Evaluation of micro-bubble size and gas hold-up in two ... › rtl › Papers › Bubble_Menguc_2006.pdfRadiative Transfer 101 (2006) 527–539 Evaluation of micro-bubble size and

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Journal of Quantitative Spectroscopy &

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Radiative Transfer 101 (2006) 527–539

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Evaluation of micro-bubble size and gas hold-up in two-phasegas–liquid columns via scattered light measurements

Mustafa M. Aslana, Czarena Crofcheckb, Daniel Taoc, M. Pinar Mengüc-a,�

aDepartment of Mechanical Engineering, University of Kentucky, Lexington, KY 40506, USAbDepartment of Biosystems and Agricultural Engineering, University of Kentucky, Lexington, KY 40506, USA

cDepartment of Mining Engineering, University of Kentucky, Lexington, KY 40506, USA

Abstract

In this paper, potential use of an elliptically polarized light scattering (EPLS) method to monitor both bubble size and

gas hold-up in a bubble-laden medium is explored. It is shown that with the use of the new EPLS system, normalized

scattering matrix elements (Mij ’s) measured at different side and back-scattering angles can be used to obtain the desired

correlations between the bubble sizes and input flow parameters for a gas–liquid (GL) column, including gas flow rate and

surfactant concentrations. The bubble size distributions were first evaluated experimentally using a digital image

processing system for different gas flows and surfactant concentrations. These images showed that the bubbles were not

necessarily spherical. We investigated the possibility of modeling the bubbles as effective spheres. The scattering matrix

elements were calculated using the Lorenz–Mie theory and the results were compared against the experimentally

determined values. It was observed that the change in the bubble size yields significant changes in M11, M33, M44, and M34profiles. An optimum single measurement angle of y ¼ 120� was determined for a gas velocity range of 0.04–0.35 cm/s(ID ¼ 4:5 cm). The choice of the optimum angle depends on frit pore size, column diameter, gas pressure, and surfactantconcentration. These results suggest that a simplified version of the present EPLS system can effectively be used as a two-

phase flow sensor to monitor bubble size and liquid hold-up in industrial systems.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Light scattering; Two-phase flow; Bubbles; Scattering matrix; Bubble size; Flow rate

1. Introduction

Two-phase gas–liquid (GL) tanks/columns/flows are extensively used in chemical, biochemical, petroleum,and mining industries [1–3]. Efficiency of mass transfer between liquid and gas depends on the total surfacearea of bubbles in the liquid. Therefore, determination of characteristics of the bubble population in a GLflow, such as bubble size distribution and gas hold-up in the liquid, is critical for evaluation of columnperformances.

There are many experimental methods devised over the years to characterize GL flows in columns [2]. Theparameters concerning column mass transfer efficiency are numerous, including bubble size distribution,

e front matter r 2006 Elsevier Ltd. All rights reserved.

srt.2006.02.068

ing author. Fax: +1859 257 3304.

ess: [email protected] (M. Pinar Mengüc-).

www.elsevier.com/locate/jqsrtdx.doi.org/10.1016/j.jqsrt.2006.02.068mailto:[email protected]:[email protected]:[email protected]

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Nomenclature

Cext extinction cross-sectionc separation distanced bubble diameterhm the height where scattering measurements were takenI scan normalized scattered light intensity from the bubbly mediumI inc Stokes’ vector of incident light to an objectI sca Stokes’ vector of scattered light from an objectI in Stokes’ vector of incident light to the systemIout Stokes’ vector of scattered light from the systemI0 Stokes’ vector of the light after polarizer 1 (P1)FðyÞ scattering matrix of the bubbly mediumk wave numberR distance between the particle and the detectorT total transmissionMij normalized scattering matrix elements of the two-phase mediumMsys system Muller matrixMP2 Muller matrix of polarizer-2MR1;MR2 Muller matrix of retarder 1 and 2n real part of refractive indexn0 relative refractive indexNT number of bubbles per unit volumeug gas velocityx size parameter (pd=l)t optical thicknessl wavelength of incident radiationb extinction coefficienty scattering angleyc critical scattering angle

M.M. Aslan et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 101 (2006) 527–539528

bubble shape, GL hold-up, pressure drop, and bubble velocities. It is critical to measure the bubble sizeand gas hold-up in order to control the efficiency of mass transfer in the GL flows in real-time [4]. The non-invasive methods to measure bubble size distributions and gas hold-up in situ include dynamic gasdisengagement techniques, photography-image analyses, radiography, light attenuation [5,6], as well asacoustic measurements [7]. These methods are relatively simple to use; however, they can be slow, expen-sive, and cannot be easily adapted for applications to opaque liquids and flotation tanks for in situmeasurements. An ideal monitoring approach should be non-destructive, in situ and economical. Mostimportantly, it should have a response time that allows for the control of the input parameters of the GL flow,so that the mass transfer is maximized in the process. In other words, a real-time measurement modality ishighly desirable.

The major optical techniques employed to characterize two-phase flow systems are the laser techniquesbased on diffraction and phase Doppler principles [8]. Phase Doppler is most widely used to measure thediameter of moving spherical bubbles and originally it was developed to measure bubble velocities [5,6,8].However, the potential change of the shape of the bubbles as they rise in the column can increase phase erroron size measurements with this method. Scattering based measurements, on the other hand, have not beenutilized extensively for industrial applications, even though there are theoretical studies in the literature forcharacterization modalities based on phase function and asymmetry parameters [9], Monte Carlo simulationof multiple scattering in bubbly media [10,11], as well as that based on the depolarization of light scatteringfrom bubbles (voids) [12]. In addition to intensity-based scattering measurements, the use of polarization of

ARTICLE IN PRESSM.M. Aslan et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 101 (2006) 527–539 529

light as a diagnostic tool was pioneered by Hoovenier’s group in Netherlands [13–15]; in later years similarstudies were also carried out by Mengüc- and co-workers [16–21].

Details of elliptically polarized light scattering (EPLS) approaches are well documented in the literature[15,18,22]. In a typical system, either the incident light is modulated to generate different polarization states orboth the incident and scattered beams are modulated using polarizers as well as quarter- or half-wave plates.Angular profiles of scattered light are measured to characterize the particles using the information about theelliptical polarization states of both the incident and scattered light. These relationships are defined by a 4� 4scattering matrix; although not all the elements are required for a satisfactory calibration [15,18,22].

In this work, we use EPLS and investigate its potential use as a possible technique for characterizingbubbles in a two-phase GL columns; particularly we are interested in measuring bubble size distributions andgas hold-up in a bubble-laden column. Our first objective is to establish a correlation between the GL columnparameters (flow rate, bubble size distribution, and the surfactant concentration) and the elliptical-polarization setting of the scattered light by the bubble-laden medium. After that, we determine the scatteringmatrix elements Mij for a range of parameters (combinations of flow rate, bubble size, and surfactantconcentration) from experiments and compare them against the theoretical results. For this purpose, we adaptthe approach outlined in [19] to modulate both incident and scattered light in order to obtain six scatteringmatrix elements. Then bubble size and gas hold-up are related with the scattering matrix elements.

Note that the experimental data can easily be correlated with the required physical parameters if themultiple and dependent scattering effects are not important. As shown later in the paper, a scattering-regimemap is drawn to show that current experimental results for bubble-laden media may need to be analyzed usingthe multiple-scattering calculations; yet the dependent scattering effects can safely be ignored.

2. Background for the elliptically polarized light scattering technique

The details of polarized light scattering models and measurements can be found in the literature [15,18,22].Stokes’ vector representation is typically used to describe how a beam of light incident on a medium laden withscattering particles changes its intensity and its degree of polarization [15,18,22]. Stokes’ vector of the scatteredlight, I sca ¼ ½I sca Qsca U sca V sca�T, which contains the flux and the polarization information can be related tothe Stokes’ vector of the incident light I inc ¼ ½I inc Qinc U inc V inc�T at given wavelength via the scatteringmatrix, FðyÞ. This relationship can be written in matrix form as

I sca ¼ 1k2R2

FðyÞI inc, (1)

where the scattering matrix for an axisymmetric medium is

FðyÞ ¼

F 11ðyÞ F12ðyÞ 0 0F 12ðyÞ F22ðyÞ 0 0

0 0 F 33ðyÞ F34ðyÞ0 0 �F34ðyÞ F44ðyÞ

266664

377775. (2)

The scattering matrix elements ðF 11;F12;F22;F 33;F 34, and F44) can be calculated from the scatteringamplitudes that relate two perpendicular components of the incident electromagnetic (EM) wave with twoperpendicular components of the scattered EM wave for elliptical bubbles using the expressions in [15]. Eq. (1)provides a methodology for determining the far-field scattering amplitudes for the medium (e.g. agglomerates[16], cotton fibers [19], nanopowders [20], carbon nanotubes [21]).

In this paper, the normalized scattering matrix elements Mij were calculated, defined as

½M � ¼

M11 M12 0 0

M12 M22 0 0

0 0 M33 M34

0 0 �M34 M44

26664

37775 ¼

F 11 F12=F 11 0 0

F12=F 11 F22=F 11 0 0

0 0 F 33=F11 F34=F 11

0 0 �F34=F 11 F44=F 11

266664

377775. (3)

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The six normalized scattering matrix elements; M11, M12, M22, M33, M34, and M44 are employed tocharacterize axi-symmetric ellipsoidal bubbles in two-phase GL flows.

3. Experimental methods

3.1. Experimental setup

Experiments were carried out using the setup shown in Fig. 1, which consists of a glass column with a frit forbubble generation and optical components for light scattering measurements. The glass bubble column wasfabricated by ACE-Glass (Vineland, NJ) with internal diameter of 4.5 cm, wall thickness of 0.25 cm, andincluded a porous glass frit (25–50 mm pore size) at the base on the column. For the bubble column we choseglass rather than Plexiglass in order to eliminate depolarization of the incident and scattered light transmittedthrough the column. The column was located on a tilting stage and two translation stages to align it vertically.A compressed nitrogen gas cylinder was used to provide a constant gas flow rate (3.5–522ml/min), which ismeasured with a Bel-Art Riteflow flow-meter (model no. 40407-0075) before introducing into the column.

Optical components of the system included two polarizers (P1 and P2) and two retarders (R1 and R2). Theywere used to modulate incident and scattered light so that the elliptical polarization setting of the lightscattered by the bubbles could be determined. Polarization setting and angle of incident light were modulatedby retarder-1 (R1); the first polarizer (P1) was fixed at 45� in the incident beam path. Scattered light from thebubbles in the water column was filtered by retarder-2 (R2) and polarizer-2 (P2). A 20mW helium neon laserðl ¼ 632 nmÞ was employed as the light source. Scattered light that passes through R2 and P2 was detected bya photomultiplier tube (PMT; Hamamatsu R446) as a function of scattering angle, y. Since the incident light isplane polarized at þ45�, the Stokes’ vector for scattered light that carries both the intensity and thepolarization information in normalized form can be written as

Ioutðy; a;b1;b2Þ ¼1

k2R2M sysðy; a; b1; b2ÞI in

¼ 1k2R2

MP2ðaÞMR2ðb1ÞFðyÞMR1ðb2ÞI0, ð4Þ

where MR1, MR2, and MP2 make up the Mueller matrix of retarder-1 (R1) and -2 (R2) and polarizer-2 (P2),respectively. The scattering matrix, FðyÞ, of the medium (bubbles in water) is given by Eq. (3) for an isotropic

Fig. 1. Gas–liquid (GL) phase column and optics used in the experimental system to obtain intensity and polarization information.


and symmetric medium. The components of the Stokes’ vector of light at the sensor for the optical system arewritten as

Iouti ðy; a;b1;b2Þ ¼1

k2R2½Msysi2 ðy; a;b1;b2Þ þM

sysi4 ðy; a; b1; b2Þ�; i ¼ 1; 2; 3 and 4. (5)

3.2. Experimental procedures

Experiments were conducted for different superficial gas velocities ðugÞ between 0.04 and 0.35 cm/s with fourdifferent surfactant concentrations (10, 20, 100, and 200 ppm). The data were collected for scattering anglesbetween 90� and 160� with slow scanning rate (5 steps per second). The height ðhmÞ at which the scatteringmeasurements taken was 50 cm from the frit surface. Time average gate of the lock-in amplifier was adjusted insuch a way that the oscillations of scattering light intensity sensed by the PMT were minimized. Scanningexperiments were repeated six times for each flow rate at different polarizer and retarder orientations (sixequations, six unknowns). The optimum orientations of the polarizer and retarders (a, b1, and b2) werealready given in [19].

Digital pictures (4 mega-pixels) were taken before and after each flow rate/surfactant combinationexperiment using a Nikon D100 camera with 105mm Nikkor lens. The camera was focused on the center ofthe glass column at the same height where scattering measurements were taken ðhm ¼ 50 cmÞ. Using AdobePhotoshop and SIAMS-600 image processing programs, the mean bubble size for each flow rate wasdetermined. Images were converted to gray scale and the intensity levels of the gray images were adjusted toseparate bubbles from the background. The background was removed and the intensity levels were adjusted asecond time. These images were further processed with the SIAMS-600 software, where the bubble imageswere converted to binary image files and then the scale was defined to relate image bubble size with the actualbubble size. The diameter of each bubble, based on equivalent surface area of the bubble, was calculated andfor each picture maximum, minimum, mean area equivalent bubble diameters (d32), and the shape factorswere calculated.

Even though local gas hold-up changes along the radial direction of the column depending on columndiameter and gas flow rate [23], we assume the change is negligible mainly because of the small columndiameter. Therefore, global gas hold-up was calculated based on liquid heights before and during gasintroduction.

4. Results and discussions

4.1. Relationship between flow rate and scattered light intensity

The experimentally measured scattered light intensity values are shown in Fig. 2 for different flow rates atscattering angles of 90� and 150�, where the dashed lines indicate the experimental maximums and minimums.Based on these measurements, there appears to be two distinct regions that define the light scattering behaviordepending on the gas flow rate and the scattering angle measurements taken. The results are presented for twodifferent surfactant concentrations. For the higher surfactant concentration at 90� measurements, if the gasflow rate is lower than 0.11 cm/s, the bubble size increases with increasing flow rate. However, if the flow rateis higher than 0.11 cm/s, as the flow rate increases the average bubble diameter decreases as the number ofsmall bubbles increase. The increase in number of smaller bubbles yields optically dense medium and thescattered light intensity measured decreases. On the other hand, the measurements at 150� show a linearrelation between the gas velocity and the intensities measured at both surfactant concentrations.

Depending on the surfactant concentration and the flow rate, the GL medium can become optically thick,where multiple-scattering effects become pronounced. At that point, it becomes important to select the rightscattering angle to measure the intensity, so that scattered light intensity can provide information about theflow rate. Fig. 2 shows that gas velocity may not be measured reliably using only the intensity at a givenscattering angle. The reason for this is that the optical thickness of a GL two-phase medium may become toolarge at high flow rates.

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0

1

2

3

4

5

Surfactant Concentration = 5 ppm

Nor

mal

ized

Inte

nsity

0

1

2

3

4

5

6Surfactant Concentration = 200 ppm

Nor

mal

ized

Inte

nsity

Iscan at �=90°

Iscan at � =150°

Gas velocity (cm/sec)

0.20.1 0.3 0.4 0.1

Gas velocity (cm/sec)

0.2 0.3 0.4

Iscan at �=90°

Iscan at � =150°

Fig. 2. Scattered light intensities at scattering angles of 90� and 150� for surfactant concentrations of 5 and 200 ppm. Dashed lines show

maximum and minimum of the experimental data.

0.2 0.6 1.0

0

5

10

15

20

25 Bubble size distribution

Den

sity

func

tion

0.0 0.4

Bubble diameter, d32 (mm)

0.8 1.2

Fig. 3. Bubble size distribution for gas velocity of 0.04 cm/s, where the bubble image is included as an inset.


The size distribution of bubbles and the corresponding digital image are shown in Fig. 3 for the gas velocityof 0.04 cm/s. The size distribution is bimodal and the location of the peaks shifts as the flow rate changes.When the flow rate increases, the major peak (for smaller diameter bubbles) shifts to the left and the minor(larger diameters) peak disappears. In order to simplify the calculations, bubble size distribution is assumed asmonodisperse and only the mean bubble diameters are used in the rest of the plots. The second peak of the sizedistribution is ignored in the calculations as the larger bubble size density is significantly low compared to thebubbles represented within the first peak.

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Fig. 4. Digital images of the bubbles at (a) the lowest flow rate and surfactant concentration and (b) the highest flow rate and surfactant

concentration. The images represent 9 by 9mm area.

M.M. Aslan et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 101 (2006) 527–539 533

Fig. 4 shows bubble images for two extreme cases, the lowest flow rate and surfactant concentration and forthe highest flow rate and surfactant concentration. The gas velocity affects both bubble size and number ofbubbles in the water. As surfactant concentration increases, the gas hold-up increases and the bubble diameterdecreases. When the flow rate increases, mean bubble diameter decreases logarithmically, but gas hold-upincreases linearly (Fig. 5). Bubble diameter does not decrease if gas velocity is larger than 0.2 cm/s for allsurfactant concentrations.

The bubble images shown in Fig. 4(a) and (b) correspond to single and multiple scattering regimes,respectively. Note that bubbles are not necessarily spherical, although they can be approximated to a degree asspherical. The knowledge of the optical thickness of the medium is important to reduce the light scatteringmeasurements to engineering parameters. Total transmission T over a distance l due to the scattering andabsorption is related to the optical thickness t if multiple scattering is neglected

T ¼ expð�blÞ ¼ expð�tÞ, (6)where t ¼ bl ¼ NTCextl, b is the extinction coefficient, Cext is extinction cross-section of bubbles, and NT isnumber of particles per unit volume. In Fig. 5, the single and multiple-scattering regimes are indicated bydashed lines, illustrating how the experimental results are related. It is obvious that most of the bubbleexperiments fall into the multiple-scattering regime. Even though we can carry out multiple-scatteringcalculations [10], we try to use only the single-scattering calculations and correlations to come out with simplemodels to be used with on-line sensors.

4.2. Two-phase light scattering experiments

In the independent scattering regime, the separation distance between the bubbles is much larger than thebubble diameter (Fig. 4(a)) and, therefore, the interaction of the incident electromagnetic wave with anindividual bubbles is considered to be independent from other bubbles. For these conditions, the Lorenz–Miesolution can be used as a basis for theoretical predictions if they are considered as spherical. However, if thebubbles are separated by smaller distances (Fig. 4(b)), the scattering may become dependent and theLorenz–Mie solution may not be applicable. In this regime, a multiple-scattering algorithm, such as thosebased on Monte Carlo simulations need to be adapted [10]. Therefore, defining scattering regimes (dependentor independent) for the two-phase light scattering measurements is important. A comparison of differentscattering regimes and our experimental data is shown in Fig. 6.

The original definition of the boundary between the independent and dependent scattering regimes is givenin [24] where the particle clearance c=l ¼ 0:3, which corresponds to t ¼ 2:5 (shown as a dashed line in Fig. 6).Even though the boundary between the single- and multiple-scattering regimes may vary depending on opticalproperties of particles/bubbles and the liquid, we assume that the demarcation boundary between the single vs.

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Fig. 6. Single and multiple (independent and dependent) scattering regimes for bubbles in the liquid as a function of size parameter and

gas hold-up, experimental results are shown for the present system. Dependent/independent scattering regime demarcation is based on

Brewster and Tien [24], and the multiple scattering demarcation line based on t ¼ 0:3 is from Agarwal and Mengüc- [25].

0.10 0.15 0.20 0.25 0.30 0.350

2

4

6

8

10

12

14

16

18 10 ppm 20 ppm 100 ppm 200 ppm

Gas

hol

d-up

(%

)

(a)

0.05 0.10 0.15 0.20 0.25 0.30 0.350.250.300.350.400.450.500.550.600.650.700.750.800.85

(b)

10 ppm 20 ppm 100 ppm 200 ppm

Mea

n bu

bble

dia

met

er d

av (

mm

)

0.05 0.20

0.0

3.0

(c)

Opt

ical

Thi

ckne

ss,τ

10ppm20ppm100ppm200ppm

2.5

2.0

1.5

1.0

0.5

0.150.10

Gas Velocity vγ (cm/sec.)

0.25 0.30 0.35

0.05

Gas velocity vg (cm/sec) Gas velocity vγ (cm/sec)

Multiple scattering

Fig. 5. The relationship between gas velocity and (a) gas hold-up, (b) mean bubble diameter, and (c) optical thickness. Dashed line

demarks multiple scattering limits.



multiple-scattering regimes to be calculated using t ¼ 0:3 (shown as a solid line in Fig. 6). This assumption isbased on the experimental results presented for latex particles [25] and may need to be revised after furtherresearch with bubble columns. Our experimental data were mostly in the independent multiple-scatteringzone, yet, the lower flow rates fall in the single-scattering regime. All of our experiments are conducted withinthe independent scattering regime and therefore the Lorenz–Mie theory applies. Multiple scattering, asdiscussed above, is not modeled here, although there are resources available to do so [10].

4.3. Characteristic of scattering matrix elements ðMijÞ at side- and back-scattering angles

In most light scattering applications, particle index of refraction is higher than that of the medium. In thepresent case, the index of refraction of the gas bubbles is smaller than that of the liquid (the relative index ofrefraction n0 ¼ 0:751 for nitrogen bubbles in water). Therefore, total reflection plays an important role onscattering [26] and critical scattering angle yields two distinct regions as a function of scattering angle. Rangeof region one where normal scattering occurs varies from y ¼ 0� to yc and the region two is from y ¼ yc to180�. The critical scattering angle is defined as: yc ¼ 2 cos�1ðn0Þ, which is yc ¼ 82:8� for nitrogen gas bubbles inwater. If the scattering measurements are taken in the region two, then there would be no total reflection effectbetween y ¼ 902160� (side to back scattering). For this reason, measurements were taken at side- and back-scattering angles. Another reason for choosing the back-scattering angles is the optical thickness of the GLflows. The medium (bubbles in water) becomes optically thick when gas velocity and surfactant concentrationsare increased (Fig. 5(c)), which makes measurements in the forward angles more difficult and prone to error.

After the intensity values are measured, they are converted to scattering matrix elements; the correspondingMij values are plotted for each flow rate (corresponding to a mean bubble size). Fig. 7 depicts the results for asurfactant concentration of 100 ppm; solid curves are for ray tracing results obtained for a 0.5mm diameternitrogen bubbles in water. Details of the ray-tracing/Monte Carlo method are given in the literature [10,11]. Inthe model calculations, the influence of possible nonsphericity of bubbles, light absorption and multiple lightscattering effects are neglected. Refractive index of nitrogen is assumed 1.000297 at l ¼ 632 nm. Depending onthe surfactant concentration and gas velocity, bubble shape changes from sphere to disk-like shape with amaximum aspect ratio of 1.46 (for large bubbles at high flow rates) as observed from the digital bubblepictures. Given this range, the results for two extreme shape cases (sphere and disk with aspect ratio of 1.46)are obtained. Modeling results show that the shape effect on scattering patterns is small because cross-sectionof bubbles in the plane where measurements were taken are close to circular. Shape effect can be observedmore clearly if the measurements at different azimuthal angles are conducted, as the compressed bubbles arenot randomly oriented; yet those measurements are very difficult for the bubbles rising in a column because ofthe column geometry.

With the change in mean bubble diameter, M11 profiles change as well, as expected. However, in back-scattering angles, for example at around y ¼ 145�, the M11 values are relatively less sensitive to change inbubble diameter. On the other hand, the profile of M22 may reveal the deviation of the bubble shape frompresumed spheres and helps to establish the demarcation between the single- and the multiple-scattering zones.When the flow rate increases, we observe from the digital images that bubble size changes from spheres tooblate spheroids (Fig. 7).

The theoretical degree of linear polarization ðDLP ¼ �M12Þ that represents single scattering gives an upperborder for light scattering measurements taken for a medium with many bubbles. DLP (�M12) does not showany trend which correlated with the gas velocity as DLP is small for all gas velocities. Yet, if the gas velocity ishigh, M12 information becomes less coherent due to multiple-scattering effects. The degree of circularpolarization (DCP ¼M33 or M44) increases when mean bubble size increases. The M44 curve at lowest flowrate is close to the predictions from ray tracing. Overall, M33 and M44 seem to be more reliable parameters tomonitor gas velocity between scattering angles 110� and 150�.

M34 represents how much of linearly polarized light is converted to circularly polarized light by bubbles.The ray-tracing curves for M34 always get close to zero between y ¼ 90� and 160�, because for scatteringangles greater than the critical angle ðy4yc ¼ 82:8�Þ, the bubbles cannot transform linearly polarized light tocircularly polarized light via scattering [12]. However, experimentally measured M34 values are not zero

ARTICLE IN PRESS

100 110 120 130 140 150

1.0

1.5

2.5Experimental

100 130 140

0.4

0.8

2.0

100 110 120 130 140 150 110

0.0

100 120 140

0.0

Scattering angle140

Scattering angle

2.0

0.5

0.00.8

0.4

0.0

-0.4

-0.8

0.4

0.2

-0.2

-0.4

-0.6

-0.8

-1.0150

-0.4

-0.2

0.0

0.2

0.4

-0.8

-0.4

0.4

0.8

0.0

1.2

1.6

M22

M44

110 120 150

M34

150140130120100

150130120110100

M12

M33

�g = 0.1395 cm/sec.�g = 0.1056 cm/sec.�g = 0.0778 cm/sec.�g = 0.0547 cm/sec.�g = 0.0369 cm/sec.

Monte-Carlo, Ray-tracing

disk(aspect ratio = 1.46) Sphere

130110

M11

Fig. 7. Scattering matrix elements ðMijÞ calculated from experimental intensity measurements between 90� and 160� at different gasvelocities and a surfactant concentration of 100 ppm.


because increased gas velocity generates more bubbles, contributing to multiple scattering. The dynamic rangeof the experimentally measured M34 appears to be large enough to be used to monitor gas velocity.

In order to understand relationship between gas velocity and Mij elements, additional single angle scatteredmeasurements were conducted at y ¼ 120� where it is possible to separate gas velocity curves. Gas velocitiesmeasured for different surfactant concentrations are first converted to mean bubble diameters and gas hold-up; then they were plotted against the measured Mij values, as shown in Figs. 8 and 9.

Fig. 8 depicts that it is possible to predict bubble diameter based on scattering measurements: M11, M22,M33, M44, and M34 are sensitive to bubble diameter variations at low gas velocities with medium-to-lowsurfactant concentrations. At high superficial gas velocities (ug40:2 cm=s), there is little to no change in thesize of the bubbles as the flow rate increases (Fig. 5), which yields small changes in the matrix elements. InFig. 8, error bars shown for all Mij elements correspond to �20% variations. The accuracy of results in Fig. 8depends on calibration measurements made using the digital bubble images. Given this, we expect �20% is areasonable figure, as it gives a reasonable representation of potential variations in the predictions.

Gas hold-up is another parameter that can be related to the gas velocity (as previously shown in Fig. 5).Fig. 9 depicts how the gas fraction in water affects the scattering at 120�. It should be understood that theaverage gas hold-up measurements performed here may have additional errors. This is because the amount ofgas hold-up is calculated from the height variation of the column liquid plus gas levels, which in turn yieldsonly an average gas hold-up value for the entire column. Yet, the gas hold-up values determined fromscattering measurements correspond to the center of the column for the given measurement height ðhm). Even

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3.0

10 ppm

20 ppm

100 ppm

200 ppm

10 ppm

20 ppm

100 ppm

200 ppm

10 ppm

20 ppm

100 ppm

200 ppm

-0.3

0.3

Average Bubble Diameter (mm)0.5

-0.1

0.1

Average Bubble Diameter (mm)

M11

M33

M12 M34

M44

M223.5

2.5

2.0

1.5

1.0

0.5

0.2

0.0

-0.2

-0.4

0.1

0.0

-0.1

-0.2

-0.3

0.3 0.4 0.5 0.6 0.7 0.8

-0.2

0.0

0.2

-0.6

0.0

0.6

0.4

0.6

0.8

1.0

1.20.80.70.60.50.40.3 0.3 0.4 0.5 0.6 0.7 0.8

0.3 0.4 0.6 0.7 0.8

Fig. 8. Scattering matrix elements ðMijÞ at 120� as a function of mean bubble diameter (mm). The solid lines indicate curve-fittedexpressions.

M.M. Aslan et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 101 (2006) 527–539 537

though the gas hold-up increases linearly with increasing gas velocity, effect of gas hold-up on Mij depends onsurfactant concentration. For a low-medium surfactant concentration, M11, M33, and M44 increase as gashold-up increases. M12 decreases rapidly and M34 increases when bubble size increases with increasing flowrate and surfactant concentration. The profiles of M22 changes drastically at higher surfactant concentrations,unlike other scattering matrix elements, because the shape factor of bubbles is decreasing with increasing gasvelocity and the number of bubbles increases (multiple-scattering regime). M34 decreases at single-scatteringregion but it decreases in the multiple-scattering zone. Monitoring gas hold-up based on Mij measurements ispossible at some gas velocities for known surfactant concentrations if the local gas hold-up can be determinedfrom bubble images.

5. Conclusions

An elliptically polarized light scattering (EPLS) approach was utilized for monitoring the mean bubble sizeand total gas hold-up in GL columns. Experiments were conducted which showed that the profiles ofscattering matrix elements were sensitive to the bubble size and gas hold-up. M11, M33, and M44 valuesat y ¼ 120� were found to be quite effective for such application on GL systems with low-to-medium flowrates and surfactant concentrations. On the other hand, M22 values at y ¼ 120� can be used to monitor gashold-up at high flow rates and surfactant concentrations. There are two disadvantages associated with the

ARTICLE IN PRESS

0.12 0.16

0.6

1.2

1.8

2.4

3.0

10 ppm

20 ppm

100 ppm

200 ppm

10 ppm

20 ppm

100 ppm

200 ppm

10 ppm

20 ppm

100 ppm

200 ppm

0.04 0.08 0.12 0.16

0.2

0.4

0.6

0.8

0.04 0.08 0.12 0.16

0.0

0.2

0.04 0.08 0.12 0.16

0.4

0.6

0.12 0.16

0.0

0.1

0.04 0.08 0.12 0.16

0.1

0.2

M11

M33

M12

M34

M44

M22

-0.2

-0.4

-0.1

-0.2

-0.3

0.04 0.08

Gas hold-up Gas hold-up0.04 0.08

-0.2

-0.1

0.0

-0.6

-0.4

-0.2

0.0

0.2

Fig. 9. Scattering matrix elements ðMijÞ at scattering angle of 120� as a function of gas hold-up.


M12-based monitoring: (1) M12 value decreases at low surfactant concentration with increasing gas hold-up,yet it increases when surfactant concentration increases; and, (2) because of multiple scattering affects, itsvalue can be very small and may not show any a trend as a function of gas flow rates and surfactantconcentrations.

The results show that the present EPLS concept is very promising for optically thin columns and has manyadvantages over imaging techniques when in situ measurements of bubble size are necessary at high flow rateswith high surfactant concentrations. For optically denser bubble-laden media, the reliability of this techniquecan be improved by incorporating multiple scattering algorithms [10] in data reduction. Alternatively, themeasurements in large GL columns can be performed on smaller pilot columns where a small amount of themixture is circulated through a smaller column out side the main system.

Acknowledgements

This work is partially sponsored by the Center for Advanced Separation Technologies, US Department ofEnergy (DE-FC26-01NT41091). The authors wish to thank Dr. Rodolphe Vaillon for valuable discussionsand Janakiraman Swamy for his help with data analysis.


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http://tools.ecn.purdue.edu/ME/heattransfer/Menguc.pdf

Evaluation of micro-bubble size and gas hold-up in two-phase gas-liquid columns via scattered light measurementsIntroductionBackground for the elliptically polarized light scattering techniqueExperimental methodsExperimental setupExperimental procedures

Results and discussionsRelationship between flow rate and scattered light intensityTwo-phase light scattering experimentsCharacteristic of scattering matrix elements (Mij) at side- and back-scattering angles

ConclusionsAcknowledgementsReferences

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Evaluation of micro-bubble size and gas hold-up in two ... › rtl › Papers › Bubble_Menguc_2006.pdfRadiative Transfer 101 (2006) 527–539 Evaluation of micro-bubble size and