J. Aerosol Sci,, Vol. 14. No. 6. pp. 703-712. 1983. 002t-8502:'83 $3.00+0.00 Printed in Great Britain. ~. 1983 Pergamon Press Ltd.

C O L L E C T I O N O F H Y D R O P H I L I C A N D H Y D R O P H O B I C C H A R G E D S U B M I C R O N P A R T I C L E S BY C H A R G E D W A T E R

D R O P L E T S

H. C. WANG*, K. H. LEONG*, J. J. STUKEL*~ and P. K. HOPKE*'~

*Department of Civil Engineering, i'Institute for Environmental Studies, :~Department of Mechanical Engineering, University of Illinois at Urbana-Champaign, Urhana, IL 61801, U.S.A.

(First received 4 February 1983 and in revised form 3 April 1983)

Al~tract--An experimental system capable of measuring the collection efficiency of charged submicron particles by charged water droplets is described. Collection efficiencies are measured for both hydrophilic and hydrophobic particles to clarify the effect of wettability on collection. Excellent agreement with the theory is obtained for hydrophilic submicron particles when the Coulombic force is dominant. No significant difference in collection efficiencies between hydrophilic and hydrophobic particles is observed. It is concluded that the wettability of submicron particles ltas no effect on its collection by water drops when Coulombic attraction is the dominant mechanism.

C Cm Ec Ee e

H K Kl K2 Kc M N n

Q R t

v Z E

subscript c subscript p subscript pl subscript p2 subscript pm superscript '

N O M E N C L A T U R E

Cunningham slip correction factor, dimensionless particle mass concentration,/~g m- 3 collision efficiency of a single collector, dimensionless collection efficiency of a single collector, dimensionless elementary charge unit, 1.6 x 10-19 Coulomb height of the aerosol chamber, m correction factor for doubly charged particles, dimensionless fraction of singly charged particles, dimensionless fraction of doubly charged particles, dimensionless Coulombic parameter, dimensionless total particle mass collected in the metal cup,/~g ion number concentration, =¢k. era-3 total number of droplets collected in the metal cup charge, Coulomb radius,/am charging time, s relative velocity between the particles and collectors, m s- 1 electrical mobility, Coulomb-m N - 1 s- electrical permittivity constant, Coulomb 2 N - t s- t fluid viscosity, kgm- ~ s- J properties of collectors properties of particles ploperties of singly charged particles properties of doubly charged particles mean properties of particles properties of particles after corona charging

INTRODUCTION

In recent years, the removal of submicron particles from anthropogenic emissions has attracted increasing attention. These particles are the most difficult to control and can be the most detrimental to human health when inhaled (Friedlander, 1977). By utilizing electrostatic force, the charged droplet scrubber (CDS) shows considerable promise in collecting submicron particles at moderate cost (Pilat, 1975). The particle collection efficiency of a single droplet, defined as the ratio of the number of particles collected to that swept out geometrically by the droplet, is usually used to predict the overall efficiency of a CDS. The collection of particles by a single droplet consists of two processes: (1) the collision of particles with the droplet and (2) the adhesion of particles to the droplet.

The mechanisms that may affect the first process include inertial impaction, interception,

703

704 H.C. WANO et al.

gravity, electrostatic attraction, Brownian and turbulent diffusion, diffusiophoresis and thermophoresis. The relative importance of these mechanisms was theoretically investigated by several authors under various conditions (Kraemer and Johnstone, 1955; Nielsen and Hill, 1976; Prem and Pilat, 1978). Coulombic attraction was found to be the dominant mechanism for charged submicron particles when collected by charged water droplets as in a CDS. For this situation, it is well documented that the theoretical collision efficiency is a linear function of the nondimensional Coulombic parameter (Kc) that was introduced by Kraemer and Johnstone (1955). They showed that single collector collision efficiencies of over 1000 °, o can easily be achieved by adequate charging of collector and particles. Most experimental studies on this subject used metal spheres as collectors (Kraemer and Johnstone, 1955; Robig and Porstend6rfer, 1979). Water droplets cannot be charged as high as metal spheres (Leong et al., 1982a). The overall theoretical efficiencies are over 99.9 °, o even with a value of the single collector efficiency of 160 ~o in the penetration formulae for electrostatic scrubbers (Calvert et al., 1978) and charged droplet scrubbers (Pilat, 1975). However, in actual electrostatic scrubbers Calvert et al. (1978) found that charging the particles increased the collection efficiency for 0.5 #m radius particles only from about 80 to 90°,0. Pilat (1975) obtained an increase from 35 to 87 ~o for 0.3/~m radius particles in a charged droplet scrubber in which both the droplets and particles were charged. The efficiencies obtained for both the above cases are significantly below the theoretical efficiencies (> 99 ~o) for fine particles. These theoretical values, however, did not take into account the particle--drop surface interactions which may lead to nonadhesion and hence lower efficiencies. This will be especially true for nonwettable particles and the above examples are for such nonwettable particles. In fact, collection efficiencies of scrubbers were found to be lower for nonwettable particles compared to wettable ones (Hesketh, 1974). The adhesion of particles to the droplet depends on the surface properties of the droplets and the particles. For hydrophilic particles, the adhesion efficiency, which is defined as the ratio of the number of particles collected to that collided with the droplet, is 1 because these particles tend to penetrate inside the droplet immediately after coming in contact with the liquid (Weber, 1968). The behavior of hydrophobic submicron particles has not been investigated. In addition, no systematic verification of the electrostatic collection theory was reported by examining the individual dependence of particle size, particle charge, and droplet size, respectively.

The present paper describes an experimental system capable of measuring the collection efficiency of charged submicron particles by charged water droplets. To clarify the wettability effects, both hydrophilic and hydrophobic particles are used. The results of hydrophilic particles are compared with the well documented electrostatic collection theory (Kraemer and Johnstone, 1955; Nielsen and Hill, 1976; Prem and Pilat, 1978).

EXPERIMENTAL DESIGN

The experimental arrangement is shown schematically in Fig. 1. Widely spaced, charged droplets of uniform size are generated and fall through a cloud of monodisperse, charged particles that are continuously monitored by an aerosol electrometer and a condensation nuclei counter (CNC). The droplets are collected in a Faraday cup at the bottom of the chamber and analyzed for the mass of particles collected by fluorescence spectroscopy. The major components of the experiments are the aerosol generator, the aerosol conditioning system, the droplet generator and the aerosol chamber.

Selection of particle material

The experimental determination of the collection efficiency of submicron particles requires the measurement of trace amounts of particle mass collected by the droplets. Fluorescence spectroscopy is one of the most sensitive and selective methods that is suitable for this experiment. Uranine (sodium fluorescein) is highly fluorescent, freely soluble in water and thus chosen as a hydrophilic particle material. After experimenting with several organic

Hydrophilic and hydrophobic charged submicron particles 705

S WET TEST METER

VACUUI~ [

FILTERED ~ AIR

DROP GENERATOR

t

AEROSOL GENERATOR

I I ELECTROSTATIC

CLASSI FIER

[TOP BOX

A ~ A L L VALVE

FILTER "~= DIFFUSION CHARGER

~EROSOL [ ~ C :Rt~IBER I ~ ELECTROMETER

I I CONDENSATION NUCLEI l COUNTER

VENTILATION ~ T-] [ ~ .ooo - |

B ~ J ~--- FILTERED

COUNTER H ELECTROMETER ]METER~ L ~ I ~ C O L L E C T O R B O X ] / / AIR

INSULATIONJ 3,5~cm

U J ' - 15cm " I

Fig. I. Schematic diagram of an experimental arrangement.

compounds, carbazole was found to be suitable for generating hydrophobic aerosol particles. The solubility of carbazole in water is 1/600,000 at 25°C (Katritzky, 1963).

Aerosol oenerator

Hydrophilic particles were generated using an improved constant output atomizer that was previously described by Leong et al. (1982b). A 1 ~ solution of uranine is forced through the atomizer by a constant pressure feed. The droplets are heated and passed through a diffusion dryer. Water was vaporized by the heater and then absorbed in the diffusion dryer by silica gel. Polydisperse uranine particles are thus generated. This method cannot be used for the generation of hydrophobic particles, since solvents other than water may change the surface properties of the droplets and modify the collection efficiency of hydrophobic particles. This problem can be avoided by utilizing the vaporization--condensation method. Carbazole is sublimed at 180°C in a tube furnace, and the vapor is carried by a nitrogen stream to a condensation region where particles are formed and diluted with a large volume of cool, clean air. A device similar to a virtual impactor was used to remove large particles.

Aerosol conditioning sys tem

The aerosol conditioning system enables the selection of particles of a specified size and charge• This system consists of an electrostatic classifier (TSI 3071) and a diffusion charger (Liu et al., 1976). The ranges of diameter and charge on particles used in this work is

706 H.C. WANG et al.

0.075-0.2#m and 1-13.5e (e = 1.602 x 10-19Coulomb), respectively. Grounded copper tubing is employed after the diffusion charger to avoid charge accumulation on the walls.

Droplet generator

Figure 2 shows a schematic diagram of the droplet generator that is based on the design of Stern (1980). Water from a reservoir is forced through a needle by a constant pressure feed. Droplets are formed at the tip of the needle and dislodged by a concentric stream of air flowing continuously from an orifice around the needle tip. Uniform charges on each droplet are obtained by induction charging and can be varied by adjusting the high voltage. The maximum charge that can be placed on the droplet in the current system is approx. 1/3 of the Rayleigh limit (Rayleigh, 1882). Spark-over occurs when a higher voltage is provided. With a constant feed and high voltage, the size of the droplets is controlled by the air flow rate and is measured by a microscope after collecting the droplets in a dish filled with castor oil (Wang, 1978). In this work, the range of the droplet diameter is 137-5130/am and the range of charge on each droplet is 3.1 x 10-12-3.5 x 10 -11 Coulomb.

Aerosol chamber

The design ofthe stainless-steel aerosol chamber is shown in Fig. 1. The droplet generator mounted on the top of the system produces sprays of droplets continuously and only those in the central region pass into the aerosol chamber. The distance between the droplet generator and the top end of the aerosol chamber is sufficient (64 cm) to allow all of the droplets to reach within 10 ~o of their terminal velocity before entering the aerosol chamber (Cataneo and Semonin, 1969).

The droplets that collide with particles when passing through the chamber are collected in an electrically isolated stainless-steel cup. The total integrated charge on the droplets collected is measured by an electrometer (Keithley 616) connected to the cup. The pulse from the discharge of each charged droplet is counted by a counter and yields the total number of droplets collected. The average charge on each droplet is then calculated from the total collected charge and total number of droplets. This method is accurate since the droplet generator produces droplets with constant charge (+ 5 70). The aerosol mass collected by these droplets is measured by fluorescence spectroscopy.

The aerosol is introduced continuously near the top of the chamber and flows out at the bottom. This continuous flow system does not have the disadvantage of the closed chamber, where the particle concentration decreases with time because of coagulation or diffusion to the chamber wall (Leong et al., 1981). Slight positive pressure in the top box and collector box is provided to prevent contamination. A sampling test is done by taking samples from the top, middle, and bottom of the chamber. Concentration variation of ~< 2 °0 in radial direction and ~< 3 7o in axial direction are observed under all experimental conditions.

PRESSURE REGULATOR

"1 NEEDLE-.~ ~] _[~ ~ FlOW METER FILTER II!l!lll[ltlllllllllllllll

COMPRESSED AIR

FLOW METER VALVE

~b GROUND

Fig. 2. Schematic design of a modified charged droplet generator.

Hydrophilic and hydrophobic charged submicron particles 707

The particle concentration is determined by a polycarbonate filter (0.1/am pore size, Nuclepore Corp.) using a wet test meter to measure the total volume of aerosol filtered. The mass collected on the filter is analyzed by fluorescence spectroscopy. The particle concentration and charge were also continuously monitored using a condensation nuclei counter (TSI 3020) and an aerosol electrometer (TSI 3068) while sampling through a port located halfway between the top and bottom of the chamber. These measurements give an independent determination of the average charge on each particle.

Analytical methods

The particle mass collected on the filter and in the stainless-steel cup were analyzed by fluorescence spectroscopy (Perkin-Elmer, MFP-44B). The detection limits for uranine and carbazole by this instrument are approx. 0.05 and 0.1 #g l - t , respectively.

The fluorescence of uranine in water shows a strong dependence on pH when the pH is less than 9 (Wohlers et al., 1959), whereas no dependence is observed for pH above 9. Hence, a basic solution is required in order to obtain repeatable analytical results. All of the solutions were prepared from 0.01 M NaOH to ensure a pH > 10 in all cases. For carbazole, 100~/o ethanol was used as the solvent. All background concentrations, including drop water, cleaned cup, filter blink and all containers employed in this experiment, were checked and no uranine was detected. A small detectable background was observed for carbazole because of its relative high vapor pressure and was accounted for in the calculation of the experimental results.

The number of droplets that must be collected to obtain 20 times the detectable mass is estimated prior to the experiment. Immediately after collecting the required number of the droplets, 5 ml of solvent was added to the cup. The volume of droplets collected in the cup was negligible compared to the volume of solvent added. For example, 500 droplets of 500/~m diameter have a volume of 0.003 ml so only a 0.66 % error may occur. To dissolve all of the mass collected on the filter, 250 ml of solvent was added to the sample. Detailed experimental procedures were given by Wang (1982).

THEORY

The collision efficiency of a collector is defined as the ratio of the number of particles that collide with the collector to the number of particles swept out geometrically by the collector. When the Coulombic force is the dominant collision mechanism as in this work, the collision efficiency, Ec, can be expressed as (Kraemer and Johnstone, 1955)

E¢ = 4 K c, (1)

where Ke is the nondimensional Coulombic parameter. Substituting the expression for K c (Kraemer and Johnstone, 1955), and rearranging the terms, E c is given by

v]r 7, Ec knRc ~ (2) LOr#Rpj

where C is the Cunningham correction factor, 5, the permittivity constant, and r/, the viscosity of air. The charge and radius of the collector, Qc and R c, are measured directly in this work. The relative velocity, V, is the difference of the droplet terminal velocity and the aerosol flow velocity (3-5 cms -1) in this work. Qp and Rp are the charge and radius of the particle, respectively. The term in the second bracket of the above equation is simply the electrical mobility of the particle and is assigned a definite value for all the particles coming from the electrostatic classifier. The particles classified by the electrostatic classifier are primarily singly charged. A small portion of doubly charged particles with the same electrical mobility but larger in size are also classified. Since aerosol particles classified by the electrostatic classifier have the same electrical mobility, it is reasonable to assume that all of the particles that leave the diffusion charger have the same electrical mobility. This assumption is justified

708 H.C. WANG et al.

in the Appendix. Consequently, the electrical mobility of the aerosol increases linearly with the mean charge on the particles. The collision efficiency can then be calculated.

RESULTS AND DISCUSSION

The collection efficiency of a collector is defined as the product of collision and adhesion efficiency. The experimental collection efficiency, E e, in this work is given by

M E e = m t R c 2 H C m , (3)

where M is the total aerosol mass collected by n droplets, H, the height of the aerosol chamber, and C m, the aerosol mass concentration in the chamber.

For hydrophilic particles, the adhesion efficiency is unity and the collection efficiency is identical to the collision efficiency. Therefore, systematic verification of equation (2) can be done by examining individually the dependence of the collection efficiency on the four independent variables, Qp, Qc, Rpand R c. Figure 3 shows the collection efficiencies of 500/am droplets with a mean charge of (2.77 _ 0.06) x 10- t t Coulomb as a function of the particle diameter with one elementary unit charge. The theoretical collision efficiencies are also plotted. Since both the charges on droplets and particles and the size of droplets are fixed, the collision efficiency actually only depends on the value of C / R p. The experimental data are in good agreement with theory.

The effect of particle charge on the collection efficiency is illustrated in Fig. 4 using 500/am droplets with a mean charge of (3.36-I-0.11) x 10- t l Coulomb to collect 0.2/am diameter uranine particles with various charges. The theoretical collision efficiencies are included. A linear relationship is obtained between the particle charge and the collection efficiency. However, the linearity no longer exists at low values ( < 0.05) of collection efficiency because of the contribution of other mechanisms, such as the phoretic forces (Wang e t al., 1983).

By fixing the particle size, the particle charge and the droplet charge, the collection efficiency as a function of the diameter of droplets can be investigated. The same charge on various sizes of droplets cannot be easily obtained in the current system. The charge on the different size droplets used in the experiments varied from 3.16 x 10- 12 on 137/am droplets to 4.59 x 10- t2 Coulomb on 407/am droplets. The droplets with a mean charge of (4.18

06

0.5

1 I I I I

Experimental Results With 95 % Confidence Interval

~Theoretical Results

I 0 4 - -

0.3

0.2

O.

[ I I I I 06 008 0.10 012 014 0.16 018 0.20 0.22

Particle Diameter (/.Lm)

Fig. 3. Collection efficiency for 500/~m diameter droplets with a mean charge of 2.77 × 10 t~ Coulomb as a function of the diameter of uranine particles with one elementary charge.

Hydrophilic and hydrophobic charged submicron particles 709

0.6 t I I I I I

0 . 5 - -

0 . 4 - - ._o .o

laJ = 0 . 3 - - .2

O 0.2-- ith 95 %

I I I I I 1 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Particle Charge (Elementary Unit)

Fig. 4. Collection efficiency for 500/~m diameter droplets with a mean charge of 3.36 x 10 -~1 Coulomb as a function of the charge on uranine particles o f 0.2/zm diameter.

+ 1.10) x 10-12 Coulomb were used to collect 0.2/~m particles with a mean charge of 6.11 elementary units. Since the collection efficiency varies linearly with the droplet charge, the values of the collection efficiencies were linearly adjusted to the mean charge of droplets and plotted as a function of the diameter of the droplets in Fig. 5. The theoretical collision efficiencies that vary with 1/(R~ V) are also included. Good agreement is obtained between theoretical results and experimental data. This implies that the droplets do fall at terminal velocity. Moreover, the collection efficiencies are shown to be independent of the flow field with Reynolds number 3.5-66 corresponding to the droplets (137-500 #m) falling at terminal

I0

I - -

I, iJ

tJ I - -

0

Experimental Result With 9 5 ~ Confidence i n t e r v a l

- -Theoret ica l Result

I I I I I I00 200 300 400 500 600

Droplet Diameter {/J.m)

Fig. 5. Collection efficiency of 0.2/am diameter uranine particles with a mean charge of 6.11 elementary units as a function of the diameter of droplets with a mean charge of 4.]8 × 10-12

Coulomb.

710 H.C. WANG et al.

LLJ

0

I 0

I - -

161 - -

i i

Results With 9,~'o Confidence Experimentol Inlervol For Corbozole

F.~per*rnentol Results With 9 5 % Confidence Intervol For Uronine

,t

: I I I°162 16' l Io

Collision Efficiency ( 4 K c )

Fig. 6. Collection efficiency of 500/an diameter droplets as a function of collision efficiency for uranine and carbazole particles of 0.2/~m diameter.

velocity (Fig. 5). These results agree with the theoretical predictions of Nielsen and Hill (1976) and the experimental results of Robig and Porstend6rfer (1979) with higher Reynolds number (32-3200).

Figure 6 shows the collection efficiencies of 500/am droplets as a function of theoretical collision efficiencies (4 Kc) for both uranine and carbazole particles of 0.2 #m diameter. The charges on the particles and droplets are varied in the range of 1-13.5 e and 4.0 x 10-12-3.5 x 10-11 Coulomb, respectively. Since the particle concentration is low, no bounce-off of particles that collide with other particles previously deposited on the droplet surface is expected (Stulov et al., 1978). The substantial scatter in the data for carbazole particles is caused by the fluctuations of the background contamination that are approximately accounted for in the collection calculation. However, considering the 95 ~ confidence interval, the results agree with the theoretical collision efficiencies. Since the carbazole particles can be collected as efficiently as the uranine particles, the wettability of submicron particles has no effect on its collection by water droplets. Hence, the particle-drop surface interactions are not the causes of the low collection efficiencies observed by Pilat (1975) and Calvert et al. (1978). Other possible reasons for the low collection may be the nonuniformity of the droplet distribution or the existence of collision-free paths for particles in the collection chamber.

CONCLUSION

The work in this paper has been directed towards experimentally checking the collection efficiencies of both hydrophilic and hydrophobic charged submicron particles by charged water droplets. An experimental system that enables collection efficiencies to be measured directly and accurately is described. During the course of this work, the model for collection by Coulombic forces is verified systematically using hydrophilic particles. The collection of hydrophobic submicron particles was examined under the same experimental conditions as hydrophilic particles. No significant difference in collection efficiencies was observed. It is concluded that the wettability has no effect on the collection of submicron particles. Hence, the surface properties are not the causes of the low observed collection (Pilat, 1975; Calvert et

al., 1978). Possible causes are the nonuniform distribution of the charged droplets and the increasing wall loss of scrubbing liquid due to charge effects. This suggests that the

Hydrophilic and hydrophobic charged submicron particles 711

f o r m u l a t i o n s f r equen t ly used to pred ic t the overal l efficiency o f wet s c rubbe r s are n o t di rect ly app l i cab l e to charged d ro p l e t sc rubbers . F u r t h e r e x p e r i m e n t s will be c o n d u c t e d to e luc ida te

the cause o f the lower t h a n expected co l l ec t ion efficiency o f charged d rop l e t sc rubbers .

Acknowledgements--This project has been financed with Federal funds as part of the program of the Advanced Environmental Control Technology Research Center, University of Illinois at U-C, which is supported under Cooperative Agreement CR 806819 with the Environmental Protection Agency. The contents do not necessarily reflect the views and policies of the Environmental Protection Agency nor does the mention of trade names or commercial products constitute endorsement or recommendation for use.

R E F E R E N C E S

Calvert, S., Yung, S. C., Barbarika, H. and Patterson, P. G. (1978) Evaluation of four novel fine particulate collection devices. EPA-600/2-7 8-062, NTIS PB-281320. Research Triangle Park, North Carolina.

Cataneo, R. and Semonin, R. G. (1969) J. Rech. Atmos. 4, 57. Friedlander, S. K. (1977) Smoke, Dust and Haze. Fundamentals of Aerosol Behavior. Wiley-Interscience, New York. Hesketh, H. E. (1974) J. Air Pollut. Control Ass. 24, 939. Katritzky, A. R., Ed. (1963) Physical Method in Heterocyclic Compounds, p. 18. Academic Press, New York. Kraemer; H. F. and Johnstone, H. F. (1955) Ind. Engne Chem. 47, 2426. Leong, K. H., Stukel, J. J. and Hopke, P. K. (1981) Advanced Environmental Control Technology Research Center

Publication No. 81-2. University of Illinois, Urbana, Illinois. Leong. K. H., Stukel, J. J. and Hopke, P. K. (1982a) Envir. $ci. Technol. 16, 384. Leong. K. H., Wang, H. C., Stukel, J. J. and Hopke, P. K. (1982b) Am. ind. HYO. Ass. J. 43, 135. Liu, B. Y. H. and Pui, D. Y. H. (1974) J. Colloid Interface Sci. 47, 155. Liu, B. Y. H., Pui, D. Y. H. and Kapadia, A. (1976) Particle Technology Laboratory Publication No. 303. University

of Minnesota, Minneapolis, Minnesota. Liu, B. Y. H., Whithy, K. T. and Yu, H. H. S. (1967) J. appl. Phys. 3g, 1952. Nielsen, K. A. and Hill, J. C. (1976) Ind. Enono Chem. Fundam. 15, 148. Pilat, M. J. (1975) J. Air Pollut. Control Ass. 25, 176. Prem, A. and Pilat, M. J. (1978) Atmos. Envir. 12, 1981. Rayleigh, Lord (1882) Phil. Mag. 14, 184. Robig, G. and Porstend6rfer, J. (1979) J. Colloid Interface Sci. 69, 183. Stern, R. A. (1980) Chemical System Laboratory Tech. Report, ARCSL-TR-80042. Stulov, L. D., Murashkevich, F. I. and Fuchs, N. (1978) J. Aerosol $ci. 9, 1. Wang, P. K. (1978) A theoretical and experimental study on the scavenging of aerosol particlesby water drops. Ph.D

Thesis. University of California, Los Angeles, California. Wang, H. C. (1982) Collection of hydrophilic and hydrophobic charged submicron imrticles by charged water

droplets. M.S. Thesis, University of Illinois, Urhana, Illinois. Wang, H. C., Leong, K. H., Stukel, J. J. and Hopke, P. K. (1983) Atmos. Envir., submitted for publication. Weber, E. (1968) Staub Reinhalt. Luft. 2g, 37. Wohlers, H C., Kass, T. E. and Johnson, K. R. (1959) Symposium on Air Pollution Control. ASTM Special

Publication No. 281.

A P P E N D I X

The particles classified by the electrostatic classifier are primarily singly charged. Therefore, their concentration can be determined with an aerosol electrometer. If all particles are singly charged, the concentration determined by the electrometer is called apparent concentration. A correction factor, K, defined as the ratio of the actual concentration to the apparent concentration, has been introduced and determined by Liu and Pui (1974).

Let K a, K2 be the fraction of singly and doubly charged particles. Then, K t, K2 can be expressed in terms of K as

K: ffi 2 - 1/K,

K 2 ffi (1 - K)/K.

The values of K a and K 2 are functions of K only and depend on the experimental conditions. ~ f o r e , for one experimental run, these values can be assumed constant before and after corona charging. The most probable factor affecting K ~ and K2 in the corona charging device is the different deposition losses for these two commponding sizes of particles. Since the maximum deposition loss measured for any experimental condition is less than 8 ~, the different rate of losses for singly and doubly charged particles is negligible. The following discussions are based on the assumption of a constant K value.

Let the subscripts 1 and 2 denote the properties of singly and doubly charged particles, respectively. Then, the mean electrical mobility, Zpm, of the particles passing through the electrostatic classifier is given by

Zpm = Qpl C~ = Qp2 C2 67trlRpl 6~tr/Rp2

or

Zp~. = QplC1Kt + Qp2C2K2. 6nr/Rpl 6~trlRp2

712 H. C. WANG et al.

Table 1. The ratio of R' /R for various values of Nt, K, and particle diameter

Diameter Nt 106 107 (#m) K 0.5 0.7 0.9 0.5 0.7 0.9

0.200 0.993 0.997 0.998 1.019 1.011 1.005 0.160 0.997 0.997 0.999 1.023 1.013 1.006 0.130 0.998 0.999 1.000 1.024 1.013 1.006 0.100 1.000 1.000 1.000 1.026 1.014 1.007 0.075 1.002 1.001 0.999 1.025 1.013 1.006

Introducing a mean charge Qpm given by

Qpm = QplKt + Qp2K2,

the equation of mean electrical mobility can be rearranged and expressed as

] k6n)lRp~ / LK~ + (Qp2/Qp0K2 + (QpdQp2)K~'+ K2 3"

It is convenient to denote the term in the bracket, [ ], of the above equation as R. For the particles before corona charging, the ratio of Qp2 (double charge) over Qpl (single charge) is 2. The expression of R becomes

R - Cl + 2C2 (Rpl/Rp2)" KI + 2K2

The electrical mobility of particles increases after corona charging because of the increase in charge on each particle. Let prime' denote the properties of particles after corona charging. Assuming that K 1 and K2 do not change during the charging process, the mean electrical mobility, Z~,~, can be obtained by the same method as above:

\6~r/Rpl )

In the above equation, Q ~ is the mean charge on particles after corona charging and R' can be expressed as

C 1 C2(Rpl/Rp2) R' +

K , + (Q'p2/Q'pl)K2 (Q'pl/Q'p2)K, + K 2 '

where Qpl and Qp2 are the charges obtained by the particles with originally single and double charge, respectively. There is no easy way to measure Qpl and Qp2 directly. An empirical equation for diffusion charging has been reported by Liu et al. (1967) as

Qp = 18.0eRpln (1 +2.04 x lO-SRpNt) ,

where N is the number concentration of the ions to which the particle has been exposed and t is the charging time. The corona charging device employed here is essentially identical to that reported by Liu et al. (1976) with an Nt value between 106 and 107 $cm -3. Then the charge obtained after diffusion charging can be estimated from the above equation by taking the initial charges on the particles into account.

An error analysis of R and R' is done for various size, K and Nt values. The results are tabulated in Table 1. Since the difference between R and R' is within 3 50, it is safe to assume R = R'. The ratio of the mean electrical mobility before and after corona charging, is given by

Zpm/ Z'pm = Qp~/ Q'pm