Article
pubs.acs.org/IECR
Experimental Investigations in Liquid−Liquid Dispersion System:
Effects of Dispersed Phase Viscosity and Impeller Speed
Mohd Izzudin Izzat Zainal Abidin, Abdul Aziz Abdul Raman,* and Mohamad Iskandr Mohamad Nor
Department of Chemical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur 50603, Malaysia
ABSTRACT: Experimental investigation was conducted on a liquid−liquid dispersion in a stirred vessel in which the effects of
dispersed phase viscosity were studied. Different grades of silicone oils were used to create oil-in-water dispersion by using
Rushton turbine as an impeller, and drop sizes were measured by laser diffraction technique. Dispersion with higher uniformity of
drop sizes was produced at low viscosity and high impeller speed. The dispersed phase viscosity influenced the equilibrium Sauter
mean diameter, d32 by contributing to drops stabilization. The decrement of d32 with an increase in impeller speed is larger for
high dispersed phase viscosities. It shows the influence of number and size of drop fragments formed after drop breakup on the
mean drop size. Correlations relating d32 and dispersed phase viscosity were proposed with an accuracy of more than 90%
between the predicted and experimental values.
1.0. INTRODUCTION
A liquid−liquid dispersion operation is required in industrial
processes such as extraction, suspension polymerization, and
multiphase reactions.1 The drop size distribution of a dispersion
is related to the interfacial area which controls the amount of
mass transferred between the phases.2 Therefore, accurate
prediction of interfacial area in dispersions is important in
determining the mass transfer and reaction rates.3,4
Drop breakup and coalescence occur simultaneously during a
liquid−liquid dispersion process, and the dynamic equilibrium
between both processes determines the final drop size
distribution of the dispersion. A drop in moving fluid
experiences turbulent pressure fluctuations, and viscous stress
which tend to cause drop breakup. The drop then resists the
deformation by its surface force and internal viscous force if its
viscosity is high.5 Drop coalescence occurs when two drops
collide and combine into bigger drops, involving drainage and
rupture of the intervening liquid film between the drops which
is governed by the physical properties of the drops.6 The mean
drop size and distribution are influenced by several factors, such
as operating parameters of stirring process and properties of
liquids which include viscosity and interfacial tension.7 An
accurate prediction equation could be developed by understanding how mean drop size and distribution are by different
factors to allow better control of drop size and uniformity of the
distribution.8
development of models or correlations which relate the Sauter
mean diameter d32 to different influencing factors.
Most of the previous works involving prediction of drop size
have applied the concept of turbulent energy cascade to
estimate the maximum stable diameter dmax referring to the
Hinze and Kolmogrov theory.14 On the basis of the theory,
drops in the inertial region of turbulence have the maximum
diameter dmax which is related to a dimensionless Weber
number We and mean energy dissipation rate εT as shown in eq
1;15
dmax
∝ εT−0.4 ∝ We−0.6
D
ρc N 2D3
We =
σ
(2)
The mean energy dissipation rate, εT at constant power number
can be determined from power consumption P as shown in eq
316
εT =
P
ρc VT
(3)
The εT or mean flow which is characterized by the impeller tip
speed ND2 is usually used to develop scale-up correlations for
liquid−liquid systems, but the use of each of the parameters
alone is not sufficient.16 Zhou and Kresta16 suggested that the
interaction between energy dissipation rate and mean flow had
to be considered, in which both εT and ND2 were included for a
better correlation. They also claimed that the maximum energy
dissipation rate εmax should be used instead of εT as εmax was
more suitable to describe the breakup across different impellers.
However, there are arguments whether one can easily and
accurately measures εmax. Therefore, scale-up correlations were
2.0. BACKGROUND
Available works in liquid−liquid dispersion have mainly focused
on investigating effects of various influencing factors such as
dispersed phase fraction, viscosity, and impeller design on the
mean drop size and distribution.3,9−11 The main physical
properties of liquids which influence mean drop size are
interfacial tension and viscosity. Earlier works on liquid−liquid
dispersion however have often been conducted for dilute and
low dispersed phase viscosity12,13 in which the surface force
dominates drops stabilization and the internal viscous force can
be neglected. Usually, the outcome of these works led to the
© 2014 American Chemical Society
(1)
Received:
Revised:
Accepted:
Published:
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March 16, 2014
March 19, 2014
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developed in this work by relating d32 to εT and the mean flow,
ND2.
Sauter mean diameter (d32 = ∑d3i /∑d2i ) is preferred in
characterizing dispersion as it relates interfacial area of
dispersed phase to its volume.7 A relation between d32 and
We is obtained based on the fact that dmax is directly
proportional to d32, as proven by several researchers:17,18
d32
∝ We−0.6
D
or
d32
= C1We−0.6
D
number and drop size of drop fragments produced after
breakup.28 Relevant studies on effects of viscosity have been
conducted in a surfactant-free system by Calabrese et al.29 and
Podgorska1 and in a surfactant-stabilized system which focused
only on drop breakup.30,31 The objectives of this research work
are to investigate the effects of viscosity on drop breakup and
mean drop size apart from obtaining the correlations relating
d32 to the influencing parameters. The studies were conducted
at different power inputs to gain better understanding on the
effects of viscosity on drop breakup.
Various grades of silicone oils with different viscosities
(moderate to high) were used to study the effects of viscosity
on mean drop size and distribution. Silicone oil was used as it
exhibits nearly constant interfacial tension at different
viscosities with its density not too much different from the
density of the continuous phase used in this work. Since the
works focused on drop breakup only, surfactant was added to
the system to prevent coalescence.32 Different techniques are
available for drop size measurement which can be categorized
based on their measurement principles.33 Laser diffraction is
one of the laser system techniques that yields fast and accurate
measurements. It is based on the measurement and
interpretation of angular distribution of light diffracted by the
drops, referring to Fraunhoffer diffraction theory. This
technique was used in this work because of its versatility,
broad dynamic range, and high reproducibility.34
(4)
Equation 4 is a well-known relation and has been widely used
to correlate d32 for a dilute system with low dispersed phase
viscosity. The constant C1 in eq 4 needs to be evaluated
experimentally where the published values in the literature are
in the range of 0.05−0.08119 at low dispersed-phase viscosity.
Although several researchers20,21 have successfully applied eq 4
to correlate their data, some have discovered that the exponent
of We in eq 4 should be modified at different operating
parameters where the applications of d32 ∝ We−0.6 have been
argued at high dispersed phase fractions.21−23 At high phase
ratio, the value of the We exponent has been found to be lower
than −0.6.24 This is because the application of eq 4 is limited to
a dilute and low viscosity system, based on the assumption that
d32 depends only on dmax linearly. Without this assumption,
Pacek et al.21 suggested that a general equation should be used
where the exponent of We should be determined experimentally;
d32
= C2(1 + C3ϕ)We−α
D
3.0. EXPERIMENTAL PROCEDURES
Experiments were conducted in a clear cylindrical flat bottom
stirred tank with an internal diameter of T = 0.20 m, equipped
with four identical baffles with width equal to T/10 each. The
tank was filled with distilled water as continuous phase to a
height of H = T. A standard six-blade stainless steel Rushton
turbine with diameter D = 0.08 m was used with bottom
clearance equal to T/3. Lighting was provided by four
fluorescent lights at the corners of the vessel to allow
observation of the dispersion process. Various grades of silicone
oils (20, 350, and 500 mPas) supplied by Sigma Aldrich were
used as dispersed phase. Silicone oils have a high refractive
index which makes them suitable for measurement by laser
diffraction and image analysis techniques. The interfacial
tensions of the oils were measured using the du Nouy ring
method. The properties of the oils are tabulated in Table 1.
(5)
Equation 5 is applicable when the effects of viscous force are
negligible, especially for an inviscid liquid.5 However, the
viscous force has significant effects on the cohesive stress at
high viscosity, which stabilizes the drops and should be
considered in the relation. The effects of viscosity can be
included in the prediction model by introducing a dimensionless viscosity number Vi which represents the ratio of viscous to
surface forces.25
⎛ ρ ⎞0.5 μ ND
Vi = ⎜⎜ c ⎟⎟ d
σ
⎝ ρd ⎠
(6)
The viscosity number is added into the d32 relation to account
for drop stabilization by both surface and viscous forces as
shown in the relation25
0.6
⎡
⎛ d32 ⎞1/3⎤
d32
−0.6⎢
= C4We
1 + C5Vi⎜ ⎟ ⎥
⎝ D ⎠ ⎥⎦
D
⎢⎣
Table 1. Properties of the Silicone Oils
(7)
When the viscosity term in eq 7 is too small and approaching
zero, the equation reverts to eq 4. The relation is limited to
dilute dispersions (ϕ < 0.01)26 but could be modified to
account for the effects of dispersed phase fraction.
The effects of dispersed phase viscosity are important as it is
one of the main factors that influence the final drop size besides
interfacial tension. However, most works on liquid−liquid
dispersion have focused on low viscosity dispersed phase which
has a narrow range of applications, and studies at high dispersed
phase are limited. Viscous and nonviscous drops undergo
breakup process in different ways where the number of
fragments formed after breakup is different.27 Therefore, d32 is
not only influenced by the rate of drop breakup but also the
properties (at 25 °C)
silicone oil
20
silicone oil
350
silicone oil
500
viscosity, μd (mPas)
interfacial tension, σ (kg/s2)
density, ρ (kg/m3)
refractive index
20
0.017
1001
1.39
350
0.0182
970
1.403
500
0.0189
970
1.403
Approximately 0.3% w/w of sodium dodecyl sulfate (SDS) was
diluted by distilled water before being added to the oil. The
temperature in the vessel was monitored during the mixing
process to make sure that there was no significant temperature
increase. The required amount of silicone oil (equivalent to ϕ =
0.01) was added into the distilled water near the impeller
region by using a syringe. The impeller speeds were varied from
300 rpm to 500 rpm, which are equivalent to Reynold’s
numbers in the range of 33 000 to 55 000. The Reynold’s
number is calculated as Re = ρcND2/μc. The minimum impeller
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mPas were much taller (see Figure 2) compared to 350 and 500
mPas which show that the drop sizes for low viscosity are more
uniform and the drop size distribution also broadens as μd
increases. Besides, at constant impeller speed, the size of the
smallest drops decreased while the volume percentage
increased as μd decreased. For example, at 400 rpm, the d50
(50% of drops were below this diameter) for 20 mPas, 350
mPas, and 500 mPas was 82.93, 126.32, and 273.31 μm,
respectively. Therefore, it shows that low viscosity produces
dispersion with smaller drops compared to high viscosity, which
leads to higher surface area. Similar trends were reported by
Podgorska1 and El-Hamouz et al.35 Since the interfacial tension
differences between the three oils were minimal, the influence
on drop-size distribution by reducing the rate of drop breakup
comes from μd.
As the impeller speed increased, the curves shifted to the left
which was toward the lower drop sizes range. This is because
smaller and finer drops were produced and the size frequency
increased at high impeller speed. It occurs as a result of
increased in drop breakup rate when the power input to the
system is increased. For example, at μd = 20 mPas, d50
decreased as the impeller speed increased where d50 at the
impeller speed of 300, 400, and 500 rpm was 290.65 μm,
126.32 and 117.18 μm respectively. The observations were
expected as increase in the power input to the impeller leads to
increase in shear and energy dissipation rate. In this condition,
turbulent pressure fluctuation which is the main external force
that causes drop breakup increases.
4.2. Effect of Dispersed Phase Viscosity on Mean
Drop Size. The d32 for every μd are tabulated in Table 3 at
different impeller speeds. As seen in Table 3, larger d32 was
produced as μd increased from 20 to 500 mPas at the same
impeller speed, leading to smaller surface area in the dispersion.
The observation can be explained by how the dispersed phase
viscosity affects the rate of drop breakup where drops are
stabilized not only by the surface force but also the internal
viscous force at high viscosity. The viscous force of the drops
provide additional cohesive force, and thus more energy is
required to overcome the cohesive force, reducing drop
breakup.37 Drops with higher viscosity also have lower drop
breakup probability, where the breakup events area in the
stirred vessel is smaller, compared to drops with low viscosity
due to the stability of the oil.4
4.3. Sauter Mean Diameter as a Function of We. A
dimensionless size ratio (d32/D) was plotted against the
dimensionless Weber number, We for every dispersed-phase
viscosities as shown in Figure 3. The data fitted well into eq 4
with slightly smaller We exponents. The constants C1 and We
exponents as in eq 4 were obtained for the three μd and are
shown in Table 4.
The exponents of We obtained from the data were between
−0.65 to −0.68 for low to high μd which were close to the
theoretical value of −0.6 as in eq 4. As seen in Table 4, the
value of C1 for μd = 20 mPas was in the range 0.05−0.081 that
was reported in the literature for low viscosity as discussed
earlier. It shows that the system satisfies the theoretical
conditions which are based on a breakup dominant process.
The constant C1 increased to 0.174 and 0.364 as μd increased,
values which were out of the range as the reported values were
only for a low viscosity system. The increment of C1 was due to
the increase in d32 at higher μd. It can be concluded from the
result that eq 4 could be applied in a high viscosity system with
slight modifications of the values of the We exponent.
speed was chosen to be above the minimum speed required for
a complete dispersion, and the maximum speed was chosen
below the speed where air entrainment starts to occur in the
vessel. The power number determined for the Rushton turbine
was 5.8 in the turbulence region. The details of the experiments
are shown in Table 2.
Table 2. Details of the Experiment
experimental conditions
symbol
value
mixing time, min
impeller diameter, m
tank diameter, m
tank height, m
impeller clearance, m
baffle width, m
liquid height, m
dispersed phase fraction
SDS concentration, wt %
θ
D
T
H
C
B
HL
ϕ
60
0.08
0.2
0.4
0.067
0.02
0.2
0.01
0.3%
3.1. Drop Size Measurements by Laser Diffraction.
Samples of the dispersion were collected at a fixed position near
the impeller region where the rate of drop breakup is high. The
samples were taken to a Malvern Mastersizer 2000 for drop size
measurement process. The laser diffraction equipment is wellknown and widely used in this area by several researchers.20,26,30,35,36 It is capable of measuring drops in the range of
0.02−2000 μm with an accuracy of ±1%. The equipment
requires the information on the refractive index of the dispersed
phase (see Table 1). Drop size distribution curves and Sauter
mean diameter d32 for all dispersions were produced and
determined from the measurement.
Figure 1. Schematic Diagram of the Stirred Vessel.
4.0. RESULTS AND DISCUSSION
4.1. Drop Size Distributions at Different Impeller
Speeds. The drop size distribution curves at different impeller
speed for each dispersed phase viscosities were plotted as
shown in Figure 2a,b,c. The curves show the range of drop sizes
in the dispersion. In Figure 2 the curves shifted to the right
where the size of the drops was larger as the dispersed phase
viscosity increased. In most cases, the distribution curves for 20
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Figure 2. DSD for (a) 20 mPas, (b) 350 mPas, and (c) 500 mPas.
act to keep the drops to its original shape. Thus, the rates of
drop breakup increase as N increases and smaller d32 is
produced. The behavior can also be explained based on
circulation time, θc where it is related to N by θc ∝ 1/ND2.38
Therefore, the circulation time in the vessel becomes shorter as
N increases, resulting in more circulations or flows in the vessel.
Therefore, the drops take less time to travel to the impeller
region, which is the most important zone that controls drop
breakup and where the rate of drop breakup is high.39
In Figure 4, a straight line was used to fit each of the data sets
in order to show the slope which represents the change in d32 as
a function of impeller speed. Interestingly, different slopes were
obtained for different dispersed phase viscosities, which were
−0.149, −0.455, and −0.881, where the largest slope was
achieved by 500 mPas followed by 350 mPas. It means that
high viscosity drops undergo larger change in d32 as the
impeller speed increases, although d32 for high viscosity is
Table 3. Sauter Mean Diameter, d32 for Different Impeller
Speeds
Sauter mean diameter, d32, μm
impeller speed, RPM
μd = 20 mPas
μd = 350 mPas
μd = 500 mPas
300
350
400
450
500
91.66
68.71
64.48
60.35
58.58
170.89
117.63
96.41
77.56
77.12
256.75
229.36
169.67
114.11
94.04
4.4. Effect of Impeller Speed on d32 at Increasing
Dispersed Phase Viscosity. The d32 data for each μd was
plotted against impeller rotational speed N in Figure 4. It is
observed that d32 decreased as N increased for every μd. An
increase in N gives higher energy dissipation into the system
where the energy is used to overcome the cohesive forces which
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Andersson27 pointed out that a viscous drop in turbulent flow
undergoes deformation by forming a thin liquid thread before it
breaks into many smaller fragments, while a nonviscous drop
breaks into three fragments only. Thus, a high-viscosity drop
produces more daughter droplets, and therefore larger d32
changes were observed as N increased. Similar trends of the
slopes were observed by Sechremeli et al.41 but at different
dispersed phase fractions. The slope of d32 versus N for ϕ = 0.1
which produced bigger d32 was larger than the slope for ϕ = 0.1
with smaller d32.
4.5. Sauter Mean Diameter as a Function of Energy
Dissipation Rate and Mean Flow. Both mean energy
dissipation rate εT and mean flow ND2 were used to develop
correlations for scale-up, and the graph of d32 vs εT (ND2) is
shown in Figure 5. Zhou and Kresta16 reported that εT could
Figure 3. d32/D vs We.
Table 4. Constants and R2 Values of Data Fitting into the
Generalized Form of d32/D = C1Wen
viscosity, μd (mPas)
C1
N
R2
20
350
500
0.06
0.174
0.364
−0.65
−0.65
−0.68
0.900
0.951
0.950
Figure 5. Graph d32 vs εT (ND2).
also give reasonably good correlation when it was used with
mean flow, ND, or ND2 just like in the case of εmax. The
correlations for each μd were obtained with an R2 value of 0.87
for 20 mPa·s and above 0.9 for 350 and 500 mPa·s as shown
below:
d32 = 34.31(εTND2)−0.2
for 20 mPa·s
(9)
d32 = 27.48(εTND2)−0.4
for 350 mPa·s
(10)
d32 = 28.51(εTND2)−0.52
for 500 mPa·s
(11)
It is seen from eq 9 to eq 11 that the power of εT (ND2)
decreases from 20 mPa·s to 500 mPa·s resulting in a bigger
difference between d32 value when the impeller speed is
increased. It shows how much d32 at different μd is affected by
the power input to the system. Therefore the change in d32 is
bigger as N is increased at high viscosity, as explained in the
previous section. A model was developed to represent the three
scale-up correlations in a single equation by adding viscosity
number Vi:
Figure 4. Graph d32 vs impeller speed.
bigger compared to that for low viscosity. On the basis of the
findings, the changes in drop breakup rates are varied at
different viscosities.
Different values of the slopes can be explained by the
influence of drop diameter on drop breakup rate. The breakup
of two drop diameters was investigated by Hermann et al.4and
Maaß et al.40 by using computational fluid dynamics (CFD). It
was observed that a smaller drop is more stable than a larger
drop. The region of drop breakup is larger for a bigger drop
diameter leading to an increase in drop breakup probabilities.
Since low viscosity produced smaller d32 in this study, the drops
were more stable and the change in d32 was smaller as the
impeller speed increased, as shown in Figure 3. Besides,
d32
= 0.000014[1 + 1.428(εT ND2)−0.7 ]Vi 0.27
(12)
D
The predicted d32 data obtained from eq 12 was plotted
against the experimental data as shown in Figure 6. It can be
observed that reasonably good fits were achieved for μd = 20
and 350 mPas and there was little scattering for 500 mPas.
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Although the d32 model (eq 13) is able to give reasonably
good estimation of d32 at different impeller speed and dispersed
phase viscosity, the deviations between the predicted and
experimental values at high impeller speed are quite significant
(see Figure 7). Thus, another correlation relating d32 to μd and
impeller speed has been developed. In this model, viscosity
number Vi is used instead of viscosity ratio to represent the
effects of dispersed phase viscosity. Since there are small
differences in the interfacial tension values at different μd, the
use of viscosity number may be more suitable as it represents
the ratio of viscous to surface forces.25 The proposed model is
d32
= 1.588(1 + 0.0227Vi1.4)We−1.05
(14)
D
The comparison between the predicted and experimental d32
is shown in Figure 8. As seen in Figure 8, the predicted d32
Figure 6. d32/D experimental vs d32/D predicted.
4.6. Mean Drop Size Correlations. The correlation of d32
was developed as a function of We and viscosity ratio, μd/μc to
represent the effects of dispersed phase viscosity. The exponent
of We and other constants were determined by linear
regression. The data are best correlated by the following
equation
⎡
⎛ μ ⎞0.9⎤
d32
⎢
= 0.285 1 + 0.0035⎜⎜ d ⎟⎟ ⎥We−0.83
⎢
D
⎝ μc ⎠ ⎥⎦
⎣
(13)
In eq 13, the value of the We exponent is −0.83, which is
slightly smaller but quite close to the value in the theoretical
relation (−0.6). An almost similar value of We exponent
(−0.85) was obtained by Singh et al.18 in their model which
related d32 to dispersed phase fraction, ϕ. Figure 7 shows that
eq 13 gives good prediction of d32 at low μd where almost all
the points are in the range of less than 10% deviation from the
experimental d32 values. The overall percentage of similarity
between experimental and predicted d32 by eq 13 is 92.25%.
Figure 8. d32/D experimental vs d32/D predicted.
values by eq 14 are in good agreement with the experimental
d32 values. The points for μd = 500 mPas are nearer to the 10%
line, which means that the deviations between the predicted
experimental d32 at high μd are reduced. Therefore, the model
(eq 14) gives better d32 estimation compared to eq 13 at high
μd. It also shows that the use of viscosity number Vi as a
parameter to represent the effects of dispersed phase viscosity
on mean drop size is more suitable at high μd compared to
viscosity ratio only.
In eq 14, the value of the We exponent (−1.05) is smaller
than the value in the theoretical relation (−0.6). The value
obtained in the model deviates from the theoretical model
because the model developed in this work covers high viscosity
dispersed phase while the theoretical relation only applies at
low viscosity. Although eq 13 gives better accuracy at low μd, a
higher percentage of similarity (95.5%) between the predicted
and experimental d32 was achieved by eq 14 for the ranges of μd
investigated in this work. Both correlations developed in this
work show that the predicted d32 correlated well with the
experimental d32 with slight scatters for 500 mPas points. At
high μd, it can be observed that both correlations underpredicted d32 values where the deviations between the predicted
and experimental d32 values were quite significant. Similar
observations were reported at this μd value by Wang et al.25 and
Figure 7. d32/D experimental vs d32/D predicted.
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Calabrese et al.,29 where their models showed scattering of d32
values at μd ≥ 500 mPas. The authors explained that this
behavior might be caused by different nature of the silicone oil
where the oil tends to change its nature from Newtonian to
viscoelastic at high viscosity. Therefore, the use of a single
model to represent the d32 data from low to high μd might not
be suitable because of different mechanisms in the model.
ρd = dispersed phase density (kg/m3)
μc = continuous phase viscosity (mPas)
ϕ = dispersed phase fraction (dimensionless)
εT = mean energy dissipation rate per unit mass (m2/s3)
μd = dispersed phase viscosity (mPas)
■
5.0. CONCLUSIONS
The drop size distribution for dispersion of moderate to high
dispersed phase viscosity was presented at different impeller
speeds. Smaller drop sizes with higher uniformity were
produced at low dispersed phase viscosity and high impeller
speed. Since the silicone oils used in the study exhibited almost
constant interfacial tension, the change in d32 at different
dispersed phase viscosity showed the contribution of viscous
force on the stabilization of drops against breakup.
The data showed that the theoretical value of the We
exponent (−0.6) was slightly modified at a higher dispersed
phase fraction as the theoretical value is only valid for dilute
and inviscid systems.
Although decrease in d32 as the impeller speed increased was
observed for all μd, the percentage of d32 decrement was
different. It shows that the drop breakup mechanism is varied at
different viscosities, proving that the mean drop size is also
influenced by the size and number of daughter droplets formed
after a drop breakup.
Scale-up models based on εT and mean flows were developed
at different μd which fit reasonably well into individual models.
Therefore, it is agreed that both parameters should be used
together in a d32 scale-up model. Two d32 correlations were
proposed on the basis of the framework of the classical relation
with the addition of μd/μc and Vi as parameters to represent the
effects of dispersed phase viscosity. The predicted d32 values by
both correlations correlated well with the experimental d32
values with slight scatters at high μd. The accuracy of both
correlations were higher than 90%.
■
REFERENCES
(1) Podgórska, W. Modelling of High Viscosity Oil Drop Breakage
Process in Intermittent Turbulence. Chem. Eng. Sci. 2006, 61 (9),
2986−2993, DOI: 10.1016/j.ces.2005.10.048.
(2) Eastwood, C. D.; Armi, L.; Lasheras, J. C. The Breakup of
Immiscible Fluids in Turbulent Flows. J. Fluid Mech. 2004, 502, 309−
333, DOI: 10.1017/s0022112003007730.
(3) Maaß, S.; Paul, N.; Kraume, M. Influence of The Dispersed Phase
Fraction on Experimental and Predicted Drop Size Distributions in
Breakage Dominated Stirred Systems. Chem. Eng. Sci. 2012, 76, 140−
153, DOI: 10.1016/j.ces.2012.03.050.
(4) Hermann, S.; Maaß, S.; Zedel, D.; Walle, A.; Schafer, M.; Kraume,
M. Experimental and Numerical Investigations of Drop Breakage
Mechanism. 1st International Symposium on Multiscale Multiphase
Process Engineering (MMPE), Kanazawa, Japan, 4−7 October 2011.
(5) Leng, D. E.; Calabrese, R. V.Immiscible Liquid−Liquid Systems.
In Handbook of Industrial Mixing: Science and Practice; Paul, E. L.,
Atiemo-Obeng, V. A., Kresta, S. M., Eds.; John Wiley and Sons: NJ,
2004; pp 639−696.
(6) Pacek, A. W.; Chamsart, S.; Nienow, A. W.; Bakker, A. The
Influence of Impeller Type on Mean Drop Size and Drop Size
Distribution in an Agitated Vessel. Chem. Eng. Sci. 1999, 54, 4211−
4222, DOI: 10.1016/S0009-2509(99)00156-6.
(7) Liu, S.; Li, D. Drop Coalescence in Turbulent Dispersions. Chem.
Eng. Sci. 1999, 54, 5667−5675, DOI: 10.1016/S0009-2509(99)001001.
(8) Chatzi, E. G.; Boutris, C. J.; Kiparissides, C. On-Line Monitoring
of Drop Size Distributions in Agitated Vessels. 1. Effects of
Temperature and Impeller Speed. Ind. Eng. Chem. Res. 1991, 30,
536−543, DOI: 10.1021/ie00051a015.
(9) Podgórska, W., Influence of the impeller type on drop size in
liquid−liquid dispersions. In 13th European Conference on Mixing,
London, April 14−17, 2009.
(10) Desnoyer, C.; Masbernat, O.; Gourdon, C. Experimental Study
of Drop Size Distributions at High Phase Ratio in Liquid−Liquid
Dispersions. Chem. Eng. Sci. 2003, 58 (7), 1353−1363, DOI: 10.1016/
s0009-2509(02)00461-x.
(11) Quadros, P. A.; Baptista, C. M. S. G. Effective interfacial area in
agitated liquid−liquid continuous reactors. Chem. Eng. Sci. 2003, 58
(17), 3935−3945, DOI: 10.1016/s0009-2509(03)00302-6.
(12) Giapos, A.; Pachatouridis, C.; Stamatoudis, M. Effect of the
Number of Impeller Blades on the Drop Sizes in Agitated Dispersions.
Chem. Eng. Res. Des. 2005, 83 (12), 1425−1430, DOI: 10.1205/
cherd.04167.
(13) Chen, H. T.; Middleman, S. Drop size distribution in agitated
Liquid−Liquid Systems. AIChE. J. 1967, 13, 989 DOI: 10.1002/
aic.690130529.
(14) Khakpay, A.; Abolghasemi, H. The Effects of Impeller Speed
and Holdup on Mean Drop Size in a Mixer Settler with Spiral-type
Impeller. Can. J. Chem. Eng. 2010, 88 (3), 329−334, DOI: 10.1002/
cjce.20287.
(15) Shinnar, R. On The Behaviour of Liquid Dispersions in Mixing
Vessels. J. Fluid Mech. 1961, 10, 259−275, DOI: 10.1017/
S0022112061000214.
(16) Zhou, G.; Kresta, S. M. Correlation of Mean Drop Size and
Minimum Drop Size With The Turbulence Energy Dissipation and
The Flow in an Agitated Tank. Chem. Eng. Sci. 1997, 53 (11), 2063−
2079, DOI: 10.1016/S0009-2509(97)00438-7.
(17) Calabrese, R. V.; Wang, C. Y.; Bryner, N. P. Drop Breakup in
Stirred-Tank Contactors, Part III: Correlation for Mean Size and Drop
Size Distributions. AIChE J. 1986, 32, 677−681, DOI: 10.1002/
aic.690320418.
AUTHOR INFORMATION
Corresponding Author
*Tel.: 603-79675300. E-mail: [email protected].
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
The authors are grateful to the University of Malaya High
Impact Research Grant (HIR-MOHE-D000038-16001) from
the Ministry of Higher Education Malaysia which financially
supported this work.
■
NOMENCLATURE
d32 = Sauter mean diameter (μm)
dmax = maximum stable diameter (μm)
D = impeller diameter (m)
N = impeller rotational speed, (1/s)
P = power consumption (kgm2/s3)
VT = volume of liquid in the tank(m3)
Vi = viscosity number, (ρc/ρd)0.5(μdND/σ), (dimensionless)
We = Weber number, ρcN2D3/σ, (dimensionless)
Greek letters
σ = interfacial tension (kg/s2)
ρc = continuous phase density (kg/m3)
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Industrial & Engineering Chemistry Research
Article
(18) Singh, K. K.; Mahajani, S. M.; Shenoy, K. T.; Ghosh, S. K.
Representative Drop Sizes and Drop Size Distributions in A/O
Dispersions in Continuous Flow Stirred Tank. Hydrometallurgy 2008,
90 (2), 121−136, DOI: 10.1016/j.hydromet.2007.10.003.
(19) Chatzi, E. G.; Boutris, C. J.; Kiparissides, C. On-Line
Monitoring of Drop Size Distributions in Agitated Vessels: 2. Effect
of Stabilizer Concentration. Ind. Eng. Chem. Res. 1991, 30, 1307−1313,
DOI: 10.1021/ie00054a035.
(20) Angle, C. W.; Hamza, H. A. Predicting the Sizes of TolueneDiluted Heavy Oil Emulsions in Turbulent Flow Part 2: Hinze−
Kolmogorov Based Model Adapted for Increased Oil Fractions and
Energy Dissipation in a Stirred Tank. Chem. Eng. Sci. 2006, 61 (22),
7325−7335, DOI: 10.1016/j.ces.2006.01.014.
(21) Pacek, A. W.; Man, C. C.; Nienow, A. W. On the Sauter Mean
Diameter and Size Distributions in Turbulent Liquid−Liquid
Dispersions in a Stirred Vessel. Chem. Eng. Sci. 1998, 53 (11),
2005−2011, DOI: 10.1016/S0009-2509(98)00068-2.
(22) Lovick, J.; Mouza, A. A.; Paras, S. V.; Lye, G. J.; Angeli, P. Drop
Size Distribution in Highly Concentrated Liquid−Liquid Dispersions
Using a Light Back Scattering Method. J. Chem. Technol. Biot. 2005, 80
(5), 545−552, DOI: 10.1002/jctb.1205.
(23) Baldyga, J.; Bourne, J. R.; Pacek, A. W.; Amanullah, A.; Nienow,
A. W. Effects of Agitation and Scale-up on Drop Size in Turbulent
Dispersions: Allowance for Intermittency. Chem. Eng. Sci. 2001, 56,
3377−3385, DOI: 10.1016/S0009-2509(01)00027-6.
(24) Razzaghi, K.; Shahraki, F. On the Effect of Phase Fraction on
Drop Size Distribution of Liquid−liquid Dispersions in Agitated
Vessels. Chem. Eng. Res. Des. 2010, 88 (7), 803−808, DOI: 10.1016/
j.cherd.2009.12.002.
(25) Wang, C. Y.; Calabrese, R. V. Drop Breakup in Stirred-Tank
Contactors Part II: Relative Influence of Viscosity and Interfacial
Tension. AIChE J. 1986, 32 (4), 667−676, DOI: 10.1002/
aic.690320417.
(26) Angle, C. W.; Hamza, H. A. Drop Sizes During Turbulent
Mixing of Toluene−Heavy Oil Fractions in Water. AIChE J. 2006, 52
(7), 2639−2650, DOI: 10.1002/aic.10862.
(27) Andersson, R.; Andersson, B. On The Breakup of Fluid Particles
in Turbulent Flows. AIChE J. 2006, 52 (6), 2020−2030,
DOI: 10.1002/aic.10831.
(28) Stamatoudis, M.; Tavlarides, L. L. Effect of Continuous-Phase
Viscosity on the Drop Sizes of Liquid−Liquid Dispersions in Agitated
Vessels. Ind. Eng. Chem. Res. 1985, 24, 1175−1181, DOI: 10.1021/
i200031a047.
(29) Calabrese, R. V.; Chang, T. P. K.; Dang, P. T. Drop Breakup in
Turbulent Stirred Tank Contactor: Part 1: Effect of Dispersed Phase
Viscosity. AIChE J. 1986, 32 (4), 657−666, DOI: 10.1002/
aic.690320416.
(30) El-Hamouz, A.; Cooke, M.; Kowalski, A.; Sharratt, P. Dispersion
of Silicone Oil in Water Surfactant Solution: Effect of Impeller Speed,
Oil Viscosity and Addition Point on Drop Size Distribution. Chem.
Eng. Process. Process Intensif. 2009, 48 (2), 633−642, DOI: 10.1016/
j.cep.2008.07.008.
(31) Briceño, M.; Salager, J. L.; Bertrand, J. Influence of Dispersed
Phase Content and Viscosity on the Mixing of Concentrated Oil-inWater Emulsions in the Transition Flow Regime. Chem. Eng. Res. Des.
2001, 79 (8), 943−948, DOI: 10.1205/02638760152721794.
(32) Tobin, T.; Muradlihar, R.; Wright, H.; Ramkrishna, D.
Determination of Coalescence Frequencies in Liquid−Liquid Dispersions: Effect of Drop Size Dependence. Chem. Eng. Sci. 1990, 45
(12), 3491−3504, DOI: 10.1016/0009-2509(90)87154-K.
(33) Zainal Abidin, M. I. I.; Abdul Raman, A. A.; Mohamad Nor, M.
I. Review on Measurement Techniques for Drop Size Distribution in a
Stirred Vessel. Ind. Eng. Chem. Res. 2013, 52 (46), 16085−16094,
DOI: 10.1021/ie401548z.
(34) Li, M.; White, G.; Wilkinson, D.; Roberts, K. J. Scale up Study of
Retreat Curve Impeller Stirred Tanks Using LDA Measurements and
CFD Simulation. Chem. Eng. J. 2005, 108 (1−2), 81−90,
DOI: 10.1080/02726350590955912.
(35) El-Hamouz, A. Effect of Surfactant Concentration and
Operating Temperature on the Drop Size Distribution of Silicon Oil
Water Dispersion. J. Disper. Sci. Technol. 2007, 28 (5), 797−804,
DOI: 10.1080/01932690701345893.
(36) Jahanzad, F.; Sajjadi, S.; Brooks, B. W. Comparative Study of
Particle Size in Suspension Polymerization and Corresponding
Monomer-Water Dispersion. Ind. Eng. Chem. Res. 2005, 44, 4112−
4119, DOI: 10.1021/ie048827f.
(37) Hashim, S.; Brooks, B. W. Drop Mixing in Suspension
Polymerisation. Chem. Eng. Sci. 2002, 57, 3703−3714,
DOI: 10.1016/S0009-2509(02)00242-7.
(38) Roberts, R.; Gray, M.; Thompson, B.; Kresta, S. The Effects of
Impeller and Tank Geometry of Circulatory Time Distributions in
Stirred Tanks. Trans. I Chem. E. 1995, 73, 512−518.
(39) Witchterle, K. Drop Breakup by Impellers. Chem. Eng. Sci. 1995,
50 (22), 3581−3586, DOI: 10.1016/0009-2509(95)00208-M.
(40) Maaß, S.; Wollny, S.; Sperling, R.; Kraume, M. Numerical and
Experimental Analysis of Particle Strain and Breakage in Turbulent
Dispersions. Chem. Eng. Res. Des. 2009, 87 (4), 565−572,
DOI: 10.1016/j.cherd.2009.01.002.
(41) Sechremeli, D.; Stampouli, A.; Stamatoudis, M. Comparison of
Mean Drop Sizes and Drop Size Distributions in Agitated Liquid−
Liquid Dispersions Produced by Disk and Open Type Impellers.
Chem. Eng. J. 2006, 117 (2), 117−122, DOI: 10.1016/
j.cej.2005.12.015.
6561
dx.doi.org/10.1021/ie5002845 | Ind. Eng. Chem. Res. 2014, 53, 6554−6561