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LIQUID-LIQUID MIXING IN STIRRED
VESSELS: A REVIEW
a
a
b
Reza Afshar Ghotli , Abdul A. A. Raman , Shaliza Ibrahim &
Saeid Baroutian
c
a
Department of Chemical Engineering, Faculty of Engineering ,
University of Malaya , Kuala Lumpur , Malaysia
b
Department of Civil Engineering, Faculty of Engineering ,
University of Malaya , Kuala Lumpur , Malaysia
c
SCION , Rotorua , New Zealand
Published online: 30 Jan 2013.
To cite this article: Reza Afshar Ghotli , Abdul A. A. Raman , Shaliza Ibrahim & Saeid Baroutian (2013)
LIQUID-LIQUID MIXING IN STIRRED VESSELS: A REVIEW, Chemical Engineering Communications, 200:5,
595-627, DOI: 10.1080/00986445.2012.717313
To link to this article: http://dx.doi.org/10.1080/00986445.2012.717313
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Chem. Eng. Comm., 200:595–627, 2013
Copyright # Taylor & Francis Group, LLC
ISSN: 0098-6445 print=1563-5201 online
DOI: 10.1080/00986445.2012.717313
Liquid-Liquid Mixing in Stirred Vessels: A Review
REZA AFSHAR GHOTLI,1 ABDUL A. A. RAMAN,1
SHALIZA IBRAHIM,2 AND SAEID BAROUTIAN3
Downloaded by [University of Malaya] at 08:19 02 January 2014
1
Department of Chemical Engineering, Faculty of Engineering,
University of Malaya, Kuala Lumpur, Malaysia
2
Department of Civil Engineering, Faculty of Engineering,
University of Malaya, Kuala Lumpur, Malaysia
3
SCION, Rotorua, New Zealand
Liquid-liquid mixing is a key process in industries that is commonly accomplished in
mechanical agitation systems. Liquid-liquid mixing performance in a stirred tank
can be evaluated by various parameters, namely minimum agitation speed, mixing
time, circulation time, power consumption, drop size distribution, breakup and
coalescence, interfacial area, and phase inversion. The importance of these
liquid-liquid mixing parameters, the measurement method, and the results are discussed briefly. Input parameters such as impeller type, power number, flow pattern,
number of impellers, and dispersed phase volume fraction, in addition to physical
properties of phases such as viscosity and density, are reviewed. Scale-up aspects
are also included.
Keywords Impellers; Liquid-liquid dispersion; Mixing performance; Stirred vessel
Introduction
Mixing is a key and common process to improve homogeneity and uniformity of systems. Mixing occurs when materials are moved from one area to another in a vessel
(Chen et al., 2005; Rushton, 1956). Nonuniformity of systems can be explained as a
gradient of properties such as concentration, viscosity, temperature, color, concentration, phase, and temperature (Paul et al., 2004). Mixing operations can be divided
into three main categories, gas-liquid, solid-liquid, and liquid-liquid mixing, the latter
of which is the main focus of the present review. Liquid-liquid mixing plays an important role in producing and increasing essential interfacial area to improve mass and
heat transfer between phases (O’Rourke and MacLoughlin, 2005; Paul et al., 2004).
Liquid-liquid mixing is divided into miscible and immiscible liquid-liquid mixing
(van de Vusse, 1955). The term ‘‘blending’’ is used to describe miscible liquid mixing,
while the term ‘‘mixing’’ is used for dispersions of immiscible liquids or the formation of emulsions (Jakobsen, 2008; Rushton, 1956). The dispersion of immiscible
liquids is used to mix water and hydrocarbons and acidic or alkaline solutions
combined with organic liquids (Coker, 2001) and produce various types of emulsion
Address correspondence to Abdul A. A. Raman, Department of Chemical Engineering,
Faculty of Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia. E-mail:
[email protected]
595
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596
R. Afshar Ghotli et al.
products (Jakobsen, 2008). Liquid-liquid mixing is applicable for special process
objectives such as solvent extraction and removal or addition of heat (Paul et al.,
2004). The fluid dynamic characteristics of liquid-liquid mixing produces several
phenomena such as drop breakup and coalescence (Wichterle, 1995; Wang and
Calabrese, 1986; Sathyagal et al., 1996), mean flow pattern and turbulence (Ibrahim
and Nienow, 1995; Norwood and Metzner, 1960), drop suspension, interfacial area,
and drop size distribution (DSD) (Podgorska and Baldyga, 2001; Fernandes and
Sharma, 1967), possible phase inversion (Norato et al., 1998), and the influence of
system composition as well as of small amounts of impurities (Laurenzi et al.,
2009). These phenomena are complicated and cause liquid-liquid dispersion to be
one of the most difficult processes in a number of industries. On the other hand,
blending of miscible liquid is a very simple operation that is achieved by two mutually soluble liquids in the absence of resistivity to dissolution at the fluid interface
(Paul et al., 2004). Generally, blending of miscible liquids happens slowly by molecular diffusion and natural convection. Thus, agitation systems can apply forced
convection to obtain homogeneity more rapidly (Rushton, 1956).
Tanks and vessels are the most accessible and universal equipment used in a wide
range of process industries such as esterification and hydrolysis (Paul et al., 2004).
Because natural diffusion in liquids is slow, agitators that provide high shear and
good pumping capacity are common choices for liquid-liquid dispersion and emulsification because they improve diffusivity. Nevertheless, it is possible to waste large
amounts of input energy through inappropriate system selection (Holland and Bragg,
1995). Furthermore, inadequate understanding of mixing could result in undesirable
product quality and increased production costs. Mixing operations are often complex. They not only require understanding the fluid flow aspects, but also consideration of the mechanical equipment and power requirements (Chen et al., 2005).
Parameters That Define Liquid-Liquid Mixing Performance
Mixing Time
Mixing time is one of the most significant parameters in liquid-liquid mixing and
scale-up because it is also the time required to obtain a defined degree of uniformity
(Montante et al., 2005; Jakobsen, 2008). It is the time required to achieve desirable
mixing and homogeneity throughout the tank. Impeller speed, the diameter of the
vessels and impellers, the number and placement of baffles, and fluid characteristics
such as viscosity are the effective parameters for determining mixing time (Jakobsen,
2008; Doran, 1995).
Several mixing time correlations have already been developed to estimate and
compute the mixing time in different standard-baffled mixing vessels and with various types of impellers such as Rushton turbines, pitched blades, and propellers
(Coker, 2001). There are, however, some limitations to the wide application of these
correlations. Most of these equations are based on experiments with standard tank
geometries and a single impeller. Consequently, they are not useful for
multiple-impeller systems. Furthermore, comparison of the different research results
is not a simple task because such factors as measurement and experimental methods,
tank and impeller geometry, location of tracer injection, and detection method vary
widely from study to study (Jahoda et al., 2007). Nere et al. (2003) did an expanded
review of mixing time correlations and divided them into five categories: (i) models
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Liquid-Liquid Mixing in Stirred Vessels
597
based on experimental data with various design and operating parameters; drawbacks of these models are due to limited application and not being reliable for other
systems, especially in scale-up; (ii) models based on bulk flow, which assumes that
the process is controlled by the bulk or convective flow; (iii) models based on dispersion; (iv) models that segregate the whole stirred vessel into a network of interconnected zones; and (v) CFD models. Drawbacks and effectiveness of these models are
extensively discussed by Nere et al. (2003).
Several methods such as the decolorization reaction of iodine and sodium thiosulfate in water (Nomura et al., 1997; Yao et al., 1998; Hiraoka et al., 2001; Kato
et al., 2005), electrical conductivity probes (Kramers et al., 1953; Biggs, 1963;
Wesselingh, 1975; Kumaresan et al., 2005; Woziwodzki, 2011), temperature pulse
(Mayr et al., 1992: Karcz et al., 2005; Szoplik and Karcz, 2005; Slemenik Perse
and Žumer, 2001), planar laser-induced fluorescence (PLIF) (Alvarez et al., 2002;
Crimaldi, 2008; Zadghaffari et al., 2009), particle image velocimetry (PIV) (Zalc
et al., 2001; Alvarez et al., 2005), acid-base neutralization reaction (Rice et al.,
1964; Norwood and Metzner, 1960; Lamberto et al., 1996; Szalai et al., 2004;
Woziwodzki and Je˛drzejczak, 2011), and electrical resistance tomography (ERT)
(Pakzad et al., 2008) have been used for mixing time determination. Mixing time
may vary for each technique as a result of the variety of homogeneity degree measurements (Coker, 2001). Commonly, these methods are based on visual observation. A small amount of tracer is added to the bulk fluid and is monitored.
Various types of tracers, principally hot water (Hoogendoorn and den Hartog,
1967; Mayr et al., 1992; Karcz et al., 2005), sodium chloride solution (Kumaresan
et al., 2005; Woziwodzki et al., 2010), or fluorescent dye (rhodamine) (Alvarez
et al., 2002, 2005; Szalai et al., 2004; Hu et al., 2010), have been employed for determination of mixing time. The radioactive tracer technique was suggested as a good
alternative by Nere et al. (2003) due to its nonintrusiveness and ability to be used
with nontransparent vessels. Very frequently, results differ considerably because of
the number and location of probes used to take samples as well as tracer injection
time and location (Lamberto et al., 1999).
In addition, various parameters, such as impeller design, impeller diameter, tank
diameter, impeller clearance, impeller eccentricity, baffles, and presence of a draft
tube can affect mixing time. Van de Vusse et al. (1955) demonstrated that at low stirrer speeds baffling has little effect on mixing time. Kumaresan et al. (2005) observed
that an increase in the number of baffles causes a slight reduction in mixing time.
They also presented evidence of a considerable reduction in mixing time, even up
to 60%, for a hydrofoil impeller surrounded by a long draft tube compared to a
pitched-blade impeller. Ochieng et al. (2008) also reported 50% reduction in mixing
time using a draft tube with a single Rushton turbine with only a small clearance
between the impeller and the tank bottom. They used two conductivity and decolorization methods. Their results showed 35% reduction in mixing time at low impeller
clearance in comparison with the standard configuration. The comparison of mixing
time for pitched-blade turbines (down flow (PTD) and up flow (PTU)) with that for
a disk turbine by Rewatkar and Joshi (1991) indicated that the pitched-blade turbines are more energy efficient than the disk turbine. Better performance of the
pitched-blade turbines was explained on the basis of the flow pattern produced by
these impellers. Increasing the impeller diameter causes a reduction in mixing time
values. Increasing the impeller diameter results in larger average circulation velocity,
and thus causes a decrease in the mixing time value. Patwardhan and Joshi (1999)
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598
R. Afshar Ghotli et al.
also determined the mixing time for around 40 axial-flow impellers. The impellers
were varied in angle, twist, width, diameter, location, and pumping direction. The
changes in blade angle showed that use of impellers with a blade angle of 50 resulted
in the shortest mixing time. Mixing time decreased with each incremental increase in
impeller blade width. They also observed that an increase in the ratio of impeller
diameter (D) to tank diameter (T) up to D=T ¼ 1=2 for a pitched-blade turbine
(PBTD 45) impeller at impeller clearance (C) ¼ T=3 caused the mixing time to
decrease. However, if the D=T ratio is increased beyond D=T ¼ 1=2, mixing time
tends to begin increasing. Further results showed that mixing time increased with
clearance reduction. Determination of mixing time by Zhao et al. (2011) in a kerosene and water system indicated an increase in mixing time with a pitched-blade turbine PTU impeller. The PTU transfers the flow upward, and as kerosene is lighter
than water it thus tends to coalesce and stay on the surface, resulting in poor dispersion of the oil and increasing mixing time. Furthermore, the experimental data indicated a reduction in mixing time by decreasing the impeller clearance in the range of
T=3 to T=6. Investigation of mixing time for miscible liquids in batch operation by
van de Vusse et al. (1955) showed that in the turbulent flow region, mixing time is
directly related to impeller pumping capacity.
Impeller clearance reduction and use of a draft tube decrease mixing time and
result in better mixing (Ochieng and Onyango, 2008). The axial mixing improves
at low clearance because of interaction between the flow stream and the bottom wall,
which produces a one-loop flow pattern (Montante et al., 2001). Enhancement of
axial velocity and the one-loop flow pattern causes the transfer rate of the tracer
through the tank to intensify from the bottom to the top area. Subsequently,
reduction in mixing time results in better mixing (Ochieng and Onyango, 2008).
The review showed that mixing time is strongly affected by any changes in geometrical ratio such as D=T and C=T and impeller design.
Circulation Time
Evaluation of the mean bulk fluid motion produced by the pumping of liquid with
impellers in mixing vessels is done by circulation time. Determination of circulation
and mixing times are helpful in recognizing the scalar transport in a tank. The mean
circulation time describes an average value for all the fluid components in the vessel
and also indicates how fast the bulk fluids are transported through a tank. On the
other hand, mixing time determines the time at which the whole of the tank is perfectly mixed or when the system reaches uniformity. Generally, the mean circulation
time is significantly shorter than mixing time in a tank (Jakobsen, 2008). For example,
mixing time for a single-phase liquid in a stirred vessel is approximately four times the
circulation time (Doran, 1995; Nienow, 1997). The evaluation of mixing time and circulation time performed by Partwardhan and Joshi (1999) also revealed that the mixing time for a 45 -pitch down-flow blade impeller (PBTD45) is slightly more than
three times the circulation time. Circulation time is related to the total volumetric flow
rate and entrainment flow of the tank and the pumping capacity of the impeller, and is
defined by the following assumption (Jakobsen, 2008):
hC ¼
V
Q
ð1Þ
Liquid-Liquid Mixing in Stirred Vessels
599
Pacek et al. (1999) reported that for the same impeller diameter and energy dissipation rates, mixing systems with low power numbers produced smaller drop size.
Because use of the lower power number impellers results in shorter circulation time;
the drops move to the impeller vicinity more often.
Several correlations have been developed for different systems and impellers.
For example, the model recommended by Calabrese (1997) and Smit (1994) illustrated that the time to obtain equilibrium is dependent on how frequently the drops
pass through the impeller area. Nienow (1990, 1997) suggested a simple correlation
to evaluate the circulation time, hc:
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hC ¼
V
FIND3
ð2Þ
Another model can be found in works by Roberts et al. (1995), Paul et al. (2004),
and Patwardhan and Joshi (1999). Several approaches have been recommended to
model the blending process. These approaches can be classified as circulation models, eddy diffusion models, network of zones models, and computational fluid
dynamics (CFD) models (Patwardhan and Joshi, 1999).
Several techniques have been used to estimate the circulation number, tc.
Chavan and Ulbrecht (1973) used the measurement-of-pressure-loss technique.
Measurement of average axial velocity along the radius of the tank was used by
Seichter (1981). The thermal technique and the conductivity method were also used
by Nienow (1990) and Delaplace et al. (2000).
Minimum Agitation Speed
Ensuring that the agitation speed is high enough to gain complete liquid-liquid dispersion is essential. Therefore, determination of minimum agitation speed, Nmin,
becomes significant in mixing vessels. For example, Skelland and Seksaria (1978)
reported that an impeller speed of even 1000 rpm is insufficient for complete dispersion. Hu et al. (2006) revealed that increasing the agitation speed causes phase inversion. The speed at which the dispersed phase becomes completely unified with the
bulk of fluid has been defined as minimum agitation speed (Armenante and Huang,
1992). Skelland and Sekasaria (1978) also showed the dependency of the minimum
agitation speed on interfacial tension.
Skelland and Lee (1978) collected samples from various points within the tank
and evaluated the mixing index in terms of the modified average of sample concentration. The average was correlated with the minimum agitation speed required for
complete dispersion calculated from the mixing index (Armenante and Huang,
1992). Godfrey et al. (1984) indicated 5% reproducibility for their visual technique
results. But visual methods have some disadvantages, such as the influence of investigator bias and faults and the difficulty of obtaining the minimum agitation speed,
Nmin, when the dispersed phase is heavier than the continuous phase (Armenante
and Huang, 1992). Armenante and Huang (1992) took samples from the vessel to
determine the volume fraction of the dispersed phase and plotted these data against
agitation speed to evaluate the minimum agitation speed for complete dispersion of
two immiscible liquids in a mixing tank. Their results were in good agreement with
the previous work by Skelland and Lee (1978) for liquid-liquid systems.
600
R. Afshar Ghotli et al.
In addition to experimental methods, a number of studies have suggested correlations for different types of impellers to predict minimum agitation speed (Nagata,
1950; Skelland and Ramsay, 1986; Skelland and Lee, 1978; Skelland and Seksaria,
1978; Armenante et al., 1992; Hobler and Palugniok, 1970). Table I shows some
of these equations. Skelland and Seksaria (1978) established minimum agitation
speed correlations for different types of impellers in baffled vessels. Regardless of
uniformity, impeller speed for complete dispersion was defined as:
1=9
Nmin ¼ C0 Da0 l1=9
c ld
r0:3 Dq0:25
ð3Þ
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where Co and a0 depend on impeller types and their locations. The following equation was also obtained from dimensional analysis:
a1 1=9 0:25 0:3
D1=2 N
T
lc
Dq
r
¼
C
1
D
qc
D2 qc g
ld
g1=2
ð4Þ
where C1 ¼ Chbsckd and a1 ¼ a þ c þ b. h, s, and b are constant and ratio of W=D,
H=T, and B=T, respectively; a1 was calculated from a0 in Equation (3) as a1 ¼ a0
1.1, and C1 was found experimentally for different types of impellers and locations
(Skelland and Seksaria, 1978).
Skelland and Ramsay (1986) developed Equation (3) to:
Nmin
a 0:42 0:42 0:08 0:04 0:05
T g Dq lM r /
¼C
D
D0:71 q0:54
M
ð5Þ
Later, Skelland and Moeti (1989) showed the suitability of Equation (5) for
evaluating the minimum agitation speed for a system with reduced interfacial tension
because of nonionic, anionic, and cationic surfactants. Furthermore, Skelland and
Kanel (1990) noted that Equation (5) was also appropriate for a system with a continuous phase of pseudoplastic fluid and a dispersed phase of Newtonian fluid.
Skelland and Ramsay (1986) also expressed the following for minimum agitation
speed for complete dispersion:
ðFrÞmin ¼ C 2
2a
T
/0:106 ðGa:BoÞ0:084
D
ð6Þ
A comparison of different equations with experimental data by Kamil et al.
(2001) indicated that the best prediction of minimum impeller speed for liquid-liquid
systems could be achieved from Equation (6) above. But, Paul et al. (2004) recommended Equation (4) in the absence of direct experimental data. They believed that
it expresses more specific impeller arrangements than the other reported works.
Due to the dependency of empirical correlations on laboratory-scale measurements, the extension to industrial-scale stirred tanks is unreliable and may cause
incorrect predictions. Thus, it is necessary to use numerical simulation techniques
to be able to eliminate scale-up and scale-down problems (Cheng et al., 2011).
Several attempts have done to predict the minimum agitation speed for complete
dispersion through liquid-liquid mixing (Wang and Mao, 2005; Laurenzi et al., 2009;
Abu-Farah et al., 2010). Recently, Cheng et al. (2011) also suggested reproducible
601
Cylindrical, flat-bottomed
vessel, D=T ¼ 1=2–1=4
Unbaffled squared vessel,
D=T ¼ 1=3
Cylindrical flat-bottomed
vessels, 0.26 D=T 0.47
Skelland and
Seksaria, 1978
Godfrey et al.,
1984
Skelland and
Ramsay, 1986
6-flat-blade turbine
Propellers Pitched-blade
turbine Flat-blade turbines
Curved-blade turbine
6-blade disk turbine
6-blade disk turbine
6-blade disk turbine
Baffled vessel, D=T ¼ 1=3
Baffled vessel, D=T ¼ 1=3
6-blade disk turbine
4-flat-blade turbine
Impeller type
Unbaffled, flat-bottom
vessel, D=T ¼ 1=3
Baffled vessel, D=T ¼ 12–1=4
Tank geometry
van Heuven and
Beek, 1971
Hobler and
Palugniok,
1970
Esch et al., 1971
Nagata, 1950
Author
lc
qc
Nmin ¼ C
Nmin
L
qc rD
l2c
D
0:14 0:33
gqc DqrD3
l2c
D
M
D0:71 q0:54
M
T a g0:42 Dq0:42 l0:08 r0:04 /0:05
lc
¼k
qc D2
r Dq0:25
1=9 1=9 0:3
Nmin ¼ C0 Da 0 lc ld
Nmin
Nmin
D
T 0:633 D 0:964 C 0:116
lc
qc rgc D 0:39
¼ 119
l2c
qc D2
0:38
0:38 0:08 0:08
3:28g Dq lc r ð1 þ 2:5/Þ0:9
¼
D0:77 q0:54
M
lc
D 2 qc
Dq
qc
Equation
1=9 0:26
Nmin ¼ 2:075 105
Nmin ¼ 6D2=3
Table I. Correlations to predict minimum agitation speed in liquid-liquid stirred vessels
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602
R. Afshar Ghotli et al.
and quantitative numerical criteria for complete dispersion in immiscible liquid-liquid
systems.
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Power Consumption
The amount of energy required per unit of time in a mechanical agitation tank bioreactor, chemical reactor, or similar process is understood as power drawn or power
consumption (Ascanio et al., 2004). The power number, a dimensionless group, has
a significant effect on the definition of power consumption (Yapici et al., 2008). The
vital roles of the power drawn for the process and the mechanical design of the mixing
tank have been the subject of many studies since 1880 (Bujalski et al., 1987). As
Bujulski et al. (1987) cited at their work, Unwin in 1880 showed close relationships
between power drawn (P) and tank diameter (T) and speed (N) for low-viscosity fluids:
P / N 3 D5
ð7Þ
Power consumption strongly depends on system characteristics such as stirred
tank size and geometry, baffle design, impeller type, impeller diameter, impeller
speed, impeller location, and physical properties of liquids (Jakobsen, 2008). For
example, although suitable baffles in a tank with radial impellers will generate strong
top to bottom flow stream, they also cause increase in power consumption (Oldshue,
1986; Kumaresan et al., 2005; Lu et al., 1997). Using axial flow impellers reduced the
requirement to install baffles, and they were employed only in turbulent mixing.
Thus, in a stirred tank with axial flow impellers the power consumption is less than
that with radial flow impellers (Oldshue, 1986). Szopolik (2004) showed that increasing the impeller eccentricity in an unbaffled stirred tank causes an increase in power
consumption and a decrease in mixing time. A 10% increase in impeller diameter
increases the power consumption more than 60%. Moreover, a 10% increase in
impeller speed enhances the power consumption more than 30%. For Newtonian
fluids, power consumption in a laminar flow system is directly related to the fluid
viscosity, but it is independent of the density (Doran, 1995). As opposed to laminar
flow, in turbulent flow the power requirement is not related to the viscosity but is
dependent on fluid density (Doran, 1995).
Since achievement of fully developed turbulence may be impossible, evaluation
of power consumption for non-Newtonian fluids is more difficult. The viscosity of
non-Newtonian liquids alters with shear conditions, and it is necessary to use the
corrected correlations for Reynolds number based on apparent viscosity (Doran,
1995).
Experimentally, power consumption (P) is usually calculated directly from
measurements of torque (s) and impeller shaft speed (N):
P ¼ 2pNs
ð8Þ
Several techniques have been utilized to determine power consumption (Ascanio
et al., 2004): strain gauges and telemetry (Karcz and Major, 1998; Moucha et al.,
2003; Fentiman et al., 1998), load cell setup associated with a torque table with a
controlled traversing mechanism (Patil et al., 2004; Kumaresan and Joshi, 2006;
Kumaresan et al., 2005), calorimeter (Oosterhuis and Kossen, 1981; Bourne et al.,
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Liquid-Liquid Mixing in Stirred Vessels
603
Figure 1. Effect of Reynolds number on Power number (Yapici et al., 2008).
1981), torquemeter (Pinho et al., 1997; Ravelet et al., 2007; Vasconcelos et al., 1999),
and dynamometer (Wang et al., 2009; Zhao et al., 2011).
Various approaches are utilized to simulate the flow in a stirred tank (Ranade, 1996;
Brucato et al., 1998; Yapici et al., 2008). Yapici et al. (2008) utilized Navier-Stokes equations instead of the turbulence model to simulate the relations between power number
and Reynolds number and flow regimes. They plotted power number versus Reynolds
number for a standard tank configuration. For a Reynolds number smaller than 20,
in the laminar flow regime, the curve was linear. By increasing the Reynolds number
to around 10,000 and changing the flow regime to turbulent, the power curve becomes
horizontal. Furthermore, the results and predictions for power are in excellent agreement
with experimental data reported by Bates et al. (1963). Figure 1 displays the relation
between power and Reynolds number. The solid line shows the experimental data
reported by Bates et al. (1963) compared with the results predicted by Yapici et al. (2008).
Drop Size Distribution (SD)
Drop size distribution or granulometry of emulsions is defined by a typical mean
diameter based on statistical analysis. It is also convenient to introduce a mean or
average drop diameter instead of having to specify the complete drop size distribution (Kreith and Berger, 1999). Whenever the interfacial area is a controlling
factor for mass transfer and chemical reactions, the mean surface diameter or Sauter
mean diameter (SMD or d32) becomes significant (Lemenand et al., 2003).
Several empirical correlations have been reported for d32. The main focus in
most studies was on Rushton turbines. Obviously, data for the other types of impellers are scarce (Paul et al., 2004). In recent years more focus can be seen on other
types of impellers (El-Hamouz et al., 2009; Pacek et al., 1999; Quadros and Baptista,
2003). Typically, Sauter mean diameter is defined as (Paul et al., 2004):
Pi¼m
ni di3
d32 ¼ Pi¼1
i¼m
2
i¼1 ni di
ð9Þ
604
R. Afshar Ghotli et al.
The number of size classes describing the drop size distribution is m, ni is the
number of drops, and di is the nominal diameter of drops in size class i. The
subscripts imply that d32 is formed from the ratio of the third to second moments
of the DSD. The mean diameter of choice is often d32, since it is directly related
to u and av by the following equation (Paul et al., 2004):
d32 ¼
6u
aV
ð10Þ
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Normal and tangential stresses cause deformation in the interface of the continuous and dispersed phases in advance of droplet breakup. The diameter of a spherical
droplet enables tolerating a strain as intense as the pressure gradient from both sides
of the interface, which is called the Laplace pressure (Lemenand et al., 2003):
PL ¼
4r
d
ð11Þ
In turbulent conditions, a drop diameter consequently reaches a point at which
additional deforming stress will not reduce drop size. The maximum stability of drop
diameter in the impeller region is the so-called maximum diameter, dmax. Under
steady conditions, drop size distribution is not a function of time. If a drop considerably larger than dmax is formed by coalescence, it will normally break up in a
short time. Furthermore, if a drop is notably smaller than dmin, it will coalesce.
Consequently, dispersion is in dynamic equilibrium, and a steady-state drop size
distribution is maintained (Liu and Li, 1999).
Several studies have been carried out on the effect of dispersed phase
viscosity because of its considerable effect on maximum drop size (Cull et al.,
2002; Vladisavljević et al., 2010; El-Hamouz et al., 2009). The viscosity of the
dispersed phase could contribute to drop stability, and its effect is often explained
by a viscosity number that can be neglected for a system with small variance of
viscosity between the phases (Cull et al., 2002). For example, Lagisetty et al.
(1986) derived an expression for maximum stable drop diameter, dmax, by considering the viscosity of the dispersed phase, which was suitable for a wide range of
variables. Ludwig et al. (1997) investigated droplet size and drop size distribution.
They reported the tendency of drop size to decrease with increasing viscosity in an
oil-water system, which means that increasing the viscosity of the continuous phase
causes a reduction in drop size and a large interfacial area.
The dimensionless Weber number, WeT, could be described and quantified as
the interaction between external stresses on the interface and the interface resistance
during breakup (Lemenand et al., 2003). Hinze (1955) developed a theory for the turbulent flow regime to predict maximum drop size. Maximum drop size, dmax, could
be related to the Weber number in agitation tanks. The Weber number is described
as follows (Lovick et al., 2005):
WeT ¼
qc N 2 D3
r
ð12Þ
The equilibrium values were also achieved in a shorter time with the equilibrium
d32 / W0:6
(El-Hamouz et al., 2009). Several correlations were shown by Paul et al.
e
Liquid-Liquid Mixing in Stirred Vessels
605
(2004) to evaluate the drop diameter size. The following correlation is derived for
low dispersed phase viscosities (Sathyagal et al., 1996):
dmax
¼ C We0:6
T
D
ð13Þ
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where C is a constant. The model of Lagisetty et al. (1986) proposed a value of 0.125
for the constant mean, while Calabrese et al. (1986b) suggested a value of 0.0883.
Arai et al. (1977), Lagisetty et al. (1986), and Calabrese et al. (1986b) reported an
increase in maximum drop size with increase in dispersed phase viscosity (Sathyagal
et al., 1996). Calabrese et al. (1986b) correlated an equation through a wide range of
experimental results with consideration of the viscosity for high viscosity systems
(Sathyagal et al., 1996):
dmax
¼ 2:1ðld =lc Þ3=8 Re3=4
D
ð14Þ
To consider the effect of increasing the dispersed phase volume fraction, u,
which can lead the system to coalesce, correlation (13) was employed to determine
the relation between Weber number, WeT, and the maximum drop size, dmax (Lovick
et al., 2005). In the following expression D is the impeller diameter and C1 and C2 are
constants:
dmax
¼ C1 ð1 þ C2 uÞ We0:6
T
D
ð15Þ
The results of Musgrove et al. (2000) with low viscous dispersed phase in a range
of 0.005 to 0.05 Pa.s showed that the influence of interfacial tension is practically
correlated by We0.6.
Numerous models have been used to determine the mean diameter size and drop
size distribution. For example, DeRoussel et al. (2001) presented models to calculate
changes in diameter. The mean drop size becomes smaller with increased viscosity in
the dispersed phase or drop and with reductions in interfacial tension. Their results
were in good agreement with experimental data.
Various practical methods such as light transmission, in situ photography, and
sample withdrawal have been employed to observe drop size distribution development in mixing vessels (O’Rourke and MacLoughlin, 2005; Paul et al., 2004). The
main focus of these techniques was on the measurement of the final steady-state drop
size distribution (O’Rourke and MacLoughlin, 2005). Direct photography is still
used frequently by researchers to measure drop size distribution (Ribeiro et al.,
2004; Zhao et al., 1993; O’Rourke and MacLoughlin, 2005). However, in these techniques, when the holdup (volume fraction) is high or drop size is small, resolution is
poor (Zhao et al., 1993). They are utilized typically for volume fractions less than
10% (O’Rourke and MacLoughlin, 2005). Table II shows some of the methods for
determining drop size and drop size distribution.
El-Hamouz et al. (2009) carried out experiments in stirred vessels using sawtooth
and pitched-blade turbines in a silicone oil-water surfactant solution. The results
showed that the sawtooth impeller produced smaller droplets than the pitched-blade
turbine. This result becomes significant because the power number for the pitched
606
R. Afshar Ghotli et al.
Table II. Some methods for determination of drop size and drop size distribution
Method
.
.
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.
.
.
.
.
Purpose
Reference
Electrical resistance or
capacitance tomography
Measure drop size and
Bolton et al., 1999;
distribution of dispersed phase
Hasan and
Azzopardi, 2007
Standard camera
Measure transient mean
Pacek et al., 1994
photography method
distribution size during phase
inversion
In situ endoscope
Measure transient drop size
Gäbler et al., 2006
technique
distributions as a function of
power input, dispersed phase
fraction, and pH
3-D ORM technique,
Drop distribution measurements Lovick et al., 2005
which provides fast in situ
even at high concentrations of
and on-line results
dispersed phase
Focus beam reflectance
Estimation of drop size
Maaß et al., 2010
measurement
distributions
Fiber optical FBR sensor
Encapsulation
Relationship between drop size Mlynek and
and location in agitated
Resnick, 1972
liquid-liquid system
blade is greater. Hence, for the same operating conditions, smaller drop sizes should
be created. The researchers concluded that their observations could be a result of
higher local shear rates for the sawtooth. The experiments undertaken by Pacek
et al. (1999) with two chlorobenzene-water and sunflower oil-water systems indicated
at the same mean specific energy dissipation rate, low power number impellers,
which are called ultrahigh shear impellers, produced similar and smaller drop sizes
at equilibrium compared to two high-shear impellers, a standard Rushton turbine,
and another six-blade disk impeller. They also concluded the low power number
impellers reached the equilibrium point faster and the drop size distributions were
narrower than those produced by the Rushton turbine and the other six-blade disk
impeller. Lovick et al. (2005) evaluated the drop size distribution in mixtures of tap
water and kerosene as the dispersed phase using a six-bladed Rushton turbine for up
to 60% dispersed phase at impeller speeds in the range of 350–550 rpm. Their results
revealed a reduction tendency in the maximum and the Sauter mean drop diameters
with increasing impeller speed, which was in good agreement with the results of
Mlynek and Resnick (1972). Lovick et al. (2005) also demonstrated that phase
fractions did not greatly influence drop size.
Breakup and Coalescence
Drop breakup and coalescence are two fundamental phenomena that accompany the
evolution of turbulent liquid-liquid dispersions. Quantitative understanding of drop
Liquid-Liquid Mixing in Stirred Vessels
607
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Figure 2. Mechanism of breakup (Briscoe et al., 1999).
breakage and coalescence rates is demanded to control the evolution of drop size
distributions and therefore the performance of liquid-liquid systems (Sathyagal
et al., 1996). Generally, when two or more drops join together and produce one
or more larger drops, coalescence occurs. Coalescence could happen because of collisions between suspended drops in a moving phase (Paul et al., 2004). Coalescence is
controlled by various physiochemical effects, such as double layers and the presence
of surface-active agents (Paul et al., 2004). The process of drop breakage has been
studied using the framework of population balances. In this approach, breakage
events of each individual drop are taken into account, providing a mathematical
equation for the evolution of the number density in drop size in a purely breaking
dispersion (Sathyagal et al., 1996). The mechanism of break up phenomena is shown
in Figure 2.
When steady-state dispersion is achieved, breakage and coalescence reach a
dynamic equilibrium without any more change in mean drop size or drop size distribution (Pacek et al., 1999). They thus control the steady-state drop size distribution
(Liu et al., 2005). If equilibrium did not occur, any changes in agitation speed or
increments in concentration of the dispersed phase, which is known as the volume
fraction, u, or holdup will cause the coalescence rate to become increasingly dominant over that of breakage. This is in good agreement with Mlynek and Resnick’s
(1972) observation that an increase in impeller speed and drop size reduced the
coalescence rate, whereas an increase in holdup caused an increase. If a very low
fraction volume is dispersed into the continuous phase, drops do not affect the continuous phase and interaction between drops happened infrequently (Wichterle,
1995), and the drop size was controlled by breakup in the impeller region (Nienow,
2004). On the other hand, higher volume fractions of the dispersed phase also lead to
increases in the interaction rate between droplets and consequently to intensification
of the breakup and coalescence processes.
It is known that dmax and dmin can be monitored under equilibrium conditions.
Drops smaller than dmin will coalesce, whereas those larger than dmax will break up.
The Sauter mean diameter, d32, is directly proportional to dmax in coalescence processes.
While the breakup process is dominant, d32 is related to dmin (Liu and Li, 1999). The
most frequent equation for calculation of dmax was expressed by Hinze (1955):
dmax
3=5
c
¼ A1
e2=5
q
ð16Þ
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608
R. Afshar Ghotli et al.
where A1 is also a constant and should be determined experimentally; c is interfacial
tension, N=m; q is density, kg=m3; and e is energy dissipation, m2=s3.
Transient breakage drop size distributions were experimentally measured by
Sathyagal et al. (1996), using an image analysis technique. The breakage rate
functions were determined using an inverse-problem approach.
Results of the inverse problem showed that the breakage rate is considerably
increased with the drop size and stirrer speed. Furthermore, the breakage rate
declines steeply with only a small increase in interfacial tension. Increasing the drop
viscosity causes breakage to a broader size distribution of daughter drops. Gäbler
et al. (2006) studied coalescence behavior in a toluene-water system by changing
droplet surface potential with pH variation. Their result showed higher pH impeded
coalescence significantly.
Several techniques can be found to study coalescence behavior. Sathyagal et al.
(1996) utilized very dilute systems to make collisions of droplets improbable. Kumar
et al. (1991) used surfactants to immobilize the droplet surface. These techniques
have some disadvantages. Liquid-liquid systems might be changed considerably by
such dilution and the use of surfactants (Gäbler et al., 2006).
Several model equations have been developed for determination of breakage and
coalescence under different conditions by investigators such as Laso et al. (1987),
Coulaloglou and Tavlarides (1977), Nambiar et al. (1990), Tsouris and Tavlarides
(1994), and Lasheras et al. (2002). The most widely used equation for drop breakage
and coalescence rate g(dp) in turbulent systems was created by Coulaloglou and
Tavlarides (1977).
Interfacial Area
Mixing of immiscible liquids happens as a result of intensification of an interfacial
area. A large interfacial area considerably affects control and increases the rate of
mass and energy transfer as well as chemical reactions such as nitration, sulfonation,
alkylation, hydrogenation, and halogenation. The parameter of interfacial area is
defined in Equation (10) in terms of a ratio of the dispersed phase volume fraction
(holdup), u, and the Sauter mean drop diameter of the dispersed phase, d32.
When light is passed into a tank, it would be tapered by the dispersed phase
particles. As a result, computation of interfacial area per volume could be possible
by measuring the transmitted light.
To evaluate dispersed phase drops at a low dispersed phase volume fraction in
turbulent systems, Sprow (1967) suggested the following equation:
d32
¼ AWe0:6
D
ð17Þ
where A is constant determined by experimental values.
For laminar flow liquid-liquid dispersion, a simple equation was derived by
Starks (1999) for evaluation of interfacial area. Prior techniques for calculation of
interfacial area are based on optical, photographic, or electrolytic resistance
measurement (Quadros and Baptista, 2003). Numerical results and simulation by
McLaughin and Rushton (1973) indicated that the interfacial area of liquid-liquid
mixing can be obtained only if the light detector receives parallel light. Furthermore,
Eckert et al. (1985) employed a modified technique involving a light probe. These
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Liquid-Liquid Mixing in Stirred Vessels
609
physical techniques display only local values of the interfacial area, which may not
be representative of the entire system. Additionally, these methods might require
measurement systems inside the tanks that could modify normal flow patterns and
results (Quadros and Baptista, 2003). Because air bubbles affect light transmission
negatively, this method is not an appropriate choice for systems in which air is
entrained (Eckert et al., 1985). Nanda et al. (1966) used chemical reactions for the
first time to evaluate the interfacial area in gas-liquid mixing. Fernandes and Sharma
(1967) used this technique to determine the interfacial area in liquid-liquid reactors
for extraction processes. Van Woezik and Westerterp (2000) and Quadros and
Baptista (2003) also used this technique. The chemical method allows quantifying
interfacial area via the mass transfer between phases. It would be profitable to determine the total value of the interfacial area in heterogeneous systems without any
obstruction in flow pattern. But it may influence the mass transfer and physiochemical characteristics of materials and also it is not useful for determination of drop size
(Quadros and Baptista, 2003). It is proven that photographic and video techniques
are the most accurate methods for determining interfacial area and drop size. These
methods require taking many pictures and lengthy analysis. Other methods include
light transmittance and light scattering (Lovick et al., 2005). Although literature
reports show faster determination using the latter methods (Skelland and Moeti,
1990), they are, however, not attractive as drop size data are not captured.
High-shear impellers such as the Rushton turbine could be appropriate for an
application that demands high interfacial area (small drop diameters). Retreat-curve
impellers are a good choice for applications with moderate interfacial area, such as
emulsion polymerization. Impellers using broad-blade paddles are an acceptable
choice for applications requiring larger drops in a narrow size distribution (Paul
et al., 2004). Interfacial area values determined by Fernandes and Sharma (1967)
showed that the interfacial area generated by a Rushton turbine was larger than
the propeller and droplet size was smaller. Quadros and Baptista (2003) employed
a chemical method for the same purpose. The mean drop size diameter in the transitional regime declined drastically with reductions in Weber number. However, this
trend is not observed when the dispersed drops diminish very gradually at greater
Weber number. The model proposed by Quadros and Baptista (2003) does not
depend on agitator system or holdup fraction. The average drop size diameter was
smaller for a four-paddle impeller and was intensified by holdup fraction. The model
could be appropriate for dispersions in aromatic nitration reactors.
Phase Inversion
Generally, in two-phase liquid-liquid systems, one of the phases is water or aqueous
and another phase consists of an organic liquid such as oil. Two types of dispersion
are possible: oil in water (O=W) and water in oil (W=O). In the first one, oil drops are
dispersed in water as a continuous phase. For the latter, phase dispersion is reversed.
Based on system properties and operational conditions such as phase volume ratio
and input energy, either of them might occur (Liu et al., 2005). Whenever an interchange happens spontaneously between two phases of liquid-liquid dispersion, phase
inversion will take place by means of dispersed phase inversion to the continuous
phase, and vice versa (Liu et al., 2005). Increasing the dispersed phase volume fraction and either impeller speed or power input could lead to phase inversion (Hu et al.,
2006). Figure 3 is a schematic of phase inversion progression. Phase inversion may be
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610
R. Afshar Ghotli et al.
Figure 3. Progression of phase inversion (Paul et al., 2004).
desired for product quality or avoided to maintain high mass transfer and reaction in
some processes (Paul et al., 2004). For example, in solvent extraction in mixersettlers, because of interruption in the settling process, phase inversion could be
undesirable. However, in some processes such as the preparation of waterborne
dispersions of polymer resin, phase inversion could be desirable (Hu et al., 2006).
Investigators such as Selker and Sleicher (1965), Kato et al. (1991), and
Kinugasa et al. (1997) studied the effect of variables such as viscosity, density,
agitation speed, and the materials and geometry of the mixing apparatus. Prior studies have shown that in an immiscible liquid system, there is a wide range of volume
fractions in which either phase could be the stable dispersed phase. This range is
known as the ambivalent range (Selker and Sleicher, 1965; Liu et al., 2005; Yeo
et al., 2002a). The ambivalent range is specified by the volume fraction of the dispersed phase and the amount of energy input into the system (Liu et al., 2005). Selker
and Sleicher (1965) illustrated the dependency of the ambivalent range on viscosity.
Kato et al. (1991) examined phase inversion phenomena in mixing vessels. They
reported that when the agitation speed was less than 400 rpm, the aqueous phase
became continuous, whereas when it was higher than 1050 rpm, the phase that
had the higher viscosity became dispersed. The significant influence of surface-active
agents on phase inversion phenomena was reported by Kato et al. (1991). Skelland
and Seksaria (1978) claimed that once the minimum agitation speed was determined,
further increases in speed did not cause phase inversion. Deshpande and Kumar
(2003), through experimental data, postulated that for sufficiently intense turbulence, phase inversion depends only on the properties of the liquid-liquid system.
The ambivalence region was determined by plotting the initially dispersed phase
volume fraction at phase inversion in terms of the impeller speed by Norato et al.
(1998), and it revealed the hysteresis effect in phase inversion from O=W to W=O
and W=O to O=W dispersions. They also concluded that, depending on the physical
properties of the dispersed and continuous phases, phase inversion could be caused
by either reduction or increase of agitation speed. Phase inversion was investigated
by Liu et al. (2005) by laser-induced fluorescence.
Phase inversion from O=W dispersion to W=O was recorded using a high-speed
video camera. Liu et al.’s results illustrated that phase inversion is a gradual transition that happens over 1 to 2 s, and depending on local phase distribution, may
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Liquid-Liquid Mixing in Stirred Vessels
611
not take place globally. During phase inversion, two contradictory processes, drop
coalescence and breakup, and the inclusion and escape of small drops in larger drops
are significant. The structure of the dispersion is extremely complex. A large number
of secondary dispersions and multi-dispersions appear during phase inversion, which
includes water-oil-water secondary dispersions (Nienow et al., 1994; Norato et al.,
1998). Phenomena that are accompanied by phase inversion, such as secondary dispersions and drop coalescence and breakup, were also observed by Hu et al. (2006)
using laser-induced fluorescence (LIF). Pacek et al. (1994) utilized a video technique
to observe quick changes in the drop size distribution of liquid-liquid dispersion
during phase inversion.
As a result of the significant role of phase inversion, few models have been
established to predict ambivalent range and phase inversion accurately. Many investigators tried to evaluate the limits of the ambivalent range by correlating data and
preparing a physical model to explain these data (Liu et al., 2005). The width of the
ambivalent range was correlated to impeller speed and interfacial tension by Luhning
and Sawistowski (1971). Kumar et al. (1991) suggested an alternative method to plot
ambivalence behavior. Juswandi (1995) recommended a stochastic model to simulate
phase inversion. Arashmid and Jeffreys (1980) suggested a correlation to evaluate the
volume fraction and agitation conditions for inversion. Yeo et al. (2002b) defined a
method for predicting phase inversion of concentrated liquid-liquid dispersions by
means of a Monte Carlo technique. The two-region model was also proposed by
Hue et al. (2005) to predict the phase inversion volume fraction and width of the
ambivalent range of concentrated liquid-liquid dispersions in agitated vessels.
Parameters That Effect Liquid-Liquid Mixing Performance
Impellers
A wide range of impellers has been designed and produced to achieve efficient
mixing commercially. Impeller selection depends on a number of factors, such as
viscosity of fluid, operating conditions, and system flow regime (Paul et al., 2004).
Power number is one of the determinant factors in impeller selection. The impeller
power number is also related to some dimensionless groups such Reynolds number
and Froude number and such geometrical ratios as D=T, C=T, and H=T (Bujalski
et al., 1987). For systems with a Reynolds number higher than 300 for baffled mixing
tanks, the central vortex can be eliminated and the Froude number neglected
(Edwards et al., 1997). When a vortex occurs within the mixing tank, the Froude
number, which is described in Equation (18), becomes important:
Fr number ¼
N2 D
g
ð18Þ
Under the same operating conditions, the geometrical ratios also could be
neglected. Thus, impeller power number (P0) is significantly related to Reynolds
number (Re), which reveals the ratio of inertial forces to viscous forces (Chen
et al., 2005). Equation (19) is the power number equation (Bujalski et al., 1987;
Kramers et al., 1953; Edwards et al., 1997):
P0 ¼
P
qN 3 D5
ð19Þ
612
R. Afshar Ghotli et al.
After computing the data, power number versus Reynolds number can be easily
plotted for various mixing tank designs with different impellers (Paul et al., 2004).
Table III reveals some power number values for the Rushton turbine and other
impeller types.
Turbine impellers are a good choice for dispersion of immiscible liquids, even
those that are quite viscous. Impellers exhibit differing flow patterns and shear levels
depending on whether they are axial flow, radial flow, hydrofoil, or high-shear
designs. Impeller flow patterns have considerable effect on mixing. Axial and radial
flows are two main categories defined for top-entry mixers. Axial-flow impellers
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Table III. Some previous power number values for different types of impellers
Impeller type
Power number
value
Down pumping 45 pitched-blade
turbines (PBT)
Down pumping 45 4-pitched-blade
turbine
Down pumping 45 6-pitched-blade
turbine
Sawtooth impeller
Concave blade (semicircular) impeller
Concave blade (semicircular) impeller
Concave blade (semicircular) impeller
2.8
Concave blade (semicircular) impeller
Chemineer HE-3
Chemineer HE-3
Chemineer HE-3
Lightnin A6000 impellers
3.0
0.27
0.305
0.30
0.23
Lightnin A310 fluid foil impeller
0.30
Lightnin A315
Lightnin A315
Lightnin A315
Lightnin A315
Propeller
Propeller
Curved pitched-blade turbine
Convex pitched-blade turbine
Standard 6-blade Rushton turbine
Standard 6-blade Rushton turbine
Standard 6-blade Rushton turbine
Standard 6-blade Rushton turbine
Standard 6-blade Rushton turbine
Standard 6-blade Rushton turbine
0.75
0.76
0.75
0.80
0.67
0.89
2.41
2.29
5.0
5.0
5.18
6.0
5.58
5.4
Reference
1.7
Montante et al., 2005
0.99
El-Hamouz et al., 2009
2.1
Ranade et al., 1992
0.32
2.8
3.8
El-Hamouz et al., 2009
Chen and Chen, 2000
Warmoeskerken and Smith,
1989
Karcz and
Kaminska-Brzoska, 1994
Mhetras et al., 1994
Coker, 2001
Jaworski et al., 1996
Ibrahim and Nienow, 1995
Weetman and Oldshue,
1988
Weetman and Oldshue,
1988
Cooke and Heggs, 2005
Bakker, 1992
Nienow, 1990
Paul et al., 2004
Shiue and Wong, 1984
Ranade et al., 1992
Ranade et al., 1992
Ranade et al., 1992
Pacek et al., 1999
Bujalski et al., 1987
Rewatkar et al., 1990
Karcz and Major, 1998
Wu et al., 2001
Chen and Chen, 2000
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Liquid-Liquid Mixing in Stirred Vessels
613
discharge fluid axially, parallel to the impeller shaft. The fluid is pumped through the
impeller toward the bottom of the vessel. Then, the flow moves along the bottom and
rises up to form a single loop (Jakobsen, 2008; Paul et al., 2004). On the other hand,
radial impellers form two circulating loops, one below and one above the impeller. Mixing takes place between the two loops, but less strongly than within each loop. Radial
flow impellers are applicable for low- to medium-viscosity liquid dispersion and high
speeds as well. In comparison with axial-flow impellers, radial-flow impellers induce
higher shear and turbulence with less pumping (Paul et al., 2004). Impellers with a central disk could be able to draw more power and also create more uniform flow than
open style impellers. Furthermore, the disk allows increasing the number of blades
(Chen et al., 2005; Paul et al., 2004). Axial flow impellers could be used for liquid blending at low viscosity and high speed (Paul et al., 2004).
Propellers are the oldest axial-flow impeller design. They are generally available in a
three-bladed marine type. Pitched-blade turbines are capable of operating in largediameter tanks and at high speed with low power consumption. Pitched-blade turbines
are able to operate in large diameters and high speeds with low power consumption
(Chen et al., 2005). The pitched-blade turbine is occasionally used interchangeably with
axial- and radial-flow impellers. If the D=T ratio exceeds 0.55, pitched-blade impellers
produce the same flow pattern as radial impellers (Edwards and Baker, 1997; Paul
et al., 2004). In applications where axial flow is significant and needs to have low shear,
hydrofoil impellers could be preferable. The specific blade shape results in a lower power
number and higher flow per power unit than the pitched-blade turbine. The low pumping capacity of high-shear impellers causes them to be used along with axial-flow impellers to produce high-shear and uniform distribution. Typical models for these impellers
are the bar turbine with low shear, the Chemshear impeller with intermediate shear, and
the sawtooth with high shear preparation (Paul et al., 2004). Figure 4 shows typical
impeller types for each category. Table IV demonstrates the effect of different parameters on flow pattern based on the review.
The literature review showed that although occasionally other designs have been
used, most experimental work on liquid-liquid systems has been carried out with
Figure 4. Common impeller types.
614
Flow pattern
Mean flow
. Turbulence characteristics
.
Purpose
Result
Reference
40 axial flow
.
By increasing the D=T ratio, the radial flow Patwardhan and Joshi,
produced by the impeller becomes
significant and leads to change in overall
flow pattern
. Disk turbine
. Strong dependency of power number on
Rewatkar et al.,
Power consumption in mechanically
(DT)
the flow pattern
agitated contactors
. Pitched-blade
. Larger impeller diameter (T=2) produces
down-flow
different flow pattern close to impeller
turbine (PTD)
. Similar flow pattern for very large blade
width impeller with radial flow and
. Pitched-blade
dissipation of energy behind the blades
up-flow turbine
becomes very high
(PTU)
. Strong effect of impeller clearance on
flow pattern and thus on power number
Anchor impeller
Power consumption with anchor
Influence of clearance on power input due Espinosa-Solares et al.,
mixers—effect of bottom clearance
to changes in flow patterns
Rushton turbine Influences of clearance and rotational
Montante et al.,
Reduction in C=T ratio from 0.2 to 0.15
speed on flow patterns
changes flow pattern from double-loop
circulation to single loop (axial flow)
Rushton turbine Investigation of effect of impeller
At low clearance single-loop flow pattern
Ochieng et al.,
clearance on velocity field and mixing
causes an increase in axial flow and
reduction in mixing time at a constant
power number
Impeller type
Table IV. Effects of different parameters on flow pattern
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2008
1999
1997
1990
1999
615
Paddle stirrer
Turbomixer
. Propeller
Rushton turbine
.
.
.
At low Re, fluids of different rheological
properties should all give radial flow
. Increasing the viscoelasticity of fluid
caused change of pitched-blade turbine
flow pattern to radial flow
. Due to entrance of Re to transition
region by increasing viscosity, flow pattern of pitched-blade turbines, axial flow
hydrofoils, and Intermig showed tendency to radial flow impeller; Rushton
turbine kept typical radial flow pattern
through the whole Re range under most
conditions
Effect of Reynolds number on flow
Axial flow pattern at higher Re changed to
pattern
radial at lower Re, and for Re around 500
when axial flow changed to radial the
flow stream direction was unsteady
Study of performance of several types of At low agitation speeds, baffling has small
agitators for mixing of miscible liquids
effect on flow pattern
in batch operation
Effects of clearance and rotational speed Did not observe any influence on flow
on flow patterns in the vessel
pattern or mean velocities by changing
impeller speed
6-blade
Investigation of power curves and flow
Rushton
patterns in Newtonian fluids
turbine
Pitched-blade
45 up down
pumping types
Intermig
Hydrofoil
impeller (A310)
Chemineer
HE3
Pitched-blade
turbine
.
.
.
.
.
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Montante et al., 1999
van de Vusse, 1955
Schäfer et al., 1998
Ibrahim and Nienow, 1995
616
R. Afshar Ghotli et al.
six-flat-blade Rushton turbines. Table V lists some of the previous liquid-liquid
experiments undertaken in stirred vessels.
In large-capacity tanks, to achieve reasonable power distribution, dispersion
uniformity, gas handling, heat transfer, and cost efficiency, multiple agitators are
employed (Vasconcelos et al., 1999). The flow in a multiple-impeller system is considerably different than that in a single-impeller system (Harvey et al., 1997).
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Liquid Phase Holdup
Increasing the dispersed phase volume fraction can enhance drop size distribution
through coalescence (Lovick et al., 2005; van Woezik and Westerterp, 2000), primarily
by decreasing turbulence intensity or increasing collision frequency (van Woezik and
Westerterp, 2000). The effect of increasing the dispersed phase has already been illustrated in Equation (15) (Lovick et al., 2005). Drop size increment was observed up
to a 40% dispersed phase volume fraction by Weinstein and Treybal (1973). The
experiment performed by Boye et al. (1996) with xylene-in-water dispersions revealed
that at a dispersed phase volume above 50% by volume caused the behavior of the dispersion to assume non-Newtonian flow properties. This behavior was attributed to a
change in the drop breakage mechanism from turbulent eddy at less than 50% concentration to boundary layer at more than 50% concentration. They also argued that d32
increased in the turbulent flow with an increase in the volume concentration of the dispersed phase but the opposite effect was seen in the non-turbulent area.
Experiments performed by Lemenand et al. (2003) for a range of 0 to15% dispersed phase concentration suggested that the Sauter diameter is independent of
the volume fraction of the dispersed phase. Brown and Pitt (1970) believed that
the dispersed phase volume fraction and impeller speed had little effect on d32.
Lovick et al. (2005) also did not observe any considerable influence of dispersed
phase fraction volume on drop size. Probably, the various results are due to different
properties of fluids and vessels (Lovick et al., 2005).
However, it seems that the dispersed phase volume fraction has an important role
in drop size and coalescence. Thus, in some experiments, a lower ratio of dispersed
phase was used because of the reduced effect of coalescence on maximum stable drop
size (Baldyga et al., 2001; Musgrove et al., 2000). Increasing the dispersed phase
volume fraction could also lead to phase inversion in the system (Hu et al., 2006;
Liu and Li, 1999; Pacek et al., 1999). Also, as mentioned previously, the volume fraction of the dispersed phase is an important factor in determining the ambivalent range
(Liu et al., 2005). Volume fraction of dispersed phase also has an influence on mixing
time. Results of Zhao et al. (2011) in a kerosene-water system indicated an increase in
mixing time at volume fractions of 10 to 20%, longer than that for single-phase systems; at lower volume fraction of dispersed phase, a reversed trend was observed.
Increasing the dispersed phase volume resulted in lower average density and higher
apparent viscosity, but higher mixing time (Zhao et al., 2011).
Viscosity of Fluids
Viscosity has a significant effect on flow behavior such as pumping, mixing, mass
transfer, heat transfer, and aeration of fluids (Doran, 1995). One of several factors
affecting the selection of impeller type is viscosity (Jakobsen, 2008). Mixing power
for non-aerated fluids is also affected by viscosity (Doran, 1995). The effect of
617
Benzaldehyde
Ethyl acetate
Dow Corning
200 silicone fluids
Water
Chlorobenzene
Sunflower oil
Water
.
.
.
.
.
.
.
Kerosene
Water
.
.
.
Silicon oil
Water
.
.
Vessels
Aim
Ref.
(Continued )
Effects of impeller type, speed,
Skelland and Lee,
Cylindrical flat-bottom
size, and location and liquid
1978
baffled vessel V ¼ 0.01 m3
properties on degree of mixing
of two immiscible liquids in a
baffled vessel
6-flat-blade RT
Mean drop size and drop size
Pacek et al., 1999
Cylindrical flat-bottom
distributions considered in both
6-flat-blade disk turbine
baffled vessel V ¼ 0.0015
viscous and non-viscous
Axial flow hydrofoil
and 0.0026 m3
dispersed phases
Chemineer HE3
Ultra High shear Chemineer CS2, CS4
6-flat-blade RT
Musgrove et al.,
Standard baffled cylindrical Influence of impeller type and
agitation conditions on drop
2000
Pitched-blade turbine
torisperical-based tank
size of immiscible liquid
(closed top) V ¼ 0.004
dispersions
and 0.02 m3
6-flat-blade RT
Cylindrical flat-bottom
Comparison of direct sampling
O’Rourke and
baffled vessel
and in situ video microscopy to MacLoughlin,
V ¼ 0.003 m3
analyze evolving droplet size
2005
distributions in lean silicone
oil-water dispersions
6-flat-blade RT
Standard baffled cylindrical Drop size distribution at high
Lovick et al., 2005
tank V ¼ 0.002 m3
dispersed phase fractions of
organic in water mixtures
Impeller type
3-bladed propellers
6-pitched-blade turbine
. 6-flat-blade RT turbine
. 6-curved-blade turbine
.
Silicone oil (Dow .
Corning)
.
. Water
.
.
.
.
.
.
.
.
System
Table V. Some previous liquid-liquid experimental work carried out in mixing tanks
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618
Toluene
Water
Silicon oil
Water surfactant
solution
. Water
. Corn syrup solution
.
.
.
.
n-Tetradecane
Diesel fuel
. Water
.
.
System
Table V. Continued
6-bladed Rushton
turbine
Pitched blade 45
Intermig
Hydrofoil impeller
(A310)
Chemineer HE3
.
.
.
.
.
Sawtooth
4-pitched-blade turbine
6-flat-blade RT
6-flat-blade RT
.
.
.
.
Impeller type
Aim
Study of dependency of drop size
distributions on power input,
phase fraction, and especially
pH in terms of breakage and
coalescence behavior
Standard baffled cylindrical Investigation of fluid dynamic
tank (closed top)
characteristics of a stirred tank
V ¼ 0.001 m3
of standard geometry for
dispersion of organics in water
at different impeller speeds and
flow features of both
continuous and dispersed
phases
Effect of impeller speed, oil
Standard ESCO mixer
viscosity, and addition point on
(ESCO Labor AG)
drop size distribution
V ¼ 0.006 m3
Cylindrical baffled Perspex Power curve and flow pattern
determination for a range of
vessel V ¼ 0.02 m3
impellers in Newtonian fluid
Cylindrical flat-bottom
baffled vessel
V ¼ 0.0026 m3
Vessels
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Ibrahim and
Nienow, 1995
El-Hamouz et al.,
2009
Laurenzi et al., 2009
Gäbler et al., 2006
Ref.
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Liquid-Liquid Mixing in Stirred Vessels
619
viscosity on drop size has been considered by many investigators; they showed that
the drops will stabilize and their size increase with a higher viscosity dispersed phase
(Davies, 1985; Calabrese et al., 1986a; Pacek et al., 1999). El-Hamouz et al. (2009)
found that the lower dispersed oil viscosity reaches the equilibrium point faster than
the viscous dispersed phase. Experimental study by Zhao et al. (2011) indicated that
mixing time increased with higher viscosity of the dispersed phase. They believed
that increasing the viscosity of the dispersed phase has a greater effect on the flow
field and turbulence than an alteration in density. Viscosity can obstruct coalescence
in the system. Consequently, smaller drops will be produced (van Woezik and Westerterp, 2000). Although Sathyagal et al. (1996) reported that increasing the viscosity
of the dispersed phase reduced the breakage rate, they claimed that the effect of viscosity is not as strong as other variables such as stirrer speed and interfacial tension.
Maggioris et al. (2000) postulated that increasing the viscosity of the continuous
phase causes the coalescence rate to intensify.
Metzner and Otto (1957) introduced an equation to achieve an appropriate
shear rate in the tank where the average shear rate in the tank, cav, is directly related
to the impeller speed and KS is a shear rate constant of the impeller:
cav ¼ KS N
ð20Þ
The constant is normally dependent on the impeller geometry but usually independent of the fluid properties (Ayazi Shamlou and Edwards, 1989; Boye et al., 1996).
Calderbank (1958) defined the following viscosity factor where C has to be
determined experimentally. The value of viscosity factor was in the range of 0.0 to
0.4 (Godfrey et al., 1989; van Woezik and Westerterp, 2000):
FðlÞ ¼ ðld =lc ÞC
ð21Þ
Liu and Li (1999) also reported that when md=mc is small, drop coalescence will
occur more rapidly because of increased interfacial mobility.
Density of Fluids
Liquid density and the density difference between two immiscible liquids is one of the
parameters that affect phase inversion (McClarey and Mansoori, 1978; Liu et al.,
2005), minimum agitation speed (Nagata, 1950; Skelland and Seksaria, 1978; Skelland
and Ramsay, 1986), drop breakage (Musgrove et al., 2000), mixing power consumption (Doran, 1995; Coker, 2001), and drop size (van Woezik and Westerterp, 2000).
Musgrove et al. (2000) indicated that although dispersed phase density does influence
drop breakage, it can be consider a secondary effect, for example, when a dispersed
phase such as chlorobenzene, which is denser than water, is forced into a different part
of the trailing vortices than a dispersed phase that is less dense than water. In the laminar region the power requirement is independent of fluid density, although it is
directly proportional to viscosity (Doran, 1995). However, for turbulent flow, the
power is not dependent on viscosity, but is directly related to density (Doran, 1995).
Table I shows the relation of minimum agitation speed to the density difference
between the dispersed and continuous phases. As can be seen from the equations, the
minimum agitation speed is directly related to (Dq)a, where the value of ‘‘a’’ is
between 0.25 and 0.42 (Nagata, 1950; van Heuven and Beek, 1971; Skelland and
620
R. Afshar Ghotli et al.
Seksaria, 1978; Godfrey et al., 1984; Skelland and Ramsay, 1986; Skelland and
Moeti, 1989; Kamil et al., 2001). Although, Nagata (1950) reported that the minimum agitation speed is independent of interfacial tension (r), Johnstone and Thring
(1957) claimed that, for low differences viscosities and densities, the required power
at specific speed is a function of interfacial tension. Zhao et al. (2011) illustrated that
higher density of dispersed phase causes increase in mixing time.
Keey (1967) defined a correlation to evaluate the average density in two-liquidphase systems (Boye et al., 1996):
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qM ¼ uqd þ ð1 uÞqc
ð22Þ
The blend time for immiscible liquid mixing is directly related to the fluid
viscosity and inversely related to the density (Paul et al., 2004). Van Woezik and
Westerterp (2000) showed that the differences in interfacial area could be described
to differences in viscosity and density. They also explained that continuous phase
density and the ratio of the viscosities of the two phases could affect drop size
(van Woezik and Westerterp, 2000).
Liquid-Liquid Mixer Scaleup
Agitation System Design
Mixing in agitation tanks could be carried out in continuous, batch, or fed-batch
mode. When mass transfer is limited, proper mixing could reduce investment and
operating cost while providing high yields (Paul et al., 2004). Equipment design,
construction, and installation demand significant amounts of time, resources, and
finances (Anderson, 2000). The objectives of the process should be defined. An
understanding of process requirements and information about the physical properties of the fluids to be processed is also essential (Paul et al., 2004).
The impeller type selected will depend on tank size and the process applications
and will influence mixing tank design. More than one impeller may be required for
tanks with a high aspect ratio (liquid depth in vessel (Z)=tank diameter (T) > 1.5) or
for large blending tanks. Typically, side-entry propeller impellers are suggested.
Impeller size, in combination with mixer speed, should be determined to obtain
desirable results. Because they affect flow pattern generation, the size and type of
wall baffles should be chosen to create an effective flow pattern. Available data
on impeller characteristics can guide evaluation of power and drive size. Consequently, mixer design can be completed when the mechanical design of the shaft,
impeller blade thickness, baffle thickness and supports, inlet=outlet nozzles, bearings, seals, gearbox, and support structures are known.
Based on the viscosity of liquids, design of mixing systems is divided into two main
groups. Liquids exhibiting viscosity up to 10,000 cP could be blended appropriately
using internal pumping from turbine impellers within the vessel. Liquids with high viscosity require close-clearance impellers such as helical ribbons (Paul et al., 2004).
Scale-Up
The key role of scale-up is extension from the laboratory scale to a large-scale mixing
system. Because any change in the scale-up could lead to dramatic alterations of
Liquid-Liquid Mixing in Stirred Vessels
621
results, the effect of each parameter must be investigated. For example, the drop size
distribution defines the interfacial area, which is frequently the restrictive factor for
mass transfer, a fundamental factor for industrial systems and scale-up (Maaß et al.,
2010), or upon scale-up mixing time will be increased in the larger tank, although a
larger impeller will reduce mixing time (Jakobsen, 2008). Dilute systems are the simplest systems to scale up. Many processes have been scaled profitably by employing
following rule based on industrial experience (Paul et al., 2004):
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NDX ¼ constant
ð23Þ
It could be used for tanks with Reynolds number greater than 104, and vessels
must be geometrically similar.
Over the years several criteria have been established for the optimal scale-up of
stirred tanks based on similarities of geometries, dynamics, and kinematics (Oldshue,
1986; Jakobsen, 2008).
Classically, geometric similarity and constant tip speed and, second, power input
are commonly used (Okufi et al., 1990; El-Hamouz et al., 2009). Podgorska and
Baldyga (2001) considered circulation time instead of the following four criteria
for scale-up: equal power input per unit mass and geometric similarity, (ii) equal
average circulation time and geometric similarity, (iii) equal power input per unit
mass, equal average circulation time, and no geometric similarity, and (iv) equal
impeller tip speed and geometric similarity. Small changes in the drop size distribution were observed in fast coalescing systems by using criteria (i) and (iii). None
of these criteria are suitable slow coalescing systems (Cull et al., 2002). Scale-up
based on geometric similarity and constant tip speed assumes that where the velocity
gradients are the sharpest, the relevant shear that generates the limiting drop size
occurs in the agitator area. These are assumed to scale with the peripheral velocity
of the impeller when coalescence rates are low. The disadvantage of this methodology is that changes in geometry necessitate a pilot-scale evaluation. Failure to take
bulk circulation time into account can result in larger drops being formed on
scale-up (El-Hamouz et al., 2009).
Generally, either power per unit volume (P=V) or torque per unit volume (Tq=V)
should be held constant on scale-up. Scale-up methods established on constant blend
time demand that the agitation speed in the plant vessel be similar to that of the laboratory vessels. If constant P=V is utilized to scale up a reacting system, the vessels
might be sized for longer residence time than the laboratory ones. Increasing mixing
time causes considerable change in the flow regime, which could affect mixing quality.
Furthermore, incrementing the Weber number by a factor of 48.4 might reduce drop
size in the dispersed phase on scale-up of an immiscible liquid system. Constant tip
speed and equivalent Tq=V are employed just for flow velocities in the impeller
region, which must be the same as in the laboratory tank. It should be noted that
at constant P=V, the agitation speed and shear rate are altered considerably (Holland
and Bragg, 1995; Paul et al., 2004). A study of the equilibrium transient drop sizes in
the turbulent regime by Wang and Calabrese (1986) showed that the equilibrium time
increased on scale-up. Baldyga et al. (2001) proved that scale-up causes an increase in
Reynolds number, makes larger turbulent fluctuations, and results in smaller drops.
Zlokarnik (2001) believed that the scale-up criterion based on the same mixing time is
not reliable; thus he proposed two dimensionless groups to choose the impeller (Nere
et al., 2003). It may be expected with proportional increase in a given liquid-liquid
622
R. Afshar Ghotli et al.
system and the same tip speed the same specific interracial area is produced in the vessels, but Fernandes and Sharma (1967) believed that increasing the reactor size causes
a reduction in specific interfacial area (Starks, 1999).
Fundamentally, scale-up of a process is very complex. For this reason, the
relationship of parameters in the system must be carefully considered. If the scale-up
would not achieve desirable products, the production process would be costly and
time consuming, which would have significant influence on the marketing of products. For example, in 1989, the cost of poor mixing for chemical industries was
approximately $1–$10 billion in the U.S. or around $100 million per year for a large
multinational chemical company because of yield reductions (Paul et al., 2004).
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Conclusion
In this review, the effects of minimum agitation speed, mixing time, circulation time,
power consumption, drop size distribution, breakup and coalescence, interfacial area,
and phase inversion on liquid-liquid mixing efficiency were investigated. The measurement method has been investigated briefly. Impeller characteristics, volume fraction of
the dispersed phase, and such physical properties of liquid phases as viscosity and density are parameters that could affect mixing efficiency. It is noteworthy that despite the
fact that in recent years various types of impellers have been tried experimentally, the
Rushton turbine still attracts significant interest. Therefore, it seems that more attention should be paid to other types of impellers and their effects on mixing quality.
Future work should focus on scale-up and design of mixing equipment and accessories
with the specific intent to reduce the cost and investment in each process.
Nomenclature
av
Bo
D
d
d32
dmax
Fl
Fr number
Ga
g
KS
N
Nmin
P
P0
PL
Q
Re
T
V
WeT
interfacial area
Bond number, D2gDq=r
impeller diameter, m
diameter of spherical droplet
Sauter mean drop diameter of the dispersed phase, mm
maximum diameter of drop size, mm
flow number, dimensionless
Froude number, dimensionless
Galileo number, D3qMgDq=l2M
acceleration due to gravity, m=s2
shear rate constant of the impeller
impeller speed, rev=s
minimum agitation speed of impeller for complete
liquid-liquid dispersion, rev=s
power consumption, kg m2=s3
impeller power number, dimensionless
Laplace pressure
pumping capacity of the impeller, m3 s1
Reynolds number
tank diameter, m
total volumetric flow rate, m3; liquid volume, m
Weber number
Liquid-Liquid Mixing in Stirred Vessels
623
Greek letters
cav
average shear rate in the tank
Dq
density difference between continuous and dispersed phase, kg=m3
e
energy dissipation, m2=s3
hC
circulation time, s
lc
continuous phase viscosity, mPa s
ld
dispersed phase viscosity,
mPa s
lc
1:5ld /
lM
lM ¼ 1/ 1 þ l þl
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d
qc
qd
qM
r
s
u
c
continuous phase density, kg=m3
disperse phase density, kg=m3
qM ¼ /qd þ (1 /)qc, kg=m3
interfacial tension, Nm1
torque, kgm2 s2
dispersed phase volume fraction (holdup)
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