Representative drop sizes and drop size distributions in A/O dispersions in continuous flow stirred tank

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1 Representative drop sizes and drop size distributions in A/O dispersions in continuous flow stirred tank K.K. Singh a, S.M. Mahajani a,, K.T. Shenoy b, S.K. Ghosh b a epartment of Chemical Engineering, Indian Institute of Technology, Powai, Mumbai, , India b Chemical Engineering ivision, Bhabha Atomic Research Centre, Trombay, Mumbai, , India Abstract This work presents experimental studies of drop size distributions in aqueous in organic (A/O) dispersions produced in a continuous flow stirred tank agitated by a four-bladed top shrouded turbine with trapezoidal blades. The organic phase is a mixture of n-paraffin, tributyl phosphate (TBP) and di-2-ethyl hexyl phosphoric acid (2EHPA), the aqueous phase is dilute phosphoric acid. rop size measurements have been performed for different values of impeller speed, feed phase ratio and mean residence time at two locations in the tank, near the wall. Surfactant stabilization of the dispersion has been used as the drop size measuring technique. Log-normal distributions are found to fit the experimental drop size distributions. Experimental results have been used to obtain the empirical correlations for representative drop sizes Sauter mean diameter and maximum stable diameter. Keywords: Liquid liquid dispersion; Phosphoric acid; 2EHPA; TBP; Surfactant stabilization; rop size 1. Introduction Liquid liquid dispersions in continuous flow stirred tanks play an important role in hydrometallurgical plants using mixer settlers, wherein the objective is to preferentially extract a valuable component from one liquid phase into another immiscible liquid phase. The overall extraction affected by the mixer or the stage efficiency depends, among other things, on specific interfacial area available for mass transfer that in turn depends on sizes of the drops of the dispersed phase. The sizes of the drops depend on several factors such as impeller geometry, impeller speed, impeller location in the tank, feed phase ratio and physical properties of the phases. For an optimum design, a quantitative description of the effect of all these factors on the drop sizes is required. In a stirred tank due to inhomogeneous dissipation of power (Cutter, 1966), drop sizes exhibit spatial variations. At a given location also, owing to continuous redispersion and coalescence, a distribution of drop sizes is observed. Therefore, to get an overall picture of the quality of dispersion it makes sense to talk of a representative drop size of the dispersion. The Sauter mean diameter ( ) and the maximum stable drop diameter (d max ) are the two choices of the representative drop diameter. While the first is the ratio of third moment of drop size distribution to second moment of drop size distribution, the second represents the maximum drop size that can be observed for the

2 122 level of turbulence prevailing in the dispersion. The Sauter mean diameter assumes more importance because it is directly related to specific interfacial area ā by the following expression: ¼ 6/P a ð1þ where ϕ is the holdup of the dispersed phase. In many instances, direct proportionality between the two representative drop diameters has been reported (Brown and Pitt, 1972; Nishikawa et al., 1987a; Collias and Pruddhornme, 1992; Zerfa and Brooks, 1996; Calabrese et al., 1986a). Therefore, correlation for either of the representative diameters can be used to compute the other representative diameter. Experimental measurements of drop size distributions in stirred tanks are indispensable in view of the exorbitant computational demands of a fully predictive model that will solve the discretized population balance equations along with the flow and turbulence equations on a fine grid in the computational domain. The number of equations to be solved will be very large as there will be one equation for each drop class. This approach has not been attempted so far. A simplification can be achieved by solving the flow equation on the fine grid followed by solution of population balance equations on a very coarse grid. Some studies using this simplified approach have been reported (Alopaeus et al., 1999; Maggioris et al., 2000; Alopaeus et al., 2002). This still does not obviate the need of experimental measurements entirely as the breakage and coalescence models (Coulaloglou and Tavlarides, 1977) embedded in the population balance equations contain model constants which need to be estimated for a given system by using the experimental data. The purpose of the present study is to investigate the effect of three operating parameters impeller speed, feed phase ratio and mean residence time, on the drop size and drop size distributions and to develop suitable system specific correlations. The experimental data generated in this study will also be used to develop and validate the population balance models. This study considers aqueous in organic (A/O) dispersions. Though the A/O dispersions are not preferred in continuous plants as during settling they tend to give thicker dispersion band for the same specific settling rate (Lott et al., 1972) thereby requiring large settlers which adversely affect the plant economics, still in many instances the end stages in a mixer settler cascade are preferably operated as A/O system to avoid loss of costly organic solvent through entrainment. Since the study aims at developing suitable correlations for the representative drop sizes, it is worthwhile to review different correlations for representative drop sizes in liquid liquid dispersion in stirred tanks reported in the literature and the semiempirical theory behind the functional form used in the majority of the correlations. 2. Literature review Owing to the immense industrial importance of liquid liquid dispersions, several studies on experimental measurements of drop size in liquid liquid dispersions in stirred tanks have been reported in literature. Some of these studies are summarized in Table 1. Majority of them (Vermeulen et al., 1955; Rodger et al., 1956; Weinstein and Treybal, 1973; Mlynek and Resnick, 1972; Fernandes and Sharma, 1967; Brown and Pitt, 1974; McManamey, 1978; Calabrese et al., 1986a,b; Wang and Calabrese 1986; Nishikaw et al., 1987a,b; Laso et al., 1987; Chatzi et al., 1991; Zhou and Kresta, 1998; Pacek et al., 1999; Ruiz et al., 2002; esnoyer et al., 2003; Giapos et al., 2005; Sechremeli et al., 2006) have been done on batch vessels. Only few of them have been done on continuous flow stirred tanks (Wienstein and Treybal, 1973; Fernandes and Sharma, 1967; Quadros and Baptista, 2003). In most of the cases, the experimental data have been correlated using the functional form developed by Hinze (1955) and modified by subsequent researchers (Shinnar and Church, 1960; oulah, 1975). In some cases, altogether different functional forms are reported (Wienstein and Treybal, 1973; Quadros and Baptista, 2003). Since model of Hinze (1955) has been used in majority of cases, it is briefly discussed below for sake of completeness. The model is essentially based on identification and quantification of the restoring and disrupting forces acting on a drop of diameter d in a turbulent flow field. The dynamic pressure fluctuations or turbulent pressure fluctuations cause a stress τ t to act on the surface of the drop. Owing to the deformation of drop, an internal flow within the drop is established giving rise to an internal dynamic pressure. This dynamic pressure is of the same order of magnitude as the external pffiffiffiffiffiffiffiffiffiffistress and causes flow velocities of the order of s t =q d.the viscous stresses passociated ffiffiffiffiffiffiffiffiffiffi with this flow are of the order of ðl d =dþ s t =q d and tend to counteract the deformation of the drop. Further more, interfacial tension σ also gives rise to a surface stress of order of magnitude σ / d to counteract pffiffiffiffiffiffiffiffiffiffi the deformation. These three stresses τ t, ðl d =dþ s t =q d and σ / d govern the deformation and breakup of the drop. Combination of these three stresses gives two dimensionless groups

3 123 which control drop deformation and breakup. These groups are: We ¼ ds t r l d Vi ¼ pffiffiffiffiffiffiffiffiffiffi dq d r ð2þ ð3þ The first group is the called generalized Weber group, which is the ratio of the disrupting force due to turbulence to the restoring force due to interfacial tension. The second group is termed as viscosity group. Breakup of drop is assumed to occur when generalized Weber group assumes a critical value We crit, expression for which can be given as: We crit ¼ c 1 ½1 þ uðviþš ð4þ where φ is a function of Vi and reduces to zero when Vi 0. The effect of dispersed phase viscosity is thus to increase the critical Weber number. The dynamic turbulent pressure fluctuations as seen by a drop are caused by changes in velocity over a distance equal to the diameter of the drop. If these fluctuations are assumed to be responsible for the breakup of drops then P substitution of q cu 2 for τ t on dimensional ground in Eq. (2) leads to: We crit ¼ q cdmax 0 r P u 2 ð5þ 0 where d max is the maximum stable drop diameter i.e. the drop diameter for which Weber number is equal to the 0 critical Weber number. For drops larger than d max, the Weber number will be more than the critical number and hence they will not be stable and will under go breakage. P u 2 is the average value of the square of velocity differences over a distance equal to maximum stable 0 drop diameter, d max. It is assumed that the drops are broken by eddies having sizes of the order of the drop diameter. While the smaller eddies collide with the drops but fail to break them, the larger eddies convey the drops rather than breaking them. Therefore, if it is assumed that the drop sizes are of the order of the length scale of the inertial subrange of the turbulence spectrum, P u 2 of Eq. (5) will be independent of viscosity and can be expressed as P u 2 ~ dmax 0 e 2=3 ð6þ where e is specific turbulence energy dissipation rate. If Vi 0, then combining Eqs. (4), (5) and (6), maximum stable drop diameter can be expressed as: dmax 0 q c 3=5e 2=5 ¼ c 2 : ð7þ r For stirred tanks having agitator of diameter, rotating at speed of N with fully established turbulence: e~n 3 2 : ð8þ This reduces Eq. (7) to dmax 0 ¼ c r 3=5 3 0:8 N 1:2 ð9þ q c which can be rearranged further to d 0 max ¼ c 3We 0:6 I ð10þ where, We I is a dimensionless group called the impeller Weber number and is defined as We I ¼ N 2 3 q c : ð11þ r Eq. (10) is the most popular functional form to correlate maximum stable drop diameter in dilute dispersions. Frame work of Hinze (1955) has been extended to account for the drops that are smaller than the characteristic length scale of eddies in inertial subrange of turbulence spectrum (Shinnar and Church, 1960). In this case u P 2 depends on viscosity also and can be expressed, instead of Eq. (6), as follows: P u 2 ~ e dmax 0 2: ð12þ m d 0 max Using Eqs. (4), (5), (8) and (12) where ¼ c 4Re 1=3 I We 1=3 I Re I ¼ N2 m ð13þ ð14þ where, Re I is a dimensionless number called impeller Reynolds number. Another important parameter, effects of which can be significant in dispersions encountered in practice is the dispersed phase holdup. A high value of dispersed phase hold up is likely to increase the maximum stable drop diameter both by damping of

4 Table 1 Summary of some of the studies on liquid liquid dispersions in mechanically agitated contactors Reference Experimental Correlations Remarks Vermeulen et al. (1955) Several systems both A/O and O/A were studied in batch experiments. Paddle impeller was used. Hold up values were between 0.1 to 0.4. rop size measurement was done using light transmission technique. N 2 d 5=3 4=3 q m ¼ 0:016 rf 5=3 / f / ¼ d d /¼0:1 q m ¼ 0:6q d þ 0:4q c Effect of holdup on drop size was accounted for through a function f ϕ. Plot of f ϕ versus ϕ was reported. 124 Rodger et al. (1956) Fernandes and Sharma (1967) Mlynek and Resnick (1972) Wienstein and Treybal (1973) Seventeen different O/A dispersions were studied in batch experiments. Turbine impeller was used in the study. Holdup was equal to 0.5 in all experiments. irect photography and light transmission were used as drop size measurement techniques. ispersions of several esters in caustic soda were studied. Batch and a few continuous experiments were done to study the overall specific interfacial area by following a fast pseudo first order reaction. ifferent impellers disk turbines, paddle impellers and propellers were studied. Experiments in tanks of different sizes were also done to study the effect of scale. Holdup was varied between Batch experiments were done with mixture of CCl 4 and iso-octane as dispersed and distilled water as continuous phase. Rushton turbine impeller was used. Holdup varied between and Measurement of drop size was done by encapsulation of drops in a polymeric film using a specially designed trap. Eight different systems, O/A and A/O were studied. Both batch and continuous experiments were done. Holdup varied between Light transmission method was used for drop size measurement. Turbine impeller was used. P a ¼ K 3 N 2 0:36 q c k 1 m 5 d t r T m c t o P aant 1=2 / P aan/ ¼ 0:058We 0:6 I ð1 þ 5:4/ Þ 1 6 ¼ 10 ð 2:316þ0:672/ Þ mc 0:0722 e 0:194 r 0:196 q c ¼ 10 ð 2:066þ0:732/ Þ mc 0:047 e 0:204 r q c q exp 3:6 W q c 0:274 Correlation for specific interfacial area was obtained. Settling times were also measured and included in the correlation to obtain good fit. t 0 is the reference settling time equal to 1 min. No practical difference between batch and continuous operation drop sizes was observed. First correlation is for turbines, paddles and propellers of Tb40 cm, the second correlation is for turbines with TN40 cm. Variation in local drop sizes was found to be small. First equation is for batch vessels. The second equation is for continuous vessels. In drop size correlations for continuous systems, residence time was not included, to account for its effect a separate correlation for hold up in terms of residence time was proposed. Brown and Pitt (1974) Three O/A systems with MIBK, kerosene, n-butanol as dispersed phase and water as continuous phase were investigated. Holdup was equal to Photoelectric probe was used for drop size measurement. isk turbine impeller was used. d 5=3 32 Nt c q e 1=3 t c ¼ c T 2=3 8=3 ¼ 0:0122 r e2=3 W T T rop sizes were measured at impeller tip. t c is the circulation time given by second equation. The term in the second bracket of left hand side of first equation was include to account for the effect of geometrical parameters in the correlation for drop size. McManamey (1978) Used experimental data of other authors. ¼ c r 0:6 e 0:4 i q Showed that the whole power dissipation should be assumed to occur in the impeller swept volume only and this value should be use to correlate the drop size.

5 Calabrese et al. (1986a) Study was aimed at finding effect of dispersed phase viscosity on drop size. Silicone oils with viscosity less than 0.5 Pas were called moderately viscous, with 1 Pas intermediately viscous and more than 4 Pas as highly viscous. Five different grades of silicone oil in water were used to obtain dispersed phases of varied viscosity. Hold up was Batch experiments were done with direct photography as drop size measuring technique. Rushton turbine impeller was used. " ¼ 1 þ 11:5 q # 1=2 c l d e 1=3 d 1=3 5=3 32 d 0 q d r ¼ 2:1 l 3=8 d q c N 2 3=4 l c l c ¼ 0:6d max ¼ 0:5d max ata for intermediately viscous oils showed a lot of scatter and could not be correlated. First and third equations are for moderately viscous oils. The second and fourth equations are for highly viscous oil. ependence of on μ d for highly viscous oils was different from as expected from a semiempirical model. Log-normal drop size distributions were obtained. d 0 is the diameter of inviscid drop. Wang and Calabrese (1986) Calabrese et al. (1986b) Objective of the study was to establish relative importance of dispersed phase viscosity and interfacial tension on drop size. Silicone oils were dispersed in water, methanol and their solution. Batch experiments were done with Rushton turbine impeller. Holdup was less than irect photography was used for drop size measurement. Total 349 data from published studies, including that of previous two studies, were used to obtain the correlation of broader utility. " # ¼ 0:066We 0:66 I 1 þ 13:8Vi 0:82 d 0:33 0:59 32 V i ¼ l dn q 1=2 c r q d μ d varied between Pas and σ varied between N/m. Transition from low to moderate viscosity behavior to high viscosity behavior was found to shift toward high viscosity as σ reduced. The equation is valid for μ d b0.5 Pas. For μ d =1 Pas, a lot of scatter was observed. " #3 1 5 Unlike two previous studies, correlation here accounts for the ¼0:054 ð d þ3/ ÞWe 0:6 I 1þ 4:42ð1 2:5/ ÞV i effect of high hold up. Nishikawa et al. (1987a) Nishikawa et al. (1987b) Laso et al. (1987) Honey bee's wax was used as dispersed phase in high temperature batch mixing experiments with Rushton turbine impeller. istilled water or millet jelly was used as the continuous phase. Holdup was varied between Measurement technique used was stabilization of dispersion by siphoning it into chilled water followed by imaging under the microscope. Honey bee's wax was used as dispersed phase in the distilled water as continuous phase. Batch experiments were done with disk turbine in tanks of different sizes to study the effect of scale. Measurement technique used was stabilization of dispersion by siphoning it into chilled water followed by imaging under the microscope. ispersed phase was a mixture of CCl 4 with n-heptane or 1-octanol or MIBK. Continuous phase was water. Batch studies with flat blade turbine in a baffled tank. rop size measurement was done by siphoning the dispersion into a capillary, photographing it and sending it back to the tank. 6 ¼ 0:105e 2= þ 2:5/ 2=3 ld 5 l d 8 r 5 T l c d l c c q 3 ¼ 0:0371e 1=4 d þ 3:5/ 3=4 ld 5 l d 8 r 8 l c d l c c q ¼ 0:5d max ¼ 0:45d max 2 ¼ 0:105e T 1 1 5B T 1 þ 2:5 2 / A l d 5 l d 8 r 5 T T 0 T 0 l c d l c c q 1 ¼ 0:0371e 4 d T 4 1 þ 3:5 T 1 1 B 2 / A l d 5 l d 8 r 8 T 0 T 0 l c d l c c q It was argued that depending on value of specific power input dispersions can be coalescence or breakup controlled. As specific power input increases transition from breakup controlled to coalescence controlled takes place. First and third equations are for breakup controlled and second and fourth for coalescence controlled regime. Note that correlation for coalescence controlled regime is not dimensionless. Correlation for transition value of specific power input was also given. The correlations of the previous study were modified to incorporate the terms for the effect of scale. The first equation is for breakup controlled regime, the second equation is for coalescence controlled regime. T 0 is the reference tank diameter equal to 25 cm. ¼ 0:118We 0:4 I / 0:27 l 0:056 Holdup values not mentioned clearly, however from one of d the presented data it seems to be l c (continued on next page) 125

6 126 Table 1 (continued) Reference Experimental Correlations Remarks Chatzi et al. (1991) Zhou and Kresta (1998) Pacek et al. (1999) Ruiz et al. (2002) Batch experiments with styrene as the dispersed phase, water with 0.1 g/l PVA as the continuous phase. Holdup was equal to Impeller used was Rushton turbine. rop sizes were measured with particle size analyzer. Batch experiments with water as the continuous and silicone oil as the dispersed phase. Four different impellers A310, HE3, PBT and RT were used. Holdup was PPA (Phase oppler Particle Analyzer) was used for drop size measurement. Batch experiments were done with water as the continuous phase and chlorobenzene or sunflower oil as the dispersed phase. ifferent impellers high shear (RT), high flow (Chemineer HE3) and ultra high shear (Chemineer CS) were used. Measurements were done by direct photography near the tank wall. ispersed phase holdup ranged between 0.01to Batch experiments were done with 0.25 M sodium sulfonate solution as continuous phase and a 1:1 mixture of salicylaldoxime (LIX-860 N-IC) and a ketoxime (LIX84-IC) in an aliphatic diluent (ESCAI 103) as the dispersed phase. ispersed phase holdup ranged between Pump-mix double shrouded impeller with eight curved blades was used in the study. Single point measurement was done by siphoning dispersion in a gelatin solution followed by quick cooling in an ice bath to freeze the drops. ¼ 0:045 ð F0:003 ÞWe 0:6 I rop size distributions observed were bimodal. ¼ 118:6 e max N 2 0:270 Objective of the study was to compare different scale-up criteria such that data for different impellers can be represented by a single correlation. Relation between and d max was not found to be strictly linear. ae b d max ¼ 0:353We 0:6 I Values of the exponent, ranging between to -0.72, were tabulated as a function of impeller type, dispersed phase and dispersed phase holdup. Number volume distributions were found to be log normal. Effects of temperature, extractant concentration and ph were also investigated. Increase in temperature caused drop size to reduce. Extractant concentration in the investigated range of 7-20% (w/w) did not affect the drop size. Reduction in ph resulted in smaller drops.

7 esnoyer et al. (2003) Batch experiments with a mixture of TBP and Sobesso 150 as the continuous phase and 20 g/l NiCl 2 (a fast coalescing system) or 3 M HCl (a slow coalescing system) solution as the dispersed phase. Hold up values ranged between Impeller used was PBTU. rop size measurements were done using laser granulometer. ¼ 0:28We 0:6 I ð1 þ 0:92/ Þ ¼ 0:14We 0:6 I ð1 þ 0:48/ Þ ¼ f ð/ ÞWe n ð/ Þ=2 I Though the Sauter mean diameters could be correlated using the frame work of Hinze (1955) and oulah (1975), they could be better correlated with the functional form given in the third equation with exponent of Weber number showing dependence on holdup value. The first equation is for NiCl 2 as the dispersed phase and second for HCl as the dispersed phase. Quadros and Baptista (2003) Giapos et al. (2005) Sechremeli et al. (2006) Experiments to determine interfacial area in continuous flow stirred tank with di-isobutylene diluted with benzene as the dispersed and sulfuric acid as the aqueous phase. Impellers used were straight blade paddles with two or four number of blades. A chemical method was used to determine overall interfacial area under different operating conditions. Hold up values ranged between Impeller speeds were varied to cover a large range of Weber number. Batch experiments were done to understand the effect of number of blades on drop size for kerosene in distilled water dispersions. irect photography was employed to measured drop size which was rendered possible due to low values of holdups ranging between isk turbines with 2, 4, 6 and 8 number of blades were used in this study. Batch were done to compare drop sizes produced by a disk turbine and an open impeller having same diameter and blade width. istilled water was used as continuous and kerosene as the dispersed phase. irect photography was used to measure drop size. Holdup values ranged between ( ) c 2 1 ¼ 6/ 1 þ c 2 / 2 þ c 3 / We I / ¼ 0:0336We 0:6 I ð1 þ 13:76/ Þ ¼ 0:0286We 0:6 I ð1 þ 13:24/ Þ The first functional form was found to represent the Sauter mean diameters over a wide range of Weber number. However, for high Weber numbers (We N1900), Sauter mean diameter could be correlated using the frame work of Hinze and oulah. The second correlation is for two blade paddle while the third correlation is for four blade paddle. ~N a The exponent a was found to vary between 0.62 to 1.23 depending upon the value of holdup. As expected, an impeller with more number of blades gave finer drops compared to an impeller having less number of blade and rotating at the same speed. ~N a Values of exponent were found to range between For open impeller (power number=4), the Sauter mean diameters were larger by 6-82% than the closed impeller (power number=5). Proportionality between d max and was not observed. 127

8 128 turbulence and enhancement of frequency of drop coalescence by increasing drop population density in the continuous phase. Considering damping of turbulence in concentrated dispersions, oulah (1975) proposed the following expression to account for the increase in drop size with increase in hold up of dispersed phase. d max d 0 max ¼ ð1 þ 2:5/ Þ q 6=5 c ð15þ q m which can be generalized to the following functional form considering terms of ϕ 2 onward negligible d max dmax 0 ¼ 1 þ c 5 / þ c 6 / 2 : ð16þ 0 Using Eq. (10) for d max and Eq. (16), the functional form of the maximum stable drop diameter for high holdup of dispersed phase assumes the following form d max ¼ c 3 1 þ c 5 / þ c 6 / 2 We 0:6 I : ð17þ This functional form has been the most extensively used by different researchers to correlate their experimental data for concentrated dispersions. Functional form of Eq. (17) assumes that the dispersed phase is not viscous or that the viscosity of the dispersed phase does not contribute to the stabilization of the drop. Several studies, however, have focused on stabilization due to dispersed phase viscosity (Calabrese et al., 1986a,b; Wang and Calabrese 1986). One of such studies (Calabrese et al. 1986b), based on a large number of experimental data, proposes the following expression for the Sauter mean diameter: where " #3 1 5 ¼0:054 ð d þ3/ ÞWe 0:6 I 1þ4:42ð1 2:5/ ÞV i V i ¼ l dn r q c q d ð18þ 1=2 : ð19þ Note that, the first part of the right hand side of Eq. (18) uses the frame work of Hinze (1955) as modified by oulah (1975), the second part, the term in the bracket, accounts for the stabilization effect of the dispersed phase viscosity. Apart from the models discussed above, there exists another class of models that views the drop deformation and breakage process as Vigot element in which the stabilization effect of interfacial tension is represented by a spring element and stabilization effect due to dispersed phase viscosity as the dash pot. Both of them act in parallel to resist the deforming stress due to turbulence (Arai et al., 1977; Lagisetty et al., 1986). These models have been extended to account for effect on drop size of dispersed phase rheologies (Lagisetty et al., 1986; Koshy et al., 1988b, Gandhi and Kumar 1990), presence of surfactants (Koshy et al., 1988a) and circulation patterns (Kumar et al., 1992). Some models accounting for breakage mechanisms different from that due to turbulent pressure fluctuations have also been proposed (Kumar et al., 1991; Wichterle, 1995; Kumar et al., 1998). A few studies focusing on the fine details like the effect of intermittency of turbulence on representative drop diameter have also been presented (Baldyga and Bourne, 1993). However, as far the functional form used to fit the experimental data is concerned, the model of Hinze (1955) as extended by oulah (1975) continues to be the most popular one. 3. Experimental Fig. 1 shows the schematic diagram of the experimental setup used in this study. The experimental setup consists of a cylindrical tank of 240 mm diameter and 240 mm height. Four baffles, each of 220 mm height, having width equal to 10% of tank diameter, are provided to prevent vortex formation and enhance mixing. At the bottom plate of the tank is a suction orifice with diameter equal to 1/4 of the tank diameter. The suction orifice provides connectivity between the tank and a cylindrical chamber called suction box (65 mm diameter and equal height), which in turn is connected with two feed tanks. One of the feed tanks contains organic phase and the other aqueous phase. A four-bladed top shrouded turbine with trapezoidal blades, a pump-mix impeller, is used in the study. iameter of the turbine is 148 mm, blade width is 31 mm and blade length is 37 mm. Shaft diameter is 12 mm, hub height is 13 mm and hub outer diameter is 20 mm. Thickness of disk and blade is 2 mm. The offbottom clearance of the impeller is equal to half of the mixer height. In this position, the impeller has a power number of 3.0. The mixer has two ports for sample withdrawal with rubber-clip arrangement one in the plane of the impeller disk and the other in a plane halfway between the impeller disk and bottom of the mixer. Organic phase used in the experiments is a mixture of n-paraffin, 2EHPA and TBP. The aqueous phase is 30% phosphoric acid. The physical properties

9 129 Fig. 1. Schematic diagram of the experimental setup. of the phases are given in Table 2. At steady state, the dispersion created in the mixer overflows from the central opening (diameter equal to half of the tank diameter) in the top baffle to a horizontal settler through a full width launder. In the settler, separation of phases occurs and the clear organic flows from the top to the organic storage tank, the aqueous phase flows from bottom to the aqueous storage tank through an interface controller. From the storage tanks the phases are pumped back to the respective feed tanks from where they are again sucked into the mixer by the pumping action of the pump-mix impeller. The flow rates are maintained at desired values using the valves and flowmeters located downstream of the pumps. Thus the system is operated in a closed loop. Before starting the actual experiments, phases were equilibrated by running the system for 24 h. All the experiments were conducted with aqueous as the dispersed phase. Filling the mixer fully with organic at the time of startup ensured organic continuity. Total 27 experiments were conducted for different impeller speeds, feed phase ratios and mean residence times of the phases in the mixer. The range over which these variables were varied is given in Table 2. Unlike the batch mixing studies where impeller speed can be varied over a wide range (between the speed required for visual homogenization and speed at which air entrapment takes place), the upper limit of the speed in the continuous mixing studies is limited by the phase separation characteristics of the dispersion in the settler. Owing to a low interfacial tension, the systems studied here is easy to disperse and difficult to separate and even at low impeller speeds the dispersion band tends to flood the settler. This effectively limits the upper limit of speed variation and hence the relatively narrow range of impeller speed as given in Table 2. For each experiment, attainment of steady state was observed by following the thickness of the dispersion band in the settler which was measured every 15 min and steady state was deemed to have been achieved when three consecutive measurements were almost same. Typical time required to attain the steady state was about 3 h. After attainment of steady state, samples of dispersion were withdrawn from sample ports into measuring cylinders. From the volumes of the settled phases, local values of the hold up were computed. To Table 2 Physical properties of the phases (at 25 C) and range of variables studied Phase ρ (kg/m 3 ) μ (cp) σ s (N/m) Organic Aqueous N (rpm) τ (min) ϕ f Range of variables

10 130 For each case, at least three hundred drops were measured to ensure good statistical accuracy. Fig. 2 shows a typical image of the stabilized dispersion. A similar method of measuring the drop size in emulsions produced in simple shear flow has been reported recently (Nandi et al., 2006). At the end of each experiment, impeller was stopped and the valves connecting the feed tanks to the mixer were simultaneously closed. Following the settling of the dispersion, the volume occupied by the separated phases were measured to compute the average holdup in the mixer. From the measurements of the counted drops, maximum drop diameter, Sauter mean diameter and drop size distribution were obtained. The Sauter mean diameter was obtained using the following expression: Fig. 2. A typical image of the stabilized dispersion. ¼ P d 3 P d 2 : ð20þ measure the drop sizes, the sample of dispersion was withdrawn into petri dish containing the organic phase laden with a surfactant (sorbitan monooleate) presence of which prevented the coalescence of drops and thus stabilized the dispersion. The dish containing stabilized dispersion was kept under a microscope mounted on a camera which in turn was connected to a personal computer. Since the field of view of this imaging system was small, the full image of the stabilized dispersion was not obtained in a single frame. Therefore, by systematically moving the dish under the microscope several images, sufficient to give adequate numbers of drops, of the stabilized dispersion were captured. Utmost care was taken to avoid imaging the same area twice. The images were analyzed using an image processing software. 4. Results and discussion 4.1. Characteristic drop diameter Most of the studies on drop size distribution in agitated tanks have been performed in batch mode. In these studies the dispersed phase holdup is an independent variable. However, in continuous flow agitated tanks, the hold up in the tank is not an independent variable as it may change with, apart from feed phase ratio, impeller speed and mean residence time. Using the holdup in tank as a correlating variable for continuous flow agitated tanks will therefore not indicate the true dependence of drop diameter on speed and mean residence time. Considering this, the feed phase fraction, instead of holdup in the tank, is used to correlate the drop diameter. To decipher the functional form of the relationship between the Sauter Fig. 3. Comparison of Sauter mean diameters at upper and lower sampling locations, as predicted by Eqs. (21) and (22).

11 131 mean diameter and the three independent variables, the experimental data were used to train a neural network based on back propagation algorithm. The response of the trained neural network indicated that the Sauter mean diameter could be correlated as a quadratic function of the feed holdup, a power law function of the impeller speed and an exponential function of mean residence time. This led to the selection of the functional form for the correlation of the Sauter mean diameter, as given in (21) (23). Note that this functional form resembles the form suggested by Eq. (17) albeit with vessel holdup replaced with the feed holdup and an additional multiplicative function to account for the effect of mean residence time on Sauter mean diameter. The values of coefficients and exponents were obtained by using Gauss Newton algorithm. The final correlations are given below: ¼ 1: N 1:681 1 þ 2:6539/ f þ1:3986/ 2 ð21þ f exp ð0:4457sþ for the upper sampling location and ¼ 2: N 1: :8785/ f þ 4:2848/ 2 f exp ð0:4148sþ ð22þ for the lower sampling location. Fig. 3 shows the comparison of Sauter mean diameters as predicted by Eqs. (21) and (22) with±10% error bars around the diameters observed at the upper sampling location. As can be seen the diameters at the upper sampling location, owing to it being in the plane of the impeller discharge stream, are marginally smaller than the diameters at the lower sampling location. However, difference being small, it can be assumed that the quality of dispersion is more or less homogeneous and it is better to have a single correlation for Sauter mean diameter for practical utility. This correlation was found to be: ¼ 1: N 1:7025 1þ0:392/ f þ3:2435/ 2 f exp ð0:4302sþ: ð23þ Fig. 4 shows the parity plot for Eq. (23). The quantitative estimate of the goodness of the fit of correlation given by Eq. (23) is given in Table 3. The ±95% confidence intervals (raper and Smith, 1966) of the regressed model constants are given in Table 4. As can be seen that for most of the constants the confidence intervals are reasonably narrow thereby indicating good statistical accuracy of the correlation given by Eq. (23). Since in the present study effects of impeller diameter and physical properties on drop size have not been investigated, Weber number will not be a proper correlating variable. However, in order to be in line with the correlation reported in literature, it would be interesting to recast Eq. (23) in terms of Weber number, as follows ¼ 2: We 0:85125 I 1þ0:392/ f þ3:2435/ 2 f expð0:4302sþ: ð24þ In the above correlations τ is the mean residence time, in minutes, of the phases in the mixer. The above correlations show that the characteristic drop size reduces with increase in speed and increases with an increase in feed holdup. This is in conformity with the trend of semiempirical model represented by Eq. (17). The exponent on N is also close to the value of 1.2 as suggested by the semiempirical model. The correlations show that, for the range of the experiments, the drop size increases with increase in mean residence time. This appears to be contradictory to the expectation that increasing mean residence time should ensure longer interaction between the impeller and the droplets and hence should result into a smaller Fig. 4. Parity plot for the Sauter mean diameter predicted by Eq. (23).

12 132 Table 3 Goodness of fit of different correlations presented in this work Equation For E max E avg Beyond ±15% 21 Sauter mean diameter at the upper sampling location /27 22 Sauter mean diameter at the lower sampling location /27 23 Average Sauter mean diameter /54 25 Local holdup at the upper sampling location /27 26 Local holdup at the lower sampling location /27 27 Vessel average holdup /27 28 Relationship between Sauter mean diameter and d max /54 30 Variance of the log-normal drop size distributions /54 31 Mean of the log-normal drop size distributions /54 characteristic drop size. This will be explained in the next section. It would be interesting to compare the correlation of Eq. (23) with some of the correlations compiled in Table 1 for their effectiveness to predict the experimental data reported in this work. Fig. 5 shows this comparison. As can be seen from Fig. 5, whereas the correlation of Eq. (23) gives predictions closer to the experimental data, the other correlations reported earlier exhibit large deviations. This is not surprising considering that the drop size distributions in stirred liquid liquid dispersions are highly system specific due to their being dependent on the physical properties of the phases, phase continuity, impeller type, mode of operation and geometric configuration of the mixer. Among the compared correlations, the correlation obtained with TBP containing organic as the continuous phase and an acidic phase as the dispersed phase (esnoyer et al., 2003) exhibits the least deviation form the correlation given by Eq. (23). This may be attributed to the identical phase continuity and similar nature of the phases Holdup To have an estimate of the specific interfacial area, in addition to the correlation for the Sauter mean diameter, the correlation for dispersed phase hold up in the mixer is also required. Whereas, in a batch mixer, hold up of the dispersed phase varies from one location to another (Wang and Mao, 2005; Wang et al., 2006), for a continuous flow stirred tank both local and vessel average values, in general, can be different from the feed holdup. The local and vessel average values will depend on the impeller speed, mean residence time and feed holdup. The local and vessel average holdup in the present study could be correlated as a power law function of the independent variables. These correlations are as follows: / ¼ 2:0274/ 0:3569 f N 1:1288 s 0:1153 ð25þ for the upper sampling location and / ¼ 2:3173/ 0:3583 f N 1:2389 s 0:1389 ð26þ for the lower sampling location and P / ¼ 2:1214/ 0:4012 f N 1:097 s 0:0631 ð27þ for vessel average holdup values. Apart from being useful in predicting the specific interfacial area, these correlations are important in deciding the intrastage recycle flow rate in order to have a desired phase ratio in the mixer. As expected, the local and vessel average holdup increase with increasing feed holdup. In the present case, the heavy phase being the dispersed phase and the outlet of dispersion being from the top of the mixer, the holdup values in the tank were observed to be larger than the feed holdup. For any system, increasing influence of impeller should tend to bridge the gap between the holdup in the vessel and the feed holdup. The increasing influence of the impeller can be due to increasing impeller speed or increasing mean residence time. For the case of heavy phase as dispersed phase and outlet from the top of the mixer, the hold up in the vessel Table 4 Confidence intervals for model constants of Eqs. (23) and (27) Equation Model constant Regressed value ±95% confidence interval 23 Multiplicative constant on right hand side ( , ) 23 Exponent on N ( , ) 23 Coefficient of ϕ f (0.1851, ) 23 2 Coefficient of ϕ f (2.7371, ) 23 Coefficient of τ (0.3824, ) 27 Multiplicative constant on right hand side (2.1091, ) 27 Exponent on ϕ f (0.3876, ) 27 Exponent on N ( , ) 27 Exponent on τ ( , )

13 133 Fig. 5. Comparison of correlation of Eq. (23) with some of the correlations reported earlier. should, therefore, reduce with increasing impeller speed and increasing mean residence time. This explains the negative exponents on N and τ in Eqs. (25) (27). Now the dependence of the Sauter mean diameter on mean residence time, as seen earlier, can be explained. The increasing residence time reduces the dispersed phase holdup in the mixer. This will tend to reduce the drop size. However, the heavy phase being the dispersed phase, the effective density of the dispersion also reduces and for the same impeller speed power introduced in the system also reduces. This reduction in the power input tends to increase the drop size. The eventual trend of dependence of drop size on mean residence time will, therefore, depend on the relative importance of these two opposing effects and can be either positive, as seen in the present case, or negative. At high impeller speeds, the holdup in the tank will be very close to the feed holdup irrespective of the mean residence time and in that case it is quite likely that the mean residence time will not have an effect on the drop size. This probably explains the similar drop sizes observed for both batch and continuous mixers in an earlier study (Fernandes and Sharma, 1967). Eqs. (21), (22) and (23) when used with Eqs. (25), (26) and (27), respectively, give the local and vessel average specific interfacial area for specified values of the independent variable (impeller speed, mean residence time and feed holdup). Quantitative estimate of goodness of fit of Eqs. (25) (27) is given in Table 3. The ± 95% confidence intervals of the evaluated model constants of Eq. (27) are given in Table Relationship between and d max Several studies report on direct proportionality between the Sauter mean diameter and maximum stable drop diameter (Brown and Pitt, 1972; Nishikawa et al.,1987a; Collias and Pruddhornme, 1992; Zerfa and Brooks, 1996; Calabrese et al., 1986a). However, a few studies contradict this view (Zhou and Fig. 6. Relationship between the maximum drop diameter and the Sauter mean diameter.

14 134 Fig. 7. Comparison of experimental and log-normal drop size distributions for Q o =300 lph, Q a =200 lph, N=120 rpm, class interval equal to 20 μm. Kresta, 1998; Sechremeli et al., 2006). The system studied here, however, tends to exhibit the direct proportionality between the two representative diameters, as shown in Fig. 6. Considering the inherent uncertainty associated with measurement of d max (there is only one drop with diameter equal to d max and hence there are fair chances that it can escape imaging), the linear fit of Fig. 6 is reasonably good. The two representative diameters can be correlated by the following equation: ¼ 0:5446d max : ð28þ The constant of Eq. (28) compares well with the values reported in the literature, as reported for some of the previous studies summarized in the Table rop size distributions Several distributions were tried but log-normal distributions were found to give the best fit to the experimentally observed drop size distributions. The number probability density of this distribution is given by: " # fðdþ ¼ 1 ðlnd lp Þ 2 pffiffiffiffiffi exp ds 2p 2s 2 : ð29þ Figs. 7 and 8 show the graphical comparison of experimental and log-normal drop size distributions for two of the cases. A good agreement between the number probability density as predicted by log-normal distribution and experimental distribution can be observed. s and μ of Eq. (29) could be correlated as a power law function of impeller speed, feed holdup and mean residence time as follows: s ¼ 0:806 N 0:838 / 0:0578 f s 0:0788 ð30þ l P ¼ 6:3873 N 0:2078 / 0:1406 f s 0:1508 : ð31þ Goodness of fit of Eqs. (30) and (31) is quantified in Table 3. Fig. 8. Comparison of experimental and log-normal drop size distributions for Q o =400 lph, Q a =150 lph, N=120 rpm, class interval equal to 20 μm.

15 Conclusions Measurements of drop size distributions have been performed for aqueous in organic dispersions in continuous flow stirred tank with a mixture of n-paraffin, 2EHPA and TBP as the organic phase and dilute phosphoric acid as the aqueous phase. Surfactant stabilization has been used as drop size measuring technique. The experimentally measured drop size distributions exhibit log-normal behavior in droplet number density. The characteristic drop sizes exhibit insignificant spatial variations. The Sauter mean diameters have been correlated with impeller speed, dispersed phase feed fraction and mean residence time. Local and vessel average values of hold up have also been correlated. Proportionality between the Sauter mean diameter and the maximum stable diameter is observed. Nomenclature ā Specific interfacial area [L 1 ] c i Constant [ ] Impeller diameter [L] d roplet diameter [L] d 0 iameter of inviscid drop in correlation of Calabrese et al. (1986a) [L] Sauter mean diameter [L] d max Maximum stable drop diameter [L] 0 d max Maximum stable drop diameter in dilute dispersions [L] E avg Average percentage error [ ] E max Maximum percentage error [ ] f(d) Number probability density distribution [L 1 ] f(ϕ) A function of hold up in correlation of esnoyer et al. (2003) [ ] K A constant in correlation of Rodger et al. (1956) [ ] n(ϕ) A function of hold up in correlation of esnoyer et al. (2003) [ ] N Impeller speed [T 1 ] Q a Aqueous phase flow rate [L 3 T 1 ] Q o Organic phase flow rate [L 3 T 1 ] Re I Impeller Reynolds number [ ] t Settling time in correlation of Rodger et al. (1956) [T] t 0 Reference settling time (equal to 1 min) in correlation of Rodger et al. (1956) [T] T Tank diameter [L] T 0 Reference tank diameter (25 cm) in correlation of Nishikawa et al. (1987b) [L] t c Circulation time in correlation of Brown et al. (1974) [T] P u 2 V i W We We crit We I Average relative velocity between two points separatedbyadistancedin turbulent field [L 2 T 2 ] Viscosity group [ ] Width of the impeller blade [L] Generalized Weber group [ ] Critical Weber number [ ] Impeller Weber number [ ] Greek letters e Specific turbulent energy dissipation rate [L 2 T 3 ] e i Specific turbulent energy dissipation rate in impeller region [L 2 T 3 ] e max Maximum specific turbulent energy dissipation rate [L 2 T 3 ] μ Mean of log-normal drop size distributions [ ] μ d Viscosity of dispersed phase [ML 1 T 1 ] μ c Viscosity of continuous phase [ML 1 T 1 ] ν Kinematic viscosity [L 2 T 1 ] ϕ Local dispersed phase holdup [ ] ϕ Vessel average dispersed phase holdup [ ] ϕ f ispersed phase feed holdup [ ] φ Function of V i [ ] ψ A scale-up function in correlation of Rodger et al. (1956) [ ] ρ c ensity of continuous phase [ML 3 ] ρ d ensity of dispersed phase [ML 3 ] ρ m Effective density of the dispersion [ML 3 ] σ Interfacial tension [MT 2 ] σ s Surface tension [MT 2 ] τ Mean residence time [T] τ t Stress on droplet surface due to turbulent flow field [ML 1 T 2 ] References Alopaeus, V., Koskinen, J., Kosiken, K.I., Simulation of the population balance for liquid liquid systems in a nonideal stirred tank. Part I. escription and qualitative validation of the model. Chem. Eng. Sci. 54, Alopaeus, V., Koskinen, J., Kosiken, K.I., Majander, J., Simulation of the population balance for liquid liquid systems in a nonideal stirred tank. Part II. Parameter fitting and use of the multiblock model for dense dispersion. Chem. Eng. Sci. 57, Arai, K., Konno, M., Matunaga, Y., Saito, S., Effect of dispersed phase viscosity on the maximum stable drop size for breakup in turbulent flow. J. Chem. Eng. Jpn. 10 (4), 325. Baldyga, J., Bourne, J.R., rop breakup and intermittent turbulence. J. Chem. Eng. Jpn. 26 (6), 738. Brown,., Pitt, K., rop size distribution of stirred noncoalescing liquid liquid system. Chem. Eng. Sci. 27, 577. Brown,.E., Pitt, K., Effect of impeller geometry on drop breakup in a stirred liquid liquid contactor. Chem. Eng. Sci. 29, 345.

16 136 Calabrese, R.V., Chang, T.P.K., ang, P.T., 1986a. rop breakup in turbulent stirred tank contactors, Part-I: effect of dispersed phase viscosity. AIChE J. 32, 657. Calabrese, R.V., Wang, C.Y., Bryner, N.P., 1986b. rop breakup in turbulent stirred tank contactors, Part-III: correlation for mean size and drop size distributions. AIChE J. 32, 677. Chatzi, E.G., Boutris, C.J., Kiparissides, C., Online monitoring of drop size distributions in agitated vessels. Effect of temperature and impeller speed. Ind. Eng. Chem. Res. 30, 536. Collias,.I., Pruddhornme, R.K., iagnostic techniques of mixing effectiveness: the effect of shear and elongation in drop production in mixing tanks. Chem. Eng. Sci. 47 (6), Coulaloglou, C.A., Tavlarides, L.L., escription of interaction processes in agitated liquid liquid dispersions. Chem. Eng. Sci. 32, Cutter, L.A., Flow and turbulence in a stirred tanks. AIChEJ 12, 35. esnoyer, C., Masbernat, O., Gourdon, C., Experimental study of drop size distribution at high phase ratio in liquid liquid dispersions. Chem. Eng. Sci. 58, oulah, S.M., An effect of hold-up on drop sizes in liquid liquid dispersions. Ind. Eng. Chem. Fund. 14 (2), 137. raper, N.R., Smith, H., Applied regression analysis. John Wiley & Sons Inc., New York. Fernandes, J.B., Sharma, M.M., Effective interfacial area in agitated liquid liquid contactors. Chem. Eng. Sci. 22, Gandhi, K.S., Kumar, R., An elongational flow model for drop breakage in stirred turbulent dispersions. Chem. Eng. Sci. 45 (9), Giapos, A., Pachatouridis, C., Stamatoudis, M., Effect of the number of impeller blades on the drop sizes in agitated dispersions. Chem. Eng. Res. es. 83 (A12), Hinze, J.O., Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1, 289. Koshy, A., as, T.R., Kumar, R., 1988a. Effect of surfactant on drop breakage in turbulent liquid dispersions. Chem. Eng. Sci. 43 (3), 649. Koshy, A., as, T.R., Kumar, R., Gandhi, K.S., 1988b. Breakage of viscoelastic drops in turbulent stirred dispersions. Chem. Eng. Sci. 43 (10), Kumar, S., Kumar, R., Gandhi, K.S., Alternative mechanisms of drop breakage in stirred vessels. Chem. Eng. Sci. 46, Kumar, S., Kumar, R., Gandhi, K.S., A multi-stage model for drop breakage in stirred vessels. Chem. Eng. Sci. 47 (5), 971. Kumar, S., Ganvir, V., Satyanand, C., Kumar, R., Gandhi, K.S., Alternative mechanisms of drop breakup in stirred vessels. Chem. Eng. Sci. 53 (18), Lagisetty, J.S., as, P.K., Kumar, R., Gandhi, K.S., Breakage of viscous and non-newtonian drops in stirred dispersions. Chem. Eng. Sci. 41, 65. Laso, M., Steiner, L., Hartland, S., ynamic simulation of agitated liquid liquid dispersions II. Experimental determination of breakage and coalescence rates in a stirred tank. Chem. Eng. Sci. 42 (10), Lott, J.B., Warwick, G.I., Scuffham, J.B., esign of large scale mixer settlers. Trans. Soc. Mining Engrs. 252, Maggioris,., Goulas, A., Alexopoulos, A.H., Chatzi, E.G., Kiparissides, C., Prediction of particle size distribution in suspension polymerisation reactors: effect of turbulence nonhomoeniety. Chem. Eng. Sci. 55, McManamey, W.J., Sauter mean and maximum drop diameters of liquid liquid dispersions in turbulent agitated vessels at low dispersed phase holdup. Chem. Eng. Sci. 34, 432. Mlynek, Y., Resnick, W., rop size in an agitated liquid liquid system. AIChE J. 18, 122. Nandi, A., Mehra, A., Khakhar,.V., Coalescence in a surfactantless emulsion under simple shear flow. AIChE J. 52 (3), 885. Nishikawa, M., Mori, F., Fujieda, S., 1987a. Average drop size in a liquid liquid phase mixing vessel. J. Chem. Eng. Jpn. 20 (1), 82. Nishikawa, M., Mori, F., Fujieda, S., Kayama, T., 1987b. Scaleup of liquid liquid phase mixing vessel. J. Chem. Eng. Jpn. 20 (5), 454. Pacek, A.W., Chasart, 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. 54, Quadros, P.A., Baptista, C.M.S.G., Effective interfacial area in agitated liquid liquid continuous reactors. Chem. Eng. Sci. 58 (17), Rodger, W.A., Trice, V.G., Rushton, J.H., Effect of fluid motion on interfacial area of dispersions. Chem. Eng. Prog. 52 (12), 515. Ruiz, M.C., Lermanda, P., Padilla, R., rop size distribution in a batch mixer under breakage conditions. Hydrometallurgy 63, Sechremeli,., 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. 117, Shinnar, R., Church, J.M., Statistical theories of turbulence in predicting particle size in agitated dispersions. Ind. Eng. Chem. Res. 52, 253. Vermeulen, T., Williams, G.M., Langlois, G.E., Interfacial area in liquid liquid and gas liquid agitation. Chem. Eng. Prog. 51 (2), 85-F. Wang, C.Y., Calabrese, R.V., rop breakup in turbulent stirred tank contactors. Part II: relative influence of viscosity and interfacial tension. AIChE J. 32 (4), 667. Wang, F., Mao, Z., Numerical and experimental investigation of liquid liquid two-phase flow in stirred tanks. Ind. Eng. Chem. Res. 44, Wang, F., Mao, Z., Wang, Y., Yang, C., Measurement of phase holdups in liquid liquid solid three-phase stirred tanks and CF simulations. Chem. Eng. Sci. 61, Weinstein, B., Treybal, R.E., Liquid liquid contacting in unbaffled agitated vessels. AIChE J. 19, 304. Wichterle, K., rop breakup by impellers. Chem. Eng. Sci. 50 (22), Zerfa, M., Brooks, B.W., Prediction of vinyl chloride drop sizes in stabilized liquid liquid dispersions. Chem. Eng. Sci. 51 (12), 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. 53 (11), l063.