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ARTICLE IN PRESS
Journal of Quantitative Spectroscopy &
0022-4073/$ - se
doi:10.1016/j.jq
�CorrespondE-mail addr
Radiative Transfer 101 (2006) 527–539
www.elsevier.com/locate/jqsrt
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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ARTICLE IN PRESS
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
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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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Spectroscopy & Radiative Transfer 101 (2006) 527–539530
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.
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Spectroscopy & Radiative Transfer 101 (2006) 527–539 531
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.
M.M. Aslan et al. / Journal of Quantitative Spectroscopy &
Radiative Transfer 101 (2006) 527–539532
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.
M.M. Aslan et al. / Journal of Quantitative Spectroscopy &
Radiative Transfer 101 (2006) 527–539534
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ARTICLE IN PRESSM.M. Aslan et al. / Journal of Quantitative
Spectroscopy & Radiative Transfer 101 (2006) 527–539 535
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
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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.
M.M. Aslan et al. / Journal of Quantitative Spectroscopy &
Radiative Transfer 101 (2006) 527–539536
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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ARTICLE IN PRESS
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
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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.
M.M. Aslan et al. / Journal of Quantitative Spectroscopy &
Radiative Transfer 101 (2006) 527–539538
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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ARTICLE IN PRESSM.M. Aslan et al. / Journal of Quantitative
Spectroscopy & Radiative Transfer 101 (2006) 527–539 539
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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