Analysis of Dispersion and Propagation of Fine and Ultra ... · Analysis of Dispersion and Propagation of Fine and Ultra Fine Particle Aerosols from a Busy Road Submitted by Galina

Queensland University of Technology

School of Physical and Chemical Sciences

Analysis of Dispersion and Propagation of Fine and Ultra Fine Particle Aerosols from a Busy

Road

Submitted by Galina GRAMOTNEV, School of Physical and Chemical Sciences, Queensland University of Technology in partial fulfilment of the requirements of the

degree of Doctor of Philosophy

January 2007

ii

Keywords Combustion aerosols, urban aerosols, outdoor aerosols, background aerosols, nano-

particles, ultra-fine particles, particle formation, aerosol evolution, busy road,

aerosol dispersion, air quality, transport emissions, emission factors, canonical

correlations analysis, multi-variate analysis, degradation processes, turbulent

diffusion, atmospheric monitoring, hydrodynamics, statistical mechanics,

probability, particle deposition.

iii

Statement of original

authorship

The work contained in this Thesis has not been previously submitted for a degree or

diploma at any other higher education institution. To the best of my knowledge and

belief, the Thesis contains no material previously published or written by another

persons except where due reference is made.

Galina Gramotnev

iv

Acknowledgements

I note my appreciation of financial support for this research from the Queensland

University of Technology (QUT), Faculty of Science, School of Physical and

Chemical Sciences, and QUT Office of Research.

I would like to express my sincere gratitude and appreciation to Dr. Richard J.

Brown for very helpful discussions, support, useful directions, and introduction to

the theory of turbulent atmospheric processes. I also thank Mr Pierre Madl and Ms

Maricella Yip for their substantial help and consultations with respect to monitoring

equipment, and all my friends from the International Laboratory for Air Quality and

Health for their support during my PhD studies.

Special thanks go to my husband, Dr Dmitri K. Gramotnev, for the

comprehensive support during my studies and suggested ideas.

v

Abstract

Nano-particle aerosols are one of the major types of air pollutants in the urban

indoor and outdoor environments. Therefore, determination of mechanisms of

formation, dispersion, evolution, and transformation of combustion aerosols near the

major source of this type of air pollution – busy roads and road networks – is one of

the most essential and urgent goals. This Thesis addresses this particular direction of

research by filling in gaps in the existing physical understanding of aerosol

behaviour and evolution.

The applicability of the Gaussian plume model to combustion aerosols near busy

roads is discussed and used for the numerical analysis of aerosol dispersion. New

methods of determination of emission factors from the average fleet on a road and

from different types of vehicles are developed. Strong and fast evolution processes

in combustion aerosols near busy roads are discovered experimentally, interpreted,

modelled, and statistically analysed.

A new major mechanism of aerosol evolution based on the intensive thermal

fragmentation of nano-particles is proposed, discussed and modelled. A

comprehensive interpretation of mutual transformations of particle modes, a strong

maximum of the total number concentration at an optimal distance from the road,

increase of the proportion of small nano-particles far from the road is suggested.

Modelling of the new mechanism is developed on the basis of the theory of turbulent

diffusion, kinetic equations, and theory of stochastic evaporation/degradation

vi

processes.

Several new powerful statistical methods of analysis are developed for

comprehensive data analysis in the presence of strong turbulent mixing and

stochastic fluctuations of environmental factors and parameters. These methods are

based upon the moving average approach, multi-variate and canonical correlation

analyses. As a result, an important new physical insight into the

relationships/interactions between particle modes, atmospheric parameters and

traffic conditions is presented. In particular, a new definition of particle modes as

groups of particles with similar diameters, characterised by strong mutual

correlations, is introduced. Likely sources of different particle modes near a busy

road are identified and investigated. Strong anti-correlations between some of the

particle modes are discovered and interpreted using the derived fragmentation

theorem.

The results obtained in this thesis will be important for accurate prediction of

aerosol pollution levels in the outdoor and indoor environments, for the reliable

determination of human exposure and impact of transport emissions on the

environment on local and possibly global scales. This work will also be important

for the development of reliable and scientifically-based national and international

standards for nano-particle emissions.

vii

LIST OF AUTHOR PUBLICATIONS

1. Refereed journal papers

[A1]. Gramotnev, G., Brown, R., Ristovski, Z, Hitchins, J., Morawska, L. 2003.

Determination of emission factors for vehicles on a busy road. Atmospheric

Environment, 37, pp. 465-474 (Number 13 out of 25 most downloaded papers in

2004).

[A2]. Gramotnev, G., Ristovski Z., Brown, R., Madl, P. 2004. New methods of

determination of emission factors for two groups of vehicles on a busy road,

Atmospheric Environment, vol.38, pp.2607-2610.

[A3]. Gramotnev, G., Ristovski, Z. 2004. Experimental investigation of ultra fine

particle size distribution near a busy road, Atmospheric Environment, vol.38,

pp.1767-1776.

[A4]. Gramotnev, D.K., Gramotnev, G. 2005. A new mechanism of aerosol

evolution near a busy road: fragmentation of nano-particles, Journal of Aerosol

Science, vol.36, pp.323-340. (Number 9 out of 25 most downloaded papers in 2005).

[A5]. Gramotnev, D.K., Gramotnev, G. 2005. Modelling of aerosol dispersion from

a busy road in the presence of nanoparticle fragmentation, Journal of Applied

Meteorology, vol.44, pp.888–899.

[A6]. Gramotnev, G., Gramotnev, D.K. Multi-channel statistical analysis of

combustion aerosols. Part I: Canonical correlations and sources of particle modes

Atmospheric Environment (accepted 9 January 2007).

[A7]. Gramotnev, D.K., Gramotnev, G. Multi-channel statistical analysis of

combustion aerosols. Part II: Anti-correlations of particle modes and fragmentation

theorem. Atmospheric Environment (accepted 9 January 2007).

[A8]. Gramotnev, D.K., Gramotnev, G. Kinetics of stochastic degradation /

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evaporation processes in polymer-like systems with multiple bonds, J. Appl. Phys.

(submitted).

[A9]. Gramotnev, D. K., Mason, D. R., Gramotnev, G., Rasmussen A. J. Thermal

tweezers for surface manipulation with nano-scale resolution. Appl. Phys. Lett.

(accepted 2 January 2007).

[A10]. Gramotnev, G., Madl, P., Gramotnev, D. K., Urban background aerosols:

Anti-correlations of particle modes and fragmentation mechanism. Geophysical

Research Letters (submitted).

2. Full-length refereed conference papers

[A11]. Gramotnev, G., Brown, R., Ristovski, Z., Hitchins, J., Morawska, L. 2002.

Estimation of fine particles emission factors for vehicles on a road using Caline4

program. Proceedings of 4th Queensland Environmental Conference, Brisbane,

Australia, 30 & 31 May 2002, pp. 43-48.

[A12]. Gramotnev, G., Ristovski, Z., Brown, R., Morawska, L, Jamriska, M.,

Agranovski, V. 2003. A new method for obtaining fine particles emission factors

with validation from measurements near a busy road in Brisbane. Proceedings of

National Environmental Conference, Brisbane, Australia, 18 & 20 June 2003, pp.

206-211.

3. Conference papers in refereed journals

[A13]. Gramotnev, G., Ristovski, Z., Brown, R., Morawska, L., Madl, P. 2003.

New method of determination of emission factors for different types of vehicles on a

busy road. Journal of Aerosol Science, EAC 2003, vol.34s, S259-S260.

[A14]. Gramotnev, G., Ristovski, Z. 2003. Nanoparticles near a busy road:

experimental observation of the effect of formation of a new mode of particles.

Journal of Aerosol Science, EAC 2003, vol.34s, S255-S256.

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[A15]. Gramotnev, G., Ristovski, Z. and Gramotnev, A. 2003. Dependence of

concentration of nanoparticles near a busy road on meteorological parameters:

canonical correlation analysis. Journal of Aerosol Science, EAC 2003, vol.34s,

S257-S258.

[A16]. Gramotnev, G., Ristovski, Z., Morawska, L., Thomas, S. 2003. Statistical

analysis of correlations between air pollution in the city area and temperature and

humidity. Journal of Aerosol Science, EAC 2003, vol.34s, S715-S716.

[A17]. Gramotnev, G. 2004. Determination of the average emission factors for

three different types of vehicles on a busy road. Journal of Aerosol Science, EAC

2004, vol.35, S1089-S1090.

[A18]. Gramotnev, D.K., Gramotnev, G. 2004. A new mechanism of aerosol

evolution near a busy road: fragmentation of nanoparticles. Journal of Aerosol

Science, EAC 2004, vol.35, S221-S222.

[A19]. Gramotnev, D.K., Gramotnev, G. 2004. Modelling of aerosol dispersion

from a busy road in the presence of nano-particle fragmentation. Journal of Aerosol

Science, EAC 2004, vol.35, S925-S926.

4. Other conference publications

[A20]. Gramotnev, G., Brown, R., Ristovski, Z, Hitchins, J., Morawska, L. 2002.

Dispersion of fine and ultra fine particles from busy road: the comparison of

experimental and theoretical results, in Chiu-Sen Wang (Ed) Proc. of Sixth

International Aerosol Conference, Taipei, Taiwan (September 9 – 13, 2002), pp.

839-840.

[A21]. Gramotnev, G., Thomas, S., Morawska, L., Ristovski, Z. 2002. Canonical

correlation analysis of fine particle and gaseous pollution in the city area, in Chiu-

Sen Wang (Ed) Proc. of Sixth International Aerosol Conference, Taipei, Taiwan

(September 9 – 13, 2002), pp. 873-874.

[A22]. Gramotnev, D.K., Gramotnev, G. 2004. Fragmentation of nanoparticles near

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a busy road: Justification and modelling. Proceedings of 8th International

Conference on Carbonaceous Particles in the Atmosphere, Vienna, Austria, 14-16

September 2004, H3.

[A23]. Gramotnev, G., Gramotnev, D.K. 2004. New statistical method of

determination of particle modes in the presence of strong turbulent mixing.

Proceedings of 8th International Conference on Carbonaceous Particles in the

Atmosphere, Vienna, Austria, 14-16 September 2004, H4.

[A24]. Gramotnev, G., Gramotnev, D. K. 2005. Theoretical analysis of multiple

thermal fragmentation of aerosol nanoparticles from a line source: Evolution of

particle modes. Biannual AIP Congress, Canberra, Australia, February, 2005, p.210.

[A25]. Gramotnev, G., Gramotnev, D. K. 2005. Numerical and experimental

investigation of thermal fragmentation of aerosol nano-particles from vehicle

exhaust. Biannual AIP Congress, Canberra, Australia, February, 2005, p.210.

[A26]. Gramotnev, D. K., Gramotnev, G. 2005. Combustion nano-particle aerosols:

Mechanisms of evolution and modelling, Aerosol Workshop, 30 March – 1 April

2005, Sydney, Australia (invited talk).

[A27]. Gramotnev, D. K., Gramotnev, G. 2005. Time delays during multiple

thermal fragmentation of nanoparticles: evolution of particle modes. European

Aerosol Conference (EAC 2005), Ghent, Belgium, p. 690.

[A28]. Gramotnev, G., Madl, P. 2005. Multi-channel statistical analysis of

background fine particle aerosols, European Aerosol Conference (EAC 2005),

Ghent, Belgium, p. 697.

[A29]. Gramotnev, D. K., Bostrom, T. E., Devine, N., Gramotnev, G. 2005.

Experimental investigation of deposition of aerosol particles near a busy road.

European Aerosol Conference (EAC 2005), Ghent, Belgium, p. 696.

[A30]. Mason, D.R., Gramotnev, D.K., Rasmussen, A., Gramotnev, G. 2005.

Feasibility of thermal tweezers for effective manipulation of nano-particles on

surfaces. ACOLS’05, 6 December, Christchurch, New Zealand, ThC6.

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[A31]. Gramotnev, D. K., Bostrom, T. E., Gramotnev, G., Goodman, S. J.

“Deposition of Composite Aerosol Particles on Different Surfaces near a Busy

Road”, 7th International Aerosol Conference (IAC 2006), 10-15 September 2006, St.

Paul, Minnesota, USA, p.616-617.

[A32]. Gramotnev, D. K., Gramotnev, G. “Multiple thermal fragmentation of

nanoparticles: evolution of particle total number concentration”, 7th International

Aerosol Conference (IAC 2006), 10-15 September 2006, St. Paul, Minnesota, USA,

p.107-108.

[A33]. Gramotnev, G., Gramotnev, D. K. “Multi-channel statistical analysis of

combustion aerosols: Canonical correlations and sources of particle modes”, 7th

International Aerosol Conference (IAC 2006), 10-15 September 2006, St. Paul,

Minnesota, USA, p.177-178.

[A34]. Gramotnev, D. K., Gramotnev, G. “Anti-correlations of particle modes and

fragmentation theorem for combustion aerosols”, 7th International Aerosol

Conference (IAC 2006), 10-15 September 2006, St. Paul, Minnesota, USA, p.734-

735.

[A35]. Gramotnev, G., Madl, P., Gramotnev, D. K. “Anti-symmetric correlations of

particle modes in urban background aerosols”, 7th International Aerosol Conference

(IAC 2006), 10-15 September 2006, St. Paul, Minnesota, USA, p.1764-1765.

[A36]. Mason, D. R., Gramotnev, D. K., Gramotnev, G., Rasmussen, A. J.

“Thermal tweezers with dynamic evolution of the heat source”, 17th AIP Congress,

December 2006, Brisbane, Australia, abstract 461.

[A37]. Gramotnev, D. K., Bostrom, T. E., Mason, D. R., Gramotnev, G., Burchill,

M. J. “Deposition and Surface Evolution of Composite Aerosol Particles”, 17th AIP

Congress, December 2006, Brisbane, Australia, abstract 796.

[A38]. Gramotnev, D. K., Gramotnev, G. “Anti-Symmetric Correlation Pattern for

Particle Modes in Combustion and Background Aerosols: Fragmentation Theorem”,

17th AIP Congress, December 2006, Brisbane, Australia, abstract 795.

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[A39]. Gramotnev, G., Gramotnev, D. K. “Multi-Channel Statistical Analysis for

the Detailed Investigation of Combustion Aerosols”, 17th AIP Congress, December

2006, Brisbane, Australia, abstract 797.

[A40]. Gramotnev, D. K., Flegg, M. B., Gramotnev, G. “Stochastic

evaporation/degradation processes in complex structures with multiple bonds”, 17th

AIP Congress, December 2006, Brisbane, Australia, abstract 748.

xiii

LIST OF FIGURES

Fig. 3.1. Monitoring place 49

Fig. 3.2. Average wind parameters 50

Fig. 3.3. Theory and experiment (linear scale) 60

Fig. 3.4. Theory and experiment (logarithmic scale) 61

Fig. 3.5. Consultancy example 64


Fig. 5.2. Size distribution near the kerb 85

Fig. 5.3. Size distributions with experimental points (20 November 2002) 86

Fig. 5.4. Comparison of size distributions (20 November 2002) 87

Fig. 5.5. Size distributions with experimental points (23 December 2002) 89

Fig. 5.6. Comparison of size distributions (23 December 2002) 91

Fig. 5.7. Total number concentration 92


Fig. 5.9. Number concentrations (8 January 2003) 95


Fig. 6.2. Average wind parameters (25 November 2002) 105


Fig. 6.4. Moving average correlation coefficients 109

Fig. 6.5. Error curves 110

Fig. 6.6. Size distributions (20 November 2002) 116

Fig. 6.7. Size distributions (23 December 2002) 119

Fig. 6.8. Evolution pattern 123

Fig. 7.1. Geometry of the problem 132

Fig. 7.2. Fragmentation rate coefficient 135

Fig. 7.3. Total number concentrations (theoretical dependencies) 138

Fig. 7.4. Total number concentrations (comparison with experiment) 144

Fig. 8.1. Size distributions; moving average approach (25 November 2002) 159

Fig. 8.2. Moving average correlation coefficients 161

Fig. 8.3. Simple correlations with traffic 169

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Fig. 8.4. Canonical correlation coefficients 173

Fig. 8.5. Canonical weights and loadings for heavy trucks 175

Fig. 8.6. Canonical weights and loadings for cars 176

Fig. 8.7. Canonical weights and loadings for temperature 187

Fig. 8.8. Canonical weights and loadings for solar radiation 188

Fig. 9.1. Moving average cross-correlation coefficients 195

Fig. 9.2. Anti-symmetric correlation pattern 197

Fig. 9.3. Anti-correlations with 13.6 nm mode 201

Fig. 9.4. Anti-correlations with 7 nm mode 202

Fig. 9.5. Anti-symmetric correlation pattern (later evolution stage) 203

Fig. 9.6. Fragmentation theorem 206

Fig. 10.1. Evolution of the 3-particle from the 1-2 state 215

Fig. 10.2. Random graph representation 216

Fig. 10.3. Particle concentrations (no dispersion) 226

Fig. 10.4. Particle concentrations (with dispersion) 227


Fig. 11.2. Background size distribution (before sunset) 231

Fig. 11.3. Comparison of size distributions before and after sunset 232

Fig. 11.4. Moving average correlation coefficients for background 233

Fig. 11.5. Anti-symmetric correlation pattern for background 236

xv

Contents

Abstract v

List of Author Publications vii

List of Figures xiii

Contents xv

1. Introduction 1

1.1. Aims 7

2. Background and Theory 10

2.1. Ambient aerosols and their origins 10

2.2. Turbulent dispersion of air pollutants 15

2.2a. Taylor theorem and asymptotic properties

of the diffusing cloud 18

2.2b. Turbulent diffusion from a point continuous sources 20

2.2c. Continuous ground level line source 23

2.3. Dispersion of fine particles from a busy road 26

2.4. Monitoring equipment 34

2.5. Statistical approaches: correlation techniques in data analysis 36

3. Determination of average emission factors for vehicles on a busy road 45

3.1. Introduction 45

3.2. CALINE4 model 46

3.3. Experimental measurements 48

3.4. Model adaptation 50

xvi

3.4.1. Model emission factors 52

3.4.2. Determination of the emission factor 54

3.5. Comparison of numerical and experimental results 58

3.6. An example of application of the model for road design 64

3.7. Conclusions 65

4. New methods of determination of average particle emission factors

for two groups of vehicles on a busy road 68


4.2. Emission factors for two different groups of vehicles 69

4.3. Constrained optimization 73

4.4. Three types of vehicles on the road 74

4.5. Turbulent corrections to the w-factors 77

4.6. Conclusions 80

5. Experimental investigation of ultra fine particle size distribution

near a busy road 81


5.2. Experimental procedure 82

5.3. Experimental results and discussion 84

5.4. Level of confidence and errors 96

5.5. Conclusions 99

6. A new mechanism of aerosol evolution near a busy road:

fragmentation of nano-particles 101


6.2. Modes of particle size distribution 102

xvii

6.3. Maximum of the total number concentration 111

6.4. Failure of the conventional mechanisms of the aerosol evolution 113

6.5. Fragmentation model of aerosol evolution 120

6.6. Conclusions 126

6.7. Appendix for Chapter 6 127

7. Modelling of aerosol dispersion from a busy road

in the presence of nano-particle fragmentation 130


7.2. Dispersion as a chemical reaction 131

7.3. Fragmentation of particles 133

7.4. Existence conditions for the maximum

of the total number concentration 140

7.5. Comparison with the experimental results 143

7.6. Applicability conditions 150


8. Multi-channel statistical analysis of aerosol particle modes

near a busy road 155


8.2. Experimental data and particle modes 156

8.3. Moving average approach and the canonical correlation analysis 163

8.4. Sources of particle modes 169

8.5. Meteorological parameters 183


9. Correlations between particle modes: fragmentation theorem 191

xviii


9.2. Moving average approach for particle modes 192

9.3. Numerical results and their discussion 194

9.4. Fragmentation Theorem 204

10. Probabilistic time delays during multiple stochastic

degradation/evaporation processes 213


10.2. Time delays 214

10.3. Evolution time and kinetics of degradation 218

11. Multi-channel statistical analysis of background fine particle aerosols 229

12. Conclusions 239

List of main results 240

Bibliography 243

1

CHAPTER 1

INTRODUCTION

Rapid development of high-technology industry, transport, and ever increasing

consumption of energy have resulted in increasing changes to our environment, climate,

atmosphere, natural resources, etc. (Seinfeld and Pandis, 1998). All these changes

should prompt a rapid and decisive response, if we want to stop adverse effects of our

technological activities on the quality of life, environment, and health. Finding such a

response is one of the major aims of modern science, including all of its mainstream

branches such as environmental sciences, engineering, physics, chemistry, medicine,

and applied mathematics.

Transport emissions are one of the major sources of atmospheric and

environmental pollution with the global effect on climate, environment, and quality of

life (Whelan, J. 1998, Schauer, et al, 1996, Shi, et al, 1999, Shi, et al, 2001). Choking

atmospheres in major world cities and reducing air quality in residential areas of large

metropolitan centres require urgent measures on reduction, control, and effective

prediction of air pollution levels from busy roads and road networks. One of the major

types of pollutants from modern transport and road networks is combustion aerosols

comprising fine and ultra-fine particles with diameters from several nanometres to

several hundreds of nanometres (Schauer, et al, 1996, Shi, et al, 1999). It is long known

that such aerosols may have an effect on climate, mainly through cloud formation and

rainfall patterns (Seinfeld and Pandis, 1998, Jacobson, 1999). In addition, during the last

decade, researchers have established links between fine and ultra-fine particle aerosols

and noticeable health risks for humans in city areas (Pope, et al, 1995, Van Vliet, et al,

1997).

During the last several years, numerous studies have observed health effects of

particulate air pollutants. Compared to early studies that focused on severe air pollution

2

episodes (Beaver, H., 1953), recent research is more relevant to understanding health

effects of pollution at levels common to contemporary cities in the developed world.

Observed health effects include increased respiratory symptoms, decreased lung

function, increased hospitalizations and other health care visits for respiratory and

cardiovascular disease, increased respiratory morbidity as measured by absenteeism

from work and school, or other restrictions in activity, and increased cardiopulmonary

disease mortality. These health effects have been observed at levels common to many

U.S. cities including levels below current U.S. National Ambient Air Quality Standards

for particulate air pollution (Pope, et al, 1995).

It has also been found that those children who have been living within 100 m of

a freeway had significantly more coughs, wheezes, runny noses, and doctor-diagnosed

asthmas (Van Vliet, et al, 1997). In addition, the same study identified a significant

association between truck traffic density and black smoke concentration on the one hand

and chronic respiratory symptoms on the other.

Until recently, the main concern has been related to emission of relatively large

particles with diameters > 1 μm (Friedlander, 1977). Therefore the current emission

standards establish the limits on emission of overall particulate mass, rather than

concentration of particles. However, recent investigations have made it apparent that

fine and ultra-fine aerosol particles (within the ranges < 1 μm and < 0.1 μm,

respectively) emitted from combustion sources may present a significant health risk for

humans (Wichmann, and Peters, 2000, Zhiqiang, et al, 2000, Ziesenis, et al, 1998,

Borja-Aburto, et al, 1998), especially for people with specific health problems (e.g.,

heart, vascular, respiratory, etc. problems (Borja-Aburto et al, 1998). Moreover, it is

now clear that adverse health effects related to ultra-fine (< 100 nm) particles with large

number concentration but small overall mass appear to be significantly stronger than the

effects from larger (fine) particles with diameters between ~ 100 nm and ~ 1 μm (Stone,

3

2000, Brown, et al 2000). For example, proinflammatory response is greater for ultra-

fine particles, and is directly proportional to the surface area of the particles (Brown, et

al, 2001). Therefore, one of the possible explanations of increased health effects of

ultra-fine aerosol particles is related to the fact that decreasing particle diameters and

increasing their number concentrations results in a strong increase of particle surface

area per unit volume (Peters, 1997, Brown, et al, 2001, Nemmar, et al, 2002). This is

the surface area of the particles that probably drives inflammation in the short term,

resulting in significantly larger effect from ultra-fine particles having very large number

concentrations and surface area (Nemmar, et al, 2002). During a study of the

penetration of pollutant particles into the blood stream, it was found that ultra-fine

aerosol particles penetrate into the blood just in ~ 1 minute (Nemmar, et al, 2002). The

concentration in the blood reaches a maximum within ~ 10 – 20 minutes, and remains at

this maximal level for up to ~ 60 minutes (Nemmar, et al, 2002). One of the reasons for

these enhanced and fast effects is probably related to the fact that fine and ultra-fine

particles tend to penetrate much deeper into the respiratory tract (Siegmann, et al,

1999). However, the complete understanding of the observed health problems and risks

related to fine and ultra-fine particle aerosols still needs further studies including

research into physical mechanisms of particle transformation and evolution, in order to

understand which types of particles tend to play a predominant role in human exposure.

As mentioned above, the current particulate emission standards restrict the

overall particulate mass emissions. These standards are thus focusing only on PM10 and

PM2.5 (i.e., the overall particulate mass concentration for particle diameters < 10 μm and

< 2.5 μm, respectively). They are obviously of little use for the development of

regulations and policies when it comes to the strong adverse effects of fine and ultra-

fine particles, because the contribution of such particles to the overall aerosol mass is

negligible. Therefore, new standards for fine and ultra-fine particle aerosols are

4

required, based on number concentrations rather than overall particulate mass. This will

also require detailed and comprehensive understanding of the major mechanisms of

formation and evolution of combustion aerosols, transformation of particle modes,

determination of their possible sources, possible places of enhanced health risks,

mechanisms of removal and self-removal of particles from the atmosphere, etc. At the

same time, our current knowledge about fine and ultra-fine aerosol particles, their

possible sources and mechanisms of transformation is fairly limited and some times

inconsistent with experimental observations (for more detail see Chapter 2).

It is also clear that the development of adequate standards for fine and ultra-fine

particle aerosols may only help to determine and identify the existing and potential

problems with air pollution and transport and industry emissions. Solution of these

problems will be another very complex task that will require new approaches for

effective reduction and control of air pollution levels (including particulate pollutants)

and improvement of the air quality in major metropolitan centres. And this is again not

possible without the detailed understanding of processes of aerosol formation,

interaction, evolution, and eventual removal and/or self-removal from the atmosphere.

As a result, significant efforts of a number of aerosol scientists have recently

been focused on the advancement of our fundamental knowledge of behaviour of

combustion aerosols and their prediction in the urban environment. In particular,

detailed understanding of dispersion of nanoparticle aerosols is one of the most

important goals for achieving reliable and accurate forecast of aerosol pollution levels

and the resultant human exposure. One of the major physical mechanisms of dispersion

of air pollutants (including nanoparticle aerosols) in the atmosphere is turbulent

diffusion (Seinfeld & Pandis, 1998, Jacobson, 1999). If only this mechanism is taken

into account, dispersion of aerosols and gasses can be described by the Gaussian plume

model (Csanady, 1980, Pasquill and Smith, 1983, Zannetti, 1990). Several successful

5

software packages for different types of sources including point sources (industry)

(Bowers & Anderson, 1981), area sources (bushfires) (Hanna, et al, 1984), line sources

(busy roads) (Benson, 1992) have been developed for non-reactive pollutants. However,

modelling of dispersion of reactive gasses and rapidly evolving aerosols is a much more

complex problem (Bilger, 1978, Fraigneau, et al, 1995).

Previously, it was fairly commonly assumed that fine and ultra fine particle

aerosols do not undergo significant and rapid transformations (Shi et al, 1999). In this

case, particle size distributions should be more or less constant within a significant

period of time, and the Gaussian plume approximation should be applicable for the

approximate description of aerosol dispersion from different sources. In this case the

above-mentioned software packages should be applicable (after the appropriate re-

scaling) for the prediction of aerosol dispersion in the atmosphere. Therefore, the main

interest of aerosol scientists has been focused on the study of decay of the total number

concentration of particles with distance from a source, e.g., a busy road (Shi, et al,

1999, Hitchins, et al, 2000, Zhu, et al, 2002a,b). In particular, exponential decay laws

were used for the description of the total number concentration of fine particles as a

function of distance from the road (Zhu, et al, 2002a,b).

However, several recent experimental observations have suggested that the

Gaussian plume approximation is not always applicable, especially for smaller particles

within the range < 30 nm. Noticeable deviations of the size distributions of fine and

ultra fine particles near a busy road from those predicted by the Gaussian plume model

have been observed by Zhu, et al (2002a,b). This suggests that there are significant

processes of evolution of particles during their transport away from the road – see also

(Ketzel and Berkowicz, 2004). Such evolution processes may include particle formation

by means of homogeneous and heterogeneous nucleation (Alam, et al, 2003, Kulmala,

et al, 2000, Kerminen, et al, 2002, Lehtinen and Kulmala, 2003, Pirjola, 1999),

6

coagulation (Jacobson, 1999, Kostoglou & Konstandopoulos, 2001, Piskunov &

Golubev, 2002), deposition (Jacobson, 1999, Meszaros, 1999), condensation and

evaporation (Zhang et al, 2005, Uvarova, 2003).

Nevertheless, there are still noticeable discrepancies between the theoretical

predictions based on the mentioned mechanisms of aerosol evolution and the

experimental observations and monitoring data near busy roads. For example, Zhu, et al

(2002a,b) have observed a shift of one of the particle modes (maximums of the particle

size distribution) towards smaller particle diameters when the distance from the road is

increased. This observation is in obvious contradiction with the suggested coagulation

mechanism, of evolution of the particle size distribution (Zhu, et al, 2002a,b).

Contradictory suggestions regarding the nature of combustion nanoparticles have been

presented in the literature. Some of the researchers assume that particles with diameters

< 30 nm are mostly volatile (Sakurai, et al, 2003), whereas others suggest that they are

predominantly solid – graphite, carbon, or metallic ash (Pohjola, et al, 2003, Abdul-

Khalek, et al, 1998, Bagley, et al, 1996). Very few experiments on direct particle

observation and determination of their properties and structure under field conditions

have been undertaken so far, while laboratory analysis may give significantly different

results from the real-world situations with stochastically varying atmospheric conditions

and natural variability of the source (different types of vehicles, their maintenance, etc.).

Problems with such field experiments are well known. They are related to significant

fluctuations/dispersion of monitoring data associated with strong natural stochastic

processes, such as atmospheric turbulence, variability of temperature, humidity, solar

radiation, traffic conditions, etc. Therefore, deriving sensible conclusions about the

nature of different types of aerosol particles and their evolution in the presence of strong

turbulent mixing requires the development of new extensive and complex methods of

statistical analysis.

7

As a result, a number of important questions about the nature of particle modes

in combustion aerosols and their evolution/transformation and physical and chemical

structure in the real-world environment have so far been left unanswered. Some of these

questions can be listed as follows. (1) What is the predominant nature of the exhaust

nanoparticles? Are they mainly solid or volatile? (2) What are the dominant sources (if

any) of different particle modes? (3) How can we determine emission factors from

different types of vehicles on an actual road (these factors are essential for accurate

prediction of aerosol pollution levels)? (5) How do particle modes evolve with time and

distance from the source at different atmospheric, physical, and climate conditions? (6)

Are the known mechanisms sufficient for the complete description of aerosol evolution,

or we are missing something?

Detailed investigation of these and other questions is essential for accurate

forecast of aerosol pollution in the urban environment, establishment of working

emission standards and, ultimately, reduction or elimination of the impact of these

emissions on our environment, air quality and health.

Therefore, the general aim of this thesis is to gain better understanding of

behaviour of nanoparticle aerosols by means of detailed experimental, statistical and

theoretical investigation of evolution mechanisms, dispersion, and deposition of

combustion airborne nanoparticles in the real-world environment, and develop new

predictive models and statistical methods of data analysis in the presence of natural

variability of the source and environmental conditions.

The specific aims of the project can be listed as follows.

1. Adaptation of the currently available models for the analysis of dispersion of non-

reactive air pollutants from a busy road (CALINE4 model) for the reliable forecast

of aerosol pollution levels.

8

2. Development of new methods for the experimental determination of the average

emission factors per one vehicle on the road in the real-world environment, based on

the monitoring data for the total number concentration at just one point near a busy

road.

3. Development of new methods for the determination of average emission factors

from different types of vehicles on a road on the basis of monitoring data on

different days of observation.

4. Detailed experimental investigation of combustion aerosols near busy roads.

Investigation of particle modes and their evolution as the aerosol is transported

away from the road.

5. Development of new statistical methods of identification of particle modes and

analysis of mechanisms of their rapid evolution near a busy road, based on the

moving average approach in combination with the simple correlation and canonical

correlation analyses.

6. Development of a new major mechanism of aerosol evolution based on intensive

thermal fragmentation of nanoparticles. Comprehensive interpretation of a complex

pattern of aerosol evolution near a busy road.

7. Statistical determination of possible sources of nanoparticle modes in combustion

aerosols near a busy road. Determination and interpretation of mutual correlations

between different particle modes.

8. Statistical analysis of urban background aerosols, including mode analysis and their

correlations.

9. Development of a new model of aerosol dispersion near a busy road on the basis of

the theory of particle fragmentation. Determination of the applicability conditions

for the proposed model and derivation of conditions for a maximum of the total

number concentration at an optimal distance from the road.

9

10. Development of a theory of stochastic evaporation/degradation processes in

composite aggregate structures. Determination of substantial time delays during

fragmentation of composite nanoparticles. Investigation of formation of particle

modes during aerosol evolution.

10

CHAPTER 2

BACKGROUND AND THEORY

2.1 Ambient aerosols and their origins.

The term ‘aerosol’ refers to an assembly (suspension) of liquid or solid particles

in a gaseous medium. Such suspensions are usually the result of either natural processes

(e.g., marine aerosols, dust storms, etc.), or human activities mainly related to

combustion processes, use of fossil fuels, transport, airplanes, etc. (Seinfeld and Pandis,

1998, Hinds, 1982, Willeke & Baron, 1993, Fuch, 1989, Kaye, 1981).

Aerosols play a very important role in atmospheric behaviour, climate patterns,

global climate changes, air quality in large metropolitan centres, inside our homes and

at the workplace. For example, atmospheric aerosols may result in additional reflection

of sunlight from the Earth atmosphere, which may lead to a cooling effect on the global

climate. Atmospheric aerosols may lead to a substantial increase in the number of

precipitation centres, resulting in extensive cloud formation with smaller size of the

droplets. This may lead to decreased rainfall and increased reflectivity of sunlight

(increased brightness of the clouds (Seinfeld & Pandis, 1998, Jacobson, 1999). On the

other hand, aerosol particles that strongly absorb solar energy may result in an

additional heating effect, leading to intensified global warming (Seinfeld and Pandis,

1998, Jacobson, 1999). Which of these tendencies appear to be predominant in reality is

still to be determined.

On the more local scale, the most significant effect of aerosols is a decrease of

the air quality in our homes, at the workplace, and at other places of our everyday

activities and leisure. They are one of the most significant air polluting factors in

modern cities and large metropolitan centres, produced by a number of different

anthropogenic sources resulting from human activities. The most significant sources of

11

aerosol air pollution and reduction of the air quality in the urban environment are

transport and industrial emissions (Seinfeld and Pandis, 1998, Willeke & Baron, 1993).

These emissions have been shown to have a significant adverse effect on human health

and state of our environment.

Aerosols are normally classified in terms of size of the particles (Hinds, 1982,

Willeke & Baron, 1993), which usually ranges from ~ 1 nm to ~ 100 μm (Kaye, 1981).

This classification usually includes three major particle groups: coarse particles (with

diameters ≥ 1 μm), fine particles (with diameters between ~ 0.1 μm and ~ 1 μm), and

ultra-fine particles or nanoparticles (with diameters < 100 nm). Such a classification is

important because size of particles is one of the most important factors in the

determination of aerosol properties and behaviour (Mandelbrot, 1983). Moreover,

different physical laws and approaches should be used for their description and

characterisation (Cliff, et al, 1978).

Properties of the particles in the atmosphere have been of interest for physicists

and meteorologists since the late 1880s, when John Aitken measured for the first time

number concentrations of dust and fog particles. However, only during the last decade

has it become possible to measure concentrations of nano-scale particles in the

atmosphere. Aerosol number distributions have been widely measured in urban, rural

and remote environments to characterise properties of small particles starting from

diameters as small as ~ 3 nm (Seinfeld and Pandis, 1998). Unfortunately, the smallest

size range (with diameters < 3 nm) is still difficult to access, and there is no clear

understanding of concentration and composition of these particles.

Coarse particles can be detected and analysed relatively easily, and their

contribution to the overall particulate mass of an aerosol is predominant (Friedlander,

1977). They also produce significant visible effects (such as dust storms, smoke from

open fires, etc.). Aerosols of such particles may have significant health effects, cause

12

respiratory problems, result in poor visibility and equipment breakage, and lead to other

problems in the metropolitan and rural environments. Therefore, until recently, the main

efforts have been concentrated on the analysis, monitoring and forecasting of aerosols

consisting of coarse particles.

At the same time, due to relatively large size of coarse particles, they are

effectively stopped by the upper air ways of the human air tract, predominantly in the

nose, from where they can be removed very effectively (Siegmann, 1999). This

significantly reduces the adverse health effects of course particles on humans (unless

during relatively rare significant bushfire events, dust storms, etc.). On the contrary,

smaller particles may penetrate deeper into the respiratory tract (Siegmann, 1999). In

addition, the highest levels of concentration of trace elements and toxins from

anthropogenic sources are usually associated with very small particles mainly in the fine

and ultra-fine ranges, i.e., between ~ 1 nm and ~ 2.5 μm (Thomas, et al, 1997).

Commonly, urban aerosols are a mixture of emissions from industrial sources,

transport, power plants, natural sources, and particles from the gas-to-particle formation

processes. Therefore, the aerosol size distribution in urban environment is quite

variable. Extremely high concentrations of fine particles (up to ~106 cm-3) are found

close to sources, for example, near highways (Zhu et al, 2002ab), but the concentration

decreases rapidly with distance from the source (Zhu et al, 2002ab). Nevertheless,

typical particle concentrations in the urban aerosols are substantially (at least an order of

magnitude) higher than in the remote areas. The particle number distribution in the

urban environment is dominated by particles within the range less than ~ 100 nm. These

particles are of a special interest for aerosol scientists, because they are regarded to be

most harmful, their number concentrations are typically high, and a large proportion of

population in the developed countries is exposed to them on the daily basis (Hussein et

al, 2005).

13

Aerosols in rural areas are mainly of natural origin, but with moderate influence

of anthropogenic sources (Hobbs, et al, 1985) and secondary aerosol formation products

in remote continental areas (Bashurova, 1992). The number distribution is mainly

characterized by two modes ~ 0.02 μm and ~ 0.1 μm (Jaenicke, 1993), and the mass

distribution mode ~ 7 – 10 μm (Jaenicke, 1993). Similar modes are typical for remote

continental aerosols. Aerosol number concentrations are typically from ~ 2×103 cm-3 to

~ 104 cm-3 (Bashurova, 1992), with the PM10 concentrations (i.e., the mass

concentrations for particles with diameters less than 10 μm) being from ~ 10 μg/m3 to ~

20 μg/m3 (Koutsenogii & Jaenicke, 1994).

An important source of aerosols is particle nucleation and growth in relatively

clean air of rural and remote areas. The resultant particles are usually in the nanometre

range. This process is of a growing interest because of its possible effect on climate and

health. Although, despite more than 100 publications in the literature on this topic, the

nature of the nucleation process is still not entirely clear (Kulmala, et al, 2004).

Therefore, this topic of aerosol science is under intensive current investigation.

Particles over the remote oceans are largely of marine origin (Savoie, 1989). The

typical concentrations in marine atmospheric aerosols are normally within the range

between ~ 100 cm-3 and ~ 300 cm-3. The size of the particles is usually relatively large

an is typically characterized by three distinct modes: Dp < 0.1 μm, 0.1 < Dp <0.6 μm, Dp

> 0.6 μm (Fitzgerald, 1991). Particles in marine aerosols are usually of biological and

organic nature, iodine compounds, sea salt, or their combination (Fitzgerald, 1991). Due

to their usually low number concentration, these particles present little or no problems

for human health. Therefore, the main aim of their investigation is usually related to the

effect of these aerosols on climate, cloud formation, and possible spread of microscopic

species and their products in the atmosphere.

14

Background free tropospheric aerosols have received relatively little attention.

These aerosols are usually characterized by two different particle modes in the size

distribution. These are at ~ 0.01 μm and ~ 0.25 μm (Jaenicke, 1993). The middle

troposphere typically has more particles in the accumulation (~ 0.25 μm) mode,

compared to the lower troposphere. This was explained by precipitation, scavenging,

and deposition of smaller and larger particles (Leaitch and Isaac, 1991).

The described types of aerosols rarely appear separately from each other.

Typically, an observed aerosol is a mixture of these types, resulting in a complex

pattern of the corresponding particle size distribution within a huge range of particle

diameters of ~ 4 orders of magnitude. A number of different modes of particles can

appear mixing with each other and thus leading to results that may be difficult to

interpret and subdivide into separate groups originating from particular sources. On top

of this, we have the natural instability of the atmospheric and environmental parameters

(e.g., atmospheric turbulence and the corresponding strong stochastic fluctuations of the

measured parameters), which makes the aerosol analysis and interpretation especially

difficult.

Accurate prediction of concentrations and dispersion of aerosols from different

polluting sources in the urban environment is one of the major problems of modern

environmental science. Solution of this problem is complicated by changing size

distribution of the aerosol particles, caused by possible evolutionary and formation

processes. Therefore, clear understanding of these physical and chemical processes in

urban aerosols is an essential goal of modern aerosol science (Seinfeld and Pandis,

1998, Jacobson, 1999). This naturally leads us to the next section where we consider the

first (and probably the most important) mechanism of aerosol evolution – turbulent

dispersion in the atmosphere.

15

2.2 Turbulent dispersion of air pollutants

One of the major physical mechanisms of dispersion of air pollutants in the

atmosphere is turbulent diffusion (Csanady, 1980, Pasquill & Smith, 1983, Zannetti,

1990). Turbulence is stochastic (random) motion of the air caused by breakage of the

unstable laminar flow of the air/fluid due to its interaction with obstacles and/or uneven

heating (Landau & Lifshitz, 1987). Turbulent diffusion occurs when the diffusing

substance (aerosol particles) is transported by such random motion, which is similar to

random motion of separate molecules in the air, resulting in conventional molecular

diffusion (Csanady, 1980). Mathematical and physical consideration of turbulent

diffusion is the same as for molecular diffusion – the diffusing particles experience

random walk caused by their random transport by means of air parcels moving

randomly due to turbulence.

If only the mechanism of turbulent diffusion is taken into account, then

dispersion of the aerosol can be described in exactly the same way as for non-reactive

gasses – by the Gaussian plume model (Csanady, 1980, Pasquill & Smith, 1983,

Jacobson, 1999). This model is based upon the solution of the well-known diffusion

equation in a moving incompressible fluid

χ∇=χ∇•+∂χ∂ 2Dt

u , (2.1)

where χ is the volume density (or concentration) of the diffusing substance, u is the

velocity of the fluid, D is the coefficient of diffusion, and t is the time (see, for example,

Stull, 1989, Jacobson, 1999, Pasquill, 1983).

For the simplest case of one-dimensional diffusion in a uniform medium at rest

(u = 0, D = const), the solution to Eq. (2.1) can be written as:

DtxeDt

Q 4/2

2−

π=χ . (2.2)

16

This equation gives the time-dependent concentration of the diffusing

substance/particles at some moment of time t and the coordinate x. The constant Q is the

surface density (or surface concentration) of the diffusing substance at x = 0 at the

moment t = 0 (at this moment of time, all the diffusing substance is concentrated at the

plane x = 0).

It is possible to see that σ = 2 Dt is the typical distance within which the

substance (particles) have spread due to diffusion within the time interval t. This

distance can be regarded as a convenient scale of the width of the spatial distribution of

particles during their diffusion, and is termed as standard deviation for diffusing

particles from the position x = 0. Eq. (2.2) represents the Gaussian distribution that also

applies to turbulent diffusion in the atmosphere. However, in this case, the diffusion

coefficient D is much larger than that for molecular diffusion, simply because the scale

of random motion (given by the turbulence scale, i.e., typical size of the turbulent

eddies (Landau & Lifshitz, 1987, Csanady, 1980)) is much larger than for molecular

diffusion where it is given by the mean free path of the molecules. Therefore, in the

problems with turbulent diffusion in the atmosphere, molecular diffusion does not play

any noticeable role and thus can be neglected.

To determine σ in the case of turbulent diffusion of air pollutants in the real

environment, a statistical theory of diffusion has been developed, based on the history

of random-walk motion executed by the diffusing particles (Csanady, 1980). Turbulent

motion appears to be one of the most difficult problems of modern physics, and the

complete understanding of this process in the general case has not yet been achieved.

Historically, the first successful treatment of turbulent diffusion by Taylor (Taylor,

1922) was directly based on the statistical theory of Brownian motion that was

developed by Einstein in 1905 (Einstein, 1905).

17

In a process of random walk of particles (Brownian motion) or air parcels

(turbulent diffusion), the displacement of the diffusing particle is a function of time. At

the same time, the actual value of this displacement at any given time is random and can

only be specified in terms of probability distribution (Taylor, 1922). If this probability

distribution is time independent, then we have a steady-state stochastic process that has

some simple properties and can be analysed relatively easily. Turbulent diffusion is

steady-state if the temperature, mean velocity of the air, and turbulent intensity are

homogeneous over the whole turbulent field, i.e., over the whole space (Taylor, 1922,

Csanady, 1980). The concept of turbulent intensity was introduced to characterize the

“strength” of a turbulent state. Turbulent intensities are defined as follows. We

determine the average velocity of the air, i.e. the average wind velocity. Then, we

determine instantaneous values of wind components at some moment of time and the

considered point in space. The time average squares of the differences between the

instantaneous and average wind components 222 ,, wvu are called turbulent

intensities, where u, v and w are these differences between the instantaneous and

average wind components along the x-, y-, and z-axes, respectively.

If the magnitude of the mean velocity is U, we can introduce relative turbulent

intensities:

U

uix

2/12 ⎟⎠⎞⎜

⎝⎛

= ; U

viy

2/12 ⎟⎠⎞⎜

⎝⎛

= ; U

wiz

2/12 ⎟⎠⎞⎜

⎝⎛

= . (2.3)

The root-mean-square of the differences between the instantaneous and average wind

components 2/1

2 ⎟⎠⎞⎜

⎝⎛= uum ,

2/12 ⎟⎠⎞⎜

⎝⎛= vvm and

2/12 ⎟⎠⎞⎜

⎝⎛= wwm can be regarded as

characteristics of the eddies in the turbulent motion.

18

2.2.1. Taylor theorem and asymptotic properties of the diffusing cloud

Consider a point source of particles with the position vector x’. Let a particle be

released from the source at time t = 0 (the particle position vector at t = 0 is x’).

Suppose that during the diffusion time t the particle has moved to its new position x.

Then P(x – x’, t)dx is the probability that the displacement vector x – x’ ends within the

volume element dx around the point x at time t. If χ is the mean mass concentration of

the particles at the position x of the volume element dx, then

χ(x – x’, t) = QP(x – x’, t), (2.4)

where Q is the total mass of particles released at the point x’ at the moment of time t =

0.

If u is the component of the fluid velocity relative to a reference frame moving

with the average velocity of the fluid (i.e. U = 0), then in the steady-state case

0)( =tu ;

consttu =)(2 , (2.5)

with the same relationships holding for v and w.

An important characteristic of a steady-state stochastic process is its

autocorrelation function R(τ) that measures the “persistence” of a given value of a

random variable (e.g., velocity) within a time interval τ. In other words, the

autocorrelation function determines the likelihood that if a particle has a particular

velocity at some moment of time t, then this velocity will have similar magnitude and

direction at the moment of time t + τ (Csanady, 1980). It can be shown that the

autocorrelation function is given by the equation (Csanady, 1980):

2

)()()(u

tutuR τ+=τ , (2.6)

19

where the averages are taken in time. In a steady-state process, R(τ) is independent of

time t. At τ = 0 the autocorrelation function is equal to one, and R(t) → 0 when τ → +

∞.

Since the displacement of a particle is related to its velocity by

∫=t

dttutx0

')'()( ,

for the x-component (and similar for the y- and z-components), we have

∫=t

dttutudt

txd0

2')'()(2)]([ .

Taking an average over the whole ensemble of the diffusing particles of the both sides

of this equation, gives (Taylor, 1922, Csanady, 1980):

∫ ττ=t

dRudtxd

0

22

)(2 , (2.7)

where 2x is the square of displacement of a diffusing particle averaged over the whole

considered ensemble of the particles. Therefore, 2x is a function of time. On the

contrary, the other averages in Eq. (2.7) are taken over time (and thus are time-

independent).

Eq. (2.7) is the most important fundamental result of the random-walk theory of

diffusion (Brownian motion or turbulence). In the theory of turbulent diffusion it is

known as the Taylor theorem (Taylor, 1922).

For an ensemble of independently diffusing particles that are released at x = 0

and t = 0, the spread of the plume along the x-axis is given by the so-called radius of

inertia σx of the mean concentration distribution (Csanady, 1980):

∫∫∫ χ=σ dxdydztzyxxQx ),,,(1 22 . (2.8)

20

The length σx defined by Eq. (2.8) is a measure of the cloud size after some time of

turbulent diffusion (it has the same meaning as σ = 2 Dt introduced below Eq. (2.2)).

Assuming the χ(x,y,z,t) is the concentration formed by the independently

diffusing particles and substituting Eq. (2.4) into Eq. (2.8), gives:

222 ),,,( xdxdydztzyxPxx =∫∫∫=σ , (2.9)

where 2x is again the time-dependent ensemble average of the square of the particle

displacement. Therefore, using the Taylor theorem (Eq. (2.7)), Eq. (2.9) for the time-

dependent standard deviation (or the radius of inertia) of the cloud can be reduced as:

∫ τττ−=σt

x dRtut0

22 )()(2)( . (2.10)

Asymptotic properties of σx can be determined from the behaviour of R(τ) at small and

large values of τ. For example, when τ → 0 (and R → 1), Eq. (2.10) is reduced as

222 tux ≈σ (if t → 0) (2.11)

with the accuracy of ~ t4 – see (Csanady, 1980).

On the other hand, when τ → ∞, R(τ) → 0. In this case,

)(2 1022 tttux −≈σ (if t → ∞) (2.12)

where

∫ ττ=∞

00 )( dRt , ∫ τττ=

∞

001 )(1 dR

tt ).

Thus for small dispersion times (small t), the size of the plume σx increases linearly with

time, whereas for large t, it is proportional to the square root of time.

2.2.2. Turbulent diffusion from a point continuous source

Let the point source of particles be at the origin of the frame (x,y,z) and the wind

be parallel to the x-axis. We assume that the total mass of the particles released from the

source at the moment of time t = 0 is equal to Q. Then, assuming that the probability

21

distribution P(x,y,z,t) is Gaussian, the resultant average particle concentration as a

function of time and coordinates can be written as (Csanady, 1980):

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

σ−

σ−

σ−−

σσσπ=χ 2

2

2

2

2

2

2/3 222)(exp

)2(),,,(

zyxzyx

zyUtxQtzyx , (2.13)

where U is the wind speed.

If we have a continuous point source of particles, then such a source can be

represented as a number of releases of particle plumes at infinitesimally close moments

of time. In other words, we have a number of instantaneous point sources located at the

same point in space (frame origin) and releasing particles at different (infinitesimally

close) moments of time, thus producing a continuous particle release by a continuous

source.

One of the main assumptions of the mathematical analysis of turbulent diffusion

is that the motion of each of the air parcels (elements) is independent of the other

neighbouring parcels (Csanady, 1980). Therefore, in this approximation, turbulent

diffusion is a linear phenomenon, and the concentration field from multiple sources

(releasing particles at different moments of time) can be represented as a simple

superposition of the fields from each of the individual sources. Thus, the steady-state

concentration from a continuous point source is give as (Csanady, 1980):

zyxzyx

dtzyUtxqzyxσσσ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

σ−

σ−

σ−−∫

π=χ

∞ '222

)'(exp)2(

),,( 2

2

2

2

2

2

02/3 (2.14)

where q is release rate, i.e., the total mass of the particles released per unit of time.

At short distances from the source, where the size of the cloud grows linearly

with time (see Eq. (2.11)):

σx ≈ umt, σy ≈ vmt, σz ≈ wmt,

and integration of Eq. (2.14) gives (Frenkiel, 1953):

22

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎟⎠

⎞⎜⎜⎝

⎛π+×⎟⎟⎠

⎞⎜⎜⎝

⎛−

π=χ

ruUx

ruxU

ruUx

uU

rwvquzyx

mmmmmm

m

21erfexp

21

2exp

)2(),,( 22

2

2

2

22/3

where

22

22

2

222 z

wuy

vuxr

m

m

m

m ++= (2.15)

However, for a point source that is not too high above the ground level (within ~

100 m), the application of this formula is non-trivial, since at these heights the wind

speed and the turbulence parameters (e.g., diffusivity) are height-dependent (Csanady,

1980). The detailed analysis of this situation is very complex and has not been done in

the general case. Usually, the wind speed is assumed to be approximately constant with

height (Benson, 1992a,b) or has a logarithmic profile (Stull, 1989), which in a number

of situations is associated with significant errors. Even if we assume that the turbulence

is homogeneous in the first approximation, we have to take into account the surface of

the ground that works as a rigid boundary. Usually, the ground is assumed to be a

perfect reflector, and it can be introduced by a mirror-image source placed below the

ground (Csanady, 1890, Jacobson, 1999, Seinfeld & Pandis, 1998). This approach has

been confirmed by the experimental evidence (see, for example, (Csanady, 1968,

Clauser, 1956)). Therefore, the mean concentration field due to a continuous elevated

point source of strength q can be written as (Csanady, 1980):

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

σ+−

σ−+

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

σ−−

σ−

σσπ=χ 2

2

2

2

2

2

2

2

2)(

2exp

2)(

2exp

2),,(

zyzyzy

hzyhzyU

qzyx , (2.16)

where the frame origin is exactly under the point source that is located at the height h

above the ground level, and the wind speed U is assumed to be height-independent.

The practical importance of Eq. (2.16) is that it can be used for prediction of

ground level concentrations:

23

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

σ−

σ−

σσπ=χ 2

2

2

2

22exp)0,,(

zyzy

hyU

qyx . (2.17)

2.2.3 Continuous ground level line source

The considered case of dispersion from a point source is important for modelling

of dispersion of non-reactive pollutants (e.g., aerosols), for example, from an industrial

site. Another even more important situation is a line source of emission, such as a busy

road with traffic. Because traffic emissions from busy roads and road networks make a

predominant contribution to air pollution in large metropolitan areas, modelling of

aerosol dispersion from a line source is essential for our ability to forecast air pollution

levels and control air quality in the urban environment.

It is possible to think that the consideration of a line source can again be

conducted by subdividing this source into point sources and applying the equations

derived in the previous sections (Held, et al, 2001). However, application of Eqs. (2.12)

– (2.15) to the determination of mean particle concentrations from a continuous ground

line source is again substantially impeded by the fact that wind speed strongly depends

on height above the ground. Therefore Eqs. (2.12) – (2.15) are not applicable, since they

have been derived in the approximation of constant wind.

Therefore, the approximate analysis of dispersion from a ground level line

source (e.g., a busy road) is considered using the self-similarity theory and dimensional

approach (Csanady, 1980).

We choose the y-axis along the ground level line source and the z-axis

perpendicular to the ground. We also assume that the average wind velocity is parallel

to the x-axis, i.e., normal to the road. It has been shown that the vertical profile of the

wind (up to ~ 100 m above the surface of the earth) is given by the logarithmic law

(Stull, 1989):

24

0

lnzz

kuU ∗= , (2.18)

where ∗u is called friction velocity, and it depends on roughness of the surface z0 and

the Karman constant k (Stull, 1989). The roughness of the surface is approximately

estimated as 1/30 of the typical height of the obstacles on the surface (Stull, 1989).

The major parameter that determines turbulent diffusion of a plume is the length

scale Lc. The length Lc can be taken to equal the typical size of turbulent eddies, and

then the spread of the plume can be determined in terms of Lc, because the rate of

expansion of a plume (turbulent diffusivities) are determined by the typical size of

eddies. However, this choice may be ambiguous, because turbulence may have different

scales (Csanady, 1980, Landau & Lifshitz, 1987). Therefore, it is more convenient and

practical to define Lc directly as the typical spread of a plume emitted, for example,

from a point source within some particular time of dispersion. For example, we can

choose that Lc = σx, where σx is the radius of inertia of the plume – see above. It is

necessary, however, to keep in mind that the asymptotic behaviour of the radius of

inertia for a ground source is significantly different from that for an elevated point

source (Eqs. (2.8) – (2.12)). This is because of the mentioned dependence of the wind

on height above the ground and the corresponding non-homogeneity of the turbulence

(its scale, as well as the turbulent diffusivities, also changes with increasing height

above the ground) (Csanady, 1980, Stull, 1989, Zannetti, 1990, Pasquill & Smith,

1983).

Variation of Lc with distance x can then be derived as the universal “law of

growth” for the ground-level source (Csanady, 1980, ):

bkxezLL c

c =0

ln , (2.19)

where e = 2.71828, and b is the coefficient of proportionality.

Eq. (2.19) can be reduced to the form of the power law (Csanady, 1980):

25

γ×= xconstxLc )( , (2.20)

where Δ−=γ 1 , and )/ln(/1 0zLc=Δ . This form of Eq. (2.19) is more convenient for

practical use, because though the power γ depends on Lc (and thus on distance from the

road x), this dependence is usually relatively weak, because z0 << Lc. Therefore, within

reasonably large distance intervals near a road, Δ can be regarded as a constant that is

noticeably smaller than 1. As a result, the approximate dependence of plume spread is

indeed the power law of distance from the road with the power γ that is close to 1

(further confirmation of this statement will be provided in Chapter 3).

In this case, the concentration of particles in the plume will be the inverse power

law in distance from the road (Csanady, 1980):

μ−=χ Cx0 , (2.21)

where μ = 1 – Δ2, and C is the coefficient of proportionality (a constant). Because of the

same reasons as above, μ should be close to 1 and vary only weakly with distance from

the road.

This approximation and results (Eq. (2.21)) seem quite reasonable, because it is

well-known (for example, from the electrostatics) that a line source of some field results

in the decay of this field as r–1, where r is the distance from the source. In the case of

line source emitting particles, particle conservation requires approximately the same

dependencies. The small difference associated with μ being slightly smaller than 1 is

due to the presence of the boundary (ground surface). This boundary results in reflection

of particles from it, which is taken into account by introducing an additional imaginary

source below the ground level (Csanady, 1980). This is again very similar to

electrostatics considering field structure from charges in the presence of metallic

surfaces (Landau & Lifshitz, 1984).

26

As a result, dispersion from a busy road in the absence of particle

transformation/evolution and noticeable deposition is best described by the described

power law (Csanady, 1980, Zhang, et al, 2005), rather than exponential dependencies

that were some times used for this modelling (Hitchins, et al, 2000, Zhu, et al, 2002a,b).

At the same time, it is possible that deposition of nano-particles may result in a

significant loss of particles during their transport from the road, and the actual

dependence may be different (e.g., be closer to the exponential law).

2.3 Dispersion of fine particles from a busy road

Until recently, the major efforts in environmental science were focused on

gaseous air pollution or aerosols consisting of fairly large not evolving particles.

Dispersion of inert gasses (e.g., CO or NOx on the time scale of ~ tens of seconds) and

not evolving aerosols with the diameters ≥ 2.5 μm can be described by the conventional

theory of turbulent diffusion based on the Gaussian plume approximation, considered in

the previous section. The resultant most developed dispersion models for determination

concentrations of inert gasses emitted by a line source (highway) are CALINE4,

developed by California Department of Transport (Benson, 1992) and UCD2001 from

University of California (Held, et al, 2001).

CALINE4 has been designed for the analysis of carbon monoxide pollution near

a busy road, based on the knowledge of gaseous emission factors from stationary and

moving vehicles. The model considers the region directly above the road as a zone of

uniform emission that is called mixing zone (Benson, 1992). The aim of the

introduction of the mixing zone is to establish initial Gaussian dispersion parameters at

a reference distance near the edge of the roadway. CALINE4 model divides the

roadway into a series of elements from which incremental concentrations are computed

and summed (Benson, 1992). The UCD model (Held, et al, 2001) is based on an array

27

of point sources, rather than a sequence of sections of line sources (sections of the road)

used in the CALINE models. Similar to CALINE models, UCD 2001 assumes that all

pollutants are emitted from a mixing zone above the roadway (Held, et al, 2001).

However, even for the case of non-reactive pollutants that can be treated by

means of the CALINE4 or UCD models, the major problem is in the absence of

consistent experimental data on the average emission factors for fine and ultra-fine

particles from motor vehicles, that are required as an input for both the packages.

Indeed, experimental values of these emission factors presented by different researchers

vary by one or even two orders of magnitude, even for the same types of vehicles

(Graskow, et al, 1998, Gertler, et al, 2000, Gross, et al, 2000, Jamriska & Morawska,

2000). Typically, the emission factors lie within the intervals between ~ 1012 to ~ 1014

particles per vehicle per kilometre for gasoline (light-duty) vehicles, and between ~ 1014

to ~ 1015 for diesel (heavy-duty) vehicles. Thus, there is a strong need to develop

reliable methods for the determination of average emission factors for different types of

vehicles on a busy road.

Until recently (until the last couple of years), it was accepted that particle size

distributions do not change significantly with increasing distance from the road, i.e., the

particles were thought to be non-evolving (Shi, et al, 1999). Therefore, the main interest

of aerosol scientists has been focused on the study of decay of the total number

concentration of particles with distance from a busy road (Shi, et al, 1999, Hitchins, et

al, 2000, Zhu, et al, 2002a,b). In particular, exponential (Hitchins, et al, 2000, Zhu, et

al, 2002a,b) decay laws were used for the description of the total number concentration

of fine particles as a function of distance from the road (see also the end of the previous

section).

Shi, et al, (1999) measured the size distribution for particles in the range from ~

10 nm to ~ 352 nm at three distances downwind from a busy road. As a result, only an

28

insignificant shift (of only ~ 1 nm) of the size distribution was observed. However,

these measurements were conducted in an urban area with a number of other roads in

the vicinity of the measurement site, which made it difficult to see aerosol evolution

with increasing distance from the specific source (road). At the same time, in another

paper from the same group (Alam, et al, 2003), unusual strong bursts of concentration

of ultra-fine particles in the range ≤ 7 nm were registered at a significant distance from

the road. These maximums were associated with the traffic conditions and solar

radiation. An explanation of the obtained results by means of particle nucleation was

attempted. However, these measurements were not specifically focused on the

investigation of particle size distribution and its evolution with increasing distance from

a busy road (Alam, et al, 2003), which may be important for verification or disproval of

the nucleation model.

The first consistent attempt to investigate evolution of combustion aerosols near

a busy road has been undertaken in the two papers by Zhu, et al (2002a,b), where the

size distribution of particles in the range from 6 nm to 220 nm was investigated at six

distances from a busy road: 17 m, 20 m, 30 m, 90 m, 150 m, and 300 m. Concentrations

of particles were normalized to wind speed and direction (Zhu, et al, 2002a,b), and

averaged over different conditions during the observations. This research revealed

significant changes of the size distribution of fine and ultra-fine particles during their

transport from the road. A conclusion was made that both coagulation of particles and

turbulent dispersion contribute to the rapid decrease in particle number concentration

and mode transformation (Zhu, et al, 2002a,b). The process of coagulation was regarded

as the main reason for the variation of the size distribution with distance from a busy

road. Two main modes (strong maximums) of the size distribution (around ~ 10 nm and

~ 20 nm) that were observed at 17 m distance from the road, were claimed to shift

29

towards larger particle diameters as the aerosol was transported away from the road

((Zhu, et al, 2002a).

As mentioned above, concentrations were averaged over the atmospheric

conditions and normalized to wind speed and direction. This approach is important for

the determination of the general average tendencies of the aerosol evolution from a busy

road. However, it may mask effects that are sensitive to particular atmospheric

conditions and wind direction and speed. In addition, relatively large steps in distance

might have resulted in insufficient spatial and temporal resolution of the measurements.

The suggestion that particle coagulation may be used for the explanation of the

observed mode transformation (Zhu, et al, 2002a) seems questionable, since coagulation

at the considered particle concentrations is highly inefficient (Jacobson, 1999, Shi, et al,

1999, Zhang & Wexler, 2004, Zhang et al, 2004) and can hardly result in the observed

significant changes in the particle size distribution (Jacobson & Seinfeld, 2004).

It is clear that modelling of dispersion of evolving aerosol particles (or reactive

gasses) is a much more complex problem. Over the years, substantial efforts have been

made to understand chemical and physical processes inside plumes from point

(industrial) sources (see, for example, (Seigneur, et al, 1983, Kerminen and Wexler,

1995, Kumar & Russell, 1996, Bilger, 1978, Bilger, et al, 1991)). However, only a few

models have been published in the literature that could be applied for evaluation of

motor-vehicle aerosol transformation on the urban scale (Pilinis and Seinfield, 1987,

Jacobson, et al, 1996, Jacobson, 1997a,b). At the same time, application of any model to

dispersion of reacting and rapidly evolving particles will require detailed knowledge of

the actual processes occurring in the aerosol. Comprehensive understanding of these

processes has not been reached so far, and even the predominant nature of the exhaust

ultra-fine particles is still disputed by different authors (Alam et al, 2003, Sacurai et al,

30

2003, Fierz & Burtscher, 2003, Kittelson, 1998, Farrar-Khan, et al, 1992, Colbeck, et al,

1997, Wentzel, et al, 2003, Abdul-Khalek et al, 1998).

For example, diesel exhaust particles consist mainly of highly agglomerated

solid carbonaceous material, ash, and volatile organic and sulphur compounds

(Kittelson, 1998). Solid carbon is the usual product of all combustion processes

including vehicle exhaust. According to (Kittelson, 1998), solid carbon agglomerates

constitute approximately 40% of particulate emission from diesel vehicles. Unburned

fuel particles (~ 7%), and evaporated lube oil (~ 25%) appear as volatile or soluble

organic compounds that form volatile particles or volatile cover for solid particles in the

exhaust (Kittelson, 1998). Soluble organic compounds contain polycyclic aromatic

compounds and sulphurs (~ 14%) (Farrar-Khan, et al, 1992). Metal compounds in the

fuel and lube oil result in a small amount of inorganic ash (~ 13% of the overall

particulate emission) (Kittelson, 1998). The fraction of the unburned fuel and lube oil

varies with engine design and operation condition. Most of the particle mass exists in

accumulation mode (0.1 – 0.3 μm) consisting mainly of carbonaceous agglomerates.

The coarse mode (> 1 μm) contains ~ 5 – 20% of the particle mass (Kittelson, 1998).

It has also been suggested that the nuclei mode (nanoparticles) that is typically ~

5 – 50 nm usually consists of volatile organic and sulphur compounds, and probably of

solid carbon and metal compounds (Kittelson, 1998). On the other hand, solid carbon

particles ~ 20 – 30 nm have readily been observed in the products of combustion of

different materials (Colbeck, et al, 1997), and in the vehicle exhaust (Meszaros, 1999,

Wentzel, et al, 2003). Several researchers have also reported the existence of a large

number of smaller solid particles around ~ 7 nm mobility diameter. For example,

Abdul-Khalek, et al (1998) reported the experimental observation of a strong mode of

particles from diesel exhaust within this particular range. The analysis of these particles

by means of a catalytic stripper has suggested that a large number of them are solid

31

(Abdul-Khalek, et al, 1998), and the authors assumed these particles to be metallic ash

formed from oil and fuel additives. On the other hand, Bagley, et al (1996) suggested

that this mode may consist primarily of carbonaceous particles. Recent investigation by

Sakurai, et al (2003), using a thermal desorption particle beam mass spectrometer, has

demonstrated the existence of solid nuclei particles in the diesel exhaust of ~ 3 – 7 nm.

The results have been explained by evaporation of a thick volatile layer from the surface

of the solid nuclei particles (Sakurai, et al, 2003). Yet another recent experiment on

separation of volatile and solid particles in the diesel exhaust by means of a hot dilution

system has also demonstrated the existence of a large number of solid (presumably,

carbon/graphite) particles of ~ 6 nm – 10 nm mobility diameter (Fierz & Burtscher,

2003).

The assumption of the above-mentioned predominantly volatile nanoparticles

inevitably raises questions about possible mechanisms of their formation and chemical

composition. In particular, it has been suggested that sulphur could play a significant

role in formation of the volatile compounds of the diesel aerosol (Kittelson, 1998).

However, more recent attempts to estimate the effects of nucleation of sulphur nano-

particles has suggested that this process may be significant only within just a few

seconds after the exhaust gasses leave the exhaust pipe (Pohjola, et al, 2003). This study

developed a model that was based on the specific composition of the vehicle exhaust of

~ 20% organic carbon and ~ 80% elemental carbon (Kittelson, et al, 1999). The traffic

flow was taken to be ~ 13,400 vehicle/day with ~ 5% of light duty diesel vehicles. The

model estimates the mutual importance of different aerosol processes during the first 25

s of evolution of particles emitted from the vehicle exhaust. The results showed that,

under the selected conditions, binary (H2SO4 – H2O) and ternary (H2SO4 – H2O – NH3)

nucleation can be neglected, as well as condensation of sulphate. Therefore, sulphur

compounds cannot play a noticeable role (at least at the considered traffic conditions) in

32

formation of the presumably volatile particles in the nucleation mode considered by

Kittelson, et al (1998).

Condensation of insoluble organic vapour is important if its concentration

exceeds ~ 1010 cm-3 (Pohjola, et al, 2003). Condensation or evaporation of water can

also be an important process. However, its influence is strongly dependent on the

hygroscopicity of particles. The effects of coagulation is negligible. A very important

finding of this work is that after 25 s of evolution the particulate population reaches a

quasi-steady state, i.e., most of the transformation processes have finished (Pohjola, et

al, 2003).

Another very recent work by K.M. Zhang and colleagues (Zhang & Wexler,

2004, Zhang et al, 2004) analysed the results of experiments conducted by Zhu, et al

(2002a,b). It is interesting to notice that the traffic conditions in this experiment were

strongly different from those in (Pohjola, et al, 2003): ~ 15,000 vehicle/hour with ~ 5%

of heavy-duty trucks for one road (Zhu, et al, 2002b), and ~ 12,500 vehicle/hour with ~

23% of heavy-duty trucks for another road (Zhu, et al, 2002a). Therefore, the traffic

density was ~ 10 times higher than that considered in (Pohjola, et al, 2003). At the same

time, whereas the width of the roads were very similar: 25 m in (Pohjola, et al, 2003)

and 26 – 30 m in (Zhu, et al, 2002a,b). The total number concentrations of particles in

the range 6 – 220 nm at the distances of 17 m and 30 m from the roads were very high:

~ 220×103 cm-3 and ~ (150 – 180)×103 cm-3, respectively (Zhu, et al, 2002a,b).

Two stages for dilution of the emitted exhaust were considered (Zhang &

Wexler, 2004, Zhang et al, 2004). The first stage dilution ~1000:1 is caused by the

traffic turbulence within ~ 1 – 3 s immediately after the emission from the exhaust pipe.

The second stage dilution 10:1 is mainly caused by the atmospheric turbulence, and this

process usually lasts ~ 3 – 10 min (Zhang & Wexler, 2004, Zhang et al, 2004). The pre-

dilution (“in-tailpipe”) aerosol composition measurements are not yet available.

33

Therefore, this composition was estimated from total mass of emissions, using ambient

measurements (Shauer, et al, 1999, Shauer, et al, 2002). Although, as it was shown by

Zhang & Wexler (2004) and Zhang et al (2004), particle growth is very sensitive to the

initial “in-tailpipe” processes, the results of Shauer, et al (1999) and Shauer, et al (2002)

have been used as best estimates for semi-volatile, gaseous and particulate components

of the exhaust emissions for medium-duty diesel and light-duty gasoline vehicles

(Zhang & Wexler, 2004, Zhang et al, 2004). The chemical species were assumed to be

sulphate and organic compounds since they are the likely candidates to trigger

nucleation or lead to significant particle growth in such a short time (Zhang & Wexler,

2004). The effective behaviour of organic compounds has been modelled by introducing

two different volatility classes: semi-volatile and low volatile (Zhang et al, 2004). Each

class was represented by a single carbon number. Their vapour pressures and molar

volumes were assumed to be the same as for alkanes of the same carbon number, whose

thermodynamic properties are well known (Zhang et al, 2004).

As a result, investigation and modelling of the aerosol dynamical processes such

as nucleation, condensation and coagulation have been carried out (Zhang & Wexler,

2004, Zhang et al, 2004). For the first dilution stage, it was shown that the nucleation

process can take place. However, extremely rapid dilution (within ~ 1 s) results in the

equally rapid decrease of vapour concentration for the gasses responsible for the

nucleation processes. Therefore, nucleation may only occur when the dilution ratio is

around 30 – 80 (Zhang & Wexler, 2004) – during the first second of dilution of the

exhaust gasses in the ambient air. Condensation of organic compounds also occurs at

the first dilution stage, which results in rapid growth of solid and liquid nanoparticles.

Coagulation has been shown to be negligible for both stages of dilution (Zhang &

Wexler, 2004). It has also been suggested that for the second dilution stage only

condensation/evaporation can affect the aerosol size distribution (Zhang et al, 2004).

34

The model demonstrated agreement with the measured particle size distribution at 3

distances from the road, though there were some discrepancies for smaller (< 10 nm)

particles and, in some cases, for particles larger than 100 nm (Zhang et al, 2004).

As a conclusion to this section, it can be noted that there is no current generally

accepted model and/or physical understanding of the complex processes that lead to the

formation and evolution of nanoparticle combustion aerosols at different stages of this

evolution. The suggested mechanisms do not seem to be entirely agreed upon and do

not present a clear and comprehensive picture of the aerosol behaviour. At the same

time, as has been mentioned, detailed understanding of these mechanisms of aerosol

evolution is essential for the development of reliable predicting models for aerosol

pollution levels, their impact on the environment and human health.

2.4 Monitoring equipment

One of the major types of instruments used in this work were Scanning Mobility

Particle Sizers (SMPS). The SMPS system measures the size distribution of

submicrometer and nano-particle aerosols, using an electrical mobility technique. The

SMPS spectrometer system is based on the principle of the mobility of a charged

particle in an electric field. Particles entering the system pass through a bipolar charger

(or neutralizer) with a radioactive source. Then they enter a Differential Mobility

Analyser (DMA) where the aerosol is classified according to electrical mobility, with

only particles of a narrow range of mobility diameter exiting through the output slit.

This monodisperse aerosol then goes to a Condensation Particle Counter (CPC) that

determines the particle concentration at that size.

The DMA consists of a cylinder, with a negatively charged rod at the centre, the

main flow through the DMA is the laminar flow of particle free 'sheath' air. The air with

aerosol particles is injected at the outside edge of the DMA, particles with a positive

35

charge move across the sheath flow towards the central rod, at a rate determined by their

electrical mobility. Particles of a given mobility exit through the sample slit at the top of

the DMA, while all other particles exit with the exhaust flow. The size of particle

exiting through the slit being determined by the particle size, shape, charge, central rod

voltage, and flow within the DMA. Exponentially scanning the voltage on the central

rod, a full particle size distribution is built up in the logarithmic scale of particle

diameters.

Two types of the SMPS spectrometer systems have been used within this

project. These are the Model 3071 Electrostatic Classifier (SMPS 3071) with the Model

3010 Condensation Particle Counter, and Model 3085 Electrostatic Classifier (SMPS

3936) with the Model 3025 Condensation Particle Counter. All the classifying

equipment was manufactured by TSI Incorporated. The first system (SMPS 3071 and

CPC 3010) have the measurement range of particle diameters from ~ 13 nm to ~ 763

nm. The second system (SMPS 3936 with CPC 3025) allowed concentration

measurements within the diameter range from ~ 4.6 nm to ~ 163 nm.

The SMPS software (available from TSI Incorporated) calculates particle

concentrations in each channel of the size distribution by using the raw counts in the

channel, calculations for single charge probability, corrections for multiple charges,

transfer function width, DMA flow rates, the CPC flow rate, the measurement time for

the size channel, slip correction for particles, the impactor cut-point, and user-defined

efficiencies for all the pieces of equipment involved. Therefore, no additional inversion

of the obtained data sets has been carried out.

Routine calibration of the SMPS system was performed by the manufacturer

(TSI Incorporated) on a regular basis. In addition, fine calibration of the system was

conducted before each of the monitoring campaigns by adjustment of the delay time

(which is the time that it takes for an aerosol to travel from the classifier column until it

36

is detected by CPC). This time, determining sizing accuracy of SMPS, was verified under

laboratory conditions by means of monodisperse polystyrene latex spheres of 100 nm diameter

An automatic weather station (Standard Weather Station from Monitor Sensors)

was used for monitoring of local atmospheric parameters such as temperature, humidity,

wind speed, wind direction and solar radiation at the point of aerosol monitoring. The

weather station was under manufacturer’s warranty, and its calibration was conducted

by the manufacturer. All the aerosol measurements were conducted simultaneously with

the monitoring of the local atmospheric parameters. The measurements of wind

direction were normally conducted every minute, while all other parameters were

measured every 20 s. The time scales for aerosol and atmospheric monitoring were

matched in order to enable detailed statistical analyses and correlations between particle

concentrations and atmospheric parameters.

2.5 Statistical approaches: correlation techniques in data analysis

Despite a substantial body of literature on computational modelling and

experimental investigation and measurements of various types of aerosols and gaseous

pollutants, as has been discussed above, there are still significant gaps in our

understanding of aerosol behaviour. One of the main such gaps is the lack of knowledge

and understanding of generation, evolution and propagation of fine and ultra-fine

particle aerosols, and their relationship with other types of pollutants such as gasses and

coarse particles under various atmospheric conditions (e.g., temperature, humidity, solar

radiation, etc.). The analysis of these relationships will involve simultaneous

consideration of a number of different variables, some of which vary unpredictably due

to the strong stochastic processes in the atmosphere and environment (such as, for

example, turbulent diffusion and the corresponding strong fluctuations of pollutant

37

concentrations). Therefore, one of the most effective and essential approaches to data

analysis and investigation of complex and unpredictable effects associated with air

pollution should be based on the extensive use of statistical methods.

Statistical methods include a number of specific techniques, including regression

analysis and various smoothing techniques, simple correlation analysis, time-series

analysis, principal component and canonical correlation analyses, etc. (Larsen & Marx,

1986, Box & Jenkins,1976, Diggle, 1990 & Rice,1992, Srivastava & Carter, 1983).

Statistical methods are expected to provide a significant aid in the analysis of multiple

data with substantial dispersion, determination of important relationships and tendencies

for different types of air pollutants, their mutual relationships and interactions under

different and ever changing atmospheric and environmental conditions.

For example, simple statistical methods of analysis could also be useful for the

determination of correlations between different components of aerosols, and between

these components and external physical and chemical factors, such as wind,

temperature, humidity, etc. (Meszaros, 1999, Morawska, et al, 1998, Campanelli, et al,

2003, Salvadora, et al, 2004, Paatero, et al, 2005).

Simple correlation analysis establishes correlations between just two variables

(Larsen & Marx, 1986). Though it can be used for the analysis of some relationships

between variables, e.g., particle concentration and solar radiation, etc., it may be

inaccurate and unreliable when it comes to the analysis of, for example, particle

concentration that depends not only on solar radiation, but also on temperature,

humidity, particle concentration in a neighbouring mode, etc. We simply do not know if

the dependence on solar radiation is due to solar radiation and not, for example, due to

humidity, etc. This may result in unreliable conclusions. Therefore, multi-variate

analysis should be used instead, where simultaneous correlations between a number of

variables can be determined.

38

Using different types of multiple correlations or multiple regression techniques,

it is possible to represent variables or their combinations in terms of linear combinations

of other variables (Dillon & Goldstain, 1984, Srivastava & Carter, 1983). Regression

analysis and correlation analysis are closely related but are conceptually very different.

Regression analysis attempts to estimate the mean value of the dependant variable on

the basis of the known values of one or more predictor variables (Dillon & Goldstain,

1984). Correlation analysis attempts to measure the strength of linear relationship

between two variables (Dillon & Goldstain, 1984, Srivastava & Carter, 1983).

This analysis is important for the accurate predictions of concentration of

various types of particles in the atmosphere with subsequent evaluation of their effects

on human health. In addition, the establishment of statistical correlations between

various components of aerosols and other pollutants (e.g., gaseous components) may

allow the determination of main sources of such pollutants and particles with

subsequent targeting technical solutions in terms of major improvement of the quality of

the indoor and outdoor air in our cities.

Only very few papers reported analysis and forecast of aerosol and/or gaseous

pollutants on the basis of multiple and canonical correlations (Cogliani, 2000, Hien, et

al, 2002, Paatero et al, 2005). However, these papers present only a starting point for

the extensive use of these powerful techniques in the area of air pollution and air

quality. So far, no one has attempted canonical correlation analysis of fine and ultra-fine

particle aerosols, determination of their origins and mutual interactions/transformations,

their relationships with the environmental and atmospheric parameters, etc. in the

presence of strong turbulent mixing. At the same time, such an analysis may be

expected to provide further important information about the physical nature of the

diverse processes of aerosol evolution and particle transformations in the real-world

urban environment.

39

The methods of time series analysis are another powerful tool of statistical data

analysis (Diggle, 1990, Box & Jenkins, 1976). These methods can be subdivided into

two classes: those that use the time domain procedure, i.e., simply present the

dependencies of some quantity versus time, and those that use the frequency domain to

investigate the periodic properties of the obtained dependencies (series of data), using

the Fourier analysis (Diggle, 1990). Plots of autocovariance or autocorrelation versus

time (Box & Jenkins, 1976, Everitt, 1994, Jones & Rice, 1992, Paatero, et al, 2005) are

useful for the determination of possible mechanisms underlying the series (e.g.,

mechanisms for the existence of dominant frequencies in the Fourier integrals of the

obtained time dependencies).

A problem in analysing data is that the number of variables in the real situation

may be excessively large. For example, if we have 7 variables (n = 7), there are 21

correlations that must be considered. With n = 15 the number of correlation coefficients

is 105, and it keeps increasing proportionally to n2, where n is the number of variables.

This obviously may make impossible such an analysis, and data reduction techniques

may be highly useful.

One of such techniques is called principal component analysis (Dillon &

Goldstain, 1984, Srivastava & Carter, 1983). This analysis transforms the original set of

variables into a smaller set of uncorrelated linear combinations (principal components)

that is responsible for most of the variance of the original set (Dillon & Goldstain, 1984,

Srivastava & Carter, 1983). The purpose of the principal component analysis is to

determine a set of the minimum possible number of principal components that would

account for the majority of the variation of the original set of variables (Dillon &

Goldstain, 1984, Srivastava & Carter, 1983, Everitt, 1994, Campanelli, et al, 2003,

Salvadora et al, 2004).

40

The most comprehensive statistical approach for multiple data with a number of

different dependent and independent variables is the canonical correlation analysis

(Dillon & Goldstain, 1984, Srivastava & Carter, 1983, Johnson, R.A., Wichern, 2002).

This approach allows the determination of complex and intricate relationships between

a number of different variables that may vary in an unpredictable and complex way –

just as happens in the real-world environment.

Canonical correlation analysis determines correlations between two groups of

variables in the case when the variables in each of the groups depend on each other. The

canonical correlation technique was initially developed by H. Hotelling to identify and

quantify the associations between two sets of variables (Hotelling, 1935, Hotelling,

1936).

The main idea of the canonical correlation analysis is to determine two linear

combinations (one for predictor set and one for criterion set of variables), such that the

correlation between them is maximal. These linear combinations (canonical variates)

are analogous to the factors in the principal component analysis (Dillon & Goldstain,

1984, Srivastava & Carter, 1983, Everitt, 1994). The difference is that in the canonical

correlation analysis, we have two groups of variables that we try to compare and

correlate with each other. A significant advantage of this method is that it can determine

the effect of each of the mutually dependent parameters (e.g., temperature, humidity,

etc.) on some variable or a group of variables (e.g., particle concentration in different

size intervals) (Dillon & Goldstain, 1984, Johnson & Wichern, 2002). Thus it can

uncover complex relationships that reflect the structure between the predictor and the

criterion variables.

When only qualitative information about main tendencies and relationships

(without determining levels of confidence of the obtained correlations) is required, there

are no restrictions on types of data distribution (e.g., normal, uniform, log-normal, etc.).

41

However, if we need to determine levels of confidence of the obtained correlations, the

data should meet the requirements of multivariate normality and homogeneity of

variance (Dillon & Goldstain, 1984, Johnson & Wichern, 2002).

The squared canonical correlation coefficient R2 determines the contribution of

the considered group of meteorological parameters (predictor variables) to the variation

of the particle concentration (the larger the contribution of the considered parameters to

the variation of the concentration, the larger the coefficient R). Increasing number of

predictor variables that the concentration depends on, should increase R.

The canonical correlation technique can be described briefly as follows. Let m

be the number of predictors and p be the number of criterion variables, with m ≥ p. We

denote by

(X(1))′ = (X1, X2, …, Xm) - the vector of predictor variables,

(Y(1))′ = (Y1, Y2, …, Yp) - the vector of criterion variables,

μx(1) and μy

(1) – the respective mean vectors associated with the set X and

Y.

We define the following variance-covariance matrices (Dillon & Goldstain,

1984, Johnson & Wichern, 2002):

})')({( )1()1()1()1(xxxx E μ−μ−=Σ XX ,

})')({( )1()1()1()1(yyyy E μ−μ−=Σ YY ,

})')({( )1()1()1()1(yxxy E μ−μ−=Σ YX . (2.22)

The objective of the canonical correlation analysis is to find a linear combination of the

m predictor variables (of X) that is maximally correlated with a linear combination of

the p criterion variables (of Y). Let

X(1) = (a(1))′x = a11x1 + a12x2 + … + a1m xm,

Y(2) = (b(1))′y = b21y1 + b22y2 + … +b1m ym (2.23)

42

be the respective linear combination. Then the correlation between X(1) and Y(2) is given

by (Dillon & Goldstain, 1984, Johnson & Wichern, 2002):

2/1)1()1()1()1(

)1()1()2()1(

)}))((){((

)(),(

∑′∑′

∑′=ρ

yyxx

xy

bbaa

baba (2.24)

Out of the infinite number of such linear combinations we find two linear combinations

which maximize the correlation ρ(a(1), b(1)). Since ρ(a(1), b(1)) is invariant under the

operation of multiplication of a(1) and b(1) by arbitrary constants (Larsen & Marx, 1986),

we can arbitrary normalize a(1) and b(1). We would like to require that

∑′ xx)1()1( )( aa = ∑′ yy

)1()1( )( bb = 1, (2.25a)

i.e., X(1) and Y(1) have unit variances, and

E(X(1)) = E(Y(1)) = 0. (2.25b)

This problem is equivalent to solving the following canonical equations:

(∑xx-1 ∑xy ∑yy

-1 ∑yx – λI)a = 0,

(∑yy-1 ∑yx ∑xx

-1 ∑xy – λI)b = 0. (2.26)

Here, I is the identity matrix and λ is the largest eigenvalue for the characteristic

equations

|∑xx-1 ∑xy ∑yy

-1 ∑yx – λI| = 0,

|∑yy-1 ∑yx ∑xx

-1 ∑xy – λI| = 0. (2.27)

In this case, this largest λmax = λ(1) will be equal to the squared canonical correlation

coefficient ρ(1) (Dillon & Goldstain, 1984, Johnson & Wichern, 2002). The eigenvectors

for ∑xx-1 ∑xy ∑yy

-1 ∑yx and ∑yy-1 ∑yx ∑xx

-1 ∑xy, associated with the eigenvalue λ(1), are the

vectors of coefficients a(1) and b(1). The elements of the vectors a(1) and b(1) are called

the canonical weights. The magnitudes of these weights indicate the importance of a

variable from one set with respect to the other set in obtaining a maximum correlation

between the sets. The canonical weights do not depend on original scale of

43

measurement and are expressed in standardized form (Dillon & Goldstain, 1984,

Johnson & Wichern, 2002). Under the normalization restrictions (2.25a,b), calculation

of the canonical variate is conducted using the obtained standardized weights together

with the standardized x and y variables.

Therefore, the first pair of canonical variables (first canonical variate pair) is the

pair of linear combinations X(1), Y(1) having unit variances, which maximize the

correlation ρ(a(1),b(1)).

In the same fashion, the second pair of canonical variables (second canonical

variate pair) is the pair of linear combinations X(2), Y(2) with unit variances, which

maximize the correlation ρ(2) = ρ(a(2),b(2)), and are uncorrelated with the first pair of

canonical variables X(1), Y(1). In this case, (ρ(2))2 is the second largest eigenvalue for the

characteristic equations (2.27), etc. Altogether, p canonical variate pairs could be

extracted with ρ(1) ≥ ρ(2) ≥ …≥ ρ(p) (Dillon & Goldstain, 1984, Srivastava & Carter,

1983, Johnson & Wichern, 2002, Hotelling, 1935, Hotelling, 1936).

The canonical weights (the coefficients in linear combinations (2.23)) indicate

the contribution of each original variable to the variance of the respective canonical

variate. In other words, the larger the value of the canonical weight for a particular

variable, the larger the contribution of this variable to the corresponding correlation

(dependence). However, it is important to understand that some variables may obtain

small weights, because the variance in a variable has already been accounted for by

some other variable(s). This does not necessarily mean that the considered variable is

not important. It is possible that this variable’s contribution has been taken into account

through other variables. Therefore, if a variable has a small weight, then it is possible to

eliminate it from the consideration only if this does not change significantly the

canonical correlation, otherwise, the variable cannot be neglected.

44

Another important aspect is that the canonical variates are not directly

observable. Therefore, many researchers recommend the use of canonical loading for

identifying the structure of the canonical relationships (Dillon & Goldstain, 1984,

Johnson & Wichern, 2002). A canonical loading gives the simple correlation of the

original variable and its respective canonical variate (linear combination). It reflects the

degree to which a variable is represented by a canonical variate. The canonical loadings

can be computed by correlating the original variables with the canonical variate scores

(Dillon & Goldstain, 1984, Johnson & Wichern, 2002). For a proper interpretation of

the canonical solution, the inspection of both the canonical weights and the

corresponding canonical loadings is recommended (Dillon & Goldstain, 1984, Johnson

& Wichern, 2002). Large differences in magnitude and different sign between weights

and loadings can be an indication of nonlinear relationships between the variables, or

the fact that some additional variables/processes, that have not been taken into account,

may be as important for the analysis.

This complex but comprehensive and highly informative statistical approach is

expected to provide valuable information about possible mutual relationships between

particle modes, meteorological, environmental and traffic conditions. Therefore, it is

expected to also give an excellent insight into major physical and chemical processes of

aerosol transformation/evolution in the real-world environment.

45

CHAPTER 3

AVERAGE EMISSION FACTORS FOR VEHICLES ON A BUSY ROAD ([A1, A11, A12, A20])

3.1. Introduction

It is known that busy roads are one of the main contributing sources to the

overall air pollution in the urban environment (Zhiqiang, et al, 2000). As mentioned in

Chapter 2, one of the most well developed models for the analysis of turbulent diffusion

of busy road pollution is CALINE4 (Benson, 1992) that was designed by the California

Transport for the analysis of carbon monoxide pollution on the basis of knowledge of

gaseous emission factors from stationary and moving vehicles.

However, there are two main difficulties with the application of the CALINE4

model for the simulation of dispersion of fine particle aerosols from a busy road. Firstly,

gas parameters in the CALINE4 model (such as the emission factor and concentrations)

cannot be directly replaced by the corresponding parameters for particles, due to

different units for these parameters for gasses and aerosols. The second (more general

and significant) problem arises from the absence of consistent experimental data on

particulate emission factors from motor vehicles, that would be required as an input for

the CALINE4 package. Indeed, experimental values of these emission factors presented

by different researchers vary by one or even two orders of magnitude depending on type

of vehicles and conditions of measurements (Jamriska & Morawska, 2001, Cadle et al,

2001, Graskow et al, 1998, Gertler et al, 2000, Gross et al, 2000). From the same

references, typically, the emission factors lie within the interval between ~ 1012 to ~

1014 particles per vehicle per kilometre for gasoline (light-duty) vehicles, and between ~

1014 to ~ 1015 for diesel (heavy-duty) vehicles. Note also that very few attempts have

46

been made to determine average emission factors for vehicles on a real road with rather

inconclusive results: large spread of the obtained data (Gertler et al, 2000, Gross et al,

2000) and significant experimental errors ~ 70% (Jamriska & Morawska, 2001).

Therefore, the aim of this Chapter is to develop a new effective and accurate

method for the determination of the average emission factors for vehicles (average fleet)

on a road (based on the knowledge of experimental total number concentration at one

point near the road), and simultaneously re-scale the CALINE4 package to make it

suitable for the analysis of propagation of fine particle aerosols from a busy road. The

predictions obtained by means of the re-scaled CALINE4 package, and the determined

emission factors will be compared with two sets of experimental measurements.

3.2. CALINE4 model

Though the CALINE4 package based on the Gaussian plume model (Csanady,

1980) has been specifically developed for the analysis of carbon monoxide pollution

(Benson, 1992), it can be adapted for the approximate simulation of aerosol dispersion

and predictions of the total number concentrations near busy roads. This statement is

based on the following aspects.

First, unlike particles of larger size (> 1 μm), that have sedimentation velocities

between ~ 0.01 m/min and ~ 10 m/min, sedimentation velocities for fine particles are ~

1 mm per hour or less (Jacobson, 1999). Velocities of dry deposition due to turbulent

diffusion increase with decreasing size of particles. However, these velocities are only:

~ 0.3 cm/s for particles with the diameter 30 nm, and ~ 0.03 cm/s for 120 nm particles

(Jacobson, 1999). As a result, fine particle aerosols can propagate large distances from a

source without noticeable sedimentation and/or deposition.

Second, though as demonstrated in Chapters 5 – 10 below, combustion nano-

particle aerosols experience strong evolutionary processes resulting in rapid

47

transformation of particle modes, it may be expected that the total number concentration

near a busy road can be approximately described and predicted by means of the

Gaussian plume model (Csanady, 1980). This is the basis for the use of CALINE4 for

such a modelling. The accuracy of this model, its validity and usefulness should be

confirmed by the comparison of the predicted results with the observation data (see

below). Nevertheless, one should always keep in mind significant limitations of

Gaussian plume model, including its failure to predict strong mode evolution [A3,A4]

and experimentally observed maximum of the total number concentration at an optimal

distance from the road [A3-A5].

Therefore, in this Chapter, we adapt the CALINE4 model for the approximate

prediction of the total number concentration near a busy road in the Gaussian plume

approximation, while its extension to non-Gaussian dispersion will be considered below

in Chapter 7.

As mentioned above, the CALINA4 software package (Benson, 1992) enables

calculation of concentrations of carbon monoxide at different distances from a road and

presents these concentrations in parts per million (the number of CO-molecules per

million molecules of the air).

The inputs for the package are: roadway geometry, meteorological parameters

(wind speed, wind direction and its standard deviation, temperature and humidity),

background concentration (concentration of the pollutant in the absence of the traffic on

the considered road) in parts per million (ppm), traffic volume (in vehicles per hour),

and receptor positions. The program also requires CO-emission factors for vehicles on

the road in mg per vehicle per mile.

To adapt the software CALINE4 for fine particle aerosols, we need to find

scaling coefficients for emission factors and concentrations, since particle

concentrations are measured in particles per cubic centimeter, and emission factors in

48

particles per vehicle per mile. This adaptation will be done simultaneously with the

determination of the average emission factor for vehicles on the road, using the

experimental measurements of total number concentration at some distance from the

road. After this, the scaled package will be tested by comparing its predictions with the

experimental results of concentration as a function of distance from the road. Therefore,

in the next section we will discuss the experimental measurements of particle

concentrations, that will be needed for the developed methods and their verification, and

then proceed to the adaptation of CALINE4 in section 4.

3.3. Experimental measurements

The experimental measurements were taken near Gateway Motorway in the

Brisbane area, Australia. The total width of the Motorway was 27 m (with four traffic

lanes: two in each direction, separated by grass area with width ~ 7 m in the middle of

the road). The analysed road, its geometry (that should be used as an input in

CALINE4), and the surrounding area are presented in Fig. 3.1. The total number

concentration of fine and ultra-fine particles in the range from 0.015 μm to 0.7 μm was

measured at the height h = 2 m above the ground by means of a Scanning Mobility

Particle Sizer (SMPS-3071) and a condensation particle counter (CPC-3010). 11 sets of

measurements of the total number concentration (five independent measurements in

each set) were conducted at the distances of 15 m, 55 m, 15 m, 135 m, 15 m, 215 m,

15m, 295 m, 15 m, 375 m, and 15 m from the curb of Gateway Motorway during four

hours of monitoring [Hitchins et al, 2000]. All the concentration measurements were

conducted simultaneously with the measurements of the traffic flow on the road

(recorded and counted from the video tape with 75% of cars, 11% light trucks and 14%

heavy-duty vehicles on average). A weather station was used to measure temperature,

49

wind speed and wind direction at the time of concentration measurements and at the

same height above the ground, i.e. at h = 2 m.

Fig. 3.1. Gateway Motorway and the sample road. Dashed arrow indicates the direction of the

wind for calculations of emission factor. Dashed lines represent the imaginary vertical planes

parallel to the road (used in the calculations of the particle flux). The scale of the map and the

direction to the North are as indicated. The points on the road indicate the straight sections of

the road used in the CALINE4 for calculating dispersion.

The results of the measurements of wind speed and wind direction are presented

by points in Fig. 3.2a,b. The solid curves in Fig. 3.2a,b were obtained by means of the

“super smoother” method available in the S-Plus statistical package. These

dependencies (solid curves in Fig. 3.2a,b) approximately correspond to one hour

average values of wind speed and wind direction, which are used as the input

parameters in the CALINE4 model.

50

Each set of the concentration measurements took 12 minutes. The average of the

measured concentrations in each set was assumed to be the one hour average that is

substituted into CALINE4. The corresponding one hour average values for the wind

direction and speed were taken from the curves in Figs. 3.2a,b at the moments of time

corresponding to the middle of each of the 12 minute intervals.

Fig. 3.2. The dependencies of the one hour average wind speed (a) and wind direction (b) on

time during the whole period of measurements (four hours).

3.4. Model adaptation

The adaptation of the CALINE4 model to combustion aerosols can briefly be

outlined as follows. Firstly, we take experimentally measured concentrations of

particles at some distance (e.g., 15 m) from the curb of the road. Secondly, we substitute

all the known meteorological and environmental parameters, and some arbitrary

51

numbers for the emission factors into the model. Formally changing these emission

factors, we adjust them so that the output concentration at the considered distance (15

m) from the curb of the road is equal to the experimental value of concentration divided

by 1000. By doing this, we actually assume that the model gives concentration in ×103

particles/cm3. Note however that the adjusted emission factors are not measured in

particles per vehicle per mile. These are not real emission factors, but rather some input

numbers for the CALINE4 model. Therefore, the adjusted emission factors will be

called model emission factors and denoted as Em.

Thirdly, substituting the determined values of Em and the known meteorological

and environmental parameters back into the CALINE4 model, we calculate the

concentration of particles (in ×103 particles per cm3) at the considered distance from the

road (15 m) as a function of height above the ground (vertical concentration profile).

Fourthly, taking into account the vertical concentration profile, we determine the total

(integral) flux of particles through a plane that is normal to the ground, parallel to the

road, and located on the downwind side of the road (plane 1 denoted by the dashed line

in Fig. 3.1). The same flux can easily be determined from the average (real and

unknown) emission factor from a vehicle on the road, and the number of vehicles. Thus,

equating these two fluxes, we determine the unknown average emission factor, E (in

particles per vehicle per mile). Comparing this average emission factor, E, with the

previously obtained model emission factor, Em, we determine the scaling coefficient η =

Em/E. Thus, the average emission factor E (in particles per vehicle per mile) should be

multiplied by η, before substituting it into the CALINE4 model, in order to obtain

concentration in ×103 particles per cm3.

The following two subsections will present more detailed analysis of the

outlined procedure, including the calculations for the Gateway Motorway (Fig. 3.1).

52

3.4.1. Model emission factors

As mentioned above, we calculate model emission factors for vehicles on the

road using the concentration measurements at 15 m distance from the curb of the road.

The average values of the measured parameters that were used as the inputs of the

CALINE4 model in this calculation are presented in Table 3.1 for each of the six sets of

measurements at the distance 15 m from the road.

Set number 1 2 3 4 5 6

Wind speed, (m/s) 0.7 1.0 1.5 1.6 1.5 1.6

Wind direction, (degrees from the North)

17.5 358.2 351.2 1.7 21.9 35

Standard deviation of wind direction, (degrees)

55.5 53.7 48.7 37.5 41.0 38.0

Temperature, (°C) 31.0 34.8 33.4 35.5 36.8 36.4

Traffic flow, (vehicles/hour) 2928 3096 3108 3456 3216 3504

Cars, (vehicles/hour) 2064 2400 2520 2688 2256 2820

Trucks, (vehicles/hour) 444 456 312 480 624 468

Light trucks, (vehicles/hour) 420 240 276 288 336 216

Average experimental concentration, (×103 particle/cm3)

49.9 26.5 19.7 20.8 23.5 22.0

Model emission factor, Em 774 490 534 409 443 408

Table 3.1.

Wind speed and direction (one hour averages) were determined from the graphs

in Figs.2a,b, as described in Section 3. Standard deviations of the wind speed,

temperature, and experimental concentrations are not needed for calculations using the

CALINE4 model (Benson & Pinkerman, 1989). Therefore, they are not presented in

Table 3.1. Atmospheric stability was of class 1 (Benson & Pinkerman, 1989).

The background concentration was estimated from a different set of

concentration measurements on the same (left in Fig. 3.1) side of the road, but with the

53

opposite wind direction. These measurements gave the concentrations ~ 3200

particles/cm3. The reason for using this estimate is related to similar densities of the

residential and road areas on both sides of the road (see also the error analysis in end of

this section).

Standard deviation of the wind direction is an input parameter for the model.

However, the weather station gives only average values for the wind direction during a

6 minute interval (a continuous measurement) with a standard deviation sj for the same

interval. The standard deviation, s, of one hour average wind direction (used as an input

for the model) is related to sj as (Larsen & Marx, 1986):

s2 = k s jj

k−

=∑1 2

1. (3.1)

Here, k is the number of continuous measurements undertaken within one hour period,

and sj is the standard deviation for each of these measurements. The standard deviations

for one hour average wind directions, calculated by means of Eq.(3.1), are presented in

Table 3.1.

Using the CALINE4 model and the data in Table 3.1, we obtain the

corresponding model emission factors Em for each set of measurements at 15 m distance

from the curb of the road. The results of these calculations are presented in the last row

of Table 3.1. The units for these emission factors do not matter, because these factors do

not have any physical meaning, but are simply some input numbers for the CALINE4

model.

From Table 3.1, we can also see that the value of Em for the first set of data is ≈

1.5 times bigger than for the other sets. This may be interpreted by the fact that the first

set of measurements was taken during a very busy traffic hour – between 8 and 9 am,

when vehicle speed was relatively small and changed frequently. This can increase

values of Em, because it takes more time for a vehicle to travel the distance of one mile.

In addition, changing speed, and frequent acceleration of vehicles obviously results in

54

enhanced emission of particles. The lowest traffic flow for this set of measurements

(Table 3.1) is related to smaller speed of the vehicles in the heavy traffic, indicating

smaller number of vehicle passing the point of monitoring per hour.

The analysis of propagation of errors demonstrates that the values of Em are

relatively stable with respect to variations of the background concentration. Indeed,

20% variation of the average background concentration results in only ~ 4% variation of

the corresponding Em, and 50% variation of the average background results in only ~

10% variation of Em.

3.4.2. Determination of the emission factor

According to the general outline of the method, described in the beginning of

section 4, each of the six values of model emission factors Em are substituted back into

the CALINE4 model, together with the corresponding values of wind speed, wind

direction standard deviation, temperature and traffic flow (see Table 3.1). To simplify

further calculations of particle fluxes, we assume that the background concentration is

equal to zero, and the wind direction is normal to the road (i.e. 72o to the North – see the

dashed arrow in Fig. 3.1) for all six sets of parameters from Table 3.1. That is, instead

of all the values in the boxes of the third row in Table 3.1 we use 72o. This can be done

since in the calculations of the flux we do not use the experimental values of

concentrations (the seventh row in Table 3.1), but rather the determined values of Em

(the last row in Table 3.1), which are independent of the background concentration and

wind direction.

As a result, concentrations of particles (in ×103 particles/cm3) were calculated at

the distance 15 m from the curb of the road as a function of height above the ground

(vertical concentration profile) on the west of the road – Fig. 3.1. It can be seen that at

the same distance (15 m), but on the upwind side of the road (plane 2 in Fig. 3.1), the

concentrations are zero within an accuracy of the program (this accuracy is ~ 100

55

particles/cm3). This is the case for all wind speeds presented in Table 3.1 (if the wind

direction is normal to the road). This means that the flux of particles, caused by

turbulent diffusion, into the direction opposite to the wind direction is negligible.

Therefore, the overwhelming contribution to particle fluxes is due to transport by wind,

and practically all particles that are emitted by vehicles on the road are carried by wind

through the vertical plane on the downwind side of the road.

In this case, the flux F through the plane on the downwind side of the road

(plane 1 in Fig. 3.1) per segment of the road of length l is given by the equation (the

contribution of the turbulent diffusion to this flux is neglected):

F l U h c h dh≈ ∫+∞

( ) ( )0

, (3.2)

where c(h) is the concentration of particles as function of height h, calculated by means

of CALINE4 and the procedure discussed above, and U(h) is the average wind speed at

the height h.

For all six sets of parameters from Table 3.1, the vertical concentration

decreases to the background level at the height of ~ 15 m. The average wind speed can

be assumed to be constant within this height (the same is assumed in CALINE4

(Benson, 1992)). Indeed, wind starts changing with height if h >> 100h0, where h0 is

the dynamic roughness coefficient that is approximately equal to 1/30 of the average

height of obstacles on the considered surface (Csanady, 1980). In our case, the road is

located in a more or less flat region with isolated bushes and scattered buildings, which

corresponds to h0 ≈ 0.5 m (Stull,1989). Therefore, at the considered heights (up to 15 m

above the ground) variation of the wind speed with height was neglected: U(h) ≈ U0,

where U0 is the experimentally measured wind speed at the height of 2 m above the

ground level.

56

In the same approximation, the flux F was simply given by the strength of the

line source q (in particles per metre per second) multiplied by the length of the segment

of the road:

F ≈ ql = afl/v, (3.4)

where f is the number of particles emitted by one vehicle per second, a is the traffic flow

in vehicles per second, v is the average speed of vehicles on the road.

Comparing Eqs. (3.2) and (3.4), gives

af/v = U0 c h dh( ) .0

+∞∫ (3.5)

This equation determines f – the average number of particles emitted by one

vehicle per second. If we multiply f by the average time that it takes for a vehicle to

travel the distance of one kilometre (or one mile), we obtain the average (real) emission

factor, E, in particles per vehicle per kilometre (or particles per vehicle per mile).

The values of E calculated by means of the described procedure are presented in

Table 3.2 for the six sets of measurements from Table 3.1.

Set of measurements 1 2 3 4 5 6

Real emission factors, E, [1014particles/vehicle/mile]

6.51 4.64 4.84 3.78 4.07 3.41

Scaling coefficient, η = Em/E (×10-12 g/cm3)

1.19 1.06 1.10 1.08 1.09 1.20

Table 3.2. Emission factors and scaling coefficients.

From this table, the mean value of the six presented emission factors <E> = (4.5

± 0.4)×1014 particle/vehicle/mile, and the average scaling coefficient <η> = (1.12×10-12

± 0.02) g/cm3.

An additional error of <E> is associated with uncertainty of the background

concentration. However, this additional error cannot be large due to only weak

57

sensitivity of the resultant emission factor E to the uncertainty of the background

concentration (see the end of Section 3.4.1). Therefore, accurate knowledge of

background concentration is not essential for the developed method of determination of

average emission factors from busy roads. It is usually sufficient to have just a

reasonable estimate of background concentration (with an acceptable error of up to ~

100%).

Note also that the determination of the scaling coefficient η can be carried out

without using any experimental measurements. That is, the described procedure of

determining η can be used with arbitrary (hypothetical) emission factors and

meteorological parameters. Indeed, when calculating the scaling coefficient in the

beginning of this section, we assumed that the wind is normal to the road, and the

background concentration is zero. In the same way, all other parameters in Table 3.1

can be chosen arbitrarily, including the model emission factors. It can be seen that the

subsequent calculation and comparison of the corresponding particle fluxes at some

distance from the road (for different input parameters) give similar scaling coefficients

as those presented in Table 3.2, with the same mean value <η> ≈ 1.12×10-12. The only

error of this result is related to the uncertainty of calculations by means of the

CALINE4 model (i.e., by the sensitivity of the model).

Input parameters

Smallest increment

Variation of concentration,

×103 particles/cm3 wind speed, [m/s] 0.1 1.6

wind direction, [deg] 1 0.2

Std. Dev. of wind direction, [deg] 1 0.2 E [particle/mile/vehicle] 2.7×1012 0.1

traffic flow, [vehicle/hour] 5 0.1 receptor position, [m] 1 1

temperature, [°C] 1 0.1 stability class 1 1.1

Table 3.3. Sensitivity of the model.

58

Table 3.3 shows the variations of concentration resulting from the smallest

(allowed by the model) increments of each of the input parameters separately. As can be

seen from the Table, normally, CALINE4 responds with the accuracy of ~ 100 – 200

particles/cm3 with respect to the smallest increments of the input parameters. The

largest sensitivity occurs for wind speed variations and stability class – see Table 3.3.

As soon as the scaling coefficient is known, it is easy to use the CALINE4

model for the determination of average emission factors from vehicles on different

roads. To do this, we only need to measure the average total number concentration at

just one point near the road, find the model emission factor (using the CALINE4 model)

that produces this concentration for given meteorological conditions, and divide the

model emission factor by the scaling coefficient.

3.5. Comparison of numerical and experimental results

Note again that the procedure for the determination of the emission factors and

scaling of the CALINE4 model for the analysis of fine particle aerosols from a busy

road has been developed on the basis of the Gaussian plume model and experimental

measurements of particle concentrations at a particular distance from the road (in our

case it was 15 m from the curb). The obtained emission factors are valid only for the

particular road under consideration (since they depend on the average speed and type of

the vehicles). At the same time, the scaling coefficient is correct for any road and is

characteristic for the software package (CALINE4).

The described procedures were based on the assumption that the CALINE4

model can be used for the analysis of dispersion of fine particle aerosols from a busy

road. Therefore, in this section, we verify this original assumption by means of

calculating a theoretical dependence of total number concentration on distance from the

road, and comparing it with the experimental measurements. The theoretical

dependence is obtained by substituting the average model emission factor and the

59

corresponding meteorological parameters, averaged over the four hour interval of

measurements, into the CALINE4 model and calculating average particle concentration

as a function of distance from the road. The average value of Em = 510 ± 60 is obtained

by averaging the six values in Table 3.1. The average wind speed for the period of four

hours is equal to 1.3 m/sec, with wind speed standard deviation being 0.5 m/sec. The

average wind direction for the same period is 17o to the North, and the standard

deviation ≈ 46o. The average traffic flow for the period of measurement is 3218 vehicles

per hour (with the error of the mean ≈ 90 vehicles per hour), and the average

temperature is 34.9°C (summer period). The background concentration was estimated to

be ~ 3200 particles/cm3 – see above.

In the input of CALINE4, coordinates of receptor points can only be integer

numbers (in metres) that have to be entered separately for each of the points. Therefore,

it is inconvenient to use this model for plotting an actual theoretical dependence of

concentration on distance from the road. Instead, we calculate concentrations only at the

distances, corresponding to the experimental measurements (see Section 3.3). After this,

we perform similar curve fitting procedure (see below) for both experimental and

theoretical points, and compare the resultant curves.

The experimental values of concentration at the different distances from the road

are presented in Fig. 3.3. The theoretical points are not presented in the figure, as they

all lie almost exactly on the corresponding theoretical curve (curve 2 in Fig. 3.3a).

The curve-fitting procedure for the experimental and theoretical points was

based on the self-similarity theory of concentration distribution (Csanady, 1980). This

theory approximates the concentration c (in ×103 particles/cm3) as a power law in

distance from the road:

c = Kd-μ + c0 , (3.6)

60

where d is the distance from the road in metres, K and μ are constants to be determined,

and c0 is the background concentration. The constants K = 289 and μ = 0.73 (for the

experimental curve), and K = 500 and μ = 0.88 (for the theoretical curve) were

calculated by means of the non-linear regression model in the S-Plus statistical package

(Venables & Ripley, 2000).

Fig. 3.3. The experimental (solid curves 1 and 4) and theoretical (dashed curves 2 and 3)

dependencies of the total number concentration c on distance from the centre of the road. The

two sets of the experimentally measured average total number concentrations are represented by

the small dots (for the summer measurements in 1999 – experimental curve 1) and big dots (for

the winter measurements in 2002 – experimental curve 4).

61

Fig. 3.4. The experimental (solid curves) and theoretical (dashed curves) dependencies of the

average total number concentrations without the background, c – c0, on distance from the

middle of the road in the logarithmic scale. The dotted curves give the standard errors for the

experimental (solid) lines. (a) The summer set of measurements in 1999; (b) the winter set of

measurements in 2002 at the same place near Gateway Motorway, Brisbane area, Australia.

The resultant experimental and theoretical dependencies of concentration on

distance from the middle of the road are presented in Fig. 3.3 by curves 1 and 2,

respectively. The significant scatter of experimental points around curve 1 can be

explained by changing average speed and direction of the wind during the period of

measurements. Indeed, as can be seen from Figs.2a,b, variations of wind direction

62

within the four hour interval are ~ 60o, and variations of wind speed are ~ 1 m/s for the

same period.

Curves 1 and 2 in Fig. 3.3 demonstrate a good agreement between the theory,

based on the approaches developed in this Chapter, and the experimental results for

dispersion of fine and ultra-fine particle aerosols from a busy road. However, using

curves 1 and 2 in Fig. 3.3, it is difficult to judge if the theoretical curve lies within the

error range for the experimental curve or not. To answer this question, we subtract the

background concentration c0 from all the values of the number concentration and draw

the resultant dependencies c – c0 on distance from the road in the logarithmic scale –

Fig. 3.4a. The dotted curves in Fig. 3.4a give the standard errors (Hamilton, 1991) for

the experimental (solid) line. It is clear that the theoretical (dashed) line indeed lies well

within the standard error of the experimental curve, and CALINE4 with the calculated

scaling coefficient can be used for the analysis of aerosol propagation from a busy road.

At the same time, this agreement has been demonstrated so far only for one set

of measurements. Therefore, in order to have a better confirmation for the theoretical

model, another set of measurements (taken on 30 July 2002) in the same size range (for

particles from 0.015 μm to 0.7 μm) at the same place near the road was considered. The

average wind speed for the period of four hours was 1.8 m/sec, with wind speed

standard deviation of 0.8 m/sec. The average wind direction for the same period was

131o to the North with the standard deviation ≈ 50o. The average temperature was

20.5°C (winter period). The atmospheric stability was of class one. This time, the

background was simultaneously measured to be ≈ 2400 particles/cm3 with the standard

deviation ≈ 240 particles/cm3 (note that this measured value also confirms the estimate

of the background for the previous set of measurements). The measurements of the total

number concentration were taken at the following distances from the curb of the road:

15 m, 40 m, 65 m, 90 m, 115 m, 190 m, and 265 m; (the width of the road is 27 m). The

63

corresponding experimental points are presented in Fig. 3.3 by small dots (the distance

on the horizontal axis is taken from the middle of the road).

Again, using the non-linear regression model in the S-Plus statistical package

(Venables, 2000), the corresponding theoretical and experimental curves were plotted

(curves 3 and 4 in Fig. 3.3). Both these curves are noticeably lower than curves 1 and 2

(for the previous set of measurements). This is expected, since the wind speed for the

second set of measurements was noticeably larger (1.8 m/s compared to 1.3 m/s). If the

wind is taken the same for both sets of measurements, all the curves appear to be very

close to each other.

Similarly to curves 1 and 2 (for the first set of measurements), curves 3 and 4 in

Fig. 3.3 clearly demonstrate good agreement between the theoretical model and

experimental results. The dependencies of (c – c0) on distance from the centre of the

road in logarithmic scale (Fig. 3.4b) again demonstrate that the theoretical line lies

within the error for the experimental dependence. The typical difference between the

theoretical and average measured number concentrations is estimated to be ~ 10%.

The average emission factor for vehicles on the road for the second set of

measurements was again calculated from the measured average number concentration at

the distance 15 m from the curb of the road and the counted traffic flow 4212 vehicles

per hour. The calculated value of the emission factor in this case was E ≈ 4.6×1014

particle/vehicle/mile (with the uncertainty ~ 16% mainly due to uncertainty of

concentrations). This is very close to the value of the emission factor, calculated from

the summer experiment (E ≈ 4.5×1014 particle/vehicle/mile - see above).

Both the obtained values of the average emission factor are in reasonable

agreement with the previous results obtained by means of a box model (Jamriska &

Morawska, 2001), where the average emission factor was estimated as ≈ 2.8×1014

particles/vehicle/mile. The discrepancies could be explained by the larger number of

64

heavy duty vehicles in our experiments (14% compared to just 4% in (Jamriska &

Morawska, 2001), and by the significant uncertainty of the results from the box model

(~ 70% (Jamriska & Morawska, 2001)).

3.6. An example of application of the model for road design

Fig. 3.5 shows an example of the existing (solid line) and the proposed (dashed

line) road. The proposed road was designed to be parallel to the existing road in order to

take half of the traffic load. We assume that originally the traffic on the existing road is

2000 vehicles per hour and the average emission factor is 4.5×1014

particles/vehicle/mile.

-100 100 200 300 400 500

500

1000

N

E

S

W

A B C

distance, m

dist

ance

, m

exist

ing

road

prop

osed

road

Fig. 3.5. An example of existing (solid line) and proposed (dashed line) roads with the receptor

points A, B, C. Arrows (solid for the case of one road and dashed for the case of two roads)

indicate the direction of the wind that corresponds to maximum concentrations for a given point.

The length of the arrow is proportional to the concentration.

The analysis of the worst-case angle (the direction of the wind that corresponds

to maximum concentration of particles at a given point of observation) was conducted

65

by means of the CALINE4 program. As shown in the table below, the new

configuration (two parallel roads instead of one) decreased the worst-case particle

concentrations at points A and B by 34% and 50%, respectively. At the same time, the

worst case angle concentration at point C increased by 90%. This type of analysis will

aid in scientifically-based decision-making and achieving an optimal design of the

proposed roads and road networks in modern metropolitan areas.

A B C

Worst case angle, o to the North

49 229 225 One road

Concentration, 103particles/cm3

3.2 3.2 1.1

Worst case angle, o to the North

49 2 229 Two roads

instead of one Concentration, 103particles/cm3

2.1 1.6 2.1

Table 3.4. Comparison of concentration of particles at points A, B and C for two different

configurations of the roads.

3.7. Conclusions

In this Chapter, the CALINE4 software package, that was originally designed

for calculation of concentrations of carbon monoxide near a busy road, was adapted for

the analysis of aerosols of fine and ultra-fine particles, generated by vehicles on a busy

road. As a result, the scaling procedure for the available CALINE4 model was

developed and justified. A scaling coefficient relating the model and real emission

factors was determined: η ≈ 1.12×10-12 g/cm3. A new method of determination of the

average emission factor for fine particle emission from a vehicle on a road was also

developed. This method was based on experimental measurements of particle

concentration at just one point at some distance from the road. The average emission

factor of ~ 4.5×1014 particle/vehicle/mile (or 2.8×1014 particle/vehicle/km) (with the

standard deviation of ~ 10% – 15%, depending mainly on uncertainty of concentration

66

measurements) was determined for the road under consideration (Gateway Motorway,

Brisbane, Australia). This value must obviously be different for different roads, since it

depends on average speed and type of the vehicles on the road. At the same time, the

determined scaling coefficient and the whole procedure of the analysis are correct for an

arbitrary road, and arbitrary meteorological and environmental conditions, as long as we

use the CALINE4 software package.

It is important that the determined scaling coefficient gives us an easy way to

calculate an average emission factor for vehicles on a road, using only measurements of

average concentration at one point in the vicinity of the road. When applied to different

roads, this method may lead to an estimate of emission factors for different types of

vehicles.

Good agreement between the experimental results for the two sets of summer

and winter measurements and the predicted theoretical dependencies of concentration

on distance from the road has confirmed the applicability of the CALINE4 package for

the approximate prediction of total number concentrations in fine particle aerosols near

busy roads. In particular, statistical analysis of the experimental and theoretical results

has also demonstrated that the concentration of fine and ultra-fine particles reduces as a

power law in distance from the road.

The main applicability conditions for the developed model are the same as for

the CALINE4 software package (Benson & Pinkerman, 1989, Benson, 1992) using the

line source approximation. For example, it is not applicable for roads with traffic lights,

roads in canyons and tunnels, roads with very low traffic flow (e.g., one vehicle per

several minutes), etc. Another significant limitation for the applicability and reliability

for application of the Gaussian plume model, and thus CALINE4, is related to the

existence of fast processes of evolution of nano-particles, especially within the range <

100 nm – see Sections 5 – 9 and [A3-A5]. These include such processes as particle

67

condensation, evaporation, deposition, and thermal fragmentation (Sections 5 – 9).

Therefore, more accurate and reliable model of aerosol dispersion near a busy road will

be developed in Section 7 of this thesis. Nevertheless, as has been demonstrated, use of

CALINE4 and the Gaussian plume approximation gives reasonable results in terms of

prediction of the total number concentrations at different distances from the road.

Therefore, it can be used in environmental and urban planning practice for simple

evaluation of particle concentrations near major highways and suburban roads, and

determine expected impact of aerosol pollution on population exposure and health. In

addition, the considered approach and adapted CALINE4 model will be essential for the

development of the new much more accurate model based on the theory of particle

fragmentation (Section 7).

68

CHAPTER 4

NEW METHODS OF DETERMINATION OF AVERAGE PARTICLE EMISSION FACTORS FOR TWO GROUPS OF

VEHICLES ON A BUSY ROAD ([A2, A12, A13, A17])

4.1. Introduction

One of the significant problems with the determination of the impact of busy

roads and the resultant aerosol air pollution on human health and exposure in the urban

environment has been the lack of consistent knowledge of emission factors from

different types of vehicles in the real-world environment. The values of the emission

factors obtained under laboratory conditions for different types of vehicles differ by up

to ~ 3 orders of magnitude (Graskow et al, 1998, Watson et al, 1998, Ristovski et al,

1998, Cadle et al, 2001), and lie within the intervals between ~1012 to ~1014

particles/vehicle/kilometre for gasoline (light-duty) vehicles, and ~1014 to ~1015

particles/vehicle/kilometre for diesel trucks. Gross et al (2000) also estimated during

on-road measurements that the ratio of the average emission factors for trucks and cars

is ~ 48. However, the actual values for the emission factors have not been determined.

The CALINE4 model, designed for calculation of concentrations of carbon

monoxide near a busy road (Benson, 1992), has been adapted for the analysis of

aerosols of fine and ultra-fine particles (see Chapter 3 and [A1, A11, A12, A20]). The

scaling procedure for this model has been developed and justified (Chapter 3), together

with the new method for the determination of emission factor for the average fleet on

the road, based on the experimental values of the total number concentration at some

distance from the road. However, this approach is not applicable for the determination

the emission factors of different types (groups) of vehicles on the road, for example,

heavy truck and light cars. At the same time, as mentioned above, this information is

69

important for the effective forecast of aerosol pollution levels and human exposure from

busy roads.

Therefore, in this Chapter, two new methods are developed for the determination

of the average emission factors of fine and ultra-fine particles for different groups of

vehicles on a busy road. These methods are based on the experimental measurements of

the total number concentration near the road. The values of these emission factors for

heavy-duty trucks and light-duty cars are calculated, discussed, and compared with the

previous results obtained mainly in laboratory conditions. The method is also extended

to three different types of vehicles on the road (cars, light trucks and heavy-duty

diesels).

4.2. Emission factors for two different groups of vehicles

The measurements were taken near the Gateway Motorway (Brisbane, Australia)

at different traffic conditions: 18.1% of heavy-duty trucks on 30 July 2002 (weekday)

and 2.7% of heavy-duty trucks on 24 November 2002 (weekend). The total number

concentration of fine and ultra-fine particles in the range from 14 nm to 710 nm was

measured at the distance of 15 m from the kerb at 2 m height above the ground by a

scanning mobility particle sizer (SMPS-3071) and a condensation particle counter

(CPC-3010). The concentrations were measured in 110 equal intervals (channels) of

Δlog(Dp), where Dp is the particle diameter in nanometres. Five and ten scans were

taken on the weekday and weekend, respectively, and the average total number

concentration was determined. Even with such low number of scans, the developed

approaches give quite reasonable errors (see below), which is a demonstration of their

effectiveness. The time intervals within which SMPS took the concentration

measurements in one channel were τ1 ≈ 2.73 s for the weekday, and τ2 ≈ 1.36 s for the

weekend (this results in the same overall sampling time for weekday and weekend

70

measurements). The meteorological parameters (wind speed, wind direction,

temperature and humidity) were measured every 20 seconds by a weather station.

The average traffic parameters and measured concentrations with their relative

standard deviations of the mean are presented in Table 4.1. The one hour average wind

speed and direction and their standard deviations (required as inputs in CALINE 4) are

also shown in Table 4.1 (specifically indicated as “Std. Dev”). Traffic flow for each

type of vehicles (light duty vehicles, light trucks and heavy duty vehicles) has been

counted (from the video tape) within 5 min intervals eight times during the period of

measurements of 40 min. Then the average traffic flows were calculated – see Table

4.1. These small standard deviations clearly indicate the high stability of the traffic. It is

also worth mentioning that the average speed on the motorway was approximately the

same for the period of measurements on both the days (100 km/h, which is the speed

limit on the road with no traffic congestion).

30 July 24 November Concentration at 15 m, cm-3 20.3×103 (±16%) 2.2×103 (±13%) Background concentration, cm-3 2.3×103 (±4%) 0.74×103 (±9%) Traffic flow, vehicle/hr 4295 (±2%) 3694 (±2.2%) Heavy-duty trucks, vehicle/hr 776 (±2.3%) 100 (±15%) Cars, vehicle/hr 3097 (±2.3%) 3337 (±2.3%) Light trucks, vehicle/hr 422 (±9%) 257 (±9%) Wind direction, o to the North 142 (Std. Dev. = 48) 28.54

(Std. Dev. = 39.43) Wind speed, m/s 2.3 (Std. Dev. = 8) 2.2 (Std. Dev. = 0.7) Temperature, °C 22 27 Humidity, % 33 35 Emission factor, particle/vehicle/km

2.8×1014 (±23%) 0.23×1014 (±24%)

Table 4.1

Using the concentrations, meteorological and traffic parameters from Table 4.1

and the roadway geometry (Fig. 3.1), the values of the emission factors Ef for the

71

average fleet on the road were calculated by means of the CALINE4 model (Chapter 3)

– see the last row of Table 4.1.

Let us now assume that there are two groups of vehicles on the road – heavy-

duty trucks and cars. The light trucks (Table 4.1) are included in the car group. In this

case the emission factors for the average fleet (in particle/vehicle/km) for the weekday

(index 1) and weekend (index 2) can be written as

Ef1 = wt1nt1et + wc1(1 – nt1)ec, (4.1)

Ef2 = wt2nt2et + wc2(1 – nt2)ec. (4.2)

Here, nt1 and nt2 (no units) are the fractions of heavy-duty trucks in the traffic flow, ec

and et are the emission factors for cars and heavy-duty trucks (in particle/vehicle/km)

(to be determined), wt1,2 and wc1,2 (no units) are the correction factors that are

introduced to compensate for the discreteness of the traffic flow (breach of the line

source approximation). The reasons for using these factors can be understood from the

following.

The concentration measurements were taken in 110 size channels in sequence

within the time intervals τ1 and τ2 per one channel. Let Nt1,2 and Nc1,2 be the numbers of

trucks (index t) and cars (index c) passing by within the time interval for a measurement

within one channel on the weekday (index 1) and weekend (index 2). If, for example,

Nt2 < 1, then the particle concentration will be affected by the passing trucks only in a

fraction of channels that equals N. Table 4.1 gives Nt2 = 0.04. Therefore, only one of ~

25 channels in one scan “feels” the presence of a heavy truck. This effectively reduces

the contribution of et to Ef2 by a factor 0.04. Therefore the values of et,c in Eqs. (4.1) and

(4.2) are multiplied by the additional correction factors wt1,2 = min{1,Nt1,2,}, and wc1,2 =

min{1,Nc1,2}. It follows from the traffic data (Table 4.1) that in our experiments, wc1,2 =

1, wt1 ≈ 0.6, and wt2 ≈ 0.04. Note also that this determination of the correction factors

72

has been carried out in the slender plume approximation, i.e., when turbulent dispersion

of the plume is neglected (further corrections to these factors, associated with turbulent

diffusion are determined in Section 4.5).

Eqs. (4.1), (4.2) can be solved with respect to et and ec. The theory of variance

(Larsen and Marx, 1986) gives that if ΔEf1 and ΔEf2 are the standard deviations of Ef1

and Ef2, then the standard deviations of et and ec are

Δet = [wc22(1 – nt2)2ΔEf2

2 + wc12(1 – nt1)2ΔEf1

2]1/2/D0, (4.3)

Δec = [wt12nt1

2ΔEf22 + wt2nt2

2ΔEf12]1/2/D0, (4.4)

where

D0 = |nt1wt1wc2(1 – nt2) – nt2wt2wc1(1 – nt1)|.

For example, for the values of Ef1,2 presented in Table 4.1, we obtain:

et = (25 ± 6)×1014 particle/vehicle/km,

ec = (0.21 ± 0.06)×1014 particle/vehicle/km. (4.5)

Note that another possible source of errors is related to the possibility of

different contributions of the light trucks to the overall flow of cars on the weekday and

weekend. To evaluate the upper limit of this error, we take the difference between the

flow of the light trucks on weekday and weekend (i.e. 165 vehicles/hour) and include it

into the number of heavy trucks. Thus we assume that the average emission factor of

165 light trucks on the weekday is equal to that of heavy-duty trucks (which is an

obvious exaggeration). The resultant emission factor for heavy trucks appeared to be

different from that given by Eq. (4.4) by ≈ 30%, while for the cars, this difference was ≈

4%. This gives the upper (exaggerated) limit for the possible error due to differences in

the flow of the light trucks on weekday and weekend.

73

4.3. Constrained optimization

The same results can be obtained from Eqs. (4.1), (4.2) by means of the method

of constrained optimization (Kreyszig, 1999, Wolfram, 1999). In this method, et and ec,

are regarded as variables, and we wish to find intervals of their variations that are

determined by linear constraints. The four constraints are given by the two linear

equations (4.1), (4.2), and the two intervals for the emission factors for the average fleet

Ef1,2, determined by their standard deviations (Table 4.1). Numerical solution of this

problem (Wolfram, 1999) with the considered constrains gives the intervals (in

particle/vehicle/km):

18.3×1014 ≤ et ≤ 31.4×1014, 0.14×1014 ≤ ec ≤ 0.27×1014 (4.6)

that are hardly different from Eq.(4.5).

Note however, that though in the considered example the method with

constraints is equivalent to the direct solution of Eqs. (4.1) and (4.2), it may be very

important for the determination of the emission factors when the traffic conditions

during the two sets of measurements are similar: nt1 ≈ nt2. In this case, the slopes of the

two lines, given by Eqs. (4.1), (4.2) in the (et, ec) space, may be too close, and the point

of intersection of these lines (the solution to Eqs. (4.1), (4.2)) is highly sensitive to

experimental errors. As a result, the obtained values of et and ec suffer from substantial

errors (increasing when nt1 → nt2) – see Eqs. (4.3), (4.4).

In this case, using the method of constrained optimization (Kreyszig, 1999,

Wolfram, 1999), we can determine the average emission factors for two groups of

vehicles from only one set of measurements and the typical ratios for the emission

factors determined in the laboratory conditions: et/ec ≈ 36 (Watson et al, 1998), and et/ec

≈ 377 (Ristovski et al, 1998). The on-road value of et/ec ≈ 48 was estimated by Gross et

74

al (2000). The inconsistency of these results is obvious. However, they determine the

constraint 36 < et/ec < 377.

Suppose that we have only one set of measurements on the weekday (30 July

2002). Thus the second constraint is given by Eq. (4.1), while the third is again obtained

from the standard deviation of Ef1 (Table 4.1): 2.2×1014 ≤ Ef1 ≤ 3.4×1014. The solution

of this problem with constraints (Wolfram, 1999) gives in particle/vehicle/km: 17×1014

≤ et ≤ 32×1014, and 0.06×1014 ≤ ec ≤ 0.75×1014.

If we take the other set of measurements, then Eq. (4.2) is the second constraint,

whereas the third is 0.17×1014 ≤ Ef2 ≤ 0.29×1014 (Table 4.1). In this case, 6.2×1014 ≤ et ≤

78.9×1014, and 0.13×1014 ≤ ec ≤ 0.28×1014 (in particle/vehicle/km). Note however, that

in this case the accuracy of et and ec is lower than in Eq. (4.5). This is due to the fairly

loose constraint on the laboratory results for et/ec.

Note that the second method automatically gives the comparison of the

determined emission factors with the previously obtained results from the

measurements mainly in laboratory conditions (Watson et al, 1998, Ristovski et al,

1998, Gross et al, 2000).

4.4. Three types of vehicles on the road.

In this section, we extend the above approach to the case of three different types

of vehicles on the road: cars, light trucks and heavy-duty diesels. The average emission

factors for particles for these types of vehicles within the range from 14 nm to 710 nm

will be determined under field conditions. Associated errors of the results will be

evaluated.

The analysis is based on the same set of data shown in Table 4.1. On 30 July

2002 (weekday), the fractional composition of the traffic was 0.181 of heavy-duty

trucks, 0.098 of light trucks, and 0.721 of cars, while on 24 November 2002 (weekend)

it was 0.027, 0.069, and 0.903, respectively. As mentioned above, the average speed on

75

the motorway was approximately the same during the measurements on both the days

(100 km/h).

Using the average total number concentrations at the distance of 15 m from the

kerb, meteorological and traffic parameters, the average emission factors for the average

fleet were determined (see Chapter 3 and [A1]):

Ef1 = 2.8×1014 particle/vehicle/km (±23%) for weekday,

Ef2 = 0.23×1014 particle/vehicle/km (±23%) for weekend. (4.7)

If we assume that there are three types of vehicles on the road (heavy-duty

diesels, light trucks and cars), then the emission factors for the average fleet can be

written as:

Efi = wdindied + wtintiet + wcinciec, (4.8)

where ndi, nti, nci are the fractions of heavy-duty trucks, light trucks and cars in the

traffic flow, respectively, ed, et, ec are their emission factors, and wdi, wti, wci are the

correction factors that have been introduced to compensate for the breach of the line

source approximation if less than one vehicle of a particular type passes by within the

period of time corresponding to a measurement in one channel (see section 4.2), i = 1,2.

In principle, if we had experimental measurements on three different days with

different traffic conditions (i.e., i = 1,2,3), then Eqs. (4.8) could have been directly

solved for unknown emission factors ed, et, ec. Unfortunately, this often does not give

suitable results, since the traffic conditions are usually not that different on all three

days of measurements. It can be seen that in this case the resultant emission factors are

highly sensitive to experimental and statistical errors, and we may get zero or even

negative results, which is obviously a nonsense.

Therefore, the method of constrained optimization (Kreyszig, 1999) is used.

This method will allow determination of these three emission factors ed, et, ec only from

two sets of measurements, i.e. two Eqs. (4.8) (i = 1,2), and the constraints on the ratios

76

ed/ec and et/ec. The constraint for ed/ec is obtained from the literature data by taking the

maximum and minimum values of this ratio ed/ec ≈ 377 (Ristovski et al, 1998) and ed/ec

≈ 36 (Watson et al, 1998):

36 < ed/ec < 377 (4.9)

The constraint on the ratio et/ec has been determined from (Maricq, et al, 1999):

1.2 < et/ec < 3.7. (4.10)

Eqs. (4.7) determine the error intervals of the average emission factors, and they

are considered as two other constraints on Ef1 and Ef2. Eqs. (4.8) are also regarded as

two (functional) constraints on ed, et, ec. This gives us 6 constraints on three functions

ed, et, ec. In this case, the method of constrained optimization (Wolfram, 1999) gives

minimum and maximum values of the functions ed, et, ec, The resultant intervals for

possible values of ed, et, ec represent the error intervals for the emission factors.

Using the described procedure, the three average emission factors and their

uncertainties were determined as follows:

ed = (24.5 ± 6.5)×1014 particles/vehicle/km,

et = (0.6 ± 0.4)× 1014 particles/vehicle/km,

ec = (0.22 ± 0.07)× 1014 particles/vehicle/km. (4.11)

Note that the described method may even be useful if only one set of

measurements is available. In this case, we have only four constraints. As a result, the

determined emission factors for two of three types of vehicles usually have large errors.

However, the emission factor for the third type of vehicles usually has reasonable

uncertainty similar to those in Eqs. (4.11). Thus, in this case, only one of three emission

factors can be determined with reasonable accuracy.

If we assume that there are only two types of vehicles on the road (light trucks

and cars are put in one group), then ed = (25 ± 6)×1014 particles/vehicle/km, ec+t = (0.21

77

± 0.06)×1014 particles/vehicle/km (see above). Comparison of these results with Eqs.

(4.11) suggests that from the view-point of forecasting particulate pollution levels near a

busy road, subdivision of the traffic into heavy-duty diesels, light trucks, and cars (and

further) is rather excessive. Subdivision into just two groups of vehicles seems quite

sufficient within the limits of the experimental errors.

4.5. Turbulent corrections to the w-factors.

As has been mentioned in Section 4.2, the correction factors wd1,2, wt1,2 and wc1,2

were calculated under the assumption that turbulent dispersion of the plume is

neglected. That is, it was assumed that each truck/car passing by the monitoring point

affects the concentration only in one channel of the size distribution. This is a fairly

rough approximation, because it assumes that the plume emitted by any single truck/car

does not experience increase in size (dilution) due to turbulent diffusion as it is

transported from the point of emission to the point of monitoring. In reality, this is not

the case, and the emitted plume will experience two significant stages of dilution. First,

the emitted plume will experience rapid dilution in the mixing zone on the road. That is,

its width is assumed to “instantaneously” become equal to the width of the road (a

typical assumption for the CALINE4 model (Benson, 1992)). Second, the resultant

plume of the width that is equal to the width of the road will experience further increase

due to turbulent diffusion as it is transported from the road to the monitoring point

(Csanady, 1980).

As a result, every passing truck/car is likely to affect not only one channel in the

particle size distribution, but M channels, the total time of concentration measurements

in which will be equal to the time that it takes for the expanded (due to turbulent

diffusion processes) plume to pass through the monitoring point. This should result in

increasing the correction factors determined in Section 4.2.

78

It can be understood that that a correction w-factor determined in Section 4.2 is

equal to the probability for a particular vehicle (e.g., a truck) to pass by the point of

monitoring during the time that it takes for particle concentration measurement in one

channel. In the case of turbulent diffusion and increasing size of the emitted plume, this

will become the probability for a particular vehicle to pass by the point of monitoring

during the time that it takes for concentration measurements in M channels. As before,

this is correct only if the obtained w-factor is less than one. If it appears to be larger than

one, then it should be taken to equal one (similar to Section 4.2).

Dispersion of the plume in the direction of the wind can be estimated as σx ≈ umt,

where 2/1

2 ⎟⎠⎞⎜

⎝⎛= uum is the root-mean-square of turbulent wind fluctuations (Section

2.2.1). Therefore, for the typical relative turbulent intensity in the direction parallel to

the wind (Csanady, 1980)

i = um/U ≈ 0.1 (4.12)

(U is the average wind speed), the dispersion of the plume travelling the distance x form

the road to the point of observation in the direction of the wind can be estimated as

(Csanady, 1980):

σx ≈ ix ≈ 0.1x (4.13)

As a result, the total time for the expanded plume to pass through the monitoring

point is determined as T = (Lm + σx)/U, where Lm is the width of the mixing zone (in our

particular case, we will take Lm ≈ 10 m, which is the width of one of the two separated

sections of the road).

The correction factors wd1,2, wt1,2 or wc1,2 for each type of vehicle are equal to the

ratio of time T for the dispersed plume to pass through the monitoring point (which is

simultaneously the time for concentration measurements in M channels: τ1,2M) to the

average time interval between two vehicles of the considered type to pass by this point.

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Using the wind and traffic parameters from Table 4.1, the values of the correction

factors were calculated for both weekday and weekend:

wd1,t1,c1 = {1; 0.72; 1} (weekday), (4.14)

wd2,t2,c2 = {0.13; 0.33; 1} (weekend). (4.15)

Applying this method for two types of vehicles (heavy trucks and cars) and

assuming that Lm = σx = 0, we immediately obtain the same values of the correction

factors as in Section 4.2 (as expected).

Using the average emission factors for the average fleet for weekday and

weekend, meteorological and traffic parameters, and applying the method of constrained

optimization (Sections 4.3 and 4.4), the three average emission factors for different

types of vehicles and their uncertainties were determined as follows:

ed = (15 ± 4)×1014 particles/vehicle/km,

et = (0.54 ± 0.40)× 1014 particles/vehicle/km,

ec = (0.19 ± 0.08)× 1014 particles/vehicle/km. (4.16)

Assuming that there are only two types of vehicles on the road (light trucks and

cars are included in one group), then ed = (15 ± 4)×1014 particles/vehicle/km, ec+t =

(0.18 ± 0.07)×1014 particles/vehicle/km. Comparison of these results with Eqs. (4.16)

again suggests that subdivision of the traffic into heavy-duty diesels, light trucks, and

cars (and especially any further) is rather excessive. Subdivision into just two groups of

vehicles is sufficient within the limits of the experimental errors. At the same time,

neglecting the dispersion of the mixing zone results in overestimation of the emission

factors for heavy trucks, whereas determined in sections 4.3 and 4.4 values for emission

factors for light trucks and cars are not affected.

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4.6. Conclusions

In this Chapter, two new methods have been developed for the determination of

the average emission factors of fine and ultra-fine particles for two and three groups of

vehicles (heavy-duty trucks and cars) on a busy road. The first method requires

experimental measurements of particle concentrations at different traffic conditions

(e.g., on a weekday and on a weekend), whereas the second method is applicable when

the traffic conditions are not changing. However, the second method requires some

knowledge (typical range of variation) of the ratio of the average emission factors for

heavy trucks and cars (e.g., from the literature). The values of the emission factors have

been determined during the on-road measurements. Both the methods have been shown

to yield very similar results, which clearly demonstrates the advantage of the proposed

methods compared to the laboratory approaches giving strongly dispersed results.

The correction factors compensating for the discreteness of the traffic flow (i.e.,

for the breach of the line source approximation) have also been introduced and

discussed.

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CHAPTER 5

EXPERIMENTAL INVESTIGATION OF ULTRA FINE PARTICLE SIZE DISTRIBUTION NEAR A BUSY ROAD ([A3, A14])

5.1. Introduction. As was shown in Chapter 3, total number concentrations in combustion aerosols

near busy roads may be approximately estimated by means of the Gaussian plume

model. However, there is still a questions whether this model is applicable for the

analysis of separate particle modes, and how accurate and reliable it is even in terms of

predictions of the total number concentration. This question results from the insufficient

knowledge about possible interactions and transformations of aerosol nano-particles

during their transport from the road. If rapid and significant transformations take place,

then Gaussian plume model cannot be used, because it is only applicable for non-

reactive pollutants (Benson & Pinkerman, 1989, Benson, 1992).

The answer to this question lies in the detailed experimental investigation of the

particle size distribution and its evolution near a busy road. As indicated in Chapter 2,

experimental evidence has recently been obtained, demonstrating significant evolution

of particle modes in combustion aerosols near busy roads (Zhu et al, 2002a,b). This

confirms inapplicability of the Gaussian plume model for the description of dispersion

of separate particle modes in combustion aerosols. However, these results were only

first indications of possible rapid evolutionary processes in such aerosols. Moreover, as

indicated in Chapter 2, the undertaken experimental approach may not be suitable for

the detailed investigation of specific processes and the effects of separate external

parameters on particle modes in combustion aerosols. Further extensive experimental

investigation of evolution of combustion aerosols near busy roads is essential for proper

understanding and description of the mechanisms involved.

82

Therefore, the aim of this Chapter is in detailed experimental investigation of the

evolution of the particle size distribution in ultrafine aerosols near a busy road. Several

observed modes of the size distribution will be analysed. In particular, we will show

that some of the modes (e.g., the 30 nm mode and 20 nm mode) tend to shift towards

smaller particle diameters. For the first time, clear evidence of an increase of the total

particle number concentration at an optimal distance from the road will be presented.

Strong and unusual correlation between different modes of the size distribution will also

be demonstrated.

5.2. Experimental procedure.

The experimental measurements were taken near the Gateway Motorway in the

Brisbane area, Australia. The analyzed four-lane road (of the total width 27 m) and the

surrounding area are presented in Fig. 5.1. The height of the Motorway above the

surrounding ground level is ≈ 2 m. There are no any buildings around the measurement

area that is practically flat grass field with isolated scattered bushes and trees. On the

other (upwind) side of the Motorway, there is a small residential area with a parkland

(Fig. 5.1).

The total number concentration and size distribution of fine and ultra-fine

particles in the range from 4 nm to 710 nm was measured at the height h = 2 m above

the ground level (i.e. approximately at the level of the Motorway). Number

concentration and size distribution of particles were measured by means of two

scanning mobility particle sizers (SMPS) in two size ranges: from 4 nm to 163 nm in

100 equal intervals of Δlog(Dp) (where Dp is particle diameter in nanometres), and

from 14 nm to 710 nm in 110 equal intervals of Δlog(Dp). Concentrations of particles

within the larger range were measured by means of SMPS 3934 (the differential

mobility analyzer DMA 3071A and the condensation particle counter CPC 3010).

Concentrations of particles in the smaller range were measured using SMPS 3936

83

(model 3080 classifier with nano DMA 3085 and CPC 3025). The time for one full up-

scan was 2.5 minutes. An automatic weather station was used to measure temperature,

humidity, wind speed, wind direction and solar radiation at the same height h = 2 m and

~ 45 m from the middle of the road every 20 sec during the whole period of the

concentration measurements.

Fig. 5.1. Gateway Motorway with a few examples of receptor points. The wind direction is

indicated by the solid arrows (for 20 November 2002 and 23 December 2002) and dashed arrow

(for 8 January 2003). The scale of the map and the direction to the North are as indicated. The

insert presents a section of the map of the area of measurements. The arrow on the insert shows

the approximate place of measurements.

The measurements were conducted on four different days: 20 November 2002,

23 December 2002, 8 January 2003 (weekdays), and 24 November 2002 (weekend). On

20 November 2002, both SMPSes were used simultaneously, while other measurements

were taken only by means of SMPS with the smaller size range from 4 nm to 163 nm.

The concentration and size distribution measurements were taken at various distances

84

from the road with increments from 6 m to 25 m within the range between 25 m and

307 m from the centre of the road. At each distance from the road, five consecutive

measurement of the size distribution were conducted, from which the average size

distribution was determined (see the figures in the next section).

The concentration and size distribution measurements were conducted

simultaneously with counting of the traffic flow. All the measurements were taken at

approximately the same time intervals (from 11 am to 3 pm), when the traffic conditions

on the Motorway were stable and variations of meteorological parameters were small

(see below).

The main idea of the designed experiment was to determine the main features of

the aerosol evolution at given (and sufficiently constant) meteorological and traffic

parameters, such as humidity, temperature, wind speed, etc. This was the reason for

taking the measurements at different distances from the road within a relatively short

period of time (within several hours) when these parameters are approximately constant.

The validity of such a method is clearly confirmed by the high level of confidence of all

predicted features of the particle mode evolution (see Section 5.4).

5.3. Experimental results and discussion.

The average values of the meteorological and traffic parameters and their

standard deviations are presented in Table 5.1.

On 8 January, the wind was almost parallel to the road (the dashed arrow in Fig.

5.1), while on other days it had a noticeable component normal to the road (see Table 1

and the solid arrows in Fig. 5.1). In addition, the wind speed during all the

measurements was relatively small (Table 5.1).

Typical average size distributions for various distances within the range from 25

m to 307 m from the centre of the road are plotted in Figs. 5.2 – 5.4 for 20 November

85

2002. Standard deviation of the mean values of the concentrations within different

channels are ~ 20 – 25%. The Friedman super smoother method (Venables & Ripley,

2000) was used for plotting the corresponding curves.

Meteorological parameters

November 20

November 24

December 23

January 8

Wind direction (degrees to the North)

24 (±40)

25 (±45)

37 (±33)

7 (±27)

Wind speed (ms-1)

2.05 (±0.9)

2.2 (±0.8)

2.3 (±0.8)

2.6 (±1.0)

Normal wind component (ms-1)

1.15 (±0.5)

1.33 (±0.5)

2.05 (±0.7)

0.96 (±0.4)

Temperature (°C)

26.5 (±0.9)

27.1 (±0.4)

29.4 (±0.5)

28 (±1)

Humidity (%)

35 (±3)

36.7 (±0.9)

36 (±3)

42 (±4)

Solar radiation (W/m2)

800 (±300)

1000 (±200)

900 (±200)

800 (±400)

Traffic (vehicles per hour)

3900 3700 5000 4300

Number of trucks (%)

20 3 23 (morning) 10 (afternoon)

16

Table 5.1. Average meteorological and traffic conditions

Fig. 5.2. The typical size distribution in the immediate proximity to the road (12 m from the

kerb). The measurements were taken on 20 November 2002. The solid curve was plotted by

means of the Friedman super smoother (Venables and Ripley, 2000). The dashed curve was

plotted by means of the moving average approach with 5 channels in the moving interval. The

shaded band represents the standard errors of the moving average curve.

86

Fig. 5.3. The particle size distributions with the experimental values of the average (over five

scans) concentrations in each of the 100 channels on 20 November 2002 (midweek) at the

following distances from the road: (a) 45 m, (b) 57 m, (c) 70 m, (d) 82 m, (e) 107 m, (f) 132 m.

All the dependencies in these figures were plotted using Freedman super smoother The

meteorological and traffic parameters, and their standard deviations, are presented in Table 5.1.

For example, Fig. 5.2 presents the experimental results for the average (over

three scans) particle concentrations in different channels at the distance 12 m from the

kerb, as a function of particle diameter. Although the standard deviation for the points

in Fig. 5.2 is ~ 20%, the super smoother curve reveals all the major, statistically

significant features of the size distribution, i.e. maxima and minima. Indeed, for

comparison, Fig. 5.2 also presents the particle size distribution plotted by means of the

moving average approach with 5 channels in the moving interval (dashed curve). The

87

shaded band presents the standard errors associated with the moving average technique.

It can be seen that all the statistically significant maxima and minima on the moving

average dependence are also correctly displayed by the Freedman super smoother (solid

curve). However, the height of the maxima on the super smoother curve (especially in

the range from ~ 10 nm to ~ 30 nm) is noticeably smaller than what is suggested by the

experimental points and the moving average curve. Similar situation occurs for all other

dependencies below.

Fig. 5.4. The same size distributions as in Fig. 5.3 (re-drawn for comparison) without the

experimental points.

It can be seen that six different maxima (particle modes) can be seen in the size

distribution at about 7 nm, 12 nm, 20 nm, 30 nm, 50 nm, and 100 nm (Fig. 5.2). All

88

these modes, except probably for the 7 nm mode, were previously observed by different

researchers. For example, the 12 nm, 20 nm, 30 nm, and 50 nm modes were reported

previously by Zhu et al (2002a). Further evolution of all these modes as the aerosol is

transported by the wind away from the road is presented in Figs. 5.3 and 5.4.

For example, Fig. 5.3 presents the experimental results for the particle size

distributions at six distances from the road. Several distinct particle modes can be

observed in this figure. It can be shown that all of these modes are statistically

significant (for more detail see Section 5.4).

The dependencies in Figs. 5.3 were compared with each other in order to

identify the evolutionary effects on combustion aerosols. The main grounds for such

comparison are related to stability of the environmental parameters and discussed in

Section 5.4. For the convenience of the comparison and clear demonstration of the

major features of mode evolution, the obtained smoothed dependencies of particle size

distributions are re-plotted in the two figures 5.4a and 5.4b without the experimental

points. As a result, the four distinct modes at the particle diameters ~7 nm, ~12 nm, ~30

nm, and ~50 nm are displayed by the curves in Figs. 5.4a,b. As can be seen from Figs.

5.4a,b, the 12 nm mode is fairly stable in position, and shifts only insignificantly with

changing distance from the road (generally, this is in agreement with the results of Zhu

et al (2002a)). However, what is more important, is that not too far from the road this

maximum clearly increases in height with distance (curves 1 – 3 in Fig. 5.4a), despite

the fact that dispersion must result in the opposite tendency. As far as we know, this

result has not been described in the literature, and it is contrary to what was indicated

previously in (Zhu et al, 2002a).

Even more unusual behaviour is displayed by the 30 nm mode – see curve 1 in

Fig. 5.4a. As has been mentioned in the Introduction, this maximum has also been

observed by Zhu et al (2002a). However, their assumption that this maximum shifts

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noticeably to the right towards larger particle size (due to coagulation) with increasing

distance from the road has not been confirmed by our results. For example, as

demonstrated by curves 1 – 3 in Figs. 5.4a,b, the 30 nm mode slightly decreases in

height with increasing distance from 45 m to 57 m (curves 1, 2), and then, at 70 m,

noticeably shifts to the left rather than to the right (curve 3). This is indicated by a

noticeable ”shoulder” (at ~ 20 nm) on the right of the 12 nm maximum (curve 3). A

significant dip is left in place of the 30 nm mode. Further increasing distance to 82 m

(curve 4) causes further increase of the 20 nm mode and its merger with the 12 nm

mode, which results in a single broad maximum of approximately the same height as the

12 nm mode on curve 3. After this, increasing distance results in a monotonic decrease

of both the modes (curves 5 – 7).

Fig. 5.5. The particle size distributions with the experimental values of the average

concentrations on 23 December 2002 (midweek) at the following distances from the road: (a) 45

m, (b) 57 m, (c) 64 m, (d) 77 m, (e) 89 m, (f) 95 m. The meteorological and traffic parameters

are presented in Table 5.1. Curves (d) – (f) were measured in the afternoon when the number of

heavy truck was significantly lower (see Table 5.1).

90

At the same time, on the left of the 12 nm mode, there appears another

maximum at ~ 7 nm (curve 5 in Fig. 5.4b). This is the same maximum as the main

maximum in the Fig. 5.2. The comparison of Fig. 5.2 with curve 1 in Fig. 5.4a (the next

measured size distribution from the road) suggests that within the considered interval of

distances, processes of particle formation (coagulation) have occurred, resulting in a

significant decrease of the 7 nm mode in Fig. 5.2. Indeed, according to the Gaussian

plume dispersion (Chapter 3 and [A1]), the decrease of concentration within the

distance interval from 25 m to 45 m from the road (corresponding to the curve in Fig.

5.2 and curve 1 in Fig. 5.4a) must only be ≈ 1.8 times. However, the decrease of

concentration of the 7 nm particles within the same distance interval appeared to be ≈ 3

times. This suggests that there was a significant additional outflow of particles from this

mode, possibly due to particle coagulation.

The last obvious mode in Figs. 5.3 and 5.4 is represented by the maximum at ~

50 nm that can be seen at distances ≥ 60 m (curves 3 – 6 in Fig. 5.4a,b). This is the

mode that was interpreted by Zhu et al, (2002a) as the original 30 nm mode (curve 3)

shifted substantially to the right due to particle coagulation. However, as has been

demonstrated, this is not the case, since the 30 nm mode shifts in the opposite direction

(curves 1 – 4 in Figs. 5.4a,b).

In order to confirm these unexpected results, two other sets of measurements

were undertaken. Very similar behaviour of the size distribution modes was observed on

23 December 2002 (Fig. 5.5 – 5.6 ). The normal component of the wind velocity in this

case was noticeably larger than that on 20 November 2002 (Table 5.1). As a result, the

30 nm mode has appeared at significantly larger distances (~ 89 m) from the road –

curve 5 in Fig. 5.6b. Otherwise, the behaviour of this mode on 23 December is similar

to that on 20 November (compare curves 1 – 3 in Fig. 5.4a with curves 5 – 6 in Fig.

91

5.6b). Very similarly, the mode at ~ 7 nm can also be noticed in Fig. 5.6b (compare

curve 7 from Fig. 5.6b with curve 2 from Fig. 5.4a).

The overall noticeably larger concentrations in Fig. 5.6a than those in Fig. 5.4a

are due to the larger traffic flow, especially at the beginning of the experiment when

curves 1 and 2 in Fig. 5.6a were obtained.

Fig. 5.6. The same size distributions as in Fig. 5.5 (re-drawn for comparison) without the

experimental points.

The observed increase of the 12 nm and 20 nm modes within the range between

45 m and 82 m (Fig. 5.4a) is expected to affect the behaviour of the total number

concentration as a function of distance from the road. As a result, a substantial increase

of the total number concentration at these distances from the road was observed on 20

92

November 2002 (squares in Fig. 5.7a). The maximum of the total number concentration

is achieved at ≈ 82 m from the middle of the road (Fig. 5.7a). The error bars correspond

to the standard deviation of the mean values of the total number concentrations, and

confirm that the maximum is statistically significant.

Fig. 5.7. The dependencies of the total number concentration of particles on distance from the

road for the measurements on (a) 20 November 2002, and (b) 23 December 2002. The ranges of

particles are as indicated. The error bars show the standard deviation of the average (over five

measurements) total number concentrations. The experimental measurements were taken in the

sequence from the smallest distance to the largest. The double points at the distances 57 m and

132 m (in Fig. 5.7a) indicate the control sets of measurements in the end of the experiment for

the confirmation of the reliability and repeatability of the obtained results.

The dispersion of larger particles (> 163 nm) takes place in the usual fashion,

i.e., results in a monotonic decay with increasing distance (triangles in Fig. 5.7a). Note

93

that the overall concentration of these larger particles is negligible compared to the

concentration within the range < 163 nm (Fig. 5.7a). Therefore, these larger particles do

not have any effect of the observed maximum of the total number concentration.

Moreover, as can be seen (dots in Fig. 5.7a), the total number concentration within the

range > 30 nm also decays monotonically with distance, which strongly suggests that

the observed maximum of the total number concentration is caused by some

physical/chemical mechanisms resulting in increasing number of particles within the

range ≤ 30 nm (for a detailed description of such mechanisms see Sections 6 and 7). It is

important to note that the thermal rise does not have a noticeable effect on aerosol

dispersion near a busy road (confirmed experimentally by Zhu & Hinds (2005)).

The two additional points at the distances 50 m and 125 m (Fig. 5.7a) represent

two control measurements of the total number concentrations at the end of the

experiment. This was done to confirm the reproducibility of the obtained results. The

point in Fig. 5.7a at ≈ 232 m from the road does not seem to be an outlier (though this

was indicated in [A3]). On the basis of distribution of the experimental points (Fig.

5.7a) around the theoretical dependencies derived below in Chapter 7 (and in [A5]),

discarding the point at ≈ 232 m from the road (Fig. 5.7a) does not seem reasonable.

Note that Fig. 5.7b also demonstrates a tendency towards a maximum of the

total number concentration at the distances between ~ 90 m and ~ 150 m from the road.

However, with only a couple of measurements at these distances, it is difficult to state

with certainty that this maximum really exists. Nevertheless, because the normal wind

component for Fig. 5.7b is ~ 2 times larger than that for Fig. 5.7a, it is possible to

expect that the maximum of the total number concentration may occur in Fig. 5.7b at

approximately 150 m from the road.

The obtained results and dependencies are strongly affected by the type of

vehicles on the road. For example, measurements on weekend (24 November 2002)

94

resulted in noticeably different dependencies – Fig. 5.8. In particular, the 12 nm

maximum is relatively small (Fig. 5.8), which is related to the significantly smaller

number of heavy duty diesel trucks in the traffic flow. This is in agreement with the

earlier conclusion that this mode is mainly due to diesel vehicles (Zhu et al, 2002a).

Otherwise, the dependencies in Figs. 5.4a,b, 5.6b and 5.8 are fairly similar.

Fig. 5.8. The particle size distributions on 24 November 2002 (Sunday), with significantly

lower contribution of trucks (see Table 5.1). The dependencies were plotted using the Freedman

super smoother technique.

The measurements on 8 January 2003 resulted in a substantial scatter of

concentrations within channels, not allowing repeatable size distributions. This is due to

the wind being almost parallel to the road (Table 5.1 and Fig. 5.1). In this case, large

tangential component of the wind results in increased turbulence and, therefore,

fluctuations of concentration. Thus, the evolution effects are masked by strong turbulent

fluctuations. In this circumstances, significantly more than five measurements of size

distribution are required to obtain a repeatable average size distribution.

The dependence of the total number concentration on distance from the road for

8 January 2003 is shown in Fig. 5.9 by the squares for the range of particles from 4 nm

to 163 nm. In this case, methods of curve fitting based on the exponential function c =

95

k1e-αd (Hitchins et al, 2001, and Zhu et al, 2002a) or the power law c = k2d-m (Chapter 3)

with k1 = 7.0×104, α = 0.015, and k2 = 2×105, m = 0.5 can be used. The t-values (Larsen

& Marx, 1986) in these cases are as high as 17, 10, 5, and 8 for k1, α, k2, and m,

respectively. This indicates that the level of confidence for fitting both exponential and

power curves exceeds 99%.

Fig. 5.9. The total number concentrations on 8 January 2003 (almost parallel wind) within the

particle ranges: 1) from 4.6 nm to 163 nm; 2) from 7 nm to 20 nm; 3) from 21 nm to 42 nm

(includes the 30 nm mode). The curves are plotted by the Loess regression (Venables and

Ripley, 2000).

On the other hand, in order to reveal small features of the dependencies of the

total number concentration on 8 January 2003, the Loess regression (Venables &

Ripley, 2000) was used. This method is more efficient (than the Friedman super

smoother) in drawing regression curves with small features represented by a few

experimental points (Venables & Ripley, 2000). The obtained regression curves are

shown in Fig. 5.9 for the total number concentrations within the three size ranges as

functions of distance from the road. In particular, it can be seen that curve 3

corresponding to the 30 nm mode displays a tendency to levelling at the distances

96

between 25 m to 70 m. This may indicate an inflow of particles into this mode. This is

probably the reason for the small bump on curve 1 at ~ 50 m from the road. As a result,

mode evolution observed in Figs. 5.3 – 5.8 has only a very limited effect in the case of

almost parallel wind.

5.4. Level of confidence and errors

There are several sources of possible errors in the obtained experimental results.

In this section, we will consider their contribution to the level of confidence of the

features of mode evolution and will demonstrate the validity of the results.

One of the questions that may arise is that the measurements undertaken in this

chapter were not simultaneous at different distances. From this point of view, sufficient

stability of the average environmental and traffic conditions is important (this is

discussed below). However, observation of the consistent features of particle size

distributions, total number concentration, and their evolution during at least 6

independent sets of measurements on different days under different conditions (plus

another independent confirmation by the group at Lancaster University, UK) seems to

be a sufficient demonstration of the general validity of the obtained results.

Specifically, the first source of errors can be associated with changing

atmospheric parameters during the course of measurements. However, as shown in

Table 5.1, standard deviations of such parameters as humidity and temperature are small

during each of the measurement periods. These small variations of humidity and/or

temperature can hardly affect the presented curves for size distributions. This, however,

does not mean that temperature and humidity do not affect the described mode

evolution. On the contrary, they are expected to be important for understanding the

behaviour of the modes – see Chapters 6, 8, 10 and [A4, A6, A8, A9].

97

The standard deviations of speed, direction, and normal component of the wind

are large (as expected) due to strong turbulence (Table 5.1). However, the associated

random errors of particle concentrations in this case are effectively reduced by taking

the average of five scans at every distance from the road (see Section 5.2). This

statement is confirmed by the limited dispersion of experimental (average) points

around the size distribution curves (Figs. 5.3 and 5.5).

Solar radiation changed fairly noticeably (Table 5.1). However, no direct and

obvious effect of solar radiation on the observed mode evolution has been detected.

Once again, this does not mean that there is no such an effect (which should be the

matter for further investigation), but rather that the appearance and transformation of the

modes in our experiment did not correlate with the solar radiation.

Standard deviations of the overall traffic (for the traffic flow measured in 5

minute intervals) on all days of measurements were less than 10%, and the standard

deviations for trucks ~ 20%. This is a clear indication of a highly stable traffic

conditions on the considered road. Insignificant contribution of traffic variations to the

errors of the measured particle size distributions and the total number concentrations is

also demonstrated by the control measurements conducted in the end of the

measurement period on 20 November 2003 (see the additional two points at the

distances 57 m and 132 m in Fig. 5.7a). The two size distributions at the distance 57 m

for the original (curve 2 in Fig. 5.4a) and control sets of five scans were hardly

different. This is also another confirmation of the high stability of the obtained results

with respect to the fluctuations of the meteorological parameters, including wind speed

and direction.

At the same time, it is important that on 23 December 2003, traffic conditions

changed substantially for the morning and afternoon measurements (due to the next day

holiday). The number of trucks in the afternoon dropped very noticeably (see Table

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5.1). This was one of the major reasons why the 30 nm mode and 20 nm modes in Fig.

5.6b were substantially smaller than those in Fig. 5.4a. This is also likely to be a reason

for the maximum of the total number concentration in Fig. 5.7b to be significantly

smaller than in Fig. 5.7a. Nevertheless, despite such a drastic variation in the traffic

flow, the major features of the mode evolution remained unchanged (compare Fig. 5.4a

with Fig. 5.6b). This clearly demonstrates that the discovered unusual features of the

aerosol evolution are highly resilient to variations of traffic flow, and that they are not

an artefact of changing atmospheric and traffic conditions.

In addition, levels of confidence for all of the maxima of the size distributions

(modes) in Figs. 5.4, and 5.6 were determined by means of known statistical methods

(Bowman and Azzalini, 1997). Using S-Plus, the experimental point near each of the

modes are approximated by a polynomial of the fifth order (to include the neighbouring

modes). The level of confidence of the considered mode is then determined using the

two neighbouring minima and the error of the approximation (Bowman and Azzalini,

1997). The resultant values of level of confidence for the modes in Figs. 5.2 – 5.6 are

presented in Tables 5.2 and 5.3, clearly demonstrating the validity of the obtained

results and conclusions.

25 m 45 m 57 m 70 m 82 m 107 m 132 m 307 m 7 nm >99 - - - 85 91 - >99 12 nm 83 >99 >99 >99 >99 >99 >99 - 20 nm 83 - - - - - - - 27 nm >99 >99 >99 - - - - - 50 nm >99 - - 99 81 91 >99 79

Table 5.2. Levels of confidence in % for different modes on the curves in Figs. 5.2 –

5.4 (20 November 2003). The modes are shown in the first column, while the distance

from the road (corresponding to different curves in Figs. 5.2 – 5.4) are shown in the first

row.

99

45 m 57 m 64 m 77 m 89 m 95 m12 nm >99 >99 >99 >99 >99 >99 20 nm - - - - - 89 30 nm - - - - >99 - 40 – 50 nm - >99 99 >99 - -

Table 5.3. Levels of confidence in % for different modes on the curves in Figs. 5.5 –

5.6 (23 December 2003).

Finally, it can be shown that the effect of Wynnum road (Fig. 5.1) is negligible.

Indeed, the Gaussian plume approximation gives that particle concentrations should

decay as a power function of distance from the road (Chapter 3 and [A1]). Taking into

account the typical traffic flow on Wynnum road (2127 vehicle/hour with 1.8% of

heavy duty trucks), the distance to the place of measurements (600 – 800 m), and the

average emission factors for light cars and heavy-duty trucks (Chapter 4 and [A2]), we

obtain that the typical concentrations due to Wynnum road are at least ~ 10 times less

than those from the Gateway Motorway at all sampling points.

5.5. Conclusions

In this Chapter, for the first time, a detailed experimental investigation of the

evolution of particle size distribution modes in the fine and ultra-fine ranges has been

carried out near a busy road. A number of unexpected and unusual effects have been

observed. These are related to mutual transformation of different modes, resulting in

appearance, growth and disappearance of these modes at particular distances from the

road. For example, the first clear and consistent experimental evidence of existing of a

strong 7 nm mode of particles has been obtained. A strong mode at ~ 30 nm particle

diameter appears at a particular distance from the road. This mode has been shown to

consistently shift to the left, i.e. towards smaller particle diameters. As a result, the 30

nm mode is transformed into the 20 nm mode, and then into the 12 nm mode. At the

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same time, it has been shown that during the whole process of mode conversion and

transformation, the particle concentration in the 7 nm mode changes only insignificantly

(increasing at some stages) with increasing distance from the road. Therefore, since

dispersion must obviously result in a significant reduction of particle concentrations,

there is a substantial influx of particles into the 7 nm mode during the aerosol evolution

and its transport away from the road.

For the first time, clear experimental evidence of a maximum of the total

number concentration at a particular distance from the road has been obtained. This

maximum has been shown to occur due to a strong increase of particle concentration

within the range < 30 nm. The observed maximum has been demonstrated to decrease

and move away from the road with increasing normal (to the road) component of the

wind. The effect of normal wind component on the particle size distribution has also

been investigated. For example, increasing normal component of the wind results in

approximately proportional increase of the distance at which the 30 nm mode appears.

If the average wind is approximately parallel to the road, then the observed modes are

shown to significantly fluctuate due to the turbulence and stochastic nature of

fluctuations of wind direction.

Statistical analysis of the errors associated with the experiments have been

conducted, and the levels of confidence for the observed modes of particle size

distribution have been determined, clearly confirming the obtained results and

conclusions.

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CHAPTER 6

A NEW MECHANISM OF AEROSOL EVOLUTION NEAR A BUSY ROAD: FRAGMENTATION OF NANO-PARTICLES ([A4, A18, A22,

A23, A25, A26])

6.1. Introduction

As has been demonstrated in the previous Chapter 5, combustion nano-particle

aerosols may experience rapid evolutionary processes near their major source – busy

roads. Therefore, investigation and modelling of the specific mechanisms responsible

for these processes are essential for understanding and reliable prediction of aerosol

dispersion in the urban environment. However, serious doubts about the possibility of

using only the conventional mechanisms of evolution of combustion aerosols, e.g., such

as particle formation and coagulation, arise if we attempt a comprehensive explanation

of the experimental features of the aerosol evolution and particle mode transformation

(Chapter 5 and [A3]). For example, because at the considered particle concentrations

coagulation is highly inefficient (Jacobson, 1999, Jacobson and Seinfeld, 2004, Pohjola

et al, 2003, Zhang & Wexler, 2004, Zhang et al, 2004), it can hardly result in the

observed strong changes in the particle size distribution. It is also difficult to expect that

only particle formation and coagulation can be used for the interpretation of the

observed evolution of the 30 nm mode into the 20 nm mode and then into the 12 nm

mode (Chapter 5).

In this Chapter, we present further experimental evidence that the conventional

mechanisms of aerosol evolution are insufficient for a comprehensive interpretation of

the experimental observations of evolution of combustion aerosols near busy roads. A

new statistical method of analysis will be developed for the investigation of particle

modes. An alternative definition of particle modes will be presented. As a result, a

number of distinct modes strongly interacting with each other will be shown to exist in

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particle size distributions in the presence of strong turbulent mixing. A new mechanism

of mode evolution, based on thermal fragmentation of nano-particles, will be introduced

and justified. A complex pattern of the aerosol evolution will be suggested, including

several stages of particle formation, coagulation, and fragmentation.

6.2. Modes of particle size distribution

The new method of statistical analysis of particle modes near a busy road is

demonstrated and developed on an example of 50 independent scans of particle size

distribution, obtained on 25 November 2002 within the time interval of 3 hours at the

distance of 40 m from the centre of the road (Gateway Motorway, Brisbane area,

Australia). The description of the road and the environment at the point of monitoring is

presented in Chapter 5 (see also Fig. 6.1 with the indicated wind directions during this

monitoring campaign).

The size distributions of fine and ultra-fine particles in the range from 4.6 nm to

163 nm were measured at the height h = 2 m above the ground level (i.e. approximately

at the level of the Motorway). The measurements were taken by means of a scanning

mobility particle sizer SMPS 3936 and the condensation particle counter CPC 3025 in N

= 100 equal intervals of Δlog(Dp) (where Dp is particle diameter in nanometres). The

time for one full scan was 2.5 minutes. An automatic weather station was used to

measure temperature, humidity, wind speed, wind direction and solar radiation at the

same height h = 2 m and ~ 45 m from the middle of the road every 20 sec during the

whole period of the concentration measurements.

103

Fig. 6.1. The area of measurements near Gateway Motorway, Brisbane, Australia. The indicated

receptor point is at the distance 40 m from the centre of the road. The scale of the map and the

direction to the North are as indicated (the distances on the axes are given in meters). The

crosses indicate the receptor point.

The time dependencies of the wind direction and speed during the

measurements, plotted by means of the Friedman super smoother (Venables & Ripley,

2000), are presented in Figs. 6.2a,b. It can be seen that these dependencies give

approximately constant average wind directions and speeds within the time intervals

between 14:05 and 14:42 (indicated by the dashed vertical line in Fig. 6.2a,b) and

between 15:06 and 16:16 (indicated by the two dotted vertical lines in Figs. 6.2a,b).

These time intervals correspond to following two sets of scans: (i) scans from 1 to 11

(between 14:05 and 14:42), and (ii) scans from 19 to 38 (between 15:06 and 16:16). The

104

average normal and parallel (to the road) components of the wind for these sets are then

determined as: (i) v⊥ = 1.65 ± 0.16 ms-1, v|| = 1.6 ± 0.2 ms-1; (ii) v⊥ = 0.8 ± 0.1 ms-1, v|| =

2.4 ± 0.3 ms-1. We will consider these sets of scans separately because they correspond

to significantly different (on average) stages of the aerosol evolution. Indeed, since the

normal wind component for set (i) is approximately two times larger than that for set

(ii), the time that it takes for the aerosol to reach the point of observation during set (i) is

approximately twice as small. The difference between the average evolution times for

the two sets of measurements is thus ~ 25 s. The other meteorological and traffic

parameters are presented in Table 6.1 for both the sets of scans.

It is important to understand that here we consider average wind components

rather than their instantaneous values. Consideration of the instantaneous values cannot

be justified due to stochastic nature of the atmospheric turbulence (Csanady, 1980).

These strong stochastic turbulent fluctuations are typically taken into account in the

analysis through turbulent diffusion in the atmosphere, which represents a type of

averaging of these fluctuations and the resultant diffusive transport/dispersion of

aerosols (Csanady, 1980). Certainly, instantaneous evolution times for particular

aerosol/air samples (i.e., the time of aerosol transportation to the monitoring point) vary

significantly due to violent turbulent fluctuations – Fig. 6.2. However, the developed

approach is based on averaging evolution time, and thus determining averaged

evolutionary changes of aerosol nano-particles (which is analogous to considering

turbulent diffusion as opposed to instantaneous acts of stochastic transportation of

particular air portions (Csanady, 1980)). This is the reason for using average values of

wind speed and direction (Fig. 6.2), i.e., wind components v⊥ and v||, and considering

their differences for the two different selected sets of scans.

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Fig. 6.2. The time dependencies of (a) the wind direction (i.e. the angle between the wind

direction and the road), and (b) wind speed. Both the curves have been plotted by means of the

Freedman super smoother (Venables & Ripley, 2000). The measurements of the wind direction

and wind speed were taken by an automatic weather station at the rate of one measurement per

minute and three measurements per minute, respectively. The sets of 11 and 20 scan are denoted

by the dashed and two dotted vertical lines, respectively.

The corresponding average (over 11 and 20 scans) particle size distributions are

presented in Fig. 6.3a,b. Not much can be seen from these distributions, apart from the

strong maximum between ~ 10 nm and ~ 12 nm in both the figures, and a weak ~ 50 nm

mode in Fig. 6.3a. No conclusions about possible interaction of modes, and/or their

evolution can be made directly from these figures. Nevertheless, even if distinct features

of a size distribution are effectively smoothed out by strong turbulent mixing (as in

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Figs. 6.3a,b), as shown below, the statistical analysis will clearly reveal a number of

particle modes and their mutual interactions.

Fig. 6.3. The average particle size distributions of concentrations in 100 channels on 25

November 2002 at the same distance of 40 m from the centre of the road, but at significantly

different normal and parallel one hour average wind components: (a) v⊥ = 1.65 ± 0.16 ms-1, v|| =

1.6 ± 0.2 ms-1 (for the set of 11 scans); (b) v⊥ = 0.8 ± 0.1 ms-1, v|| = 2.4 ± 0.3 ms-1 (for the second

set of 20 scans). The meteorological and traffic parameters, as well as their standard deviations,

are presented in Table 6.1.

We re-define particle modes as groups of particles in neighbouring channels,

such that particle concentrations in these channels tend to fluctuate in correlation with

each other. In particular, this suggests that such groups of particles are likely to have the

same nature and/or come from the same source (i.e., are likely to be generated by the

same mechanism). Usually, this new definition does not contradict the conventional

mode definition as distinct maxima of a particle size distribution. We will see below

that in several cases it results in the same modes as those that were directly observed

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under more favourable meteorological conditions (Chapter 5 and [A3]). However, the

new definition makes more physical sense, emphasises the actual nature of the aerosol

particles, and will allow mode analysis in the case of strong turbulent mixing (Fig.

6.3a,b). If two or more modes overlap, i.e. the corresponding particles come from

different sources / physical processes, then correlations between particle concentrations

in neighbouring channels should typically reduce in the overlap region. This effect

enhances the appearance of the correlation maximums corresponding to separate

particle modes, which makes the analysis of evolution and transformation of different

types of aerosol particles much more obvious. As a result, it will be possible to clearly

see and identify particle modes even if there are no any distinct features of the

conventional size distributions (e.g., due to strong turbulent mixing – Figs. 6.3a,b).

To determine particle modes (as maximums of the correlation coefficients) from

multiple scans of size distribution in the absence of obvious features of this distribution

(Figs. 6.3a,b), correlations between particle concentrations in neighbouring channels of

the size distribution were determined using the following steps.

Step 1. Normalise particle concentrations in each channel in every scan to the

total number concentration in this scan. Thus we eliminate trivial correlations between

channel concentrations, caused by changing total number concentration.

Step 2. Select an interval of n channels out of the overall N channels in a scan

(in our case, N = 100).

Step 3. Choose two different channels from the n-channel interval, and

determine the simple correlation coefficient (Larsen and Marx, 1986) between particle

concentrations in these two channels over the M scans (in our case M = 11 or 20). In

other words, simple correlation is determined between two columns of concentrations in

two chosen channels, the number of elements in each of the columns being equal to the

number of scans M.

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Step 4. The procedure is repeated m = n!/[2!(n – 2)!] times for all possible

different pairs of channels in the n-channel interval.

Step 5. The average correlation coefficient for the considered n-channel interval

is determined.

Step 6. If n is odd, then steps 2 – 5 are repeated for all N – (n – 1) different n-

channel intervals, giving N – (n – 1) different values for average correlation coefficient.

At the same time, each n-channel interval can be characterised by an average

particle diameter. For example, if n is odd, then this will be the diameter corresponding

to the middle channel of the n-channel interval. As a result, we obtain a dependence of

the moving average of the correlation coefficient versus average particle diameter. The

number n is chosen as a compromise between mode resolution and statistical errors

(standard deviation of the moving average), both increasing with decreasing n.

The procedure was applied to the two sets of M = 11 and M = 20 scans (see

above) with N = 100 and n = 7 (m = 21). The resultant dependencies of the moving

average correlation coefficients are presented in Fig. 6.4a,b. It can clearly be seen that

despite the absence of noticeable features on the average particle size distributions

(Figs. 6.3a,b), the dependencies in Figs. 6.4a,b display a number of distinct and

pronounced maxima and minima with the level of confidence of the corresponding

correlations (Larsen & Marx, 1986) of no less than 95% for all points on the curves (see

the Appendix to this Chapter for the procedure of calculating the levels of confidence).

The corresponding error curves (representing the errors of the moving average

correlation coefficients) are presented in Figs. 6.5a,b. These clearly demonstrate that all

of the obtained maxima, except for those at ~ 14.6 nm and ~ 31 nm in Fig. 6.4a and ~

31 nm and ~ 35 nm in Fig. 6.4b, are statistically significant. A correlation maximum

was assumed to be statistically significant if the lower limit of the error band at this

109

maximum is higher than the upper limits of the error band at the two neighbouring

minima (Figs. 6.5a,b).

Fig. 6.4. The dependencies of the moving average of the correlation coefficient, R, between the

particle concentrations in different channels on particle diameter. The averaging is carried out in

each of the different intervals of 7 neighbouring channels, thus giving 94 average values of the

correlation coefficients, i.e., 94 points in the presented graphs. The curves are obtained by

simply connecting the neighbouring points. The moving average correlation coefficients are

calculated over (a) the first set of 11 scans (scans from 1 to 11); (b) the second set of 20 scans

(scans from 19 to 38).

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Fig. 6.5. The error curves determining the errors of the moving average correlation coefficients

represented in Figs. 6.4a,b. The two curves in each of the figures (a) and (b) give the limits of

the range of possible statistical errors for every considered particle diameter. This demonstrates

that all the modes are statistically significant, except for the 14.6 nm and 31 nm modes in Figs.

6.4a, and 31 nm and 35 nm modes in Figs. 6.4b.

The obtained maxima correspond to groups of particles of similar size with

strong mutual correlations, which means that concentrations of these particles tend to

increase/decrease simultaneously in strong correlation with each other. For example,

this is the case for particles within the size range from ≈ 10 nm to ≈ 15 nm in Fig. 6.4b.

These particles appear to be in strong correlation with each other, and thus can be

regarded as a mode.

Thus particle modes can be re-defined as groups of particles of similar size, that

are characterised by pronounced maxima of mutual correlations. This definition is more

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general and physically meaningful, than the previous definition of a mode as a group of

particles corresponding to a maximum on a particle size distribution.

It is important that such a large number of different particle modes (Figs. 6.4a,b)

in a single size distribution has never been obtained previously (even at more favourable

atmospheric conditions with weaker turbulent mixing (Zhu et al, 2002, Chapter 5 and

[A3]). This clearly demonstrates the effectiveness of the proposed method that provides

a new physical insight into the processes of aerosol evolution.

6.3. Maximum of the total number concentration

In Chapter 5 and [A3], for the first time, a maximum of the total number

concentration was observed at an optimal distance from the road. This means that the

total number concentration may increase with increasing distance from the road. For

example, in Chapter 5, this maximum was observed at the distance of ~ 80 m from the

road, and the total number concentration increased within the interval from ~40 m to ~

80 m from the road (for the normal component of wind ≈ 1.15 m/s). It is important that

the experiment described above in Section 6.2 clearly confirms those previous results.

Indeed, the total number concentrations calculated for the particle size

distributions presented in Figs. 6.3a,b were determined as N1 ≈ (23 ± 3)×104

particles/cm3 and N2 ≈ (40 ± 3)×104 particles/cm3, respectively. The background

particle concentration was taken to be N0 ~ 2,400 particles/cm3 (measured for the

similar conditions in (Chapter 3 and [A1]). However, the direct comparison of N1 and

N2 is not possible, since the wind conditions were different for the two sets of scans

corresponding to Figs. 6.3a,b. Therefore, the following procedure was used. Using the

calculated value of N1 and the software package CALINE4 (adjusted for predicting

aerosol dispersion near a busy road (Chapter 3 and [A1])), the model emission factor Em

= 229 from the average fleet on the road (Chapter 3 and [A1]) was determined for the

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meteorological and traffic parameters corresponding to the first set of 11 scans at the

considered distance 45 m from the centre of the road.

scans 1 to 11 scans 19 to 38

wind direction, degrees to the road

43 ± 20 18 ± 19

wind speed, ms-1 2.3 ± 0.2 2.6 ± 0.9

temperature, °C 28.2 ± 0.3 27.2 ± 0.3

humidity, % 29 ± 1 36 ± 1

solar radiation, Wm-2

860 ± 40 560 ± 80

trucks, hour-1 810 ± 140 790 ± 140

cars, hour-1 3800 ± 400 4800 ± 500

Table 6.1. Meteorological and traffic parameters.

The traffic flow for both the sets of scans is regarded to be approximately the

same. This is because the emission factors for cars are about two orders of magnitude

less than those for heavy trucks (Chapter 4 and [A2]), and increase of the number of

cars by ~ 1000 for the second set of scans (see Table 6.1) is approximately cancelled by

the simultaneous reduction of the number of trucks by ≈ 20 (Table 6.1). Therefore, the

effective traffic flow can be regarded as approximately the same. Then, using the

determined emission factor from the average fleet on the road Em and the CALINE4

model, the total number concentration was calculated for the wind parameters

corresponding to the second set of scans: 2N′ ≈ 19.6×104 particles/cm3. This is the

concentration that one would have expected for the second set of scans if the Gaussian

plume approximation were correct.

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In other words, we determine the model emission factor corresponding to the

evolution time t1, which is the time of transport of the aerosol from the road to the point

of observation for the first set of scans. Then, using this model emission factor (which

should not change significantly between the two sets of scans), we determine the

corresponding total number concentration at a different evolution time t2 ≈ t1 + 25 s,

which is the time of transport of the aerosol from the road to the point of observation for

the second set of scans.

However, we have: (N2 – N0)/( 2N′ – N0) ≈ 2.19. Thus, the Gaussian plume

approximation is not valid, and an additional strong influx of particles from some

“internal” sources exists during the evolution of the aerosol within the ~ 25 s between

the two sets of scans (see section 2). In other words, due to the presence of these

“internal” sources, the number of particles in the aerosol increases 2.19 times within the

time interval of ~ 25 s. This means that the total number concentration may increase

with increasing distance from the road, if the dispersion is not sufficient to suppress the

above increase of the number of particles. This is another confirmation of the

experimental observation of a maximum of the total number concentration at an optimal

distance from the road in (Chapter 5 and [A3]).

6.4. Failure of the conventional mechanisms of the aerosol evolution

Interpretation of the results obtained in sections 2 and 3 may present a challenge

if we intend to use only the conventional mechanisms of aerosol evolution, such as

particle formation, condensation, evaporation, coagulation, and dispersion.

For example, the observed increase of the number of particles during the

evolution of the aerosol within ~ 25 s cannot be explained by particle formation. Indeed,

if this were the case, the number of smaller particles within the range < 8 nm would

have increased much more significantly than the number of the larger particles with the

diameters > 8 nm. At the same time, the comparison of Figs. 6.3a,b suggests the

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opposite: the number of particles within the range between ~ 8 nm and ~ 30 nm

increases, whereas the number of particles with the diameters less than ~ 8 nm is

practically the same for both size distributions. In addition, it is difficult to imagine that

particles of ~ 10 – 20 nm diameter may be formed or significantly increase their

diameter due to nucleation processes within ~ 25 s near a busy road with relatively low

levels of gaseous pollutant concentrations (Fig. 6.3a,b). Therefore, there should be some

other “internal” source of particles as the aerosol is transported away from the road.

Strong differences can be seen in the mode structure for the two sets of scans in

Figs. 6.4a and 6.4b. In the range between ~ 6 nm and ~ 14 nm, and between ~ 35 nm

and ~ 80 nm, maxima in Fig. 6.4a correspond to minima in Fig. 6.4b. In addition, Fig.

6.4a displays three sharp minima of correlations at ~ 7 nm, ~ 10 nm, and ~ 70 nm. In

Fig. 6.4b, these minima disappear, turning into maxima. A very strong and broad

maximum of correlations appears between 9.5 nm and 15.5 nm (Fig. 6.4b). All this

strongly suggests the presence of fast and strong processes of evolution and

transformation of aerosol particles. For example, substantial variations of the correlation

coefficient (e.g., at ~ 10 nm or ~ 70 nm) must be linked to an inflow or outflow of

particular particles into or out of the corresponding range of diameters. This means that

within the time interval of ~ 25 s (the difference in the evolution time between the sets

of the scans – see section 2) particles in the ranges from ~ 6 nm to ~ 14 nm and from ~

35 nm to ~ 80 nm experience substantial variations of their properties and size.

It is hardly possible to expect that coagulation may be responsible for the

observed mode evolution. Indeed, according to (Jacobson and Seinfeld, 2004),

coagulation is highly inefficient at the considered particle size and concentrations (Figs.

6.3a,b) and cannot account for the drastic evolution of the particle modes (Figs. 6.4a,b).

In addition, coagulation hypothesis is in obvious contradiction with the observed

115

increase of the number of particles in the aerosol within the time interval ~ 25 s between

the two sets of scans.

Condensation/evaporation alone would be likely to shift the mode pattern in Fig.

6.4a to the right or to the left without significant changes of the mode structure

(assuming similar chemistry for the particles). However, this contradicts the results

presented in Fig. 6.4b. In addition to significant variations of the overall pattern of

minima/maxima, Fig. 6.4b displays a significantly larger shift (by more than ~ 10 nm)

of the modes in the range between ~ 35 nm and ~ 80 nm, than in the range between ~ 6

nm and ~ 14 nm (by ~ 2 – 3 nm). This would be difficult to explain using the

condensation/evaporation mechanism alone. The appearance of a strong and broad

maximum at ~ 12 nm (Fig. 6.4b) with surprisingly small errors (Fig. 6.5b) would also

be difficult to explain by condensation/evaporation.

Even more importantly, the analysis of correlations between the 5.7 nm mode

and other modes in Fig. 6.4a, and between the 7.9 nm mode and other modes in Fig.

6.4b suggests that the 7.9 nm mode in Fig. 6.4b is unlikely to result from shifting the 5.7

nm mode to the right, since these modes are characterised by strongly different

correlations with other modes (for more detail see (Chapter 7 and [A5]). In addition, the

same analysis shows that the 7.9 nm mode in Fig. 6.4b is likely to result from the 8.8

nm mode in Fig. 6.4a, shifting to the left (towards smaller particle size). At the same

time, the 5.7 nm mode simply disappears in Fig. 6.4b. This can be explained by an

assumption that the 5.7 nm mode is likely to consist of liquid volatile particles that

effectively evaporate within the evolutional time interval of 25 s between the two sets of

scans corresponding to Figs. 6.4a,b.

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Fig. 6.6. Particle size distributions obtained on 20 November 2002 at the indicated distances

from the centre of the road (reproduced from Chapter 5). The normal one hour average wind

component v⊥ = 1.15 m/s. The other meteorological and traffic parameters are presented in

Table 5.1.

From this point of view, it is interesting that 8.8 nm particles can be obtained

when a 7.9 nm (presumably solid – see below) particle coagulates with a liquid 5.7 nm

particle. Therefore, it is possible that the 8.8 nm mode in Fig. 6.4a may have resulted

from coagulation of the 5.7 nm and 7.9 nm modes near the exhaust pipe where the

concentration of particles is sufficient for this process to occur (Jacobson, 1999,

Jacobson and Seinfeld, 2004).

As the aerosol is transported away from the road, the concentration of volatile

compounds in the air is reduced, and the fluid particles (and the volatile coating of solid

particles) start evaporating. This results in shifting the 8.8 nm mode (Fig. 6.4a) to the

117

left into the 7.9 nm mode (Fig. 6.4b). The strong minimum of correlations between the

5.7 nm and 8.8 nm modes in Fig. 6.4a can be explained by the presence of both solid

and liquid particles with different (opposite) correlations.

Similarly, the conventional mechanisms of particle transformation can hardly

explain a number of previously observed features of the particle size distribution near

the same road on at least four other days of measurements (Chapter 5 and [A3]). For

example, Figs. 6.6 and 6.7 reproduced from (Chapter 5 and [A3]) clearly demonstrate

the appearance of a strong 30 nm mode at some distance from the road (curves 1 and 6

in Figs. 6.6a and 6.7b, respectively), its subsequent shift to the left into the 20 nm mode

(curves 2 and 3 in Fig. 6.6a, and curve 7 in Fig. 6.7b), and then into the 12 nm mode

(curves 3 and 4 in Fig. 6.6) with the simultaneous increase of the 7 nm mode (curves 2 –

5 in Fig. 6.6, and 7 in Fig. 6.7b). The correspondence of these curves to the

experimental points is demonstrated in (Chapter 5 and [A3]). The levels of confidence

for the observed modes and analysis of the experimental errors are also discussed in

(Chapter 5 and [A3]). As a result, the coagulation model obviously runs into severe

problems with explaining the discussed pattern of evolution (in addition to the serious

doubts about its effectiveness (Jacobson, 1999, Pihiola et al, 2003, Jacobson and

Seinfeld, 2004, Zhang & Wexler, 2004, Zhang et al, 2004)).

Fig. 6.6a clearly suggests that the 12 nm mode substantially increases with

increasing distance from the road from 45 m to 82 m. One might think that this could be

caused by particle formation from gasses due to heterogeneous nucleation of particles,

e.g., from the 7 nm mode. However, if this were the case, the 7 nm mode would have

been a source for the 12 nm sink mode. This is in contradiction with curves 4 and 5 in

Fig. 6.6b, which display an increase of the source 7 nm mode with the simultaneous

decrease of the sink 12 nm mode. Obviously, a sink mode cannot decrease with

increasing its source (unless there appears an additional mechanism depleting the sink

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mode, which in this case is unlikely). Therefore, the 7 nm mode cannot be a source for

the 12 nm mode, and increase of the 12 nm mode displayed by curves 1 – 4 in Figs.

6.6a,b cannot be explained by heterogeneous nucleation. On the other hand,

exceptionally large average correlation coefficients and noticeably reduced statistical

errors for the 12 nm (Figs. 6.4b, 6.5b) suggest that the particles in this mode should

come from the same source (must be caused by the same mechanism).

Comparison of curves 2 – 5 in Figs. 6.6a,b also suggests that typical

concentration of ~ 7 nm particles is almost independent of distance from the road

(staying at ~ 20000 cm-3), and results in a distinct maximum on curve 5. Note that at the

same time concentrations in other channels are significantly reduced by dispersion. This

strongly suggests that there is a substantial influx of particles into the 7 nm mode due to

some physical/chemical mechanisms. If these were only nucleation processes, why

would this influx increase when the neighbouring 12 nm mode starts decreasing

substantially (curve 5 in Fig. 6.6b)? Why would the maximum of the 7 nm mode (curve

5) coincide with almost two times drop in the 12 nm mode within the distance of 25 m

(compare curves 4 and 5 in Fig. 6.6a), whereas the Gaussian plume approximation

(Csanady, 1980, Gramotnev et al, 2003) suggests only 1.2 times decrease within the

same distance? Why would the influx into the 7 nm mode practically cease or at least

significantly reduce only after other modes have been seriously depleted (see the 7 nm

mode strongly decreasing on curves 6 and 7 in Fig. 6.6b)?

119

Fig. 6.7. Particle size distributions obtained on 23 December 2002 at the indicated distances

from the centre of the road (reproduced from Chapter 5). The normal one hour average wind

component v⊥ = 2.05 m/s. The other meteorological parameters are approximately the same as

for Fig. 6, and are presented in Table 5.1.

In addition, as mentioned in section 3, the experimental measurements clearly

demonstrate that the process of shifting the 30 nm mode to the left (i.e. into the 20 nm

and 12 nm modes) coincides with a substantial increase of the total number

concentration of nano-particles within the interval of distances from ~ 45 m to ~ 82 m

from the road – see Fig 6.7a from (Chapter 5 and [A3]) and section 3 above.

It is thus clear that the conventional mechanisms, such as particle formation,

condensation, evaporation, coagulation, and dispersion, cannot fully explain all the

experimentally observed effects of aerosol evolution and mode transformation near a

busy road. The discussed contradictions suggest that a new mechanism of aerosol

120

evolution is required. This mechanism will be based on thermal fragmentation of nano-

particles.

6.5. Fragmentation model of aerosol evolution

The possibility of fragmentation of soot aggregates has previously been

discussed in (Mikhailov E. F., et al, 1996, Harris & Maricq, 2002, Kostoglou &

Konstandopoulos, 2003). For example, Mikhailov et al (1996) demonstrated

experimentally that large soot aggregates (with ~ 2 μm2 – 5 μm2 projection) produced

under special laboratory conditions can experience fragmentation at ~ 100oC and

between 300oC and 500oC. Harris and Maricq (2002) showed that allowing for

fragmentation of relatively large soot nano-particles (of mobility diameter ~ 100 nm)

slightly improved the fit of the theoretical curves to the experimental data points for

particle size distributions obtained under special laboratory conditions. Kostoglou and

Konstandopoulos (2003) suggested an oxidation mechanism for fragmentation of large

soot aggregates, also under special laboratory conditions, and again with relatively

minor effect of fragmentation on particle size distribution.

In this section, fragmentation of much smaller particles will be considered and

used for the explanation of the strong changes in the size distribution modes near a busy

road during field experiments. The main idea of the fragmentation model is based on the

existence of small solid ~ 7 nm carbon/graphite primary particles. Larger carbon

particles (~ 20 – 30 nm) were readily observed in the products of combustion of

different materials (Colbeck et al, 1997), and in the vehicle exhaust (Meszaros, 1999,

Wentzel et al, 2003). However, several researchers also reported the existence of a large

number of smaller solid particles around ~ 7 nm mobility diameter. For example,

Abdul-Khalek et al (1998) reported the experimental observation of a strong mode of

particles from the diesel exhaust within the considered range. The analysis of these

121

particles by means of a catalytic stripper suggested that a large number of them are solid

(Abdul-Khalek et al, 1998), and the authors assumed these particles to be metallic ash

formed from oil and fuel additives. On the other hand, Bagley et al,(1996) suggested

that this mode may consist of primarily carbonaceous particles. More recent

investigation using a thermal desorption particle beam mass spectrometer demonstrated

the existence of solid nuclei particles in the diesel exhaust of ~ 3 – 7 nm (Sakurai et al,

2003). This was explained by evaporation of a thick volatile layer from the surface of

the solid nuclei particles (Sakurai et al, 2003). However, an alternative explanation

might be fragmentation of nano-particles. Yet another very careful recent experiment on

separation of volatile and solid particles in the diesel exhaust by means of a hot dilution

system also demonstrated the existence of a large number of solid (presumably,

carbon/graphite) particles with the mobility diameters between 6 nm – 10 nm (Fiertz

and Burtscher, 2003).

It can be expected that these small carbon/graphite particles are mainly of non-

spherical shape. For example, these may be graphite scale-like particles (Wentzel et al,

2003) with free sp2 bonds at the edges of the scale. These particles are formed in the

exhaust pipe at high temperatures. They can then coagulate by means of the covalent

bonds, and/or various types of volatile molecules or their fragments may engage the free

bonds, forming a kind of a frill. Thus the primary ~ 7 nm particles may, to a significant

extent, consist of volatile compounds. Nevertheless, it is argued that they can be

regarded as “solid”, because the volatile molecules (or their fragments) are bonded to

the carbon/graphite core by means of strong covalent bonds. More volatile molecules

can then deposit onto the primary ~ 7 nm particles (e.g., forming the 8.8 nm mode – Fig.

6.4a). However, they interact with the “frilled” primary particles by means of weak van

der Waals forces, rather than covalent bonds. Therefore, these additional condensed

molecules can also evaporate from the particle surface.

122

If the primary, ~ 7 nm particles, are non-spherical, then their coagulation near

the exhaust pipe by means of the condensed volatile compounds may result in particles

with mobility diameters (Rogak et al, 1993, Cleary et al, 1990, Okada and

Heintzenberg, 2003) that are approximately multiples of 7 (see the modes at ~ 7.9 nm,

10 – 15 nm, 20 nm, etc. in Fig. 6.4b). The suggested pattern of the evolution of the

aerosol can then be represented by the following five stages (Fig. 6.8). First, small non-

spherical carbon/graphite particles are formed inside the exhaust pipe by means of

homogeneous and heterogeneous nucleation and coagulation by means of strong

covalent bonds (stage 1). The graphite scale-like particles have free covalent bonds

around their perimeters. As mentioned above, volatile molecules and/or their fragments

engage these bonds forming the primary ~ 7 nm non-spherical (frilled) particles (stage

2). This also is likely to occur at high temperature inside the exhaust pipe. Immediately

after their emission, the exhaust gasses with the primary ~ 7 nm particles effectively

mix with the ambient air and rapidly cool down. As a result, effective condensation of

volatile molecules onto the primary nano-particles occurs (stage 3), with subsequent

coagulation of these particles by means of these volatile molecules (stage 4). As the

aerosol propagates away from the road, the concentration of volatile compounds

gradually reduces to that in the ambient air. As a result, the volatile molecules start

evaporating from the surface of the particles, and bonding may be significantly

weakened (stages 5). Eventually, the thermal energy kT may become sufficient for

fragmentation of the particles, and they break apart (stage 6).

The possibility of such thermal fragmentation becomes clear from the fact that

volatile molecules may evaporate (break away) from the surface of a particle (when the

thermal energy kT becomes of the order of the van der Waals energy of interaction

between the molecule and the particle). Since the molecules can break away from a

123

nano-particle, the bonds between particles (due to these molecules) can also eventually

break, resulting in particle fragmentation.

Fig. 6.8. Stages of the evolution of nano-particle aerosol near a busy road, according to the

fragmentation model. Stage 1: Coagulation (first type) of carbon nano-particles and formation

of the particle frill by means of covalent bonding in the exhaust pipe (i.e. at high temperature

and lack of oxygen) – formation of the original 7 nm particles. Stage 2: Heterogeneous

nucleation, i.e. further adsorption of volatile/organic/water molecules onto the surface of the 7

nm particles (due to van der Waals interaction) near the exhaust pipe where the concentration of

such molecules is large. Stage 3: Coagulation (second type) of the original 7 nm particles with

the adsorbed molecules providing bonding between the particles – formation of larger particles.

Stage 4: Evaporation of volatile/organic/water molecules in the ambient air where the

concentration of such molecules is much lower than near the exhaust pipe. Stage 5: Weakening

bonds between the 7 nm particles due to evaporation of the bonding molecules. Stage 6:

Fragmentation by means of breaking the primary 7 nm and 12 nm particles away from larger

particles.

It is important that the fragmentation is more likely to occur by means of

breaking smaller (~ 7 nm and/or ~ 12 nm) particles away from larger composite

124

particles. This is because smaller particles are likely to have smaller area of bonding. As

a result, the broad and strong maximum of correlations within the range from ~ 10 nm

to ~ 15 nm in Fig. 6.4b can be caused by fragmentation of larger particles with

diameters > 15 nm. Small errors of the moving average correlation coefficient in the

region of this maximum (Fig. 6.5b) strongly suggest that despite the breadth of this

mode, all its particles are likely to come from the same source – fragmentation of larger

particles. At the same time, it is also important to understand that fragmentation into

larger particles is also possible, and the corresponding evidence will be presented in

Chapters 9 and 11.

The shift of the modes within the range from ~ 35 nm to ~ 80 nm in Fig. 6.4b to

the left (compared to Fig. 6.4a) is likely due to fragmentation (mainly by breaking away

the ~ 7 nm and ~ 12 nm particles). On the contrary, the 98 nm mode does not change its

position noticeably. Thus, it might largely consist of a different type of particles that do

not experience thermal fragmentation at the considered temperatures (though another

possibility may be insufficient resolution of the size distribution at large particle

diameters). The modes at ~ 20 nm, ~ 26 nm, and ~ 31 nm (Figs. 6.4a,b) do not change

their positions significantly, because they are likely to be transformed one into another

by means of fragmentation. Note that the direct observation of the average particle size

distribution does not allow the resolution of, for example, the 26 nm and 31 nm modes –

they are normally seen as one mode at ~ 30 nm (Figs. 6.6 and 6.7). It is only the

developed statistical approach (see above) that reveals these modes and their mutual

transformation (the same is also true for the modes at Dp > 30 nm – compare Figs.

6.4a,b with Figs. 6.6 and 6.7).

The difficulties with interpretation of the main features of evolution of particle

size distributions in Figs. 6.6 and 6.7 are also eliminated if we assume the fragmentation

model of evolution. Indeed, as fragmentation goes on, a significant number of 7 nm and

125

12 nm particles are expected to be released. As a result, a significant increase of

concentration of particles in the 7 nm and 12 nm modes can be expected (see Figs. 6.6

and 6.7). As seen from Fig. 6.7b, the broad plateau of curves 4 and 5 (representing the

same size distribution) within the range 40 nm < Dp < 80 nm is strongly reduced by

fragmentation, resulting in curve 6 raising above the plateau of curve 5 within the range

15 nm < Dp < 40 nm. Thus the discussed 30 nm mode appears (curve 6).

Further fragmentation of particles from the 30 nm mode results in the 20 nm and

7 nm modes, and/or 12 nm mode, which is clearly shown by curves 2 – 5 in Figs. 6.6a,b

and curve 7 in Fig. 6.7b. This is also the reason for broadening the maximum of curve 4

in Fig. 6.6b. The strong influx of particles occurs into the 7 nm mode, caused by

fragmentation of 30 nm, 20 nm, and 12 nm modes. Despite dispersion, it results in

almost constant concentration of these particles within a significant range of distances

(curves 1 – 5 in Fig. 6.6 and curves 5 – 7 in Fig. 6.7b).

When the 20 nm and 30 nm modes have disintegrated, the particle influx into the

12 nm mode ceases, and this mode starts decaying with distance from the road due to

dispersion and further fragmentation – see Fig. 6.6b. This is why the 12 nm mode

significantly decreases before the 7 nm mode starts doing the same (curve 5 in Fig.

6.6b).

If we assume that the time that it takes for the volatile compounds to evaporate

does not depend on wind (if all other meteorological parameters are approximately the

same), then the distance at which the 30 nm mode appears in the size distribution must

increase approximately proportionally to increasing normal wind component. This is the

reason for the 30 nm mode appearing at ≈ 89 m from the road in Fig. 6.7b (curve 6),

compared to ≈ 45 m in Fig. 6.6a (curve 1).

The effects of nano-particle fragmentation can also be seen when the number of

heavy-duty trucks on the road is minimal – see Fig. 6.8 from (Chapter 5 and [A3]) for

126

the weekend measurements. In this case, the height of the 12 nm mode stays the same,

whereas the 20 nm mode disappears with increasing distance from 45 m to 70 m.

The observed maximum of the total number concentration at an optimal distance

from the road (Chapter 5 and [A3]) and strong increase of the total number

concentration within the evolution time of 25 s between the two sets of scans (section 3)

can also be naturally understood in the fragmentation model. Obviously, fragmentation

of the 12 nm, 20 nm, 30 nm, etc. modes should result in increasing number of smaller ~

7 nm and ~ 12 nm particles, which causes a maximum (Chapter 5 and [A3]) or strong

increase (section 3) of the total number concentration.

It is also clear that the fragmentation model could give alternative explanations

of several previously observed features of the size distribution. For example, the

observed dependencies from (Sakurai et al, 2003) could easily be re-interpreted by

means of fragmentation of larger particles into the primary 7 nm particles at

temperatures < 100 oC. In our opinion, such a re-interpretation seems more plausible

than the assumption that the 12 and 30 nm particles are ~ 95% volatile consisting of

thick shells of lubricating oil (of significantly different thicknesses) around small core

solid particles (Sakurai et al, 2003). The smaller size of the core particles of ~ 2.5 nm –

5 nm obtained at 200 oC (Sakurai et al, 2003) might be related to further reduction of

the size of primary 7 nm particles due to stripping the frill molecules off the

carbon/graphite nuclei at the temperatures > 100 oC (Sakurai et al, 2003).

6.6. Conclusions.

As a result of this work, a new method of statistical analysis of particle modes in

combustion aerosols has been developed. This method has been shown to provide a

unique insight into physical and chemical processes of evolution and transformation of

aerosol nano-particles. In particular, a new more accurate definition of modes of particle

size distribution has been introduced. A number of different modes has been revealed

127

from the experimental particle size distributions in the presence of strong turbulent

mixing. Highly unusual features of evolution of these modes and their mutual

transformation have been demonstrated and discussed.

As a result, a new mechanism of mode transformation, based on thermal

fragmentation of nano-particles, has been suggested and discussed. A comprehensive

complex pattern of aerosol evolution near a busy road has been proposed and discussed,

involving several different processes, such as particle formation, condensation,

coagulation, evaporation and, finally, thermal fragmentation. It has been demonstrated

that the presented model appears to be highly successful in explaining the major

experimental features of mode evolution. Interestingly, it can also account for the

previous experimental results on diesel nano-particles investigated by means of the

thermodesorption technique (Sakurai et al, 2003).

Appendix for Chapter 6

Here, we present an alternative approach to obtaining graphs in Figs. 6.4a,b

from Figs. 6.3a,b. Though not essential for understanding Figs. 6.4a,b, this approach

gives an interesting statistical insight into the described procedure of calculating moving

average correlation coefficient, and leads to the determination of the levels of

confidence for the correlations represented by Figs. 6.4a,b.

The alternative method of calculating moving average correlation coefficients

can be described as follows.

Step 1: As in Section 6.2, we consider an n-channel (n > 2) interval from the

overall N channels in a scan. Suppose that we again have M scans.

Step 2: Construct a column with the corresponding M different concentrations,

for example, in the first channel of the n-channel interval.

128

Step 3: Extend periodically this column, so that the resultant (extended) column

contains n – 1 sections identical to the original column with the M elements. Thus we

form a column with (n – 1)M elements.

Step 4: The remaining (n – 1) channels in the considered n-channel interval also

correspond to (n – 1) columns of M different particle concentrations corresponding to

the M scans. Then the second column with (n – 1)M elements is constructed of these (n

– 1) columns (with M elements each) by placing them one on top of another.

Step 5: A simple correlation coefficient between the two extended data columns

with (n – 1)M elements is then determined (Larsen & Marx, 1986).

Step 6: Steps 1 – 4 are repeated for the remaining n – 1 channels in the n-

channel interval, and the average correlation coefficient is again determined for the n-

channel interval.

Step 7: Steps 1 – 5 are repeated for all different n-channel interval, and the

dependence of the moving average correlation coefficient versus average particle

diameter is again obtained.

It can be shown that in terms of determining moving average correlation

coefficients, this statistical procedure is equivalent to that described in Section 6.2.

Therefore, Figs. 6.4a,b can equally be obtained either by means of the first procedure

described in Section 6.2, or the above second approach with the extension of the data

columns. However, the second approach provides significantly higher levels of

confidence of the obtained correlations due to larger number of elements in the data

columns (Larsen & Marx, 1986, Venable & Ripley, 2000). Thus the correct levels of

confidence should be determined using the second procedure. At the same time, one

should be careful when using the second procedure for the determination of statistical

errors (errors of the mean) for the obtained moving average correlation coefficients. If

these errors are calculated directly as the errors of the mean in the above procedure, they

129

appear to be smaller than those resulting from the first approach. This is because in the

second procedure we obtain only a fraction of the overall error of the moving average

correlation coefficient, and the correct estimate of the errors will require methods based

on analysis of variance (see Section 11 in (Larsen & Marx, 1986)). Thus, it is easier to

determine the errors of the average correlation coefficients, using the first approach

(Figs. 6.5a,b).

130

CHAPTER 7

MODELLING OF AEROSOL DISPERSION FROM A BUSY ROAD IN THE PRESENCE OF NANO-PARTICLE FRAGMENTATION

([A5, A19, A22, A26])

7.1. Introduction

In the previous Chapter, we have discussed and justified the new mechanism of

aerosol evolution based on intensive fragmentation of nanoparticles. It was suggested

that at least in some cases this mechanism may play a dominant role in the processes of

dispersion and transformation of nano-particle combustion aerosols, resulting in a

serious impact on human exposure and reliable forecast of aerosol pollution from busy

roads and road networks. This, in turn, may have significant implications for the

environmentally friendly urban design and minimise the effect of transport emissions on

human health. The presence of such implications can already be seen from the observed

maximum of the total number concentration at an optimal distance from the road (see

Chapters 5 and 6 and [A3, A4]). In accordance with the proposed physical interpretation

of this maximum (Chapter 6 and [A4]), it results from fragmentation of larger aerosol

particles as they are transported away from the road. Therefore, the observed maximum

of the total number concentration is mainly related to generation of small particles at

distances from the road of ~ 100 m, or so. This distance is usually of the order of, or

larger than typical setbacks for residential developments near busy roads, which may

clearly result in a significant exposure for the residents to the most harmful

nanoparticles from transport emissions.

Previously, the main interest of aerosol scientists has been focused on the study

of decay of the total number concentration of particles with distance from a busy road

(Benson, 1992, Shi et al, 1999, Hitchins et al, 2000, Zhu et al, 2002, [A1]). In

131

particular, exponential (Hitchins et al, 2000, Zhu et al, 2002) and power (Chapter 3 and

[A1]) decay laws were used for the description of the total number concentration of fine

particles as a function of distance from the road. This can approximately be done within

the range of particles > 30 nm, for which the Gaussian plume approximation (Csanady,

1980) is approximately correct (Chapter 3 and [A1]). However, this approximation

clearly fails in the range < 30 nm and, as has been suggested, this is largely due to not

taking into account intensive particle fragmentation.

Unfortunately, there are no current models for aerosol dispersion that take

particle fragmentation into account. None of the existing models can predict increase of

the total number concentrations near busy roads, and/or determine conditions at which

such increase may exist (resulting in a significant increase of exposure).

Therefore, the aim of this Chapter is to develop a simple semi-analytical model

of dispersion of fine particle aerosols from a busy road in the presence of fragmentation

of nano-particles. Rate equations for particle concentrations will be presented for the

cases when the fragmentation process is switched on abruptly and slowly (linearly) at

some distance from the road. In particular, it is demonstrated that the total number

concentration may be characterized by a significant maximum at an optimal distance

from the road. Simple analytical existence conditions of such a maximum are derived.

Comparison of the model with the available experimental results will be carried out, and

the applicability conditions will be derived and discussed; the typical fragmentation rate

coefficient will be determined to equal ≈ 0.086 s-1 with the estimated error of ~ 30%.

7.2. Dispersion as a chemical reaction

Consider a continuous ground line source of nano-particles, i.e. a road with the

wind direction at an angle θ to the road (Fig. 7.1). Initially we will assume that these

particles do not experience fragmentation/transformation in the atmosphere, i.e., we

132

assume the Gaussian plume approximation (Csanady, 1980). If the wind is normal to the

road, then the self-similarity theory (Csanady, 1980) suggests that the concentration c of

nano-particles is given by a power function of distance from the source (road):

c = C0 x–μ, (7.1)

where x is the dimensionless distance from the road in metres divided by 1 metre, C0 is

a constant depending on the strength of the source, and μ is a parameter that is close to 1

(it depends on wind speed and x; μ → 1 when x → + ∞ (Csanady, 1980)). The

numerical and experimental analysis (Chapter 3) suggested that this power dependence

is also valid for arbitrary wind direction, with the parameter μ depending on both the

wind components. In this case, the rate of changing concentration from the road (due to

dispersion of the Gaussian plume) is

dc/dx = – (μ/x)c (7.2)

(this follows from differentiation of Eq. (7.1)). This equation is valid in the stationary

frame K with the coordinates (x,y,z). Since the source is continuous and steady-state, the

concentration c is time-independent, and varies only with distance from the road (see

Eqs. (7.1) and (7.2)).

Fig. 7.1. The geometry of the problem: a road, point of observation, and wind direction.

133

Let the slender plume approximation (Csanady, 1980) be satisfied, i.e. the

normal component Ux of the wind velocity is sufficiently large, so that the aerosol

transport perpendicular to the road (along the x-axis) due to turbulent diffusion is

negligible compared to that due to the average wind (for a detailed discussion of the

applicability conditions for the model see Section 7.6). Consider another frame K′ with

coordinates (x′,y′,z′), moving away from the road with the velocity Ux, i.e., x = x′ + Uxt.

In the frame K′, the normal wind component is zero (on average), and the concentration

depends on time but not the x′-coordinate. Transformation of Eq. (7.2) to the K′ frame at

x′ = 0 (i.e., at the origin of the K′ frame) gives:

dc/dt = – kd*c, (7.3)

where kd* = μ/t.

Eq. (7.3) has the form of an equation describing a first-order chemical reaction

with the reaction rate coefficient kd*. Obviously, in the K frame, the reaction rate

coefficient for dispersion is kd = kd*/Ux = μ/x – see Eq. (7.2).

As has been demonstrated experimentally ((Csanady, 1980) and Chapter 3), μ

can approximately be regarded as a constant depending on atmospheric conditions. The

values of the constants μ and C0 are determined numerically by using, for example, the

software package CALINE4 (Benson, 1992) adapted for the analysis of dispersion of

fine particle aerosols in the absence of particle transformation (Chapter 3). Typically,

the coefficient μ ranges between ≈ 0.7 and ≈ 1.

7.3. Fragmentation of particles

In this section, fragmentation of nano-particles will be analysed together with

dispersion with the aim of modelling the observed maximum of the total number

concentration at an optimal distance from the road (Chapters 5 and 6).

134

Consider dispersion of particles A, each of which decomposes into n (different)

particles B1, B2, …, Bn (n ≥ 2):

A ⎯→⎯k B1 + B2 + … + Bn. (7.4)

According to the previous section, the variations of concentrations of A and

B1,…,n can be described by the rate equations:

d[A]/dx = – kd(x)[A] – k(x)[A], (7.5)

⎪⎩

⎪⎨

⎧

−=

−=

],)[(])[(d/][d...

],)[(])[(d/][d 11

ndn

d

BxkAxkxB

BxkAxkxB (7.6)

where the letters in the square brackets denote concentrations of the corresponding

particles, kd(x) = μ/x (see Eq. (7.2)), and k(x) is the x-dependent rate coefficient for the

reaction of fragmentation of A into B1,…,n. In other words, each of the rates of changing

concentrations [A], [B1], [B2], …, [Bn] (left-hand sides of Eqs. (7.5), (7.6)) is simply

equal to the sum of two independent increments due to dispersion (the terms with kd(x);

always negative), and due to fragmentation (the terms with k(x); negative for

fragmenting particles and positive for resulting particles).

Note that, unlike fragmentation, coagulation depends on particle concentrations,

and unless this concentrations are very large, it is highly inefficient (Jacobson, 1999,

Shi, et al, 1999, Jacobson and Seinfeld, 2004, Pihiola et al, 2003, Zhang & Wexler,

2004, Zhang et al, 2004). Thus, the reverse process of coagulation is neglected in Eqs.

(7.5) and (7.6). If required, coagulation can be considered by means of methods similar

to those used for analysis of dispersion of reactive gasses (Fraigneau, et al, 1995).

Since fragmentation is expected to switch on at some distance from the road

(where the bonds between the particles are weakened by evaporation of bonding volatile

molecules (Chapter 6), the coefficient k(x) is generally a function of distance from the

135

road x. Here, we will assume that this coefficient depends linearly on distance within

the interval (x1, x2):

⎪⎪⎩

⎪⎪⎨

⎧

>

≤≤−−

<

=

,for,

,for,

,for,0

)(

20

2112

10

1

xxk

xxxxxxxk

xx

xk (7.7)

where x1 is the distances from the road at which fragmentation starts, and x2 is the

distance at which the rate coefficient for fragmentation reaches the steady-state value k0,

i.e. the fragmentation process is completely “switched on” (Fig. 7.2a).

We use here a linear function approximation for the rate coefficient k(x), since

this allows simple analytical solution of the problem, results in lucid physical

interpretation of the results, and clearly demonstrates the general tendencies of the

solution (including the conditions for a maximum of the total number concentration –

see Section 7.4). In addition, linear function can also be used as an approximation of

other dependencies (e.g., an exponential dependence of k(x)). At the same time,

generalization to the case of a general monotonic (e.g., exponential) function k(x) does

not present major difficulties, but will in general require numerical methods of solution

of the rate equations.

Fig. 7.2. The considered linear (a) and step-wise (b) dependencies for the fragmentation rate

coefficient k(x) as a function of distance from the road, given by Eqs. (7.13), and (7.7),

respectively.

136

Here, we will mainly be interested in the total number concentration for all

particles. Therefore, Eqs. (7.6) are added together to give:

d[A]/dx = – kd(x)[A] – k(x)[A], (7.8)

d[B]/dx = nk(x)[A] – kd(x)[B], (7.9)

where [B] is the overall concentration of the fragmentation products: [B] = [B1] + [B2] +

… + [Bn].

Assuming that the concentration of the B particles before the fragmentation

process (i.e. at x ≤ x1) is zero, the solution to Eqs. (7.8) and (7.9) is

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

>+−−

≤≤−

−−

<

=

μ−

μ−

μ−

,for)],2

(exp[

,for],)(2

)(exp[

,for,

][

221

00

2112

210

0

10

xxxxxkxC

xxxxx

xxkxC

xxxC

A (7.10)

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

>+−−−

≤≤−

−−−

<

=

μ−

μ−

,for)]},2

(exp[1{

,for]},)(2

)(exp[1{

,for,0

][

221

00

2112

210

0

1

xxxxxkxnC

xxxxx

xxkxnC

xx

B (7.11)

In this case, the total number concentration [T] can be written as:

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

>+−−−−

≤≤−

−−−−

<

=

μ−

μ−

μ−

,for)]},2

(exp[)1({

,for]},)(2

)(exp[)1({

,for,

][

221

00

2112

210

0

10

xxxxxknnxC

xxxxx

xxknnxC

xxxC

T (7.12)

In the above derivation, n was assumed to be integer, corresponding to the

number of particles B that result from fragmentation of one particle A. However, if

originally we have particles A and A*, and only particles A experience fragmentation,

then Eqs. (7.10) and (7.11) do not change, while the extra term (1 – p)p-1C0x–μ should be

137

added to the total number concentration in Eq. (7.12) (where p = [A]/([A] + [A*])). This

term corresponds to the dispersion of particles A*. The resultant equation for [T] will be

exactly the same as Eq. (7.12), but generally with fractional n = p(n1 – 1) + 1, where n1

is the integer number of the B particles resulting from fragmentation of an A particle.

If the fragmentation process switches on abruptly at t = t0, i.e. at x = x0 ≡ x1 = x2,

k(x) is a step-wise function (Fig. 7.2b):

⎩⎨⎧

≥<

=,for,

,for,0)(

00

0

xxkxx

xk (7.13)

then the corresponding solutions for the rate equations (7.8) and (7.9) are obtained by a

simple limit transition x2 → x1 in Eqs. (7.10) – (7.12).

Eq. (7.13) means that all the particles reach the fragmentation stage at the same

time t0 = x0/Ux. It also assumes that the speed of transport of different particles from the

road is the same and equal to the average normal component of the wind Ux. This means

that the spread of particles (plume) in space due to turbulent diffusion is ignored (the

slender plume approximation (Csanady, 1980)). For more detailed analysis of the

applicability conditions for this assumption see Section 7.6.

The resultant typical total number concentrations as functions of distance from

the road are presented in Fig. 7.3a-d for different values of parameters μ, k0, and x1,2 at

the assumption that n = 2, i.e. each particle A disintegrates into two particles B1 and B2.

Figs. 7.3a-c are for the case when the fragmentation process switches on gradually

within several different intervals between x1 and x2 (Eq. (7.7)), whereas Fig. 7.3d

demonstrates the situation when the fragmentation process switches on abruptly at

several different distances x0 (Eq. (7.13)).

138

Fig. 7.3. Typical dependencies of the total number concentration of fine particles on distance

from a line source (busy road) in the presence of fragmentation of each of the original particles

into two. (a) – (c) Fragmentation process is “switched on” gradually, i.e., the rate coefficient

k(x) is a linear function within the interval between x1 and x2 (see Eq. (7.7)). (d) Fragmentation

is “switched on” abruptly at the distance x0 ≡ x1 = x2 from the road. C0 = 6×105 cm-3 for all the

subplots. The dotted curves in subplots (a) – (c) are identical.

(a) The effect of different values of x1,2 on the total number concentration: μ = 0.8, k0 = 0.04 m-1,

1) x1 = 0, x2 = 50 m, 2) x1 = 20 m, x2 = 70 m, 3) x1 = 40 m, x2 = 70 m, 4) x1 = 40 m, x2 = 90 m.

(b) The effect of k0 on the total number concentration: μ = 0.8, x1 = 40 m, x2 = 70 m, 1) k0 = 0,

2) k0 = 0.02 m-1, 3) k0 = 0.04 m-1, 4) k0 = 0.08 m-1. (c) The effect of μ on the total number

concentration: k0 = 0.04 m-1, x1 = 40 m, x2 = 70 m, 1) μ = 0.7, 2) μ = 0.8, 3) μ = 0.95. (d) The

effect of x0 on the total number concentration in the case of abruptly switched fragmentation

process: 1) x0 = 0, 2) x0 = 20 m, 3) x0 = 30 m, 4) x0 = 50 m, 5) x0 = 70 m; other parameters are

the same as in (a).

139

In particular, if the fragmentation process switches on (abruptly or gradually as a

linear function k(x)) immediately after the emission by the source, i.e., x1 = 0, then

strong dispersion in the immediate proximity to the source overpowers the tendency for

increasing total number concentration due to fragmentation. As a result, the

corresponding curves monotonically decrease with increasing distance from the road

(see curves 1 in Figs. 7.3a,d). However, if the distance at which the fragmentation

process switches on increases (x1 and x0 are non-zero), then an obvious ‘shoulder’

appears on the corresponding curves (see curves 2 in Figs. 7.3a,d). Further increase of

x1 and x0 may result in an appearance of a maximum of the total number concentration

at an optimal distance from the road (curves 3 – 5 in Figs. 7.3a,d).

Expectedly, decreasing slope of the linear dependence (7.7) results in a

reduction of the maximum of the total number concentration – compare curves 3 and 4

in Fig. 7.3a. Indeed, smaller slope of the dependence (7.7), results in slower

fragmentation, which leads to smaller maximum of the total number concentration.

Thus, in general, Figs. 7.3a,d suggest that the relative height of the maximum of

the total number concentration has a tendency to increase with increasing x1 and

decreasing Δx0 ≡ x2 – x1.

Similarly, the effect of variations of the steady-state rate coefficient k0 on the x-

dependencies of the total number concentration is demonstrated by Fig. 7.3b. Increasing

k0 at given values of x1 and x2 initially results in a shoulder on the curve (see curve 2 in

Fig. 7.3b), and then in a clear maximum that increases with increasing k0 (curve 3, 4 in

Fig. 7.3b). If k(x) is given by Eq. (7.13), then the corresponding dependencies of the

total number concentration on x at different values of k0 are very similar to those in Fig.

7.3b, but display derivative discontinuities similar to those in Fig. 7.3d.

The effect of different values of μ on the dependencies of the total number

concentration is demonstrated by Fig. 7.3c, where typical curves are presented for three

140

different values of μ = 0.7, 0.8, and 0.95. In general, increasing μ results in decreasing

maximum of the total number concentration (Fig. 7.3c). This is because μ usually

decreases with increasing normal component of the wind (as can be seen from the

analysis using the CALINE4 model). In this case, if Δx0 is constant, increasing normal

component of the wind results in faster (in time) switching on the fragmentation

process, which causes an increased maximum (Fig. 7.3c).

7.4. Existence conditions for the maximum of the total number concentration

The above consideration suggests that the predicted maximum of the total

number concentration depends on several parameters, namely, x1, x2, k0, μ, and the slope

of the linear dependence k(x). Firstly, assume that the fragmentation process switches

on abruptly (see Eq. (7.13)). Then the total number concentration is

⎪⎩

⎪⎨⎧

>−−−−

<=+

μ−

μ−

.for)]},(exp[)1({

,for,][][

0000

00

xxxxknnxC

xxxCBA (7.14)

Taking the derivative of Eq. (7.14) at x > x0 and equating it to zero gives

)(10xk

nn +μμ− = exp[k0(x – x0)], (7.15)

which should be satisfied at the maximum of the total number concentration.

Using the graphical method of solving Eq. (7.15), we can derive that this

equation has a solution only if

M1 ≡ μ−1

00nxk > 1, (7.16a)

or

M1 ≡ k0x0/μ > 1 (7.16b)

for n = 2, i.e. when fragmentation of each of the particles A occurs into two B particles.

141

Conditions (7.16a,b) determine the existence of a maximum of the total number

concentration in the case of a step-wise function k(x) (Eq. (7.13)). The number M1 in

this case is a fundamental number that determines the behaviour of the total number

concentration as a function of distance from the road. It also reflects the tendency of

increasing maximum of the total number concentration with increasing k0 and x0, and

decreasing μ.

For example, for curves 1 – 5 in Fig. 7.3d, M1 = 0, 1, 1.5, 2.5, and 3.5,

respectively. It can be seen that if condition (7.16b) is not satisfied (curves 1 and 2 in

Fig. 7.3d), the maximum of the total number concentration is absent, though curve 2

(with M1 = 1) displays a ‘shoulder’ near x = x0.

If the function k(x) is given by Eq. (7.7), i.e. by a linear function of x within the

interval x1 ≤ x ≤ x2, then conditions (7.16a,b) are still approximately applicable for the

determination of existence of the maximum of the total number concentration, if Δx0 ≡

x2 – x1 is noticeably smaller than Δxc. Here, Δxc is the distance within which particles A

decay into the B particles, i.e., the typical concentration of A decreases e times. In this

case, x0 in conditions (7.16a,b) should be replaced by x0 = x1 + Δx0/2.

If, on the contrary, Δx0 is large, so that the number of A particles decreases e

times within the distance that is smaller than Δx0 (i.e., Δxc < Δx0) then conditions

(7.16a,b) are not applicable, since the value of k0 does not matter in this case for the

process of fragmentation (particles A decay before k(x) reaches k0).

In this case, the typical distance within which the concentration of particles A

drops e times is

Δxc ~ kc-1, (7.17)

where kc is the average value of k(x) within the interval Δxc. On the other hand, since

k(x) is a linear function with the slope α, we have: kc = αΔxc/2. Substituting this value

142

of kc into Eq. (7.17), gives: Δxc ~ 2/(αΔxc), or Δxc ~ α/2 . As a result, the distance

from the road, at which the fragmentation process can be regarded as switched on, is xf

~ x1 + Δxc/2 ~ x1 + α2/1 . Substituting xf into condition (7.16a,b) instead of x0, and

taking into account that in this case k0 ~ kc = αΔxc/2 ~ 2/α , gives:

2)1(2/12/12 >−

μ+α≡ nxM , (7.18a)

or for n = 2 (fragmentation of one A particle into two B particles):

22/12/12 >

μ+α≡ xM . (7.18b)

Note that 2 in the right-hand side of these conditions does not follow directly from

the above derivations. It has been used, because the numerical analysis has

demonstrated that conditions (7.18a,b) are more accurate with the factor 2 .

If Δxc is noticeably larger than Δx0, then conditions (7.16a,b) and the number M1

should be used as the approximate existence conditions for the maximum of the total

number concentration. In this case, one should use x0 ≈ x1 + Δx0/2. On the contrary, if

Δxc is noticeably smaller than Δx0, then conditions (7.18a,b) and the second number M2

should be used instead. In fact, the numerical analysis shows that M1 can be used if Δx0

< Δxc/3, while M2 should be used if Δx0 ≳ Δxc. It is also important to understand that

conditions (7.16a,b) do not formally follow from conditions (7.18a,b) in the limit case

of Δxc ≈ Δx0. This is because they have been derived at different physical and

mathematical conditions. Therefore, the first number M1 depends on k0, whereas the

second number M2 depends on α – the slope of the linear function k(x).

It can also be seen from the above derivations that the inequality Δx0 > Δxc can

be expressed in terms of the slope α and k0:

143

α < k02/2. (7.19)

In this form this inequality is more convenient to use, since these are α and k0 that might

be known in practice.

As an illustration of condition (7.18b), we present the values of the number M2

for the curves in Figs. 7.3a-c. For the curves in Fig. 7.3a, M2 is equal to: (1) 0.625, (2)

1.125, (3) 1.916, (4) 1.625. Therefore, condition (7.18b) is satisfied for curves 3 and 4

in Fig. 7.3a, and these curves indeed display maximums of the total number

concentration. At the same time, condition (7.18b) is not satisfied for curves 1 and 2 in

Fig. 7.3a, and these curves do not display such a maximum (though curve 2 shows a

‘shoulder’ at ~ 70 m from the road). For curves in Fig. 7.3b, M2 equals: (1) 0.625, (2)

1.538, (3) 1.916, (4) 2.451. Curve 2 in this figure is at the border-line for condition

(7.18b), and only a small maximum can be seen in this case. For curves in Fig. 7.3c, the

values of M2 are: (1) 2.190, (2) 1.916, (3) 1.614.

These examples demonstrate the direct relationship between the maximum of

the total number concentration and values of the second number M2: increasing M2

beyond the critical value 2 results in increasing relative strength of the maximum of

the total number concentration at an optimal distance from the road.

7.5. Comparison with the experimental results

One of the most interesting results in Chapter 5 was the experimental

observation of a significant maximum of the total number concentration at some

distance from a busy road. The measured total number concentrations and their errors at

9 different distances from the centre of the road (presented in Fig. 5.7 in Chapter 5) are

reproduced in Fig. 7.4a by the experimental points. As can be seen, a significant

maximum of the total number concentration is reached at the distance ≈ 82 m from the

road.

144

Fig. 7.4. The comparison of the theoretical curves with the experimental results (points

with the error bars) from (Chapter 5 and [A3]).

(a) Dotted curves are the x-dependencies of the total number concentration of particles

for the Gaussian plumes in the absence of fragmentation and dry deposition for the two different

values of C0 = 6.69×105 cm-3 (dotted curve 1) and C0 = n6.69×105 cm-3 ≈ 12×105 cm-3 (dotted

curve 2). The other parameters are as follows: μ = 0.87, background concentration: ~ 1000 cm-3,

θ = 41o (±40o), U = 2.05 m/s (±0.9 m/s), and temperature: 26.5 oC (±0.9 oC) [A3]. The solid

curve is obtained from Eq. (7.12), i.e. in the presence of fragmentation, with the parameters: x1

= 46 m, x2 = 71 m, n = 1.8, and k0 = 0.1, which gives M2 ≈ 2.9 > 2 .

(b) Demonstration of the effect of dry deposition of particles on the theoretical

dependence and its fit to the experimental points (including the additional point at x = 232 m,

discarded in [A3] as an outlier). The solid curve is identical to that in Fig. 7.2a, while the dotted

curve is the theoretical dependence taking into account dry deposition of the 7 nm particles at x

> xm ≈ 75 m. The parameter for the dotted curve are the same as for the solid curve, except for k0

= 0.075 m-1, and n = 1.9, resulting in M2 ≈ 2.6 > 2 .

145

Explanation of this maximum by means of particle formation is not feasible

because of several reasons discussed in detail in Chapter 6 and [A4]. One such reason is

that the concentration maximum is mainly related to increasing concentration of

particles within the range between ~ 7 nm and ~ 20 nm. At the same time, if particle

formation were responsible for this effect, concentration within the range ≤ 7 nm should

have increased especially strongly (Chapter 6 and [A4]).

The second possible explanation may be related to a thermal rise of the heated

exhaust gasses due to buoyancy. This is similar to having an elevated source that may

result in a concentration maximum at some distance from the road. To demonstrate the

impossibility of using this mechanism for the explanation of the observed maximum

(Fig. 7.4a) consider a strongly exaggerated case of the road elevated by 8 m above its

actual level. Then the numerical analysis of aerosol dispersion from the road by means

of the CALINE4 model ((Benson, 1992) and Chapter 3) with the stability class 1

(unstable) suggests that the concentration maximum should have been obtained at the

distance x ~ 45 m. In this case, the concentration at x = 25 m (the first point in Fig.

7.4a) should have been smaller (by ~ 10%) than that at x = 45 m (decreasing elevation

results in decreasing maximum and shifting it closer to the road). This is in obvious

contradiction with the experimental points in Fig. 7.4a. Thus, thermal rise has nothing to

do with the observed maximum of the total number concentration, and we are left only

with the third possible interpretation – fragmentation of nano-particles. The expectation

that the thermal rise does not have a noticeable effect on aerosol dispersion near a busy

road (highway) was confirmed experimentally by Zhu & Hinds (2005).

Using the atmospheric conditions mentioned above, and the actual shape of the

road of 27 m width as the inputs in the CALINE4 model (Benson, 1992) adjusted for

the analysis of a Gaussian plume of fine particles (Chapter 3 and [A1]), we obtain that μ

≈ 0.87. We also choose C0 = 6.69×105 cm-3, x1 = 46 m, x2 = 71 m, k0 = 0.1 m-1, and n =

146

1.8, which means that only 80% of particles A experience fragmentation into two (on

average) particles B. Substituting all these parameters into Eq. (7.12), results in the

dependence of concentration on distance from the centre of the road, given by the solid

curve in Fig. 7.4a. Dotted curve 1 in Fig. 7.4a gives the dependence of concentration of

particles A on distance in the absence of fragmentation, whereas dotted curve 2

represents the same dependence, but with 1.8 times larger concentrations (i.e. with 1.8

times larger constant C0). In this case, if n = 1.8 (as assumed above), the curve for the

total number concentration [T] (solid curve in Fig. 7.4a) must obviously split from

dotted curve 1 at the distance x1 where fragmentation starts switching on, and merge

with dotted curve 2 when fragmentation finishes – see Fig. 7.4a.

In particular, it can be seen that the solid curve in Fig. 7.4a fits well to the

experimental points up to ~ 100 m from the road (the statistical consideration is

presented below). However, at distances > 100 m from the road, the theoretical solid

curve starts deviating (with the tendency upwards) from the most of the experimental

points (Fig. 7.4a).

A possible reason for this is that the theoretical model presented in Sections 7.2

and 7.3 assumes that there are no particle losses during dispersion, apart from the

fragmentation process. However, it has been suggested that fragmentation should

mainly occur by means of breaking the primary 7 nm particles away from larger

particles from the 12 nm, 20 nm, and 30 nm modes (Chapter 6 and [A4]). Thus, we

should expect that the observed maximum of [T] should be caused by generation of the

7 nm particles due to fragmentation. On the other hand, it is known that 7 nm particles

may be effectively deposited on interfaces by means of dry deposition (Jacobson, 1999),

resulting in a noticeable loss of the overall number of such particles. This however has

not been taken into account in Eqs. (7.10) – (7.12).

147

Dry deposition occurs when particles are transported by turbulent diffusion to

the 0.01 cm – 0.1 cm laminar layer that exists near any surface (Jacobson, 1999). Then

the particles cross the layer by means of molecular diffusion and stick to the surface. It

is known that the smaller the particles, the larger their deposition coefficient due to

larger molecular diffusivity. For example, for 7 nm particles, the deposition speed is v ~

0.1 m/s (Jacobson, 1999), while deposition of larger particles will be neglected.

To estimate the contribution of dry deposition to the theoretical solid curve in

Fig. 7.4a, we assume that the 7 nm particles appear as a result of fragmentation at the

distance x ≈ xm ≈ 75 m (at which the maximum of the solid curve in Fig. 7.4a is

achieved), and their concentration is approximately equal to the concentration of

particles A at the same distance in the absence of fragmentation. This assumption is

reasonable, because we took n = 1.8, i.e., 80% (on average) of all particles A

disintegrate into two particles B. If all these B particles were from the 7 nm mode, then

their concentration should have been ~ 1.8 times larger than that of particles A at the

same distance in the absence of fragmentation. However, not all particles B should

necessarily belong to the 7 nm mode, because fragmentation may occur into one 7 nm

particle and another larger composite particle that may not experience further

fragmentation, for example, due to stronger bonding. Therefore, in this estimate, it is

reasonable to assume that the concentration of the 7 nm particles at x ≈ xm ≈ 75 m is

approximately equal to that of particles A at the same distance in the absence of

fragmentation.

Thus, if dry deposition is not taken into account, then Gaussian dispersion of the

7 nm particles at x > xm must be approximately given by dotted curve 1 in Fig. 7.4a.

The contribution of dry deposition is estimated from conservation of particles.

Consider an imaginary plane at the distance xm from the road, at which the

fragmentation process is assumed to have finished. This plane is parallel to the road,

148

perpendicular to the ground, has a length l in the direction parallel to the road (along

the y-axis), and is infinitely high (along the z-axis). If the transport due to turbulent

diffusion along the x-axis is neglected compared to the average wind transport (see

Section 7.6), then the flux of the 7 nm particles through this plane is

∫=+∞

0d),()( zzxcUxF mxm l , (7.20)

where z is the vertical distance from the ground, Ux is the average x-component of the

wind (the fact that the normal wind component may depend on z is not essential for this

consideration, and Ux is assumed z-independent), c(xm, z) is the z-dependent

concentration of the 7 nm particles (it is estimated by dotted curve 1 in Fig. 7.4a at x =

xm ≈ 75 m).

As the aerosol is transported away from the road beyond x = xm, the flux of the 7

nm particles into the ground, due to dry deposition, can be estimated as

∫ ′=′=x

xd

m

xdzxcvxF )0,()( l , (7.21)

where v ≈ 0.1 m/s is the speed of dry deposition of the 7 nm particles (Jacobson, 1999),

and c(x, z = 0) is the concentration of the 7 nm particles at the ground level, estimated in

the absence of dry deposition, i.e. given by dotted curve 1 in Fig. 7.4a. The actual

ground concentration of these particles is affected by dry deposition, and will be slightly

smaller. However, this is unlikely to be an overestimate, because, for example, dry

deposition of larger particles was not taken into account, and we have probably

underestimated the concentration of 7 nm particles (e.g., because they also exist before

the beginning of fragmentation).

At a given distance from the road (and fixed meteorological parameters), the

flux of particles through a vertical plane is proportional to the concentration at the

ground level. On the other hand, for a Gaussian plume in the absence of deposition, the

149

flux through the considered plane should be independent of distance from the road (due

to particle conservation). Therefore, the ratio of the concentration cd(x, z = 0) at a

distance x from the road, including the losses due to dry deposition, to that in the

Gaussian plume in the absence of the deposition, c(x, z = 0), is given as

)()(1

)0,()0,()(

m

dd

xFxF

zxczxcxf −===≡ . (7.22)

Thus, the dependence for the total number concentration [T] in the region x > xm

in Eq. (7.12) should be multiplied by the factor f(x). The resultant new dependence of

[T] on x takes into account the effect of dry deposition of 7 nm particles.

Using the above meteorological parameters and the constant C0 = 6.69×1011 m-3

(for dotted curve 1 in Fig. 7.4a) in the CALINE4 model, the vertical concentration

profile c(xm, z) for the 7 nm particles and the corresponding flux F(xm) are calculated.

Estimating the ground concentration of the 7 nm particles from dotted curve 1 in Fig.

7.4a, the flux due to dry deposition is also calculated: Fd(x) = (1 – μ)-1C0(x1 – μ – xm1 – μ)

(see Eq. (7.21)). As a result, the factor f(x) is determined from Eq. (7.22).

If dry deposition is taken into account (as described above), the best fit of the

theoretical curve to the experimental points (Venables and Ripley, 2000) is achieved if

the value of k0 is reduced to 0.075 m-1, and n is slightly increased to n = 1.9, i.e. 90% of

particles A experience fragmentation into two (on average) particles B. The resultant

theoretical (dotted) curve taking into account dry deposition is presented in Fig. 7.4b

together with the experimental points, together with the previously discarded point at x

= 232 m. For comparison, the previous theoretical (solid) curve calculated without dry

deposition (Fig. 7.4a) is also presented in Fig. 7.4b. It can be seen that the fit of the new

curve allowing for dry deposition of the 7 nm particles at x > xm is significantly better at

distances x > 100 m, compared to that without dry deposition.

150

The statistical analysis has shown that the residual standard error of the curve

with dry deposition is about ± 1500 cm-3 (Venables and Ripley, 2000). The value for the

fragmentation rate coefficient can thus be estimated as k0 ≈ 0.075 m-1 (with the error ~

30%). If we wish to represent the fragmentation reaction as a function of time, rather

than distance from the road, then the corresponding value of the fragmentation rate

coefficient is given by k0* = k0Ux ≈ 0.086 s-1 (assuming that at the time of concentration

measurements near the maximum Ux = 1.15 m/s (Chapter 5 and [A3])).

7.6. Applicability conditions

As mentioned in Section 3, if we have a step-wise variation of the fragmentation

rate coefficient from zero to k0 (Eq. (7.13)), this means that the fragmentation stage is

reached by all particles A simultaneously at a given distance from the road. However,

even if the time that takes for different particles to reach the fragmentation stage is the

same: t0 = x0/Ux, turbulent diffusion results in stochastic motion, and different particles

reach the fragmentation stage at different distances. Thus step-wise function (7.13) must

be spread by means of turbulent diffusion, i.e. particles reaching the fragmentation stage

should be found typically within the interval x0 – σx < x < x0 + σx, where σx is the

standard deviation of the plume along the x-axis (i.e., 2σx is the increase of the size of

the plume along the x-axis due to turbulent diffusion). Use of Eq. (7.13) can only be

justified if

σx << x0. (7.23)

To estimate σx, we consider the turbulent intensities i∥ and i⊥ (Csanady, 1980)

in the directions parallel and perpendicular to the wind, respectively. These intensities

are determined by the fluctuations u∥ and u⊥ of the wind components on the directions

parallel and normal to the average direction of the wind (Csanady, 1980):

151

i∥ = 2||

1 uU − , i⊥ = 21⊥

− uU , (7.24)

where U is the magnitude of the mean velocity of the wind (Fig. 7.1).

Suppose that the average direction of the wind makes an angle θ with respect to

the road (Fig. 7.1). It can be shown that the root-mean-square fluctuation of the wind

component onto the x-axis (normal to the road) is given as

θ+θ= ⊥2222

||2 cossin uuux , (7.25)

and the corresponding turbulent intensity

ix = θ+θ= ⊥− 2222

||21 cossin iiuU x . (7.26)

The standard deviation of the plume along the x-axis σx ≈ Dixxα (Csanady,

1980), where α ≈ 0.87, and D is a dimensional coefficient of the order of 1 with the

units m1–α. This relationship and inequality (7.23) give the required applicability

condition for using Eq. (7.13).

Usually, i� ~ 0.1, and i� ~ 0.25 – 0.55 for unstable atmospheric conditions

(Csanady, 1980). Assuming that i� ~ 0.4, θ = 41o, xm ≈ 75 m (these are the parameters

corresponding to Figs. 7.4a,b), and using Eq. (7.26), we have σx ~ 12.5 m. It can be seen

that in this case, the function k(x) can hardly be regarded as step-wise due to relatively

large value of σx (the turbulent spread of the step is ~ 25 m). The approximation of a

step-wise dependence of k(x) can thus be reasonable only for near-normal wind (i.e.,

when Ux is significantly larger than Uy) and fairly stable atmospheric conditions. For

example, if θ = 90o, and i∥ ~ 0.1, then σx ≈ 4 m << xm ≈ 75 m. In more common

situations, condition (7.23) is fairly difficult to satisfy.

Turbulent spread of the step-wise function (7.13) results in different particles A

reaching the fragmentation process at different distances from the road, which on

152

average can be approximated by a linearly increasing fragmentation rate coefficient

within the interval between x1 = x0 – σx and x2 = x0 + σx. This is another reason for using

linear dependence of k(x) – see Eq. (7.7).

Therefore, condition (7.23) is not essential for the applicability of the developed

model, since if this condition is not satisfied, the model can still be used, but with the

fragmentation rate coefficient given by Eq. (7.7) with x1 = x0 – σx and x2 = x0 + σx.

If the rate coefficient k(x) is approximated by a linearly increasing function

because of gradually switching fragmentation process (see Section 3 and Eq. (7.7)), then

turbulent diffusion will result in a further reduction of the typical slope of the x-

dependence of the effective rate coefficient. In this case, a new interval between x′1 = x1

– σx and x′2 = x2 + σx should rather be used.

For example, the above estimate of σx ≈ 12.5 m for the experimental results in

Figs. 7.4a,b suggests that the interval within which the effective (average)

fragmentation rate coefficient should change from 0 to k0 could be about 25 m, which is

in agreement with the difference between x2 and x1 used for plotting curves in Figs.

7.4a,b. This may suggest that in the considered experiment, the dependence of k(x) in

the absence of turbulent diffusion should be close to a step-wise function given by Eq.

(7.13). However, turbulent diffusion has spread this function within the interval of ≈ 25

m, effectively giving the linear dependence.

The approximation of the effect of turbulent diffusion by means of a linearly

changing fragmentation rate coefficient has its limitations. It can only be used if the

interval 2σx is not larger than the interval Δxc, within which the fragmentation process

finishes (here, Δxc is calculated in the same way as in Section 7.4, but for the effective

rate coefficient k(x) varying linearly between x′1 and x′2):

Δxc > 2σx. (7.27)

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If condition (7.27) is not satisfied, but turbulent diffusion is represented by a

linearly changing k(x), then fragmentation will formally result in the total depletion of

particles A within the interval Δxc that may be significantly smaller than the actual

interval within which this depletion occurs. This actual interval should not be smaller

than 2σx – the interval within which particles A that have just reached the fragmentation

process are dispersed by turbulent diffusion. More detailed analysis of situations when

condition (7.27) is not satisfied is beyond the scope of this chapter.

As mentioned above, for the experimental results presented in Figs. 7.4a,b, we

have 2σx ≈ 25 m, and Δxc is estimated to be ≈ 26 m. Therefore, the developed theory can

approximately be used (see Figs. 7.4a,b and Section 7.5).

The finite width of the road may also contribute to an additional spatial

dispersion (along the x-axis) of particles reaching the fragmentation stage. However,

this additional dispersion may not be as strong as one could expect it to be. Thermal

fragmentation may occur when volatile molecules responsible for bonds between the

particles evaporate (Chapter 6 and [A4]). On the road (in the mixing zone), the process

of evaporation of volatile compounds may be significantly impeded by large

concentrations of these compounds. Therefore, it is possible that all particles that cross

the kerb and leave the road may have approximately the same amount of volatile

molecules that would require approximately the same time to evaporate (irrespectively

of the width of the road). Thus finite width of the road may not lead to an additional

significant spread of the dependence of k(x) in space (along the x-axis). However, this

suggestion requires further confirmation by means of more detailed theoretical and

experimental investigation.

It is possible to indicate that the obtained applicability conditions for the model

are not over-restrictive. They are typically satisfied when the average wind direction

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makes a noticeable angle with respect to the road (e.g., in the considered experiment θ =

41o). The conventional slender plume approximation (Csanady, 1980) is typically a

sufficient (but not necessary) applicability condition for the model.

7.7. Conclusions

This Chapter developed a new model for a simple semi-analytical analysis of

dispersion of ultra-fine particle aerosols from a busy road in the presence of intensive

fragmentation of nano-particles (Chapter 6 and [A4]). The possibility of existence of a

maximum of the total number concentration at an optimal distance from the road,

caused by particle fragmentation, was derived theoretically. Simple analytical existence

conditions for this maximum were determined when the fragmentation process switches

on abruptly at some distance from the road, or linearly increases within some distance

near the road. As a result, two fundamental numbers representing these existing

conditions were suggested and discussed.

An agreement between the model and the previous experimental results (Chapter

5 and [A3]) was demonstrated. In particular, it was shown that taking into account dry

deposition of particles noticeably improves the fit of the theoretical curve to the

available experimental data. As a result, the value of the fragmentation rate coefficient

was found: k0* ≈ 0.086 s-1 (± 30%).

Main applicability conditions of the developed model were derived. The

important role of turbulent diffusion for the model was analysed. In particular, it was

suggested that increasing turbulence may eventually result in breaching the applicability

of the model. At the same time, the usual approximations (e.g., the slender plume

approximation (Csanady, 1980)) should normally be sufficient (but not always

necessary) for the applicability of the model.

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CHAPTER 8

MULTI-CHANNEL CANONICAL CORRELATION ANALYSIS OF COMBUSTION AEROSOLS: SOURCES OF PARTICLE MODES

([A6])

8.1. Introduction

In Chapters 6 and 7, a new mechanism of aerosol evolution based on intensive

particle fragmentation has been developed and used for the detailed interpretation of

evolution of particle modes in combustion aerosols near a busy road. As a result, a

complex evolution pattern has been suggested. This includes several stages such as

formation of solid and liquid nano-particles inside and in the vicinity of the vehicle

exhaust, their coagulation near the exhaust pipe (where particle concentrations are

sufficient for such a process to occur (Shi et al, 1999, Jacobson, 1999, Jacobson and

Seinfeld, 2004)), evaporation of volatile compounds from the surface of solid particles

as the aerosol is transported away from the road, loss of bonding between coagulated

nano-particles due to evaporation of bonding volatile molecules and, finally, thermal

fragmentation of nano-particles (Chapter 6). Numerous experimental evidence

supporting this evolution pattern have been presented, including substantial

transformation of particle modes and their shift towards smaller particle size (Chapters

5 and 6), observation and modelling of a maximum of the total number concentration at

an optimal distance from the road (Chapters 5, 6, and 7), direct observations and

statistical confirmation of generation of strong modes that would be expected as a result

of fragmentation of larger particles (Chapter 6), etc.

A new method of statistical analysis of particle modes in combustion aerosols

near a busy road has been developed (Chapter 6), based on the moving average of the

correlation coefficients between neighbouring channels of the particle size distribution.

This method allows determination and analysis of particle modes in the presence of

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strong turbulent mixing, even if these modes are not directly seen (as distinct

maximums) on the size distribution. As a result, particle modes have been re-defined as

groups of particles of similar dimensions, corresponding to distinct maximums of the

moving average correlation coefficient (Chapter 6).

The aim of this Chapter is to develop and use new statistical approaches for the

detailed analysis of modes of particle size distribution near a busy road, including their

possible sources, mutual transformations during the aerosol evolution, correlations with

atmospheric and meteorological parameters. This will be done by means of the

extension of the previously developed method based on the moving average technique

(Chapter 6) to the multi-variate canonical correlation analysis. In particular, modes

resulting primarily from heavy diesel trucks and petrol cars will be identified, and the

dependencies of particle modes on such parameters as temperature, humidity and solar

radiation will be analysed. Physical interpretation of the obtained results is presented on

the basis of the fragmentation model of aerosol evolution.

8.2. Experimental data and particle modes

The development of the new statistical methods and their application for the

analysis of particle modes and their evolution will be conducted on the basis of the

experimental data previously discussed in Chapter 6. The data were obtained during the

field campaign on 25 November 2003 near Gateway Motorway in Brisbane, Australia.

Measurements of particle size distribution were conducted, by means of a scanning

mobility particle sizer (SMPS-3936) and condensation particle counter (CPC-3025). 50

scans (previously discussed in Chapter 6) were taken during ~ 3 hours of measurements

at the distance of ≈ 40 m from the centre of the road, within the range of particle

diameters from 4.6 nm to 163 nm in 100 equal intervals (channels) of Δlog(Dp), where

Dp is the particle diameter in nanometres. The time for one full scan was 2.5 minutes,

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with a 1 min down-scan. The width of the Motorway was ≈ 27 m , and its elevation

above the surrounding area was ≈ 2 m.

Traffic conditions were recorded on a video camera (with short breaks for

changing batteries). The traffic on the road was subdivided into two groups: heavy-duty

trucks and cars (the car group including gasoline and diesel cars and light trucks).

Numbers of vehicles in each of these two groups were determined within 2.5 min

intervals by means of direct counting from the video tape. The beginning of each of the

2.5 min intervals for traffic counting was taken L/vn seconds earlier than the beginning

of the corresponding scans. Here, L = 40 m is the distance from the centre of the road,

and vn is the one-hour average normal component of the wind. This was done in order to

take into account average time delays associated with the aerosol transport from the

road to the point of monitoring, so that to determine the traffic conditions corresponding

to particular scans. The obtained results from traffic counting were then used for the

statistical analysis of canonical correlations between particle modes, traffic and

meteorological conditions (see below).

Wind speed, wind direction, temperature, humidity, and solar radiation were

measured every 20 seconds by a automatic weather station at the same distance from the

road. In Chapter 6, the two sets of scans (out of the overall 50 scans) from 1 to 11 and

from 19 to 38 were chosen, because these sets correspond to approximately constant

(but noticeably different) one-hour average normal wind components (the variations of

the average wind components within these sets are within the standard deviation of the

mean – see also Fig. 6.2). In this paper, when considering correlations between particle

modes and traffic and meteorological conditions, we will choose slightly different sets

of scans from 6 to 16 (11 scans) and from 28 to 43 (16 scans) – Table 8.1. This new

choice has been made because of the following two reasons. First, the new sets still

correspond to approximately constant (but distinctly different) one-hour average normal

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wind components – see Fig. 6.2 from Chapter 6 and Table 8.1. Second, the recorded

traffic conditions are available for each of the scans from the new sets, and this will

allow analysis of canonical correlations between particle modes and traffic conditions.

Part (a) Part (b).

Wind direction (degrees to the road) 50 ± 20 20 ± 20 Wind speed (ms-1) 2.4± 0.2 2.6 ± 0.8 Normal component of the wind velocity, v⊥ (ms-1)

1.7 ± 0.16 1.0 ± 0.2

Parallel component of the wind velocity, v|| (ms-1)

1.7 ± 0.2 2.3 ± 0.8

Solar radiation (Wm-2) 800 ± 40 530 ± 70 Humidity (%) 30 ± 2 36 ± 1 Temperature (°C) 28 ± 1 27 ± 1 Total number concentration (cm-1) 22.6×103 39×103

Heavy-duty trucks (hour-1) 800 ± 200 790 ± 140 Cars (hour-1) 3800 ± 400 4800 ± 500

Table 8.1. Average meteorological and traffic conditions together with their standard

deviations.

Note that significantly different average normal wind components for the two

selected sets (Table 8.1) correspond to significantly different times that it takes for the

aerosol to be transported from the road to the point of observation. The aerosol

transportation time for the first set of 11 scans is smaller than that for the second set by

≈ 16 s. As a result, the two sets correspond to two different stages of the aerosol

evolution.

The average size distributions are determined for each of the two sets of 11 and

16 scans – Fig. 8.1. These distributions are plotted using the moving average method.

The concentrations in every channel in each scan are normalised to the total number

concentration in this scan. Then we choose an interval of 5 neighbouring channels (out

of the total 100 channels) and average the normalised particle concentrations over these

5 channels in the scan and over all scans within a particular set of 11 or 16 scans. Thus

we obtain an average particle concentration, which gives us one point on the size

distribution. Then another interval of 5 neighbouring channels is chosen and the

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procedure is repeated, giving another point on the size distribution. Repeating this

procedure for all 96 different 5-channel intervals, we obtain 96 average concentrations.

Connecting all these points, gives the moving-average particle size distributions for the

11-scan and 16-scan sets. The errors associated with these distributions are obtained by

calculating the errors of the mean for each of the 96 average concentrations. These

errors and the determined size distributions are represented in Fig. 8.1 by the two bands

corresponding to the sets of 11 and 16 scans.

Fig. 8.1. Average particle size distributions and their errors of the mean for the first set of 11

scans (light band) and the second set of 16 scans (dark band), obtained using the moving

average technique. Before averaging, the concentrations in each channel in every scan were

normalised to the total number concentration in the corresponding scan.

The moving average technique for plotting average particle size distributions

seems to be more efficient and accurate than that used in Chapter 6. This is because it is

highly efficient in revealing main average features and tendencies of a particle size

distribution and results in easy and straightforward way of determination of the

corresponding errors of this distribution (Fig. 8.1). Some differences between the size

distributions in Fig. 8.1 and those obtained in Chapter 6 can be explained by the

different (more accurate) smoothing technique used in this Chapter and slightly

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different normal wind components for the considered sets, which correspond to slightly

different times of aerosol evolution, especially for the second set of 16 scans. For this

second set, the average normal wind component is ≈ 1.0 m/s (see Table 8.1), while for

the slightly shifted set considered in Chapter 6 it was ≈ 0.75 m/s (rounded up to 0.8 m/s

– Chapter 6).

Note that the 5-channel intervals for plotting the moving average size

distributions (Fig. 8.1) have been chosen as a compromise between the errors of the

mean (which increase with decreasing number of channels in the interval) and the

resolution of the features of the size distribution (which decreases with increasing

number of channels in the interval). In principle, an optimal number of channels within

a selected interval of neighbouring channels should be chosen separately for each

experimental data set.

Despite the use of the improved averaging and smoothing technique, direct

observation of the particle size distributions (Fig. 8.1) can still hardly be used for clear

identification of all particle modes and especially their mutual interaction, evolution,

major tendencies and correlations, and possible sources. Therefore, in this Chapter, the

detailed analysis of particle modes and determination of their possible sources were

conducted by means of the previously developed statistical method based on the moving

average correlation coefficient (Chapter 6). In this method, particle concentrations in

each of the 100 channels in every scan are normalized to the total number concentration

in the corresponding scan. Then we choose 7 neighbouring channels out of the 100

channels in a scan. The number of channels within the interval is again determined as a

compromise between the mode resolution and statistical errors of the resultant curves

(Chapter 6). Simple correlations between particle concentrations in all possible pairs of

different channels from the 7-channel interval are determined for the sets of 11 or 16

scans, and then the average correlation coefficient is calculated. Thus, considering all

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possible different 7-channel intervals, the moving average correlation coefficient is

plotted versus particle diameter (for more detailed description of this procedure see

Chapter 6).

Fig. 8.2. The dependencies of the moving average of the correlation coefficient, R, between the

particle concentrations in neighbouring channels on particle diameter; the bands represent the

associated statistical errors (similar to Figs. 6.4 and 6.5). The moving average correlation

coefficients are calculated over (a) the first set of 11 scans (scans from 6 to 16); (b) the second

set of 16 scans (scans from 28 to 43).

The resultant dependencies of the moving average correlation coefficient on

particle diameter, together with their errors of the mean are presented in Figs. 8.2a,b for

the two sets of 11 and 16 scans, respectively. As discussed in (Chapter 6), it is

reasonable to redefine particle modes as groups of particles with similar diameters,

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corresponding to maxima of the moving average correlation coefficient. The reason for

such a definition is that particle concentrations in different channels corresponding to

these maxima tend to increase/decrease in strong (maximal) correlation with each other,

and this is an indication that these groups of particles are likely to come from the same

source and/or have the same physical/chemical nature. Therefore, these particle groups

can naturally be called “modes”. In our opinion, this is physically more reasonable than

defining particle modes as maxima of the size distributions (Fig. 8.1). At the same time,

it is important to note that modes as maxima of the moving average correlation

coefficient often (but not always) include modes as maxima of the particle size

distributions (compare Fig. 8.1 with Figs. 8.2a,b).

The dependencies in Figs. 8.2a,b appear to be somewhat different from those

considered in Figs. 6.4a,b from Chapter 6, though the major features and modes remain

the same. These differences are again due to the different choice of the sets of scans,

and the resultant differences in the one hour average normal wind components, which is

equivalent to slightly different stages of the aerosol evolution. For example, previously

obtained ~ 12 nm mode (Fig. 6.4b) was noticeably stronger and had much smaller

statistical errors of the correlation coefficient, than the same mode in Fig. 8.2b. The

existence of the ~ 12 nm mode in Fig. 6.4b was explained by means of intensive thermal

fragmentation of larger particles, resulting in generation of a large number of particles

within the range ~ 10 – 13 nm (Chapter 6). However, Fig. 8.2b corresponds to the larger

(by ≈ 0.25 m/s) one hour average normal wind component (Table 8.1). Therefore, Fig.

8.2b corresponds to ≈ 13 s earlier stage of aerosol evolution than Fig. 6.4b. In other

words, the ~ 12 nm mode in Fig. 8.2b did not have sufficient time to properly develop,

and thus it is characterized by smaller moving average correlation coefficient and larger

errors of the mean. Fig. 8.2b is thus intermediate between Fig. 6.4a and Fig. 6.4b for the

two sets of scans considered in (Chapter 6).

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Similar situation occurs for ~ 6 – 8 nm particles. Thermal fragmentation results

in an inflow of a large number of solid particles into this range (Chapter 6). This causes

large moving average correlation coefficients (Fig. 6.4b), because these particles have

the same nature (they mainly come from the process of fragmentation), and their

concentrations in different channels tend to increase/decrease in strong correlation with

each other. However, Fig. 8.2b corresponds to ~ 13 s earlier stage of evolution, and the

number of ~ 6 – 8 nm particles resulting from fragmentation is still relatively small.

This is the reason for significantly lower correlation coefficients within this range in

Fig. 8.2b, compared to Fig. 6.4b.

The correlation maximums at ~ 6 – 7 nm diameter in Figs. 8.2a and 6.4a are

unrelated to the above interpretation, because, as it will be demonstrated in the next

section, particles causing these maximums are mostly volatile. They rapidly evaporate

during the aerosol evolution, and thus do not exist in Figs. 8.2b and 6.4b. In particular,

the evaporation process results in shifting the maximum from ~ 6 – 7 nm in Fig. 8.2a to

~ 5 – 6 nm in Fig. 6.4a, because Fig. 6.4a corresponds to ~ 3 – 5 s later stage of the

evolution, compared to Fig. 8.2a. For more justification of this conclusion see below.

8.3. Moving average approach to the canonical correlation analysis

In this section, the developed moving average approach is extended to the case

of canonical correlation analysis of particle modes and their dependence of traffic and

meteorological parameters.

Canonical correlation analysis determines correlations between two groups of

variables, when the variables in each of the groups depend on each other (Dillon and

Goldstein, 1984, Johnson and Wichern, 2002). A significant advantage of this method is

that it can determine the effect of each of the mutually dependent parameters (e.g.,

traffic and/or meteorological parameters) from a group A on some variable or a group

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of variables (e.g., particle concentrations in different modes or channels) from another

B.

Canonical correlation analysis gives three major output parameters: correlation

coefficients between specially determined linear combinations of variables from group

A with linear combinations of variables from group B, canonical weights which are the

coefficients in these linear combinations, and canonical loadings which are the simple

correlation coefficients between the a variable from one of the groups and the

considered linear combination containing this variable (Dillon and Goldstein, 1984,

Johnson and Wichern, 2002). The canonical correlation coefficient R measure the

strength of association between the two groups of variables.

For example, suppose that group A contains only one variable (e.g.,

concentration in one of the particle modes) and group B contains traffic and

meteorological parameters (see below). Then R2 determines the strength of correlation

between the mode concentration and the mentioned traffic and meteorological

parameters. If R2 = 1, then the mode concentration depends only on the parameters from

group B. If however R2 < 1, then the mode concentration depends on some other factors

that are not included in group B. That is, usually, the larger the coefficient R, the larger

the contribution of the considered parameters to variations of the mode concentration.

Canonical weights determine the contributions of the corresponding variables from one

of the groups of variables to the variance (i.e., variation) of the linear combination of

the other group of variables (Dillon and Goldstein, 1984, Johnson and Wichern, 2002).

In the above example, if the canonical weight, i.e., the coefficient in front of a variable

from group B, is large and positive, then increasing/decreasing this variable results in a

significant increase/decrease of the mode concentration. Finally, canonical loadings

may be used for the assessment of stability of the obtained correlations and

relationships. For example, if the canonical loading corresponding to a variable from

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group B and the corresponding canonical weight have different signs, then the

correlation is not stable, i.e., the obtained weight cannot be used for the above

interpretation. For the detailed mathematical description of the canonical correlation

analysis see (Dillon and Goldstein, 1984, Johnson and Wichern, 2002).

The canonical correlation coefficient R is actually the correlation coefficient for

the first canonical variates, and it should have been denoted as R1 (Dillon and

Goldstein, 1984, Johnson and Wichern, 2002). However, the correlation coefficient for

the second canonical variates R2 << R1 for all cases considered below. Therefore,

correlations for the second and higher variates can be neglected (Dillon and Goldstein,

1984, Johnson and Wichern, 2002), and for the sake of simplicity, we omit index 1 in

the correlation coefficient for the first variates, denoting it simply by R.

In order to use the canonical correlation analysis for the investigation of particle

modes and their sources, the counted numbers of heavy-duty trucks and light cars

corresponding to each of the scans from the two selected sets of scans (as discussed in

Section 8.2) are included in group B of variables. For each of the scans, we determine

the average temperature, humidity, and solar radiation and also include them in group

B. Group A includes average particle concentrations in different channels. Usually,

group A will be assumed to contain only one concentration, for example, in a particular

channel under investigation.

To apply the moving average approach to the canonical correlation analysis, we

choose an interval of 7 neighbouring channels out of the overall 100 channels in one

scan. As usual, the number of channels within one interval is chosen so that to achieve a

reasonable compromise between the statistical errors (e.g., the scatter of the resultant

points on the graph) and the sufficient resolution of the major features (particle modes)

on the resultant distributions – see also Section 8.2 and (Chapter 6). Consider, for

example, the first set of 11 scans from 6 to 16 (the analysis for the second set of 16

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scans is the same). Each of the selected 7 neighbouring channels corresponds to a

column of 11 different concentrations from each of the 11 scans. Taking the average

over the 7 channels, we obtain one column with 11 different average concentrations.

The concentrations in this average column are taken as the average concentrations for

the central channel of the considered 7-channel interval.

Each scan corresponds to the determined numbers of heavy-duty trucks and light

cars (see Section 8.2), and particular (averaged over the scan time) meteorological

parameters: temperature, humidity and solar radiation. We take one channel out of the

selected 7-channel interval. This channel corresponds to a column of 11 different

concentrations corresponding to 11 different scans. Canonical correlations between this

column of concentrations (one variable in group A), and the numbers of trucks and cars

and the corresponding meteorological parameters (group B) are calculated. As a result

we determine the canonical correlation coefficient R, canonical weights and loadings

(for example, for the numbers of trucks and cars). The procedure is then repeated for the

remaining 6 channels from the selected 7-channel interval. Taking the average over the

7 channels, we can obtain the average canonical correlation coefficient, canonical

weights and loadings for the considered 7 channel interval.

This procedure is then repeated for all 94 possible different 7-channel intervals

(out of the 100 channels in each scan), and thus 94 different canonical correlation

coefficients, weights and loadings are found. As a result, we obtain moving average

canonical correlation coefficients, weights and loadings as functions of particle diameter

that is taken as the diameter for the middle channel for each of the 7-channel intervals.

Similar dependencies of moving average correlation coefficient, weights and

loadings can also be obtained by means of an alternative statistical procedure. Instead of

calculating the average concentrations for each scan within each of the 7-channel

intervals, we rearrange these 7 columns with 11 different concentrations into one

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column by placing the 7 columns one on top of another (Chapter 6). The order in which

these 7 columns are placed on top of each other does not matter. The resultant big

column will have 77 different concentration values for the sets of 11 scans. The column

with 11 different numbers of trucks on the road (corresponding to each of the 11 scans)

is then periodically repeated 7 times, resulting in another extended column with 77

numbers of trucks in it (each of the 7 “sub-columns” of this column being identical).

The same is done for the corresponding columns with the car numbers on the road,

average (over the scan time) temperature, humidity, and solar radiation. Then the

canonical correlations between the concentration column with the 77 elements (group A

with just one variable) and the other 5 similar columns for the truck and car numbers,

temperature, humidity and solar radiation (group B with 5 variables) are calculated,

resulting in the corresponding correlation coefficient, canonical weights and loadings

for all the 5 variables from group B.

The same procedure is repeated for all other 94 different 7-channel intervals.

Thus, we obtain the dependencies of the corresponding moving average canonical

correlation coefficient, weights and loadings on particle diameter. This diameter is again

taken to equal the diameter corresponding to the central channel of the considered 7-

channel interval. The same procedure is repeated for the other selected set of 16 scans

(however, in this case, each of the extended columns contains 112 elements rather than

77).

As mentioned above, the resultant dependencies of the canonical correlation

coefficient, weights and loadings on particle diameter are very similar (though not

identical) for both the procedures. The two procedures have some complementary

advantages. For example, the direct determination of levels of confidence of canonical

correlations in the first procedure is difficult, whereas this can easily be done in the

second procedure by means of the usual methods in the canonical correlation analysis

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(Dillon and Goldstein, 1984, Johnson and Wichern, 2002). On the other hand, errors of

weights are difficult to find in the second procedure, whereas the first approach

immediately provides them as the errors of the mean.

The use of canonical correlation analysis solely for descriptive purposes requires

no assumptions about the data distribution used. However, for testing levels of

confidence of the analysis results the data should meet the requirements of normality

and homogeneity of variance (Dillon & Goldstein, 1984). Therefore, all the extended

data columns for concentrations, traffic and meteorological parameters were checked

for normality using quantile-normal plots (Dillon & Goldstein, 1984), demonstrating

high correlations with quantiles (sorted values) of normal distribution. For example, the

resultant correlation coefficients for both the sets of scans (between 6 and 16 and

between 28 and 43) were within the range ≈ 0.96 ± 0.02 with the exception of a few

channels with Dp < 6 nm in the first set of 11 scans. For these few channels, the

correlation coefficients with the quantiles of the normal distribution were within the

range ≈ 0.72 ± 0.9. As a result, it was concluded that the data transformation to the

normal distribution is not required (Dillon & Goldstein, 1984).

All the data was standardised to enable quantitative conclusions and

comparisons of the canonical weights and loadings (Dillon & Goldstein, 1984, Johnson

& Wichern, 2002).

It is also important to note that similar approach is applicable not only for the

canonical correlation analysis, but also for the determination of simple moving average

correlation coefficients, for example, between the average particle concentration in a

particular channel and the number of trucks, or cars, etc. However, canonical correlation

analysis gives a much more comprehensive and reliable analysis of mutual relationships

between multiple variables in real-world situations (Dillon and Goldstein, 1984,

Johnson and Wichern, 2002), like those considered in this thesis.

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8.4. Sources of particle modes.

The dependencies of the moving average simple correlation coefficients between

the average particle concentrations in different channels on the one hand, and the

numbers of trucks and cars for the considered two sets of scans on the other, are

presented in Figs. 8.3a,b. The dotted horizontal lines represent the 80% level of

confidence, and the solid horizontal lines correspond to the 95% level of confidence.

Fig. 8.3. The dependencies of the moving average correlation coefficient, R, between channel

concentrations and numbers of trucks (curve 1) and cars (curve 2) on particle diameter. The

moving average correlation coefficients are calculated for (a) the first set of 11 scans (scans

from 6 to 16); (b) the second set of 16 scans (scans from 28 to 43).

One of the main aspects of Figs. 8.3a,b is that particles with different diameters

are characterised by substantially different simple correlations with numbers of cars and

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trucks on the road. This is an indication that the statistical approach may be highly

effective in the determination of sources of different types of particles in combustion

aerosols. That is, it should be possible to determine which particles originate

predominantly from cars, and which from trucks. The second important aspect of Figs.

8.3a,b is that the correlations drastically change with changing evolution time (compare

Figs. 8.3a and 8.3b). This is a clear indication of rapid evolution processes (e.g.,

evaporation and thermal fragmentation of nano-particles (Chapter 6) that occur as the

aerosol is transported from the road (recall that the evolution time difference between

the set of 11 scans (Fig. 8.3a) and the set of 16 scans (Fig. 8.3b) is ≈ 16 s – see Section

8.2). Thus the proposed statistical approaches can also be used for the investigation of

these processes.

For example, the curves in Fig. 8.3a suggest that at earlier stages of aerosol

evolution (~ 24 s after the emission) there is a possibility of an association between the

~ 14, 25, 40, 90 nm particles and cars (curve 2 in Fig. 8.3a), and between the ~ 6, 55

nm, ≳ 110 nm particles and trucks (curve 1 in Fig. 8.3a). However, 16 s later (Fig.

8.3b), these associations have drastically changed. For example, strong positive

correlations with trucks for the ~ 6 nm and ~ 120 nm particles for the first set of scans

(earlier stage of evolution – Fig. 8.3a) change to negative correlations for the second set

of scans (≈ 16 s later stage of evolution). This suggests that the maximum of

correlations at ~ 5 nm in Fig. 8.2b can hardly result from shifting the maximum at ~ 6 –

7 nm in Figs. 8.2a to the left, because this maximum is strongly related to trucks (solid

curve in Fig. 8.3a), whereas the maximum at ~ 5 nm in Fig. 8.2b is related to cars (Fig.

8.3b). The most logical explanation may be that the maximum of the solid curve in Fig.

8.2a at ~ 6 – 7 nm is likely to be volatile, and its particles simply evaporate within the

16 s of evolution to the stage corresponding to Fig. 8.3b. This is also in agreement with

the transformation of the dependence in Fig. 8.2a into the dependence in Fig. 6.4a

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within ~ 3 s of aerosol evolution (see the last paragraph of Section 8.2). This is also the

reason for increased correlations of particles with < 6 nm diameters with cars (Fig.

8.3b). More justification that the 6 – 7 nm mode in Fig. 8.2a is volatile is provided

below by the canonical correlation analysis.

Strong variations of correlations of large particles with > 110 nm diameter

within the same 16 s of evolution between Figs. 8.3a and 8.3b is likely to be related to

thermal fragmentation of these particles, which noticeably change the concentration of

these particles and their mutual correlations (see also below).

At the same time, using just simple correlations for the determination of possible

sources of different types of particles and their mutual transformation/evolution may not

be reliable. Indeed, only small sections of the curves in Figs. 8.3a,b lie beyond the 95%

level of confidence. The other problem is that simple correlations establish relationships

only between two variables (e.g., particle concentration and number of trucks). At the

same time, these correlations may be significantly affected by some other parameters

(e.g., number of cars and meteorological parameters), variation of which may introduce

significant errors into the resultant simple correlation coefficients. Therefore, simple

correlation analysis is not reliable and accurate for a real-world problem with numerous

independent (and dependent) variables and external factors, as in the considered case of

aerosol dispersion and evolution near a busy road.

Therefore, canonical correlation analysis should be used instead. As mentioned

in Section 8.3, the canonical correlation analysis establishes correlations between

groups of independent or dependent parameters, which gives more accurate and reliable

predictions with significantly higher levels of confidence. Thus, though Figs. 8.3a,b

may suggest some interesting tendencies and results, these must surely be verified by

the canonical correlation analysis involving the determination of correlations between

particle concentrations on the one hand (group A), and traffic and meteorological

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parameters on the other (group B). Here, we will mainly use the second procedure

described in Section 8.3 with extended columns of the particle concentrations, and the

first procedure will only be used for estimating statistical errors of canonical weights.

Five parameters affecting particle concentration are considered. These are

numbers of trucks and cars, corresponding to each scan, and average (over the

considered scan) temperature, humidity and solar radiation. Wind speed and direction

are not included, because we choose the sets of scans for which these parameters are

approximately constant (see above). This was done because increasing number of

parameters involved (in this case up to 7) results in reduction of levels of confidence of

the obtained results (Dillon & Goldstein, 1984). Therefore, the sets with constant

average wind were chosen instead, in order to determine correlations with other

parameters. Same signs of canonical weights and loadings for almost all particles (see

below) will confirm the validity of this approach.

For example, the procedures described in Section 8.3 were used for the

determination of the dependencies of the moving average canonical correlation

coefficient on particle diameter for the set of 11 scans (thick solid curve in Fig. 8.4a)

and for the set of 16 scans (thick solid curve in Fig. 8.4b).

In particular, Figs. 8.4a,b clearly demonstrate that the canonical correlation

analysis substantially improves the levels of confidence of the obtained results. Indeed,

in this case, almost the entire curves lie beyond the lines corresponding to the 95% level

of confidence. This is one of the important indications that the obtained results may be

reliable (for the discussion of stability of the obtained correlations see the analysis of

canonical weights and loadings). Only within a few relatively small regions the level of

confidence of the obtained correlations is below 95% (Figs. 8.4a,b), and this is an

indication that within these regions the statistical analysis is not reliable.

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Fig. 8.4. The dependencies of the moving average canonical correlation coefficients on particle

diameter. Group A: channel particle concentration (one variable). Solid thick curve: five

variables in group B – temperature, humidity, solar radiation, number of trucks, and number of

cars. The other three curves correspond to group B with just four variables: (1) without the

number of trucks, (2) without the number of cars, (3) without the solar radiation. (a) The

dependencies for the first set of 11 scans (scans from 6 to 16). (b) The dependencies for the

second set of scans (scans from 28 to 43). Straight horizontal lines indicate the 95% levels of

confidence when group B contains all five variables (solid lines), and for groups B with just

four variables (dash-and-dot lines).

Note that Figs. 8.4a,b demonstrate again that the obtained canonical correlations

strongly depend on particle diameter. Numerous strong maximums of the correlation

coefficient may provide important information about the nature and evolution of nano-

particles in a combustion aerosol. For example, if one of the parameters is removed

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from group B, and the corresponding moving average correlation coefficient

significantly decreases for some particular particle diameters, then this is a strong

indication that this missing parameter has a significant impact on the particle

concentration. For example, curves 1 in Figs. 8.4a,b correspond to group B without the

number of trucks on the road. Therefore, not including truck number in group B has a

significant effect on correlations within the particle diameters ~ 6 – 7 nm and ~ 11 nm

in Fig. 8.4a. Therefore, it is possible to conclude that the corresponding particle modes

in this set of scans (Fig. 8.2a), i.e., ~ 24 s after emission, are likely to be more

associated with trucks rather than cars. At the same time, particles with the diameters

between ~ 20 nm and ~ 28 nm, and between ~ 60 nm and ~ 110 nm are more related to

cars than to trucks – see curve 2 in Fig. 8.4a (although particles around ~ 90 nm also

show relation to trucks). The effect of solar radiation is most noticeable for particles

between ~ 9 nm and ~ 50 nm (curve 3 in Fig. 8.4a).

For the second set of 16 scans (~ 16 s later), the situation significantly changes.

The most noticeable aspect is the strong dependence of the particles between ~ 5 nm

and ~ 10 nm on number of cars, which was completely different for the set of 11 scans.

This suggests that something has happened within the ~ 16 s of evolution between the

two sets of scans, which has led to the drastic increase of the correlation of small

particles with cars (see also for other significant differences between Figs. 8.4a and

8.4b).

This analysis, however, gives only qualitative information about the importance

of the contribution of different parameters to variations of particle concentrations in

different channels. In order to obtain more specific quantitative information, including

signs of correlations, we need to consider canonical weights (see Section 8.3). The

dependencies of the moving average canonical weights and loadings for trucks and cars

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on particle diameter for the sets of 11 and 16 scans are presented in Figs. 8.5a,b and

Figs. 8.6a,b.

Fig. 8.5. Moving average canonical weights (solid curves) and loadings (dotted curves) for

trucks in group B with the five variables: temperature, humidity, solar radiation, number of

trucks, and number of cars. (a) The dependencies for the first set of 11 scans (from 6 to 16). (b)

The dependencies for the second set of scans (from 28 to 43). The dashed horizontal lines

indicate the 95% level of confidence for the loading curves. The horizontal solid line

corresponds to zero. The typical errors of the curves for the moving average canonical weights

(solid curves) are ~ ± 0.1.

It can be seen that the presented dependencies of canonical weights for trucks

and cars on particle diameter are rather similar to the dependencies of the simple

correlation coefficients in Figs. 8.3a,b. However, the canonical weights and loadings in

Figs. 8.5a,b and 8.6a,b provide more reliable information about ranges of particles

where the determined tendencies can be trusted. For example, for the first set (evolution

time of ~ 24 s) for particles with the diameters < 8 nm, both canonical weights and

loadings for trucks (solid and dotted curves in Fig. 8.5a) have the same (positive) signs.

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This is an indication that the corresponding correlations are likely to be stable (Dillon

and Goldstein, 1984, Johnson and Wichern, 2002), and increasing number of trucks

results in increasing number of particles within the range < 8 nm.

Fig. 8.6. Moving average canonical weights (solid curves) and loadings (dotted curves) for cars

in group B with the five variables: temperature, humidity, solar radiation, number of trucks, and

number of cars. (a) The dependencies for the first set of 11 scans (from 6 to 16). (b) The

dependencies for the second set of scans (from 28 to 43). The dashed horizontal lines indicate

the 95% level of confidence for the loading curves. The solid horizontal line corresponds to

zero. The typical errors of the canonical weights (solid curves) are ~ ± 0.1.

On the contrary, the weights and loadings for cars (thin solid and dashed curves

in Fig. 8.6a) both have negative signs within the range of particle diameters between ~ 5

nm and ~ 8 nm. Therefore, the corresponding correlations are again likely to be stable,

and increasing number of cars results in decreasing particle concentration within the

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indicated range. This could be explained by the fact that increasing number of cars on

the road should automatically results in decreasing number of trucks (due to limited

traffic flow), thus causing number of the considered particles to drop, because their

main source is heavy trucks.

Another reason for the opposite signs of traffic correlations for modes related to

cars and trucks is due to the normalisation procedure. If, for example, we consider a

mode that is predominantly related to cars, and the number of trucks changes, then there

will be additional negative correlations (due to normalisation) of the considered mode

with the trucks, because increasing number of trucks will result in increasing total

number concentrations. This, in turn, will lead to decreasing relative concentration in a

mode that is predominantly related to cars. It is important to note that this effect is

rather beneficial because it allows better distinguishing between modes coming from

different sources (different types of vehicles).

Thus, according to the statistical evidence obtained from three different methods

(see Figs. 8.3a, 8.4a, and 8.5a), the ~ 6 – 7 nm mode in Fig. 8.2a (i.e., for the first set of

measurements) is very likely to be associated with heavy-duty trucks on the road. The

comparison of Figs. 8.5a and 8.5b also shows that the large positive maximums of

canonical weights and loadings for trucks at ~ 5 – 7 nm (Fig. 8.5a) have drastically

dropped into strong negative minimums in just 16 s of evolution (Fig. 8.5b). These

maximums in Fig. 8.5a do not seem to move to the right, but rather disappear in Fig.

8.5b (shift to the left beyond the detectable range). This is a fairly clear indication that

these particles are mostly volatile, and they simply evaporate within the 16 s of

evolution between Figs. 8.5a and 8.5b. Thus, as has been mentioned in (Chapter 6) and

during the discussion of Fig. 8.3a,b, the ~ 6 – 7 nm mode in Fig. 8.2a and ~ 5 – 6 nm

mode in Fig. 6.4a are likely to be of the same nature and formed of liquid particles that

are related to heavy-duty diesel trucks on the road. These volatile particles disappear in

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Figs. 6.4b and 8.2b due to their evaporation in the ambient air, leaving instead solid

particles resulting from fragmentation of larger particles, and from shrinking 8 – 10 nm

particles caused by evaporation of the volatile shell (Chapter 6).

The ~ 10 – 14 nm modes in the first set of scans (Fig. 8.2a) seem to be more

associated with cars rather than with trucks (Figs. 8.5a and 8.6a). Indeed, the canonical

weights and loadings for cars are both positive (Fig. 8.6a), while for trucks they are both

negative (Fig. 8.5a). This suggests that decreasing number of trucks results in increasing

particle concentration in these channels, and vice versa for cars.

For the same first set of scans, the canonical weights and loadings for trucks

within the range between ~ 15 nm and ~ 25 nm provide mainly inconclusive results,

because in this case weights and loadings either have opposite signs (indicating

instability of the correlations), or are small in magnitude (also indicating possible

instabilities) – Fig. 8.5a. On the other hand, the canonical weights and loadings for cars

are both positive for particles within the range 22 – 30 nm (Fig. 8.6a), which suggests

that the 25 nm mode is associated with cars (see also Fig. 8.3a). For particles between ~

30 nm and ~ 35 nm, the level of confidence of canonical correlations (Fig. 8.4a) is

insufficient for reliable conclusions. At the same time, for the ~ 40 nm mode (Fig. 8.2a),

the truck weights and loadings are both negative (Fig. 8.5a), while the weights and

loadings for cars are both positive (Fig. 8.6a). Therefore, this mode has a tendency to be

related to cars rather than to trucks. This is also confirmed by the simple correlations in

Fig. 8.3a. There is a strong indication that the 50 – 60 nm mode is associated with

trucks (Fig. 8.5a). However, this conclusion may be put under some question by the

insufficiently large canonical correlation coefficient within this range of particle

diameters (see Fig. 8.4a). Particles within the range between ~ 60 nm and ~ 100 nm

provide inconclusive results, because they are negatively correlated with both trucks

and cars (Fig. 8.5a). Therefore, it is possible to expect that there are some other more

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dominant factors/processes affecting particle concentrations within this range, which

may overpower the effect of increasing traffic flow and result in non-linear

dependencies causing correlation instabilities (Fig. 8.6a). At the same time, there is a

clear and strong association of particles with larger diameters ≳ 120 nm with diesel

trucks – the corresponding weights and loadings are large and positive (Fig. 8.5a), while

the weights and loading for cars are both negative (Fig. 8.6a).

The described pattern of correlations is likely to be typical for the stage

preceding particle fragmentation, because this is the stage when volatile liquid shells

have not yet evaporated from the solid particles, and bonding between coagulated

particles (caused by the volatile molecules) is still strong (Chapter 6). The next 16 s of

aerosol evolution result in substantial changes of the correlation pattern – Figs. 8.5b and

8.6b. For example, the major difference between Figs. 6a and 6b is the disappearance of

the volatile ~ 6 – 7 nm mode and the substantial alterations of weights and loadings

within the range > 70 nm.

Fig. 8.6b also demonstrates a few interesting results. First, the smallest

registered particles at ~ 5 nm are clearly associated with cars – see the positive weights

and loadings for cars (Fig. 8.6b) and negative weights and loadings for trucks (Fig.

8.5b). The second region is between ~ 7 nm and ~ 9 nm, where canonical weights and

loadings for cars are large and negative (Fig. 8.6b), and the weights and loadings for

trucks are positive (Fig. 8.5b). This is an indication that these particles are more

associated with trucks. Curve 2 in Fig. 8.4b and simple correlations in Fig. 8.3b confirm

this conclusion.

The third range where some conclusions could be made is between ~ 17 nm and

~ 23 nm. Particles from this range tend to be associated with both cars and trucks – see

the corresponding weights and loadings in Fig. 8.5b and 8.6b. The last two ranges

within which more or less certain conclusions can be made are ~ 40 – 100 nm

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(association with trucks) and ~ 70 – 110 nm (association with cars) – see Figs. 8.5b and

8.6b. Note, however, that the association with trucks seems to be significantly stronger

for these ranges (compare curves in Fig. 8.5b and Fig. 8.6b).

In other regions the presented canonical correlation analysis does not give

consistent results and reasonable conclusions. This means that in those regions, particles

and their modes cannot be associated reliably and predominantly with cars or trucks, but

rather come from both these sources, or turbulent fluctuations and additional processes

(like thermal fragmentation) mask the correlations. For example, the ~ 10 – 13 nm

particles in Figs. 8.5b and 8.6b tend to be negatively correlated with both cars and

trucks. Surprisingly, this could be explained by the fragmentation mechanism of

evolution of nano-particle aerosols. Indeed, as has been mentioned in discussion of Fig.

8.2b and Fig. 6.4b (see also Chapter 6), particles from this range at the considered

evolution time and conditions are likely to result from thermal fragmentation of larger

particles. Fragmentation may only occur when volatile bonding molecules effectively

evaporate, resulting in weakening bonds between the coagulated particles, eventually

leading to their fragmentation (Chapter 6). Evaporation of volatile molecules may only

occur if the concentration of these molecules in the ambient air is below the

concentration in the saturated vapour. On the other hand, increasing traffic flow (i.e.,

numbers of cars and trucks on the road) results in increasing concentration of volatile

compounds in the air. As a result, increasing traffic flow may cause decreasing rate of

fragmentation, and thus decreasing number of particles generated by fragmentation.

Because ~ 10 – 13 nm particles in the second set of scans are assumed to be generated

by fragmentation of larger particles (Chapter 6), their concentration may decrease with

increasing numbers of cars and trucks, leading to negative correlations with both (Figs.

8.5b and 8.6b). The presented interpretation is also likely to be the key reason for

observing condensation, rather than fragmentation, at the same distances from the road

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in (Zhang, et al, 2005) – in that paper the traffic flow was ~ 5 times larger than in our

experiments.

The discussed mechanism of partial suppression of fragmentation by increased

traffic flow should affect not only the ~ 13 nm mode, but also the ~ 7 nm mode, which

also results from fragmentation of larger particles (Chapter 6). As a result, particles with

~ 6 – 7 nm diameter in Figs. 8.5b and 8.6b are also characterised by strong negative

correlations with both cars and trucks on the road. A similar situation possibly occurs

for particles within the range between ~ 30 nm and ~ 40 nm in Figs. 8.5b and 8.6b. This

may also be the reason for exceptionally large negative correlations with number of

cars, and insufficiently strong positive correlation with number of trucks in the range

between ~ 8 nm and ~ 10 nm (Fig. 8.6b).

Further confirmation of the determined particle sources and correlations can be

obtained by means of canonical correlation analysis of concentrations in different

modes. This is done by including particle concentrations in different particle modes

(Fig. 8.2a) into group A of variables. Concentration in a mode is taken as the average

concentration within the 7-channel interval with the middle channel centred at the

considered mode. This middle channel will naturally be used for identification of the

considered modes.

Table 8.2 gives examples of the canonical correlation coefficients, weights and

loadings for the first canonical variates. Particle modes included into the A group of

variables are shown in the first column of Table 8.2. Canonical weights for modes are

the coefficients in front of mode concentrations in the first canonical variate for group

A; weights for traffic are the coefficients in front of numbers of trucks and cars on the

road in the first canonical variate for group B. The canonical correlation coefficient R

(the second column of Table 8.2) is the correlation coefficient for the first canonical

variates (Dillon and Goldstein, 1984, Johnson and Wichern, 2002). The correlation

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coefficient for the second canonical variates R2 << R for all cases considered below and

correlations for the second variates can be neglected.

Particle modes,

nm

R Level of conf.

Weights for modes

Loadings for modes

Traffic Weights for traffic

Loadings for traffic

6, 53, 136

0.56 99% 0.58 0.07 0.47

0.99 0.15 0.46

TrucksCars

0.93 -0.22

0.98 -0.39

26, 31

0.35 95% 1.14 -0.27

0.95 0.28

TrucksCars

-0.14 0.96

-0.30 0.99

14, 26, 40, 88

0.66 99% 0.87 0.67 0.55 0.32

0.69 0.34 -0.20 0.18

TrucksCars

-0.58 0.71

-0.71 0.82

Table 8.2. The results of the canonical correlation analysis for different particle modes

in the first set of 11 scans (Fig. 8.2a). Group A: the considered particle modes (the first column

of Table 8.2). Group B: numbers of trucks and cars (the traffic column).

This results yet again confirm that particles from the 6 nm mode are associated

with trucks. This is because the corresponding canonical weights and loadings for trucks

are large and both positive, while for cars they are also large but negative (Table 8.2).

Therefore, increasing number of trucks results in a significant increase of particle

concentration in this mode, and vice versa for cars (the correlation is strong and stable).

Similarly, the 136 nm mode is also associated with trucks, which is in agreement

with Figs. 8.3a, 8.4a, and 8.5a. The corresponding weights and loadings are large and

positive (the correlation is thus sufficiently stable and strong).

The 53 nm mode also has the same tendency towards the association with

trucks, and this is in agreement with the comments about the same association derived

from Fig. 8.5a. However, its weight and loading are not very large (Table 8.2), and there

might be questions about its stability and strength. This is probably related to the

insufficient level of confidence for the canonical correlations of this mode, displayed by

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Fig. 8.4a. Therefore, the conclusions about this mode may not be as certain as for the 6

nm and 136 nm modes.

The 26 nm and 31 nm modes represent two components of essentially the same

~ 30 nm mode (Chapter 6) – see also Figs. 8.2a and 6.4a. However, it is interesting that

the canonical correlation analysis suggests that these components could come from

different sources. Indeed, the canonical weight for the 26 nm mode is positive with

respect to the car weight and negative with respect to the truck weight (Table 8.2).

Therefore, we can conclude that the 26 nm mode mainly comes from cars. Since the

corresponding canonical loadings have the same signs, the considered correlation is

stable. Similarly, the 31 nm mode mainly comes from heavy trucks, which is

demonstrated by the signs of the corresponding canonical weights in Table 8.2.

However, this correlation is unstable, since the weight and loading for this mode have

different signs. Therefore, more extensive experimental data will be required to confirm

this conclusion.

As can be seen from the third row of Table 8.2, all the remaining 14, 40 and 88

nm modes are related to cars (although the 40 nm mode shows instability of correlation

because of the different sign of its canonical loading). This conclusion is again

confirmed by the simple moving average correlation coefficient (Fig. 8.3a). The

association of the 14 nm and 40 nm modes with cars is also in agreement with Fig. 8.5a

(see above). However, Figs. 8.4a and 6a provide inconclusive results about the 88 nm

mode, which makes the conclusions about its association with cars more questionable,

and more experimental data and further analysis is needed.

8.5. Meteorological parameters.

As has been mentioned, the canonical correlation analysis (Figs. 8.4 – 8.6) has

been conducted for group B of 5 variables including numbers of cars and trucks on the

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road, and average (over the scan time) meteorological parameters, such as temperature,

humidity and solar radiation. Therefore, the conducted analysis has automatically

provided canonical weights and loadings for temperature, humidity and solar radiation

for all particle diameters.

However, it has been shown that for both the sets of 11 and 16 scans,

correlations of particle modes with humidity are highly unstable. Signs of canonical

weights and loadings do not normally coincide with each other, with typical values for

loadings less than 0.2 (which corresponds to the level of confidence < 95%). Stable

correlation between the particle concentrations and humidity for the first set of scans

could only be revealed within the range ~ 7 – 19 nm (with negative weights and

loadings) and within the range ~ 70 – 110 nm (with positive weights and loadings). The

situation is not better for the second set of 16 scans: only ~ 40 nm particles show stable

(negative) correlation with humidity. Therefore, it is hardly possible to talk about

reliable and useful relationships between the observed particle modes and humidity.

One of the reasons of this instability is related to the significant dependence of

humidity on traffic. For example, it has been experimentally estimated that traffic-

induced fluctuations of humidity at the distance of ~ 40 m from the road may be of the

order of a few percent. If this results in non-linear dependencies, then the canonical

correlations may become unstable.

For better understanding of these relationships, canonical correlations between

temperature/humidity and traffic have been calculated for both the sets of scans (Table

8.3). In particular, one can see strong positive association between humidity and the

number of cars for both the sets. This is because the corresponding canonical weights

and loadings for cars are large and both positive, while for trucks they are negative

(Table 8.3). Therefore, increasing number of cars results in a significant increase of

humidity. At the same time, the correlations between traffic and temperature are

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unstable, because the weight and loading for temperature have different signs – see

Table 8.3.

Temperature and humidity Trucks and cars Set R Level

of conf.

weights loadings weights loadings

1 0.73 99% 0.32 (temp) 1,12 (hum)

-0.24 (temp) 0.96 (hum)

-0.09 (trucks) 0.98 (cars)

-0.27 (trucks) 0.996 (cars)

2 0.64 99% 0.34 (temp) 1.22 (hum)

-0.54 (temp) 0.97 (hum)

-0.36 (trucks) 0.89 (cars)

-0.47 (trucks) 0.94 (cars)

Table 8.3. The results of the canonical correlation analysis between temperature and

humidity (group A) and the number of trucks and cars (group B).

Thus, it is indeed possible that correlations between humidity and particle

concentrations may be significantly affected by the additional dependence of humidity

on traffic conditions on the road. On the contrary, temperature does not display a

consistent dependence on traffic conditions. Therefore, it is possible to expect that

correlations between temperature and particle concentrations should be much more

stable and thus can be used for the analysis of temperature-related processes of aerosol

evolution.

Correlations of particle modes with temperature are illustrated by Figs. 8.7a,b by

the dependencies of the moving average canonical weights and loadings for

temperature. These dependencies show very strong and stable correlations with same

signs of canonical weights and loadings in wide ranges of particle diameters (Fig.

8.7a,b). An important feature of these dependencies are the drastic differences between

correlations for the two considered sets of scans. This means that just 16 s of evolution

(between Figs. 8.7a and 8.7b) have resulted in a significant alteration of the

temperature-related correlations. This is a clear indication of strong and fast processes

of evolution of combustion aerosols near a busy road. For example, particles in the

broad range from ~ 8 nm to ~ 20 nm (the ~ 13 nm mode) for the second set of scans are

characterised by strong and stable positive correlations with temperature (Fig. 8.7b).

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This means that increasing temperature results in increasing number of particles within

this range. On the contrary, particles within the ranges ~ 20 – 80 nm and > 100 nm are

negatively correlated with temperature (Fig. 8.7b), i.e. increasing temperature results in

decreasing concentration of these particles. This behaviour is again in a good qualitative

agreement with the fragmentation mechanism of aerosol evolution. Indeed, particles

within the ~ 8 – 20 nm range are expected to be generated by fragmentation of larger

particles. At the same time, thermal fragmentation should strongly depend on

temperature – its rate rapidly (exponentially) increasing with increasing temperature

(Chapter 10). This is the reason for strong negative correlations for fragmenting larger

particles (their concentration decreases with increasing temperature) and strong positive

correlations with particles resulting from fragmentation (their concentration increases

with increasing temperature).

An interesting feature is the strong and stable negative correlations with

temperature for very small particles with ~ 5 – 6 nm for both the sets of scans (i.e., at

both considered stages of aerosol evolution). This behaviour is unclear at this stage and

will require further investigation. It could be interpreted by the presence of a large

number of small volatile particles coming from diesels (see the discussion of Figs. 8.3a

and 8.5a). The number of these particles could increase with decreasing temperature due

to slower evaporation. However, the same is not applicable to Fig. 8.7b, where the

volatile particles have already evaporated (see the discussion of Figs. 8.6a,b). Similarly,

further investigation is needed for understanding of temperature dependence of particle

correlations in the range ~ 80 – 100 nm (Fig. 8.7b).

Temperature correlations for the first set are less understandable at this stage and

will also need further investigation. One of the possibilities is that these correlations (at

least partly) may still be related to correlations between temperature and traffic

conditions, though this is not entirely confirmed by the weights and loadings for solar

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radiation (Figs. 8.8a,b). Indeed, weights and loading for solar radiation tend to have

some similar features to those observed on the dependencies for temperature (compare

curves in Figs. 8.7a and 8.8a). These similarities may suggest the existence of processes

that are similarly related to temperature and solar radiation, and it is obvious that solar

radiation does not depend on traffic conditions.

Fig. 8.7. Moving average canonical weights (solid curves) and loadings (dotted curves) for

temperature in group B with the five variables: temperature, humidity, solar radiation, number

of trucks, and number of cars. (a) The dependencies for the first set of 11 scans (from 6 to 16).

(b) The dependencies for the second set of scans (from 28 to 43). Straight dashed horizontal

lines indicate the 95% level of confidence for the loading curves. The dash-and-dot horizontal

line corresponds to zero.

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Fig. 8.8. Moving average canonical weights (solid curves) and loadings (dotted curves) for solar

radiation in group B with the five variables: temperature, humidity, solar radiation, number of

trucks, and number of cars. (a) The dependencies for the first set of 11 scans (scans from 6 to

16). (b) The dependencies for the second set of scans (scans from 28 to 43). Straight dashed

horizontal lines indicate the 95% level of confidence for the loading curves. The dash-and-dot

horizontal line corresponds to zero.

An interesting aspect that can be drawn from the comparison of Figs. 8.7a and

8.8a is that for small particles (< 8 nm), the effect of solar radiation is opposite to that of

temperature. This may be explained again by the fact that particles in this range in the

first set of scans are mostly volatile. Such particles are expected to be formed by means

of condensation of volatile compounds onto very small core particles (beyond the

detectable range). The core particles could be formed by means of the processes of

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nucleation in the immediate proximity of the exhaust pipe (Zhang & Wexler, 2004,

Zhang et al, 2004, Pohjola, et al, 2003). The nucleation processes may be induced by

solar radiation (Shi, et al, 2001, Kulmala, et al, 2004). Therefore, the number of core

particles should have positive correlations with solar radiation. If the volatile particles

from the range < 8 nm grow from the core particles by means of condensation, then they

must also have positive correlations with solar radiation (Fig. 8.8a). On the contrary,

increasing temperature should result in increasing evaporation or decreasing

condensation processes, resulting in negative correlations of the same particles with

temperature (Fig. 8.7a).

The situation with the second set of scans is more understandable, if we use the

fragmentation model. Again, positive stable correlations with solar radiation for the

particles within the range ~ 8 – 20 nm (Fig. 8.8b) are similar to those in Fig. 8.7b.

Larger particles are predominantly characterised by negative (ranges ~ 20 – 30 nm and

> 100 nm) or unstable (inconclusive) correlations with solar radiation. Both these results

are in agreement with fragmentation of larger particles into smaller particles from the

range ~ 8 – 20 nm. This process may be expected to intensify (e.g., due to heating

and/or radiative effects) with increasing solar radiation, resulting in increased

concentration of smaller particles (positive correlations) and decreased concentration of

larger particles (negative correlations).

8.6. Conclusions.

In this Chapter, a new statistical method of analysis of nano-particle aerosols,

based on the moving average approach and canonical correlation analysis has been

developed and applied for the investigation of particle modes and their possible sources

in combustion aerosols near busy roads. This method was demonstrated to provide an

important new physical insight into the processes of evolution of combustion aerosols

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near busy roads. It enables detailed investigation of contribution of different

environmental and meteorological factors and processes on evolution of combustion

aerosols. Several particle modes were identified to originate predominantly from petrol

cars and heavy-diesel trucks. Levels of confidence and the associated statistical errors

were determined, demonstrating reliability and accuracy of the developed new

approach. The obtained results will be important for the development of effective

practical measures for reduction of human exposure to nano-particle aerosols and

development of new strategies for reduction of the impact of modern transport on our

environment.

The developed new statistical approach will also be important for further

development of our understanding of fundamental physical and chemical effects in

combustion aerosols. For example, it has led to further confirmation of the discovered

new major mechanisms of aerosol evolution – fragmentation of nano-particles.

It is also important to note that the developed approach is directly applicable not

only to the considered combustion aerosols near busy roads, but also to any other type

of anthropogenic and natural aerosols, for which the determination of possible sources

of different particle modes and investigation of evolution processes is important.

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CHAPTER 9

CORRELATIONS BETWEEN PARTICLE MODES: FRAGMENTATION THEOREM ([A7])

9.1. Introduction

As was indicated in Chapter 8, the development of new statistical methods of analysis

of combustion aerosols resulting from transport emissions near busy roads is one of the

important directions of current research in the aerosol science. This is because such methods

are expected to provide new insights into the physical and chemical processes of evolution of

airborne nano-particles, their possible sources, mutual relationships, and eventually lead to

the development of effective means for elimination or reduction of their impact of human

health and environment. For example, these methods will be important for the investigation

of fundamental processes and nature of nano-particle aerosols, including particle formation,

condensation/evaporation, coagulation, and thermal fragmentation in the real-world

environment with strong stochastic fluctuations of atmospheric and environmental

parameters (Zhang and Wexler, 2004, Zhang et al, 2004, Zhu et al, 2002, Shi et al, 1999, Shi

et al, 2001, Pohjola et al, 2003, Kulmala et al, 2004) – see also Chapters 6 and 8.

Therefore, the new statistical methods based on the moving average concentration of

particles in different channels of the size distribution (Chapters 5 and 8), and moving average

correlation coefficients, canonical weights and loadings (Chapters 6 and 8) were developed

for the determination and investigation of particle modes in combustion aerosols. These

approaches provided an excellent new physical insight into the evolution processes and

possible sources of nano-particle modes (Chapters 6 and 8).

However, these techniques mostly provide information about how particle

concentrations in neighbouring channels correlate with each other (e.g., forming a mode), or

how groups of particles with similar diameters react to variations of traffic and/or

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meteorological conditions (Chapters 6 and 8). It is more difficult to use these methods for the

direct investigation of correlations between particles with significantly different diameters

(i.e., between different channels/modes in the particle size distribution). At the same time,

such an analysis is expected to provide new important evidence of physical processes and

particle transformations during evolution of combustion aerosols.

For example, because thermal fragmentation of nano-particles was demonstrated to

play a major role at particular stages of aerosol evolution (Chapters 6 and 8), this process

should have a substantial effect on mutual correlations between particle modes. For example,

if fragmentation results in mutual transformation of some particle modes, then these modes

may be characterised by strong negative correlations (anti-correlations). This is because

increasing concentration in the fragmenting mode (e.g., due to turbulent fluctuations of

evolution time) may result in decreasing concentration in the modes resulting from

fragmentation.

Therefore, in this Chapter, we extend the developed moving average approach to the

analysis of correlations and mutual transformations/interactions between different particle

modes in combustion aerosols near busy roads. As a result, a new moving average cross-

correlation approach will be developed. Strong anti-correlations between several particle

modes will be demonstrated and investigated. A unique anti-symmetric correlations between

some particular modes will be demonstrated and investigated. The interpretation of these

anti-symmetric correlations will be conducted on the basis of the derived fragmentation

theorem, which may be regarded as one of the most convincing confirmations of the

fragmentation mechanism of evolution of combustion aerosols.

9.2. Moving average approach for particle modes.

In this Chapter we again analyse the set of monitoring data near Gateway Motorway

in the Brisbane area, Australia, which was considered in Chapters 6 and 8. The detailed

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description of the experimental procedure, the obtained monitoring data, and the

corresponding meteorological and traffic parameters are presented in Section 8.2.

The extension of the moving average approach described in Chapters 6 and 8 to the

case of correlations between particle modes and/or different channels from the size

distribution can be done as follows. We again consider multiple scans of the particle size

distribution. For example, these can be the sets of 16 scans (from 28 to 43) corresponding to

Figs. 8.2a,b from Chapter 8, or 20 scans (from 19 to 38) corresponding to Figs. 6.4a,b from

Chapter 6.

We again choose a 7-channel interval (which we will call ‘primary interval’)

corresponding to a particular mode, i.e., the central channel of this interval corresponds to

one of the maximums in Figs. 8.2a,b or 6.4a,b. We also choose another arbitrary interval

(‘secondary interval’) of 7 neighbouring channels from the overall 100 channels in the

particle size distribution. Each of the channels from any of the chosen (primary or

secondary) 7-channel intervals will correspond to a column of different particle

concentrations corresponding to each of the multiple scans. For example, for a set of 11

scans, each channel will correspond to a column of 11 different particle concentrations.

Every value of concentration in every column is normalised to the total number

concentration in the respective scan. This eliminates trivial correlations associated with

turbulent fluctuations of the total number concentration.

We select a channel from the primary 7-channel interval and calculate the simple

correlation coefficient between the concentration columns corresponding to this channel and

one of the channels from the secondary 7-channel interval. This procedure is then repeated

for all possible different pairs of channels – one from the primary interval and the other from

the secondary interval. As a result, we obtain 49 simple correlation coefficients, and their

average is calculated. Each 7-channel interval is identified by the particle diameter

corresponding to its central channel. The obtained average simple correlation coefficient is

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taken as the correlation coefficient between the two central channels from the two selected 7-

channel intervals. Then we take a different secondary interval, and repeat the whole

procedure (this is done 94 times for all possible choices of the secondary 7-channel interval

and the fixed primary interval; one of the secondary intervals coincides with the primary

interval). As a result, we obtain 94 average correlation coefficients between the selected

channel (i.e., the central channel of the selected primary interval) and all other

channels/modes. Thus we obtain a dependence of the moving average correlation coefficient

between the selected channel/mode and all other channels on particle diameter (each such

diameter is associated with the central channel of a secondary interval). These dependences

are obviously different for different primary intervals.

The statistical errors of the obtained dependencies of the moving average correlation

coefficients can be obtained by calculating the errors of the mean correlation coefficients for

each of the 94 pairs of the primary and secondary 7-channel intervals. As a result, we obtain

two error curves surrounding the main dependence, similar to how it was done for Figs.

8.2a,b and 6.4a,b.

9.3. Numerical results and their discussion

For the numerical analysis in this section, we will choose three sets of scans: 16 scans

(scans from 1 to 16), 16 scans (from 28 to 43), and 20 scans (from 19 to 38). The first set of

16 scans includes the two sets from 1 to 11 and from 6 to 16 scans, considered in Chapter 8.

We use here one joint set, instead of the two separate considered in Chapter 8, because they

both correspond to approximately the same wind, and the difference between them in terms

of the evolution time was only ~ 3 s (Chapter 8). Therefore, within the limits of errors, it is

difficult to distinguish between these two sets, and we join them in one larger set of 16 scans.

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Fig. 9.1. The dependencies of the moving average correlation coefficients for the primary intervals

centred at the following channels: 126 nm (solid curve 1), 136 nm (2 channels above 126 nm –

dashed curve 1), 113 nm (2 channels below 126 nm – dotted curve 1), 13.6 nm (solid curve 2), 13.1

nm (1 channel below 13.6 nm – dotted curve 2), and 14.1 nm (1 channel above 13.6 nm – dashed

curve 2) for the set of 16 scans from 1 to 16. The average particle diameters on the horizontal axis

correspond to the central channels of the secondary intervals. The 95% levels of confidence for the

considered simple correlations are shown by the horizontal solid lines. Average normal wind

component ≈ 1.65 m/s; evolution time ~ 24 s. The dash-and-dot horizontal line corresponds to zero

correlation coefficient.

For the first set of 16 scans (from 1 to 16), the dependence of the correlation

coefficients for the 126 nm channel (i.e., the central channel of the primary interval

corresponds to the diameter 126 nm) on particle diameter is given by the solid curve 1 in Fig.

9.1. Slight variations of the position of the primary interval does not result in drastic

alterations of the obtained dependence. For example, if we choose the 136 nm and 113 nm

channels as the central channels of the primary 7-channel interval, variations of the resultant

correlations coefficients are relatively small (dashed and dotted curves 1 in Fig. 9.1). This is

expected, because variations of position of the primary interval within the same mode are not

anticipated to produce substantial variations of correlations with other channels. Similar

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situation occurs for the curves corresponding to the primary intervals centred at the 13.1 nm,

13.6 nm, and 14.1 nm channels (dotted, solid and dashed curves 2 in Fig. 9.1). Therefore,

this approach can thus be regarded as a method for the determination of particle modes – a

mode will thus be an interval of neighbouring channels within which correlations with other

modes/channels, obtained by means of the described procedure, are approximately the same.

Curves 1 in Fig. 9.1 suggest that particles with diameters around 126 nm (the 126

mode in Fig. 8.2a) are positively correlated with the modes ~ 55 nm and ~ 6 nm. Note that

this is in agreement with the solid curve in Fig. 8.3a from Chapter 8, which demonstrates that

all these three modes are associated with trucks on the road. Therefore, the positive

correlations between these three modes on the curves 1 in Fig. 9.1 are likely due to their

mutual source – diesel trucks (Chapter 8).

Negative correlations shown by curves 1 in Fig. 9.1 for ~ 10 – 30 nm particles can be

explained by stronger association of these particles with cars (Chapter 8). Therefore, due to

limited overall traffic capacity of the road, and normalisation-induced negative correlations

(see Section 8.4), it may be expected that, for example, increasing relative concentrations of

particles associated with trucks (e.g., 126 nm mode) may result in a tendency of decreasing

relative concentrations in the channels more associated with cars, leading to negative

correlations with the 126 nm mode (curves 1 in Fig. 9.1).

As the aerosol is transported from the road, particles experience rapid processes of

transformation/evolution. These processes drastically change the correlation pattern for the

particle modes within just 16 s – see Figs. 8.2 – 8.7. Similar significant alterations are also

expected for the moving average simple correlations between the modes. For example, the

dependencies of the moving average correlation coefficient for the 126 nm mode (the

primary 7-channel interval is centred at the 126 nm channel) and for the 13.6 nm mode (the

primary interval is centred at the 13.6 nm channel) for the second set of 16 scans (from 28 to

43) are presented in Fig. 9.2 by solid curves 1 and 2, respectively.

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The dashed and dotted curves 1 are plotted for the primary interval centred at the 136

and 113 nm channels, respectively. These curves again suggest (as expected) relative

insensitivity, i.e., stability of the resultant dependencies with respect to variations of position

of the primary interval within the limits of one mode. The examples of the resultant error

curves (obtained by the approach described above in Section 9.2) are represented by the two

dashed curves around solid curve 2 in Fig. 9.2. These error curves clearly demonstrate that

the corresponding errors of the moving average correlation coefficients are typically

insignificant and may not be considered.

Fig. 9.2. Moving average simple correlation coefficient between each of the following four channels

(modes): 126 nm (solid curve 1), 136 nm (dashed curve 1), 113 nm (dotted curve 1), and 13.6 nm

(solid curve 2) and all other channels in the particle size distribution for the second set of 16 scans

(from 28 to 43). Dashed curves 2 represent an example of the error lines for the dependence given by

solid curve 2. The average particle diameter for each of the secondary intervals is taken as the

diameter corresponding to the central channel of the interval. The average normal wind component ≈

1 m/s; evolution time ~ 40 s. The horizontal straight lines indicate the 95% level of confidence of the

considered simple correlations.

The 13.6 nm and 126 nm modes are thus negatively correlated (anti-correlated) with

each other. The most interesting aspect of this figure is that the dependencies for the primary

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intervals centred at the 126 nm and 13.6 nm channels (solid curves 1 and 2, respectively) are

almost symmetric of each other with respect to the zero line (anti-symmetric correlations) –

Fig. 9.2. Moreover, all the correlation curves for the channels 113 nm, 126 nm, and 136 nm

(curves 1 in Fig. 9.2) have almost exactly the same positions of their maximums and

minimums, corresponding to the same positions of the respective minimums and maximums

of the correlation curve for the 13.6 nm mode (Fig. 9.2).

This is a non-trivial result. It means that the correlation coefficient between the 126

nm channel and, for example, 40 nm channel is the same in magnitude, but different in sign

to the correlation coefficient between 13.6 nm channel and the same 40 nm channel. The

same is correct for any other channel, but not just the 40 nm channel. This clearly

demonstrates that all the channels are related by some mutual physical process. It is

important that this process was not present or was suppressed/masked for the first set of 16

scans (from 1 to 16), because the correlations in Fig. 9.1 are not anti-symmetric. The average

normal wind component for the first set of 16 scans is 1.65 m/s, whereas for the second set of

scans (from 28 to 43) it is ≈ 1 m/s (Chapter 8). This means that the anti-symmetric

correlation pattern (Fig. 9.2) has developed within just ~ 16 s of aerosol evolution.

An explanation of anti-correlations in Fig. 9.2 should be different from that for Fig.

9.1. Because significant variations of correlations between the modes have occurred, anti-

correlations in Fig. 9.2 cannot be explained by traffic effects, similar to how it was done for

Fig. 9.1, whereas average traffic conditions have not changed noticeably between these two

sets of scans. Therefore, these are rather evolutionary processes within the 16 s of the time

difference between Figs. 9.1 and 9.2 that have resulted in anti-symmetric correlations in Fig.

9.2.

The fact that the 13.6 nm mode is negatively correlated with all larger modes

suggests that there may be a process of formation of the 13 nm mode from the larger

particles, or, vice versa, larger particles are formed by the particles from the 13 nm mode.

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This is because the observed anti-correlations between the ~ 13 nm particles and particles

with diameters > 30 nm (Fig. 9.1), and especially particles with diameters ~ 126 nm clearly

suggest that, for example, if concentration in the 13 nm mode increases, then the

concentration in the 126 nm mode decreases, and vice versa. Therefore, one of this modes

may be the source for the other, and the process of transformation should be characterised by

the typical relaxation time that is of the order of the time of evolution between the two sets of

scans, which is ≈ 16 s.

It seems to be possible to immediately dismiss such processes of particle evolution as

condensation/evaporation, homogeneous and heterogeneous nucleation, deposition and

dispersion as possible mechanisms for the observed strong anti-correlations and anti-

symmetric correlations (Fig. 9.2). It difficult to imagine (from the physical nature of these

processes) how they could result in such anti-correlations on the considered scale of particle

diameters. The only option out of the conventional mechanisms of aerosol evolution would

be coagulation. However, as has been shown by Shi, et. al. (1999), Jacobson (1999), and

Jacobson & Seinfeld (2004), coagulation at the considered levels of particle concentrations

will take at least hours (rather than 16 s) to result in noticeable changes in particle

distribution and correlation pattern. Therefore, coagulation should also be excluded from the

list of possible mechanisms.

As a result, the only suitable explanation of the observed anti-symmetric correlations

(Fig. 9.2) is thermal fragmentation of nano-particles (Chapters 6 and 8). In accordance with

the obtained results (Fig. 9.2), it can be assumed that the ~ 13 nm particles are generated due

to thermal fragmentation of larger nano-particles (e.g., the ~ 126 nm mode). As a result, it is

expected that if particles with the diameters of ~ 13 nm break away from, for example, 126

nm particles, then particle concentration in the ~ 126 nm mode decreases, while the

concentration in the ~ 13 nm mode increases, resulting in the observed anti-correlations.

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However, Fig. 9.2 also suggests that particles not only from ~ 126 nm mode, but also

within the large range (> 30 nm) experience similar anti-correlations with the ~ 13 nm mode.

This suggests that all these particles experience fragmentation resulting in breaking away ~

13 nm particles. For example, the ~ 66 nm particles have strong negative correlations with

the ~ 13 nm particles, and strong positive correlations with the ~ 126 nm particles (Fig.

9.2).This could be explained by the fact that particle concentration for the considered second

set of 16 scans decreases monotonically with increasing particle diameter –see the dark band

in Fig. 8.1. This means that during the process of fragmentation, the inflow of the particles

into, for example, the 66 nm mode due to fragmentation of the larger particles is less than the

outflow of the particles from the 66 nm mode due to its own fragmentation. Thus

fragmentation causes an overall shift of the dark band at larger particle diameters in Fig. 8.1

to the left. Therefore, fragmentation results in a simultaneous decrease of particle

concentrations in all the channels in the range > 30 nm, thus giving positive correlations

between all the modes from this range and the 126 nm mode – Fig. 9.2.

Fig. 9.3 shows the moving average correlation curves for 40, 50, 68 and 126 nm

particles from the range of particles experiencing anti-correlations with the ~ 13 nm particles

(Fig. 9.2). Curve 1 in Fig. 9.3 is identical to solid curve 1 in Fig. 9.2. The most significant

result of Fig. 9.3 is that all the presented curves demonstrate almost identical negative

correlations between the considered channels and the ~ 13 nm particles. This is a clear

indication that all the particles within the considered range > 30 nm have approximately the

same probability to fragment with the release of ~ 13 nm particles. The fragmentation

mechanism works in approximately the same way for the larger particles in a large range of

particle diameters (between ~ 30 nm and ~ 136 nm). In other words, the fraction of particles

participating in the process of fragmentation is approximately the same for all the channels in

the mentioned range. This suggests approximately the same values of the fragmentation rate

coefficient for particles in the considered range.

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Fig. 9.3. Moving average simple correlation coefficient between each of the following four channels

(modes): 126 nm (curve 1), 68 nm (curve 2), 50 nm (curve 3), and 40 nm (curve 4) and all other

channels in the particle size distribution for the second set of scans from 28 to 43. Average normal

wind component ≈ 1 m/s; evolution time ~ 40 s. The horizontal straight lines indicate the 80%

(dashed straight lines) and 95% (solid straight lines) levels of confidence of the considered simple

correlations.

Another interesting aspect of Fig. 9.3 is that decreasing average particle diameter for

the primary 7-channel interval from ~ 126 nm to ~ 40 nm results in a steady and significant

reduction of the correlation coefficients with smaller particles of ≲ 8 nm (compare curves 1 –

4).

This might be because of the tendency that smaller particles may fragment by means

of the release of smaller (~ 7 nm) primary particles (Chapter 6). If this is true, then one

should expect that further decrease of diameter of fragmenting particles below ~ 40 nm

should significantly increase anti-correlations (negative correlations) with the ~ 7 nm mode.

This is indeed the case and is demonstrated by Fig. 9.4, where correlations for the 7 nm and

32 nm modes (channels) are considered. We again obtain the two dependencies that tend to

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be approximately symmetric with respect to the zero line (Fig. 9.4). Because of the same

reasons as for Fig. 9.2, the obtained anti-correlations between the 32 nm and 7 nm modes can

be explained by fragmentation of nano-particles by means of breaking away primary ~ 7 nm

particles (Chapter 6).

Fig. 9.4. Moving average simple correlation coefficient between each of the following two channels

(modes): 32.2 nm (curve 1) and 7.37 nm (curve 2) and all other channels in the particle size

distribution for the second set of 16 scans from 28 to 43. Average normal wind component ≈ 1 m/s;

evolution time ~ 40 s. The horizontal straight lines indicate the 80% (dashed straight lines) and 95%

(solid straight lines) levels of confidence of the considered simple correlations.

As a result, Figs. 9.2 – 9.4 suggest the following possible interpretation. There are

two main types of primary particles: ~ 7 nm and ~ 13 nm. They can possibly be related to

different types of vehicles (needs to be confirmed by further analysis). These particles form

different types of larger particles. This is expected, because coagulation may occur only in

the immediate proximity to the exhaust pipe or inside it, where particle concentration is

sufficient for coagulation to occur (Jacobson, 1999, Jacobson & Sienfeld, 2004). As a result,

large composite particles are primarily formed of one type of primary particles – either ~ 7

nm or ~ 13 nm (particles from one vehicle are highly unlikely to get to the exhaust pipe of

another vehicle in sufficient concentrations). Larger particles with diameters closer to ~ 100

203

nm are mainly formed of larger primary particles, and their fragmentation results mainly in

breaking away particles from the ~ 13 nm mode. This leads to anti-correlations shown in

Figs. 9.2 and 9.3. However, at smaller diameters (~ 20 – 40 nm) there is a large number of

particles formed by the ~ 7 nm primary particles (Chapter 6). As a result, their fragmentation

leads to the anti-correlations with the ~ 7 nm mode (Fig. 9.4).

Fig. 9.5. Moving average simple correlation coefficient between each of the two channels (modes):

126 nm (solid curve) and 13.6 nm (dashed curve) and all other channels in the particle size

distribution for the third set of scans from 19 to 38. Average normal wind component ≈ 0.75 m/s;

evolution time ~ 53 s. The horizontal solid straight lines indicate the 95% levels of confidence of the

considered simple correlations.

The anti-symmetry of correlations between different particle modes is approximately

preserved for the third set of 20 scans (from 19 to 38) that corresponds to the largest

evolution time of ~ 53 s (Fig. 9.5). This is because the fragmentation process continues at

this stage of the aerosol evolution. However, the anti-symmetry has started to break down,

for example, in the region below ~ 8 nm diameter (Fig. 9.5). This is possibly because anti-

symmetry requires very specific conditions that may possibly be achieved only at some

particular stage of aerosol evolution (see the next section). Probabilistic time delays (Chapter

10) with fragmentation of intermediate particle modes resulting from fragmentation of even

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larger particles may also play a noticeable role in the formation and breach of the anti-

symmetric pattern of correlations. However, this requires further investigation.

Certainly, fragmentation mechanism does not necessarily imply that all of the larger

particles should necessarily fragment into primary particles. Some of larger particles may

have completely different origins and physical/chemical nature. The presence of such

different particles may also result in breaching anti-symmetric pattern of correlations

between the modes in the particle size distribution (for more detail see the next section).

9.4. Fragmentation Theorem

In Section 9.3, we have attempted a qualitative interpretation of the obtained anti-

symmetric pattern of mutual correlations between the modes in the particle size distribution.

Here, we will present a more rigorous mathematical derivation and justification of conditions

when such a pattern may occur. As a result, we will obtain further confirmation of the

fragmentation model of evolution of combustion aerosols.

In order to explain the observed anti-symmetric correlations between concentrations

in different channels of the size distribution (Fig. 9.2), consider again N scans of the particle

size distribution and simple correlations between two columns of particle concentrations

corresponding to two selected channels. Each such column contains N different

concentrations that are normalised to the total number concentration in the respective scan.

The sufficient and necessary condition for the anti-symmetry of the dependencies of the

moving average correlation coefficients for two different k-th and m-th channels/modes (e.g.,

126 nm channel and 13.6 nm channel in Fig. 9.2) can be written in the form:

Rkn = – Rmn, (9.1)

where Rkn is the correlation coefficient between the k-th channel (with the larger particle

diameter) and an arbitrary n-th channel of the particle size distribution, and Rmn is the

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correlation coefficient between the m-th channel (with the smaller particle diameter) and the

same n-th channel.

Using the equation for the simple correlation coefficient between the two data

columns (Larsen and Marx, 1986), we re-write Eq. (9.1) as follows:

∑∑Δ

Δ

∑Δ

Δ−=∑∑Δ

Δ

∑Δ

Δi

jnj

ni

jmj

mi

ij

nj

ni

jkj

ki

y

y

y

y

y

y

y

y2222

, (9.2)

where yki, ymi, and yni are the particle concentrations in the k-th, m-th, and an arbitrary n-th

channels of the particle size distribution, respectively, sums are taken over the N different

scans, Δyki, Δymi, and Δyni are the concentration fluctuations in the i-th scan around the mean

values ky , my , and ny calculated over the N scans.

The fragmentation theorem establishes conditions at which Eqs. (9.1) and (9.2) are

satisfied, i.e., the dependencies of the moving average correlation coefficients for two

different channels/modes are anti-symmetric (Fig. 9.2).

Conditions of the fragmentation theorem:

1. Particles taking part in fragmentation consist of primary particles that can break away

from larger composite particles. Primary particles belong to the sink mode.

2. Fragmentation occurs by means of breaking away a primary particle – one primary

particle breaks away during each act of fragmentation (Fig. 9.6). Each act of

fragmentation adds one primary particle to the sink mode and results in a transition of

the fragmenting particle to the next intermediate mode with smaller diameter (Fig.

9.6). Only the last act of fragmentation of a particle from the smallest intermediate

mode results in two primary particles being added to the sink mode.

3. Fragmentation by means of breaking away non-primary particles or more than one

primary particles at a time are assumed not to be possible.

4. The number of fragmenting intermediate particle modes can be finite (when there is a

maximal diameter of fragmenting particle, i.e. a maximal number of primary particles

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in a fragmenting particle), or infinite (when there is no maximal diameter of

fragmenting particles).

5. Fluctuations of particle concentrations in different scans in at least two different k-th

and m-th channels are caused predominantly by the process of fragmentation (for

more detailed explanation of this condition see below).

6. Particle concentrations in the k-th and m-th channels are negatively correlated with

each other: Rkm < 0 (i.e., if the concentration in the k-th channel increases, then the

concentration in the m-th channel decreases, and vice versa).

7. Fragmentation rates for particles from all the intermediate modes are equal.

Fragmentation theorem: If conditions 1 – 7 are satisfied, then the dependencies of the

moving average correlation coefficients for the k-th and m-th channels are anti-symmetric of

each other.

Fig. 9.6. Fragmentation scheme for particles in the intermediate modes into the sink mode of primary

particles by means of breaking away primary particles – one per each act of fragmentation. Each

intermediate mode is obtained from the previous mode by means of breaking away one primary

particle that is automatically added to the sink mode.

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For example, in accordance with Fig. 9.2, it is possible to expect that for the second

set of scans considered in Section 9.3, the particle diameter for the k-th mode is equal to 126

nm, whereas the m-th mode corresponds to the sink mode with the primary particles of 13.6

nm diameter. Fragmentation occurs by means of breaking the ~ 13.6 nm particles away from

the larger particles from the source mode or intermediate modes.

Proving the fragmentation theorem is equivalent to verifying the validity of the

sufficient and necessary conditions (1) and/or (2) under the conditions of the theorem 1 – 7.

In accordance with Fig. 9.6, we can write the equations for the concentration

fluctuations Δypi in an arbitrary p-th intermediate mode:

Δypi = ypi – py = addpi

outpi

inpi yyy Δ+Δ+Δ , for p ≠ 1; (9.3)

Δy1i = y1i – 1y = – outi

p

outpi yy 2

32Δ−∑ Δ

∞

= + add

iy1Δ =

= iniy1Δ + add

iy1Δ . (9.4)

Here, outpiyΔ is the variation of the concentration in the p-th intermediate mode in the i-th

scan, caused by fragmentation of particles from this mode. Therefore, this variation results in

particle outflow from the p-th intermediate mode, caused by fragmentation. Simultaneously,

this variation results in an inflow of particles into the sink mode (see Eq. (9.4)), because

fragmentation occurs through the release of primary particles. If p ≠ 1, then inpiyΔ is the

variation of the concentration in the p-th intermediate mode due to the inflow of particles

from the (p + 1)-th intermediate mode. This inflow is caused by fragmentation of the (p – 1)-

th intermediate mode. On the other hand, iniy1Δ are the variations of the concentration in the

sink mode, caused by the inflow of primary particles into the sink mode due to fragmentation

of all the intermediate modes, and outixΔ . The variations add

piyΔ (p = 1, 2, 3, …) are the

additional fluctuations of the concentrations in the sink and intermediate modes, caused by

factors/processes other than the process of fragmentation. There is a factor of 2 in front of

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outiy2Δ in Eq. (9.4), because the intermediate mode with p = 2 fragments into two primary

particles. There is no term with outiy1Δ in Eq. (9.4), because the sink mode (with p = 1) is

assumed to consist of primary particles that do not experience further fragmentation. Note

also that in Eqs. (9.3) and (9.4) the index p indicate all possible modes, i.e., p may also be

equal to m or k.

Condition 5 of the theorem states that the k-th and m-th modes (for which the anti-

symmetry of the correlation coefficients is expected) are caused predominantly by the

process of fragmentation. That is, the effect of any other mechanisms on fluctuations of the

normalised particle concentrations in these modes is negligible:

addkiyΔ = add

miyΔ = 0. (9.5)

Physically, fragmentation-induced fluctuations of particle concentrations occur

because of turbulent fluctuations. Turbulent fluctuations result in fluctuations of evolution

time for the aerosol, because they lead to stochastic variations of the transport time from the

road. As a result, each scan corresponds to slightly different evolution times, i.e., slightly

different stages of the aerosol evolution. For example, smaller evolution time always results

in smaller concentration of primary particles in the sink mode, and normally (but not always

– see below) in larger concentration of fragmenting particles. Thus we usually have anti-

correlations between the sink and the intermediate modes (some exclusions may apply – see

below).

If the fragmentation rate is the same for all the modes (condition 7), then ypif = αi pfy

for all p > 1, where ypif is the concentration of particles in the p-th mode in the i-th scan,

which take part in fragmentation, αi is some coefficient that is the same for all p > 1 (because

of the same fragmentation rate), but are different for different scans. In this case, Eq. (9.4)

for the k-th and m-th modes (for which the anti-symmetry of correlation coefficients is

investigated) can be reduced as

209

Δyki = yki – ky = (αi – 1) kfy – (αi – 1) fky )1( + , (9.6)

Δymi = ymi – my = (αi – 1) mfy – (αi – 1) fmy )1( + . (9.7)

Note again, that Eq. (9.5) is assumed to be satisfied for the k-th and m-th modes. Therefore,

the effect of any other mechanism (apart from fragmentation) of concentration fluctuations is

negligible, and therefore, concentrations of particles that do not take part in fragmentation

cancel out from the right-hand sides of Eqs. (9.6) and (9.7).

Eqs. (9.6) and (9.7) suggest that condition 6 of the fragmentation theorem is satisfied

if Δyki and Δymi have opposite signs, i.e., for example, fky )1( + < kfy , and fmy )1( + > mfy . If

this is the case, then substituting Eqs. (9.6) and (9.7) into condition (9.2), reduces it to an

obvious equality.

If m = 1, then according to condition 5 of the theorem, 01 =Δ addiy , and Eq. (9.4) gives

Δy1i = (1 – αi) ⎟⎟⎠

⎞⎜⎜⎝

⎛+∑

∞

=f

ppf yy 2

1 = (1 – αi)(Nf + fy2 ). (9.8)

Substituting Eqs. (9.6) and (9.8) into condition (9.2) again gives an equality, if fky )1( + <

kfy , i.e., Δyki and Δy1i have opposite signs (condition 6 of the theorem).

According to condition 4, fragmentation theorem is also correct if the number of

intermediate modes is finite. If this is the case, then there exists a maximal diameter of

particles that take part in fragmentation. In this case, the k-th mode may correspond either to

any of the intermediate modes, or the mode with the maximal diameter, as long as the other

conditions of the theorem are satisfied for this mode. In particular, if N is the number of

modes and k = N, then Eq. (9.6) gives

ΔyNi = yNi – Ny = (αi – 1) Nfy , (9.9)

i.e., there is no influx of particles into this mode due to fragmentation. This does not change

the above proof of the fragmentation theorem, which means that the k-th mode can indeed be

210

either one of the intermediate modes, or the mode with maximal diameter (as long as such a

diameter exists and other conditions of the fragmentation theorem are satisfied).

Note also that if k = N (mode with the maximal diameter) and m = 1 (sink mode),

then condition 6 is satisfied automatically (see Eqs. (9.8) and (9.9)).

The fragmentation theorem provides yet another mathematical confirmation of the

fragmentation mechanism of evolution of nano-particle combustion aerosols near a busy

road. It demonstrates that the anti-symmetry of the moving average correlation coefficients

for the 13.6 nm mode and 126 nm mode in Fig. 9.2 can be explained by fragmentation of

nano-particles. Though the presented proof did not take into account the moving average

procedure, it can be understood that this procedure does not breach the anti-symmetry of the

correlation dependencies. Moving averaging only smoothes out the resultant dependencies

without changing their anti-symmetry.

If n = k, then substitution of Eqs. (9.8) and (9.9) into Eq. (9.2), gives the equality 1 ≡

1. Nevertheless, Fig. 9.2 gives less than unity correlation coefficients for the 13.6 nm mode

and 126 nm mode. This is because the moving average procedure smoothers out sharp

maxima and minima of the corresponding dependencies.

Condition (9.5) is essential for the anti-symmetry of the correlation coefficient

dependencies. If this condition is not satisfied, and the additional fluctuations of the

normalised particle concentrations are noticeable, then the common factor (1 – αi) in Eqs.

(9.6) – (9.9) cannot be isolated, and substitution these fluctuations into condition (9.2) does

not result in equality. That is, the necessary and sufficient condition for anti-symmetry is not

satisfied.

The fragmentation theorem may also apply to the process of evaporation that is very

similar to fragmentation. Indeed, evaporation also occurs due to breaking small particles (this

time, separate molecules) from the larger particles (e.g., evaporating droplets). However, the

dependencies in Fig. 9.2 cannot be explained by evaporation because of the following

211

reasons. First, if it were evaporation mechanism that is responsible for the evolution and anti-

symmetry of correlation dependencies (Figs. 9.2 and 9.5), then the 13.6 nm mode should

have been positively correlated with all modes with larger particle diameters. This follows

from the fact that the corresponding particle size distributions (Fig. 6.3b and dark band in

Fig. 8.1) are monotonically decreasing functions of particle diameter within the range ≥ 13

nm. It follows from here that decreasing particle diameter (caused by evaporation) would

have resulted in a uniform shift of this size distribution towards smaller particle diameters

(i.e., to the left), which should lead to a simultaneous decrease of particle concentrations in

all channels in the range ≥ 13.6 nm (see also the discussion before Fig. 9.3). This would have

resulted in positive correlations between the 13.6 nm mode and all other larger modes

(because the concentration in all these modes, including the 13 nm mode, would have

reduced), which is a contradiction to Figs. 9.2 – 9.5 and condition (6) of the fragmentation

theorem.

Secondly, evaporation mechanisms cannot explain the increase of the total number

concentration (Chapters 6 and 7) that was observed using the same sets of data. Neither can

it explain the increase in the concentration of particles with ~ 13 – 30 nm diameters (Fig.

6.3b and dark band in Fig. 8.1).

Therefore, the fragmentation theorem presented in this section suggests that the

observed anti-symmetric pattern of moving average correlation coefficients (Fig. 9.2) is very

likely to occur as a result of particle fragmentation. It establishes conditions for observation

of such anti-symmetry, and thus provides an additional physical insight into the physical

processes during the evolution of combustion aerosols. It may be important for the

determination of possible sources and behaviour of nano-particle aerosols and particle

modes. It is demonstrated that this theorem extends beyond the fragmentation mechanism,

and can be applicable to other types of evaporation/degradation processes, such as

212

evaporation of nano-particles, degradation of polymers, large biological molecules, polymer

networks, etc. (see also Chapter 10).

213

CHAPTER 10

PROBABILISTIC TIME DELAYS DURING MULTIPLE

STOCHASTIC DEGRADATION/EVAPORATION PROCESSES ([A8,

A9, A24, A26, A27])

10.1 Introduction

Multiple stochastic degradation/evaporation processes play an essential role in a

range of physical and chemical phenomena. These include degradation of double-stranded

polymers (Metanomski et al, 1993, Mark et al, 1990, Allen & Edge, 1992 ), fractals and

polymer multi-chains (Guan et al, 1999, Wickman & Korley, 1998), double-stranded DNA

(Lindahl, 1993), dye fading (Allen, 1992), interaction of UV and ionizing radiation with

large molecules (Sinha & Hader, 2002), reversible self-arrangement and

degradation/fragmentation of polymer networks (Sijbesma et al, 1997, Sijbesma & Meijer,

2003) and particle aggregates (Wickman & Korley, 1998, Mezzenga et al, 2003, Fan et al,

2004), thermal fragmentation of nano-particles due to evaporation of bonding molecules

(Chapters 6 and 7, and A4, A5), and even economic and social degradation caused, for

example, by stochastic financial processes (Buchanan, 2002, Mantegna & Stanley, 1995,

Mantegna & Stanley, 1996).

In this Chapter, we demonstrate that stochastic decay of multiple bonds between

elements of a system (e.g., particles/molecules) may lead to significant probabilistic delays

with further degradation of the intermediate substances/structures. A strong impact of such

delays on the life-time and strength of the intermediate modes due to accumulation of the

degradation/fragmentation products in these modes is demonstrated.

214

10.2 Time delays

The analysis is conducted on the example of the thermal fragmentation of composite

aerosol nano-particles (Chapters 6 and 7, and [A4, A5]), though the obtained results will be

directly applicable to any other type of multiple stochastic degradation processes. Aerosol

nano-particles often form aggregates of primary particles that are bonded together by

means of volatile molecules (Chapters 6 and [A4]). These molecules represent multiple

bonds between the particles. Stochastic evaporation of the bonding molecules results in

weakening of the interactions between the primary particles, and they may break away

from the composite particles (Chapters 6 and [A4]), similar to evaporation of molecules

from a droplet of fluid. This happens when the binding energy between the primary

particles becomes sufficiently close to the thermal energy ~ kT. Similar situation occurs

with stochastic decay of multiple covalent and non-covalent bonds in polymer-like

structures (Metanomski et al, 1993, Mark et al, 1990, Allen & Edge, 1992, Guan, 1999,

Lindahl, 1993, Sijbesma et al, 2003).

Consider a composite particle consisting of three primary particles – Fig. 10.1a.

Thermal fragmentation of such composite particles (3-particles) occurs by means of

breaking away one of the primary particles, resulting in one primary particle and one

composite 2-particle (consisting of two primary particles). However, further fragmentation

of the intermediate 2-particles may be significantly delayed compared to that of the 3-

particles. To understand this, we assume that fragmentation may occur only if there is one

bonding molecule left between the particles (for more than one molecules, the binding

energy is too large for fragmentation to occur with reasonable probability). Let one

bonding molecule be left between particles 1 and 2 (one bond) and two molecules between

particles 2 and 3 (two bonds) – Fig. 10.1a. We will say that the 3-particle is in the 1-2 state

(in accordance with the numbers of bonding molecules). We do not distinguish between

the i-k and k-i states, since they are equivalent.

215

Fig. 10.1. a) The 1-2 state of a 3-particle consisting of three primary particles that are bonded by

one and two volatile molecules. b) Two possible ways of evolution of the 3-particle from the 1-2

state: 1-2 1-1 and 1-2 0-2. The transition 1-2 0-2 corresponds to fragmentation of the 3-

particle.

Further evolution of the 3-particle may occur along two paths: 1-2 1-1 or 1-2

0-2 (Fig. 10.1b). During the process 1-2 1-1, the 3-particle does not fragment, but just

loses one of the bonding molecules (one of the two bonds between particles 2 and 3).

Further evaporation of either of the molecules will lead to fragmentation of the 3-particle:

1-1 0-1. The 0-1 state corresponds to one free primary particle and one 2-particle. The

2-particle fragments with no delays, i.e., the corresponding rate coefficient is “switched

on” immediately after the 3-particle fragments. This is because the resultant 2-particle in

the 0-1 state contains only one bonding molecule. Thus, no fragmentation delays occur

along the path 1-2 1-1 0-1 0-0.

If however evolution takes the path: 1-2 0-2 0-1 0-0, then fragmentation of

the 2-particles in the state 0-2 is delayed. This is because the 2-particle from the 0-2 state

cannot fragment until one of the two bonding molecules evaporates. The fragmentation

delay will thus be equal to the time of evaporation of one of the two bonding molecules

(bonds).

To determine the average delay between fragmentation of the 3-particles and 2-

particles, we need to determine the corresponding delays and numbers of 3-particles going

216

through different evaporation paths, e.g., 0-3 0-0, 0-4 0-0, etc. Suppose that we have

N0 3-particles in the initial 4-4 state. After losing one bonding molecule, all 3-particles will

pass through the 3-4 state (Fig. 10.2). A 3-particle in the 3-4 state has two options for

further evolution: to go into the 2-4 state (by losing one of the three bonding molecules), or

the 3-3 state (by losing one of the four bonds), etc. Thus we obtain a random graph

representing evaporation of bonding molecules in the considered 3-particles (Fig. 10.2).

Note that the initial 4-4 state also corresponds to three monomers with quadruple hydrogen

bonds considered in (Sijbesma et al, 1997, Sijbesma & Meijer, 2003).

Fig. 10.2. The random graph representation of the processes of stochastic evaporation of

bonding molecules. The 4-4 state is the initial state for the 3-particles, and 0-0 is the final state (in

which all three primary particles are free as a result of fragmentation). The arrows (edges of the

graph) indicate the direction of possible ways of particle evolution. N0 is the initial number of the

3-particles in the 4-4 state.

This random graph can be extended to the case with an arbitrary n-n or n-m initial

state. However, increasing n,m > 4 does not change the average time delays substantially,

because the probability for a particle to go through a 0-n state decreases with increasing n.

217

To determine the average fragmentation delays, we denote the number of 3-particles

passing through a particular i-k state (a vertex of the random graph – Fig. 10.2) as Nik.

Then, due to particle conservation, the sum of all numbers Nik for the vertices between any

two neighbouring dotted lines in Fig. 10.2 is equal to N0. This gives five equations relating

11 unknowns:

N33 + N24 = N23 + N14 = N22 + N13 + N04 = N12 + N03 = N11 + N02 = N0. (10.1)

The remaining 6 equations are obtained from the consideration of probabilities for

evaporation of bonding molecules in each of the i-k states of the 3-particle. Each bonding

molecule interacts with two bonded particles and other neighbouring bonding molecules by

means of van der Waals forces. Therefore, it is reasonable to expect that the energy that

should be given to one bonding molecule in order to remove it from between the particles

(binding energy of evaporation) increases with increasing number of bonding molecules,

because of the additional interaction between these molecules. This is analogous to a

possibility of interactions between the neighbouring bonds, e.g., due to overlap of the

electron wave functions in polymer molecules. As a result, the time of evaporation of one

bonding molecule (one bond) may increase by a factor of αk, where k is the number of

bonding molecules between the particles (α1 = 1).

For example, transformation of the 1-2 state into the 1-1 state occurs when one of the

two molecules evaporates. Let the time for evaporation of a single bond between two

particles be τ1. Then the time for evaporation of either of the two bonds (one of the two

molecules) is τ2 = α2τ1/2. Thus the probability for the process 1-2 1-1 is 2/α2 times

larger than for the process 1-2 0-2. Therefore, the number of particles going through the

graph edge 1-2 1-1 (which is N11) is 2/α2 times larger than the number of particles going

through the edge 1-2 0-2 (which is N02 – N03). This gives the first of the following six

equations:

N11 = 2(N02 – N03)/α2, (N12 – N22) = 3(N03 – N04)/α3,

218

(N13 – N23 + N22) = 4N04/α4, N22 = 3α2(N13 – N14 + N04)/(2α3); (10.2)

N23 – N33 = 2α2N14/α4; N33 = 4α3N24/(3α4).

The other five equations are obtained from the similar consideration of transitions from the

1-3, 1-4, 2-3, 2-4, and 3-4 states, respectively; α3 and α4 are the factors increasing the

average time for evaporation of one of the three and one of the four molecules,

respectively. Here, we have also assumed (for simplicity) that evaporation of each of the

three (four) molecules from between the bonded particles is equally probable.

The fragmentation delays for the 2-particles originating from different 0-i states (Fig.

10.2), and the corresponding numbers of the 3-particles are given in the table.

Vertex of the graph 0-1 0-2 0-3 0-4

Fragmentation delay,

Δτ1,2,3,4

0 α2τ1/2 α2τ1/2 + α3τ1/3 α2τ1/2 + α3τ1/3 + α4τ1/4

Number of 3-particles N11 N02 – N03 N03 – N04 N04

Table 10.1. Fragmentation delays for different types of 2-particles and the numbers of such

particles.

Thus the average fragmentation delay for the intermediate 2-particles

Δτ = [Δτ1N11 + Δτ2(N02 – N03) + Δτ3(N03 – N04) + Δτ4N04]/N0. (10.3)

10.3. Evolution time and kinetics of degradation

The average time that takes for the 3-particle to evolve from the initial 4-4 state to

one of the 1-k states preceding fragmentation can also be calculated from the graph in Fig.

10.2. Different paths on the graph may lead to the same 1-k state. For example, three

different paths lead to the 1-3 state: (1) 4-4 3-4 2-4 1-4 1-3, (2) 4-4 3-4

219

2-4 2-3 1-3, and (3) 4-4 3-4 3-3 2-3 1-3. The evolution time is

determined for each of the different paths by means of calculating time for each of the

possible transitions.

For example, the time for the transition 4-4 3-4 is equal to the time of evaporation

of one of the 8 bonding molecules: τ44-34 = α4τ1/8. One may think that the time for the

process 3-4 2-4 will then be α3τ/3. However, this is not correct, because two

simultaneous processes may originate from the state 3-4: 3-4 3-3 and 3-4 2-4.

Therefore, the time for a particle to leave the state 3-4 will be

τ34-33,24 = [4/(α4τ) + 3/(α3τ)]-1 = τ(α3α4)/(4α3 + 3α4). (10.4)

Since this is the time for the particles to leave the 3-4 state, the time for a particle to go

from the 3-4 state to the 2-4 state should not exceed the time τ34-33,24. This is because at

time t > τ34-33,24, there will be no particles in the state 3-4, and thus no particles can be

transferred from this state to the 2-4 state. This suggests that the time for the process 3-4

2-4 will be equal to τ34-33,24.

This conclusion can also be confirmed mathematically by solving the following

model problem. Consider particles A with the concentration [A], which can be transformed

by two different processes into particles B1 or B2. The rate equations for these processes

are:

d[A]/dt = – (k1 + k2)[A];

d[B1]/dt = k1[A]; d[B2]/dt = k2[A], (10.5)

where k1 and k2 are the rate coefficients for the transformations A B1, and A B2,

respectively. In other words, the typical times for these transformations are τ1 = k1-1 and τ2

= k2-1. Solutions to Eqs. (10.5) are

[A] = Cexp{– t(k1 + k2)}; [ ])}(exp{1][ 2121

11 kkt

kkCk

B +−−+

= ;

220

[ ])}(exp{1][ 2121

22 kkt

kkCk

B +−−+

= , (10.6)

where C is a constant and [B1,2] are the concentrations of particles B1,2, respectively.

From these solutions, one can see that the time for the particles to leave the A state

(e.g., the 3-4 state) is (k1 + k2)-1, as well as the times for the particles to be transformed into

the states B1 and B2 (e.g., the 3-3 and 2-4 states). This is equivalent to using Eq. (10.4) for

the determination of transition time from the 3-4 state of the 3-particle. In other words, the

time that it takes for a 3-particle to go from the 3-4 state to the 2-4 state is not equal to the

time of evaporation of one of the three molecules, but rather to the time of evaporation of

one of the 7 molecules, which is given by Eq. (10.4):

τ34-24 = τ34-33 = τ34-33,24 = τ(α3α4)/(4α3 + 3α4). (10.7)

Similarly, the time for a particle to go from the state 2-4 to the state 1-4 is

τ24-14 = τ(α4α2)/(4α2 + 2α4). (10.8)

The total time for the process 4-4 1-4 is

τ14 = τ44-34 + τ34-24 + τ24-14 =

= α4τ/8 + τ(α3α4)/(4α3 + 3α4) + τ(α4α2)/(4α2 + 2α4). (10.9)

The time that it takes for the particle to reach the 1-3 state is calculated similarly.

However, in this case, a particle can reach the 1-3 state by means of three different routes:

1) 4-4 3-4 3-3 2-3 1-3; 2) 4-4 3-4 2-4 2-3 1-3; or 3) 4-4 3-4

2-4 1-4 1-3. If α2 = α3 = α4 = 1 (i.e., there is no increase in the binding energy per

one molecule due to interactions of these molecules with each other), then the times for a

particle to go through any of these routes is the same and approximately equal to τ/8 + τ/7

+ τ/6 + τ/5, which is thus the time for the particle to reach the 1-3 state. The term

approximately is used, because the actual time will be slightly larger than that determined

by this equation, because direct averaging of times corresponding to different routes in the

221

graph (Fig. 10.2) gives slightly (by a few percent) smaller estimate that the actual time

obtained from the direct solution of the kinetic equations.

If α2 ≠ α3 ≠ α4 ≠ 1, then these different routes will result in different times:

1) τ*13 = τα4/8 + τα3α4/(4α3 + 3α4) + τα3/6 + τα2α3/(3α2 + 2α3); (10.10a)

2) τ**13 = τα4/8 + τα3α4/(4α3 + 3α4) +

+ τ(α4α2)/(4α2 + 2α4) + τα2α3/(3α2 + 2α3); (10.10b)

3) τ***13 = τα4/8 + τα3α4/(4α3 + 3α4) +

+ τ(α4α2)/(4α2 + 2α4) + τα1α4/(α4 + 4α1), (10.10c)

where the number of asterisks indicate the first, second, or third route undertaken by

particles reaching the 1-3 state. If all the alphas are equal to one, these equations are

reduced, as expected, to τ/8 + τ/7 + τ/6 + τ/5. If however, this is not the case, then it is

reasonable to take an average of all these times, taking into account the number of particles

taking each of the three routes.

For route 1, the number of particles getting into the 2-3 state is equal to N33. Of

these particles, N*23-13 will reach the 1-3 state, and N*

23-22 will not. The asterisk is used to

distinguish particles taking route 1 from other particles that may also undergo the same

transitions. Thus,

N*23-13 + N*

23-22 = N33. (10.11)

In addition, from the probabilities for a particle to go into the 1-3 state or the 2-2 state, we

obtain:

N*23-22 = 3α2N*

23-13/(2α3). (10.12)

Solving these two equations, we obtain:

33

2

3

*2223

32

1

1 NN

αα

+=− ; 33

3

2

*1323

23

1

1 NN

αα

+=− , (10.13)

which determines the number of particles N*23-13 taking the first route and reaching the 1-3

state.

222

Similarly, for the second route

)(

32

1

13323

2

3

**2223 NNN −

αα

+=− ; )(

23

1

13323

3

2

**1323 NNN −

αα

+=− .

Thus the number of particles taking the second route and reaching the 1-3 state is N**23-13.

For the third route, the number of particles reaching the 1-3 state is equal to N14 –

N04.

Thus the average time for a particle to reach the 1-3 state is

τ13 ≈ [τ*13N*23-13 + τ**13N**

23-13 + τ***13(N14 – N04)]/N13. (10.14)

For the 1-2 state, we have 5 different routes of evolution:

1) 4-4 3-4 2-4 1-4 1-3 1-2;

2) 4-4 3-4 2-4 2-3 1-3 1-2;

3) 4-4 3-4 2-4 2-3 2-2 1-2;

4) 4-4 3-4 3-3 2-3 1-3 1-2;

5) 4-4 3-4 3-3 2-3 2-2 1-2; (10.15)

The corresponding times of evolution:

1) τ(1)12 = τα4/8 + τα3α4/(4α3 + 3α4) + τ(α4α2)/(4α2 + 2α4) +

+ τα1α4/(α4 + 4α1) + τα1α3/(α3 + 3α1); (10.16a)

2) τ(2)12 = τα4/8 + τα3α4/(4α3 + 3α4) + τ(α4α2)/(4α2 + 2α4) +

+ τα2α3/(3α2 + 2α3) + τα1α3/(α3 + 3α1); (10.16b)

3) τ(3)12 = τα4/8 + τα3α4/(4α3 + 3α4) + τ(α4α2)/(4α2 + 2α4) +

+ τα2α3/(3α2 + 2α3) + τα2/4; (10.16c)

4) τ(4)12 = τα4/8 + τα3α4/(4α3 + 3α4) + τα3/6 +

+ τα2α3/(3α2 + 2α3) + τα1α3/(α3 + 3α1); (10.16d)

5) τ(5)12 = τα4/8 + τα3α4/(4α3 + 3α4) + τα3/6 +

+ τα2α3/(3α2 + 2α3) + τα2/4. (10.16e)

223

Now we find the numbers of particles passing through a particular route.

1) )(

31

10414

1

3

)1(1214 NNN −

αα

+=− ; (10.17a)

2) )(

23

13

1

11424

3

2

1

3

)2(12132324 NNN −

⎟⎟⎠

⎞⎜⎜⎝

⎛αα

+⎟⎟⎠

⎞⎜⎜⎝

⎛α

α+

=−−− ; (10.17b)

3) )(

32

1

11424

2

3

)3(12222324 NNN −

αα

+=−−− ; (10.17c)

4) )(

23

13

1

1240

3

2

1

3

)4(1213233334 NNN −

⎟⎟⎠

⎞⎜⎜⎝

⎛αα

+⎟⎟⎠

⎞⎜⎜⎝

⎛α

α+

=−−−− ; (10.17d)

5) )(

32

1

1240

2

3

)5(1222233334 NNN −

αα

+=−−−− . (10.18e)

Thus, the average time of evolution for the transition from the 4-4 state to the 1-2

state is

τ12 ≈ (τ(1)12N(1)

14-12 + τ(2)12N(2)

24-23-13-12 + τ(3)12N(3)

24-23-22-12 +

+ τ(4)12N(4)

34-33-23-13-12 + τ(5)12N(5)

34-33-23-22-12)/N12. (10.19)

The time of evolution to the state 1-1 is determined simply by adding the time δτ =

α1α2τ/(α2 + 2α1) for a particle to leave the 1-2 state to all the times corresponding to the

evolution to the 1-2 state. This is because the only way the particles can get to the 1-1 state

is through the 1-2 state.

The number of particles passing from the 1-2 state into the 1-1 state is given by

N12-11 = N12/[1 + α2/(2α1)].

Therefore, to get the number of particles getting to the 1-1 state by means of 5 different

routes (10.15), we multiply the numbers of particles determined by Eqs. (10.17) by the

additional factor

224

1

22

1

1

αα

+.

Then the average time of evolution for the transition from the 4-4 state to the 1-1 state is

τ11 ≈ [(τ(1)12 + δτ)

1

2

)1(1214

21

αα

+

−N + (τ(2)

12 + δτ)

1

2

)2(12132324

21

αα+

−−−N +

+ (τ(3)12 + δτ)

1

2

)3(12222324

21

αα+

−−−N + (τ(4)

12 + δτ)

1

2

)4(1213233334

21

αα+

−−−−N +

+ (τ(5)12 + δτ)

1

2

)5(1222233334

21

αα+

−−−−N]/N11. (10.20)

Note that this procedure is to an extent similar to the determination of the

communication-related random delays in large-scale computing systems (Gu & Niculescu,

2004).

For example, consider the case with α1 = α2 = α3 = α4 = 1, i.e., there is no increase of

the binding energy and no increase of the evaporation time if there are two or more binding

molecules between two particles. In this case, if N0 = 100, then N11 = 57.1, N02 = 42.9, N12

= 85.7, N03 = 14.3, N13 = 45.7, N22 = 51.4, N23 = 85.7, N04 = 2.9, N14 = 14.3, N33 = 57.1, N24

= 42.9 are the numbers of particles passing through the corresponding graph vertices (Fig.

10.2). Then the average fragmentation delay for the 2-particles determined from Eq. (10.3)

is Δτ ≈ 0.269τ1, where τ1 is the time of evaporation of a single bonding molecule. From the

experimental observations of fragmentation, τ1 ~ 10 s (the fragmentation process occurs on

this time scale (Chapters 6 and 7, and [A4, A5])), which gives Δτ ≈ 2.7 s.

The typical binding energy E0 for a single volatile molecule between the particles is

evaluated from the Maxwell-Boltzmann distribution. We determine the probability P0(E0)

for a molecule to have the energy larger than E0 (this is the probability of fragmentation at

225

a given moment of time) by integrating the Maxwell-Boltzmann distribution between E0

and ∞. The ratio of τ1 to the average time between the collisions in the air L/c (L is the

mean free path for the molecules in the air, and c is the mean speed) must be of the order

of 1/P0(E0), or τ1 ~ L/[cP0(E0)]. Assuming that T = 300 K, L ~ 300 nm, c ≈ 467 m/s, and τ1

~ 10 s (the fragmentation rate coefficient k0 = 0.1 s-1), we get: E0 ≈ 1.045×10-19 J.

If the additional van der Waals interaction between two or more bonding molecules

increases the binding energy of evaporation per one molecule by just 5% for two molecules

and by 7% for three and more molecules, then Δτ ≈ 24 s. Thus, increasing binding energy

of evaporation due to mutual interaction of bonding molecules by just 5% – 7% results in

almost 10 times increase in the fragmentation delay. This certainly highlights a very

significant impact of such an energy increase on stochastic degradation processes,

including thermal fragmentation of nano-particles and polymer degradation.

In this example, the average evolution times that take for a 3-particle in the initial 4-4

state to reach the fragmentation stage, i.e., the states 1-4, 1-3, 1-2, and 1-1 are τ14 ≈ 23.41 s,

τ13 ≈ 33.10 s, τ12 ≈ 41.73 s, and τ11 ≈ 48.18 s, respectively. The corresponding numbers of

particles experiencing fragmentation through each of these states (if N0 = 100) are N04 ≈

11.32, N03 – N04 = 32.79, N02 – N03 ≈ 35.38, and N01 – N02 ≈ 20.51. Thus the average

evolution time τav ~ 38 s with the dispersion of the mean δτA ~ 8 s. Therefore, it is

reasonable to approximate that the fragmentation rate coefficient for the 3-particles

“switches on” at t = τav – δτA ≈ 30 s and linearly increases to its steady-state value k0 = 0.1

s-1 within the time interval 2δτA ≈ 16 s.

If the fragmentation delays for the intermediate 2-particles are assumed to be zero,

then the solution of the kinetic equations results in curves 1 – 3 in Fig. 10.3. However, if

the fragmentation delays are determined using Table 10.1, then Δτ1 = 0, Δτ2 ≈ 17.60 s, Δτ3

≈ 38.86 s, Δτ4 ≈ 51.31 s, and the average delay Δτ ≈ 24.5 s. As a result, the average

evolution time to fragmentation of the resultant 2-particles is t = τav + Δτ ≈ 62.5 s with the

226

dispersion δτB ≈ 9.5 s. Thus, we approximate that the fragmentation of the intermediate 2-

particles starts at t = τav + Δτ – δτB ≈ 53 s with the linearly increasing rate coefficient from

zero to k0 within the time interval 2δτB ≈ 19 s. The solution of the kinetic equations with

these parameters gives curves 1, 4 and 5 in Fig. 10.3.

Fig. 10.3. The time dependencies of the concentrations of the 3-particles (curve 1), intermediate 2-

particles (curves 3 and 5), and primary particles (curves 2 and 4). Curves 2 and 3: zero

fragmentation delay for the 2-particles (Δτ = 0). Curves 4 and 5: fragmentation delay for the

intermediate 2-particles Δτ = 24 s.

In particular, it can be seen that fragmentation delays have a substantial impact on

the kinetics of fragmentation/degradation processes. In the presented example, the number

(concentration) of the intermediate 2-particles in the presence of the fragmentation delays

(curve 5) increases up to ~ 5 times compared to that in the absence of this delays (curve 3).

At the same time, the time-dependent number of the primary particles in the presence of

fragmentation delays (curve 4) may be less up to 2 times compared to that at zero delays

(curve 2).

227

If the dispersion is taken into account with the parameters m = 0.87 (normal

component of the wind speed is 1 m/s) and the fragmentation rate coefficients k = 0.1 s-1,

then for the same parameters (evolution times, fragmentation delays, etc.) as for Fig. 10.3,

the dependencies of particle concentrations on distance from the road are presented in Fig.

10.4. As a result, dispersion does not introduce principle changes in the obtained pattern of

mode evolution, and this approach may thus be used for mode modelling near busy roads.

Fig. 10.4. The dependencies of the concentrations of the 3-particles (curve 1), intermediate 2-

particles (curves 3 and 5), and primary particles (curves 2 and 4) on distance from the road in the

presence of dispersion and turbulent diffusion. Fragmentation of the 3-particles starts at ≈ 30 m

from the road or, equivalently, after t = τav – δτA ≈ 30 s of evolution. The initial numbers of 3-

particles, 2-particles and primary particles at this moment are the same and equal to 100. Curves 2

and 3: zero fragmentation delay for the 2-particles (Δτ = 0). Curves 4 and 5: fragmentation delay

for the intermediate 2-particles Δτ = 24 s. Other parameters are identical to those for Fig. 10.3.

In particular, it can be seen that fragmentation delays significantly affect

concentrations of the primary particles and especially intermediate 2-particles. As a result,

the intermediate modes should be much more pronounced with fragmentation delays. The

resultant typical concentrations in these modes may increase several times, compared to

228

the situation when the fragmentation delays are ignored. This demonstrates that

fragmentation delays are one of the major effects in the process of mode formation in

combustion aerosols near busy roads.

It can also be seen that the determined fragmentation delays also strongly depend on

temperature. For example, decreasing temperature by 20 C results in τ1 ≈ 62 s, and Δτ ≈

168 s, which may effectively lead to suppression of fragmentation near a particle source.

The developed theory of fragmentation delays can naturally be extended to more

complex systems consisting of four or more particles, and include the possibility of

restoration of bonds between the particles (e.g., condensation of bonding molecules). This

will be especially important for the analysis of particle fragmentation in the presence of

significant pressure of vapour of volatile compounds, reversible self-assembling polymer

structures and networks (Sijbesma et al, 1997, Sijbesma & Meijer, 2003), and DNA repair

(Lindahl, 1993, Sinha & Hader, 2002).

229

CHAPTER 11

MULTI-CHANNEL STATISTICAL ANALYSIS OF BACKGROUND

FINE PARTICLE AEROSOLS ([A10, A28])

In this chapter, the new statistical methods for the determination and investigation of

particle modes and their mutual correlations in fine and ultra-fine particle aerosols in the

presence of strong turbulent mixing (Chapters 6, 9 and [A5,A7,A23,A25]) are applied

for the analysis of urban background aerosols. In particular, several distinct modes will

be obtained from the background particle size distribution, and their possible sources

will be discussed. Anti-symmetrical correlation pattern similar to that obtained near a

busy road in the presence of particle fragmentation (Chapter 9) will also be

demonstrated for background aerosols. Therefore, fragmentation theorem (Chapter 9)

will be used for possible interpretation of the obtained results.

The experimental measurements were conducted near Gateway Motorway in the

Brisbane area, Australia, on the upwind side of the road, so that traffic emissions from

the road did not affect the obtained background data (Fig. 11.1). There were no

buildings within ~ 150 m from the measurement area that was practically a flat grass

field with isolated scattered bushes and trees. Further away from the road, there is a

small residential area with a parkland – see Fig. 11.1. No particular sources of air

pollutants are known within at least several kilometers upwind from the place of

measurements. The distance from the curb of the road was ~ 60 m (the place of the

measurement is marked by a cross on the map – Fig. 11.1). This distance was sufficient

for not registering any noticeable particle concentrations coming directly from the road

due to turbulent diffusion.

230

Concentrations of fine particles in the background aerosol were measured within

the range from 13 nm to 763 nm at the height h = 2 m above the ground during the

afternoon of 30 July 2002. 38 scans with 113 equal intervals of Δlog(Dp), where Dp is

particle diameter in nanometers, were taken by means of a Scanning Mobility Particle

Sizer (SMPS). All the concentration measurements were conducted simultaneously with

the measurements of the temperature, humidity, solar radiation, wind speed and wind

direction every 20 seconds at the same height above the ground of ≈ 2 m.

Fig. 11.1. The area of measurements near Gateway Motorway, Brisbane, Australia. The

indicated receptor point is at the distance ~ 60 m from the curb of the road. The scale of the map

and the direction to the North are as indicated (the distances on the axes are given in meters).

The cross indicates the receptor point. The insert presents a section of the map with the area of

measurements.

231

Meteorological parameters

scans 11 to 27 scans 22 to 38

wind direction, degrees to the road

46 ± 50 35 ± 40

wind speed, ms-1 1.7 ± 0.8 1.5 ± 0.8

temperature, °C 20.4 ± 0.9 18.7 ± 0.6

humidity, % 40 ± 4 46 ± 2

solar radiation, Wm-2

200 ± 100 30 ± 30

Table 11.1. Average meteorological parameters.

38 scans in total were taken, and two separate sets of 17 scans (from 11 to 27 and

from 22 to 38) were considered. The choice of these sets was conducted primarily on

the basis changing solar radiation. The monitoring was conducted during the time of

sunset, and the second set of scans corresponded to nearly zero solar radiation, while for

the first set of scans it was still significant (Table 11.1).

Fig. 11.2. Typical size distribution in the urban background aerosol

in the Brisbane area, Australia, together with the experimental points.

232

The average particle size distributions for both the sets of scans, plotted by means

of the moving average technique, are presented in Figs. 11.2 and 11.3. The average

values of the meteorological parameters for the two sets of scans are presented in Table

11.1 together with their standard deviations.

Fig. 11.3. The moving average size distributions for the two sets of scans: (1) scans from 11 to

27 (from 2:43pm to 4:33pm - higher solar radiation), and (2) scans from 22 to 38 (from 3:54pm

to 5:44pm - negligible solar radiation). Curve 1 is identical to that in Fig. 11.2. Light and dark

bands show the standard errors of the mean for both the curves.

Only two maximums can be seen on the resultant particle size distributions – at ~

20 nm and ~ 100 nm (Fig. 11.2 and curve 1 in Fig. 11.3). Otherwise, the size

distributions do not display any significant features and/or distinct particle modes (the

maximum at ~ 20 nm is fairly small and not pronounced, which make it difficult to

analyse and interpret). Nothing can be said about possible relationships between

particles in the obtained size distribution, and their mutual dependencies. No firm

conclusions can be made about the differences between the two size distributions before

the sunset (curve 1 in Fig. 11.3) and after the sunset (curve 2 in Fig. 11.3).

233

Therefore, the statistical methods of analysis of background aerosols similar to

those developed in Chapters 6, 8, and 9 are expected to be of a significant help. As was

demonstrated (Chapters 6, 8 and 9), the methods that provide highly effective

determination and analysis of possible particle modes and mutual correlations between

different channels in the size distribution is based on the determination of the moving

average correlation coefficient. Application of this method with 7-channel moving

interval (Chapters 6 and 8) to the two background data sets of 17 scans results in the

dependencies of the moving average simple correlation coefficient displayed in Figs.

11.4a,b.

Fig. 11.4. The moving average correlation coefficients as functions of particle diameter for the

two sets of 17 scans: (a) from 11 to 27 (before the sunset), and (b) from 22 to 38 (after the

sunset). Both the dependencies were plotted using 7-channel moving interval. The shadow

bands indicate the associated errors of the mean.

234

One of the main important features of Figs. 11.4a,b is that the demonstration of

the existence of strong and distinct particle modes in the background particle size

distributions. At least five distinct modes (corresponding to particle diameters ~ 21 nm,

~ 35 nm, ~ 57 nm, ~ 105 nm, and ~ 168 nm) can be seen in Fig. 11.4a, and at least four

modes are displayed by the curve in Fig. 11.4b (at ~ 30 nm, ~ 55 nm, ~ 80 nm , and ~

168 nm). The presented error curves clearly demonstrate that all of these modes are

statistically significant.

The existence of these modes demonstrates that despite the smoothness of the

original particle size distributions with no significant distinct features, there are,

nevertheless, distinct groups of particles forming these size distributions.

Concentrations of particles in different channels within each of these groups have strong

tendencies to increase/decrease in correlation with each other. As has been mentioned in

Chapter 6, this is an indication that these particles (from each mode in Figs. 11.4a,b) are

likely to have come from the same source (origin) and/or have the same

physical/chemical nature.

It is interesting to note that the three modes in Figs. 11.4a,b with smaller particle

diameters approximately correspond to the modes previously described in Chapters 6

and 8 for transport emissions from busy roads. Therefore, it is possible that these modes

originate from transport emissions from the road network in the urban environment. At

the same time, it is important to indicate that these modes (strong maximums on the

correlation curve in Fig. 11.4a,b) correspond to relatively low particle concentrations

(Figs. 11.2 and 11.3). In addition, it is possible to see that these modes transform

noticeably with decreasing solar radiation (compare Figs. 11.4a and 11.4b).

The modes with larger particle diameters, e.g., at ~ 105 and ~ 168 nm (Fig. 11.4a)

correspond to noticeably larger number concentration (Figs. 11.2, 11.3). It may be

expected that at least some of these modes may come from natural sources, e.g., marine

235

aerosols (Seinfeld and Pandis, 1998). However, this should probably require further

confirmation by means of application of the mentioned approach to the analysis of

background aerosols at significantly different wind conditions.

A very interesting and unexpected result was obtained as a result of the

application of the moving average approach to the analysis of mutual correlations

between different particle modes (Chapter 9) in the background size distributions

displayed in Figs. 11.2 and 11.3. For example, Fig. 11.5 presents the dependencies of

the moving average cross-correlation coefficients for the two primary 7-channel

intervals centered at 40 nm (dashed curves) and 113 nm (solid curves) for the two

considered sets of scans (for more detailed description of the statistical procedure used

see Chapter 9).

The maxima for both the peaks at 40 nm and 113 nm for the dashed and solid

curves in Fig. 11.5 are slightly larger than the corresponding moving average

correlation coefficients in Fig. 11.4b. This is because for the curves in Fig. 11.4,

correlations of each channel with itself were discarded from the averaging procedure,

which results in slightly lower curves (without effecting anything else).

It can be seen that after the sunset the correlations between the different channels

in the particle size distribution have substantially changed. The dependencies for the

considered channels became almost exactly anti-symmetric of each other (Fig. 11.5b).

This is a clear indication of significantly changing processes of particle evolution. The

anti-symmetry of the correlation dependencies exists only for the pair of 40 nm and 113

nm channels. Changing to any other channels quickly breaks the anti-symmetry. Recall

that this anti-symmetry means that the correlation coefficient between the 40 nm

channel and, for example, ~ 200 nm channel is exactly the same in magnitude as the

correlation coefficient between the 113 nm channel and the same ~ 200 nm channel, but

236

opposite in signs. This is a highly non-trivial result, especially taking into account the

high degree of anti-symmetry displayed by Fig. 11.5b.

Fig. 11.5. Moving average simple correlation coefficients between the 113 nm channel and all

other channels (solid curves), and between the 40 nm channel and all other channels (dashed

curves). (a) The dependencies for the first set of scans from 11 to 27 (before the sunset), and (b)

for the second set of scans from 22 to 38 (after the sunset). The solid horizontal lines correspond

to zero correlation coefficient. The average particle diameter for each of the secondary 7-

channel intervals is taken as the diameter corresponding to the central channel of the interval.

It is important that Fig. 11.5a does not display the same anti-symmetry. This is an

indication that before the sunset the conditions and the evolution processes in the

background aerosol are not appropriate for producing such an anti-symmetry.

237

Fragmentation theorem proved in Chapter 9 was previously used for the

explanation of anti-symmetric correlation patterns similar to those in Figs. 11.5b, 9.2,

9.4 and 9.5. This theorem suggests that such anti-symmetric patterns can be explained

by fragmentation of nano-particles. Therefore, it is highly tempting to suggest that the

anti-symmetric pattern in Fig. 11.5b is also related to particle fragmentation. In our

opinion, this is indeed possible, but such a statement will nevertheless need further

confirmation by future analysis and measurements.

Note also that the reason for choosing the 40 nm and 113 nm channels in the size

distribution is because only these channels correspond to the antisymmetric cross-

correlation pattern. This means that the conditions of the fragmentation theorem

(Chapter 9) happen to be satisfied only for these channels. Therefore, it is possible that

mechanisms other than fragmentation may be at least partly responsible for fluctuations

of particle concentrations in other channels.

The breach of the anti-symmetric correlation pattern before the sunset (Fig. 11.5a)

does not necessarily mean that fragmentation does not occur before the sunset. On the

contrary, it might be even stronger due to higher temperature and solar radiation.

However, the conditions of the fragmentation theorem may only be satisfied after the

sunset, which results in the anti-symmetric pattern in Fig. 11.5b.

It is not clear at this stage if the ~ 40 nm particles are the primary particles or

belong to one of the intermediate modes (see Chapter 9). Further research in this

direction (that is however outside the scope of this thesis) is necessary. One of the

possibilities is that the ~ 40 nm particles are yet another type of primary particles from

the vehicle exhaust (coming from the upwind road networks). Such larger primary

particles may be formed in the exhaust pipe by means coagulation of smaller (~ 7 nm

and/or ~ 12 nm) particles by means of strong covalent bonds, before these bonds are

engaged by volatile fragments (Chapter 6). Because the ~ 40 nm particles are relatively

238

large, their fragmentation may be impeded by larger average bonding area, and thus

larger bonding energy (Chapter 6). Therefore, it takes longer for these particles to

fragment, and we can observe this process within several kilometers from the source

(i.e., in the background aerosol).

Another option is that these are particles of different nature (e.g., marine aerosols)

that may also experience fragmentation. However, at this stage, this option seems to be

less clear and less feasible.

In conclusion to this Chapter, it is important to note that the observed interesting

and unusual effects in the background urban aerosol in the Brisbane metropolitan area

are only the first step towards a comprehensive understanding of the nature, sources and

evolution processes in such aerosols. The presented evidence suggests that the

fragmentation mechanism of aerosol evolution may also be important for the

consideration of background urban aerosols. Unfortunately, at this stage, we do not have

sufficient proof to suggest this with certainty. The anti-symmetric correlation pattern for

the ~ 40 nm and ~ 113 nm modes is only the first piece of evidence in this direction.

Additional research will be required to confirm or reject this suggestion.

Nevertheless, the obtained results are a very important step demonstrating the

power of the developed new statistical methods in terms of providing new physical

insights into the processes of evolution and transformation of background aerosols,

which may be important for our understanding of aerosol behaviour and their impact on

the environment not only on local, but also on global scales. They have also provided

the first piece of evidence that one of the major mechanisms of evolution of background

aerosols may be fragmentation of nano-particles.

239

CHAPTER 12

CONCLUSIONS

This thesis was focused at gaining better understanding of fundamental and

applied aspects of evolution and dispersion of combustion aerosols near busy roads in

the urban environment, and development of practical methods and techniques for the

identification and investigation of the main physical mechanisms of behavior of

airborne nano-particles from vehicle exhaust with the ultimate aim of accurate

prediction of human exposure and environmental impact of combustion aerosols.

The research was based on a natural combination of experimental monitoring of

combustion aerosols and air quality in the urban environment, theoretical and numerical

modelling of aerosol dispersion and mechanisms of evolution of nano-particles, and

development and application of new statistical methods of data analysis in the presence

of strong turbulent mixing and stochastic variations of atmospheric and environmental

parameters in real-world situations. One of the major fundamental achievements of this

thesis is the suggestion, experimental investigation, and theoretical modelling of a

radically new mechanism of aerosol evolution based on intensive thermal fragmentation

of nano-particles. The significance of this new mechanism may be far beyond evolution

and transformation of combustion aerosols near busy roads (which is demonstrated by

this thesis). It may also play a major role in shaping patterns of atmospheric aerosols on

the global and local scales. At the same time, it is important to understand that the

presented theory and models will certainly need further extensive experimental and

theoretical confirmation/validation under different conditions. For example, at this stage

little is known about the actual types of volatile compounds that may be responsible for

the fragmentation mechanisms of aerosol evolution. Direct observations of solid

240

primary nano-particles and laboratory investigations of their possible

interaction/fragmentation would also be of a significant benefit in future. Therefore, this

thesis presents the first major step towards the further important research in this area.

The thesis has also developed several specific methods and approaches for the

accurate prediction of aerosol pollution levels in the urban environment, and techniques

for the determination and analysis of vehicle emissions under field conditions. Several

unique and powerful statistical methods for the investigation of dispersion, evolution

processes, and possible sources of nano-particle aerosols have been successfully

developed and applied for the analysis of combustion and background aerosols. All

these findings and methods will be important for the development of workable and

scientifically-based national and international standards for nano-particle emissions,

accurate prediction of human exposure to combustion aerosols, determination and

reduction of the environmental impact of aerosols and other types of air pollutants in the

indoor and outdoor environments.

List of main results

1. Adjustment of the software package CALINE4 (from the California Transport) for

prediction and modelling of aerosol pollution from busy roads in the Gaussian

plume approximation.

2. Development of a new method for the determination of the average emission

factors per vehicle on a road, based on the experimental measurements of particle

concentration at one point near the road. Determination of the average emission

factors for Gateway Motorway, Brisbane, Australia.

3. Development of two new methods of determination of average emission factors

from different types of vehicles (cars, light trucks, heavy-duty diesels) on a road.

241

4. Detailed experimental investigation of evolution of particle modes near a busy

road. Discovery of strong variations in the size distribution, including a maximum

of the total number concentration at an “optimal” distance from the road.

5. Development of a new mechanism of evolution of combustion aerosols, based on

intensive thermal fragmentation of nano-particles. Its theoretical justification and

experimental confirmed by means of several independent sets of data.

6. Development of a new model of dispersion of combustion aerosols near busy

roads, based on intensive particle fragmentation. Determination of the typical

fragmentation rate coefficient and existence conditions for a maximum of the total

number concentration at an optimal distance from the road.

7. Development of three major new methods of statistical analysis of mode evolution

and experimental data in the presence of strong stochastic fluctuations of external

and meteorological parameters, based on the moving average approach, simple

and canonical correlation analyses.

8. Re-definition of particle modes as groups of particles of similar dimensions and

strong mutual correlations. Statistical identification of particle modes emitted by

cars and heavy diesels. In particular, determination of a volatile ~ 7 nm mode that

exists at earlier stages of aerosol evolution and is strongly related to heavy-duty

diesel trucks.

9. Detailed canonical correlation analysis of the relationships between particle

modes and external atmospheric conditions.

10. Derivation and proof of the fragmentation theorem that provides further strong

confirmation of the fragmentation mechanism of evolution of combustion

aerosols.

242

11. Development of a theory of probabilistic time delays during stochastic

degradation/evaporation processes and their relationship to formation and

evolution of particle modes in combustion aerosols.

12. Determination and analysis of distinct particle modes in urban background

aerosols. Discovery of unique anti-symmetric dependencies of the moving

average correlation coefficients between different background modes, which are

closely related to the derived fragmentation theorem.

243

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