The extent to which dispersed-phase viscosity influences equilibrium mean drop size and drop size distribution at constant interfacial tension is determined for dilute suspensions by dispersing silicone oils of various viscosity grades in water. A mechanistic model for mean drop size is developed which predicts the moderate-viscosity data and whose parameters correlate the high-viscosity results. Trends in the mean size data coincide with those for the drop size distribution, which broadens considerably as viscosity increases and suggests a dependency on breakage mechanism.Drops are stabilized in dilute agitated liquid-liquid systems by surface and dispersed-phase viscous forces and are broken up by forces associated with the continuous-phase turbulence. Most studies have been limited to surface force stabilized dispersions, so the extent to which dispersed-phase viscosity influences mean drop size and drop size distribution is not well understood.For inviscid dispersed phases, equilibrium mean drop sizes produced by turbulent stirred-tank contacting processes are correlated by the well-known Weber number theory. This semiempirical theory, as applied to dilute suspensions, has been extended via mechanistic arguments to account for the effect of dispersedphase viscosity. A viscosity group, N,, is introduced which accounts for the importance of dispersed-phase viscosity relative to interfacial tension. Numerous experiments were conducted in four, baffled cylindrical tanks of standard geometry, equipped with six-blade Rushton turbines, by photographically examining dilute suspensions of silicone oils in water. Five grades of oil, ranging in viscosity from about 0.1 to 10 Pa -s and exhibiting the same interfacial tension with water ([0.0378 N / m), were employed. The range of variables studied includes 13,000 < Re < 101.000. 44 < We < 1.137, and 0.065 < < 0.50 m2/s3. The objectives of the experimental program were to examine the extent to which dispersed-phase viscosity influences equilibrium mean drop size and drop size distribution at constant interfacial tension, and to determine the relevance of the predicted correlating parameters and the range of applicability of the semiempirical theory.Results are compared to the data of Chen and Middleman (1967) for inviscid dispersed phases and the limited data of Arai et al. (1977) for viscous drops. Trends in the data are interpreted in light of the relevant correlating variables, the functional form of the drop size distribution, and the mechanism of drop breakup. AIChE JournalApril 1986 Vol. 32, No. 4 CONCLUSIONS AND SIGNIFICANCEThe experimental data have been analyzed and compared to the derived correlations and to literature data for inviscid dispered phases. The following conclusions apply to the range of variables studied.1. At constant conditions of agitation, the equilibrium drop size distribution broadens considerably as dispersed-phase viscosity, pd, increases. The size of the smallest drops decreases, while their number increases. The size of the largest drops ...

The relative influence of dispersed-phase viscosity and interfacial tension on equilibrium drop size and drop size distribution is studied for dilute suspensions by dispersing various silicone oils in water, methanol, and their solutions. Correlations for Sauter mean diameter, Da2, are developed in terms of system variables using the mechanistic models of Part 1. Drop sizes for low to moderate viscosity dispersed phases are normally distributed in volume and can be correlated by normalization with DS2. Trends in the distributions are explained in terms of a parameter representing the relative resistance to breakage. C. Y. Wang and R. V. Calabrese SCOPEIn Part I the effect of dispersed-phase viscosity on mean equilibrium drop size and size distribution was examined for dilute liquid-liquid systems exhibiting constant interfacial tension. Moderate (& = 0.1 and 0.5 Pa -s) and high (pi = 5. and 10 Pa . s ) viscosity dispersed phases behaved differently with respect to the dependency of mean size on system variables and the functional form of the size distribution, and were separated by a region of erratic behavior. The study was, in many respects, a survey that determined the scope of the problem and defined the relevant parameters for data correlation.This study focuses in more detail on dilute liquid-liquid systems with low to moderate (0.001 I p& I 0.5 Pa -s) viscosity dispersed phases. The major objectives are to determine the relative contribution of interfacial tension and viscosity to drop stability, and to develop practical correlations for mean size and drop size distribution that remain valid in the limit of an inviscid dispersed phase. Additionally, an intermediate NY.cia1 tension, B , to gain insight into the influence of on the transition between moderate-and high-viscosity behavior.The results of numerous experiments, conducted in the geometry of Part I using similar techniques, are reported for dilute dispersions of silicone oils in water, methanol, and their solutions. Since these oils exhibit about the same interfacial tension with a given continuous phase, it was possible to systematically vary viscosity and interfacial tension over the range 0.001 < p& < 1 Pa -s and 0.001 < cr' < 0.045 N/m.The semiempirical theory of Part I is used to develop correlations for equilibrium mean drop size and a criterion for when viscous resistance to breakage can be neglected. These are in terms of two dimensionless groups containing only system variables, namely, tank Weber number, We, and viscosity group, Vi. A parameter ER, which is a measure of the relative resistance to breakage, is defined to aid in data interpretation and the development of a correlation for equilibrium drop size distribution.The range of variables studied includes 54 < We < 7 1,000,0.004 1 < Vi < 640, and 14,000 .= Re < 83,000. The results apply to dilute (noncoalescing) suspensions produced by six-blade Rushton turbines in baffled cylindrical tanks of standard geometry. AIChE JournalApril 1986 Vol. 32, No. 4 667 CONCLUSIONS AND SIGNIFICANC...

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In Part 11, the extent to which dispersed-phase viscosity and interfacial tension influence equilibrium mean drop size and drop size distribution was determined for dilute suspensions produced in baffled cylindrical tanks of standard geometry equipped with six-blade Rushton turbines. Low to moderate viscosity (pd 5 0.5 Pa-s) dispersed-phase systems behaved similarly in that Sauter mean diameter could be correlated using the mechanistic arguments of Part I, and drop sizes, normalized with respect to D,z, could be correlated by a normal distribution in volume. Limited moderate viscosity data were reported in Part I but were not used to develop the correlations of Part 11. The objective of this study is to combine the low to moderate viscosity data of Parts I and I1 with those obtained by other investigators to obtain correlations of broader utility, and to extend these via mechanistic arguments so that they apply to nondilute systems. Dilute DispersionsSeveral investigators have studied the behavior of dilute liquid-liquid systems in the geometry of Parts I and I1 (see Figure 1 of Part I). Chen and Middleman (1967) conducted a detailed study of surface forced stabilized (low pd) dispersions encompassing a broad range of operating conditions. They considered dispersed phases with viscosities up to about 0.025 Pa. s but did not account for viscous resistance to breakage when correlating their data. Sprow (1967) NY.employed in these studies differed from that of Parts I and I1 in only two respects. Baffles were mounted flush to tank walls and bottom. Chen and Middleman varied the ratio of impeller to tank diameter ( L I T ) and Sprow obtained most of his data forFor dilute suspensions, coalescence rates are negligible. Equilibrium drop sizes are determined by breakup that occurs primarily in the impeller region. Small modifications in baffle placement should be relatively unimportant and the L/ T ratio should be of secondary importance. Chen and Middleman found that the effect of L/Tfell within the scatter in their data for the range 0.21 5 L / T 5 0.73. However, it should be noted that Okamot0 et al. (198 1) report that energy dissipation rates become more uniform as LIT increases. Therefore, the ratio of the maximum to mean energy dissipation rate per unit mass increases as L/ T decreases. For a given t, drops will experience higher local turbulent energy as LIT decreases, indicating that D,, should decrease with L f T. Mean drop size correlationsThe low to moderate viscosity data reported in Parts I and I1 and by the cited investigators were fit to models developed in Part 11. The range of variables investigated in each study is summarized in Table 1. The table provides Two models were fitted to the 349 data sets via nonlinear least-squares regression. These are the semitheoretical model LIT = 0.29.

Drops are stabilized in agitated liquid-liquid systems by both surface and internal viscous forces. The dispersion of an inviscid liquid into a turbulent continuous phase in static mixers has been studied but the effect of dispersed phase viscosity is not well understood. Systematic experiments have been conducted in a Kenics mixer by photographically examining dilute suspensions of viscous oils in water to determine how viscosity and conditions of agitation affect equilibrium mean drop size and size distribution. A semiempirical theory is developed which correlates the mean size data and collapses to the well-known Weber number result in the inviscid limit. A correlation for drop size distribution in terms of cumulative volume frequency is developed by normalization with the Sauter mean diameter D32. Measurements at the mixer entrance indicate that the method of introduction of the dispersed phase should be considered when evaluating mixer performance. IntroductionWhile the determination of interfacial area for liquid-liquid dispersions produced in turbulent stirred-tank contactors has commanded considerable attention (Tavlarides and Stamatoudis, 1981), few studies have focused upon continuous, in-line mixers. Yet static mixers offer an attractive alternative to stirred vessels due to narrower residence time distribution, lower capital and operating costs, and minimal maintenance requirements.Middleman (1974) measured drop size distributions in Kenics mixers by producing dilute suspensions of six different organic liquids in water. He found that equilibrium was achieved after about n, = 10 mixer elements. For inviscid dispersed phases (&, 5 1 mPa . s) the equilibrium data were well correlated by where We = p,v2D,/cr is the system Weber number. Middleman derived Eq. 1 by assuming that the disruptive energy acting upon a drop was due to inertial subrange eddies and that drop stability was due only to interfacial tension. A slight dependency Corrcspondcnce concerning thib paper should be addresscd to R V. Calabrcsc on Reynolds number resulted and was ignored. As expected, Eq. 1 failed to correlate his data for 5 5 & , 5 26 mPa -s. Equilibrium drop size distributions were found to be normally distributed in volume and were correlated by normalization with the Sauter mean diameter D3*. Additional data for benzene-water dispersions (&, = 0.6 mPa . s) showed that mean drop diameter was independent of dispersed phase volume fraction for 0.01 -=c @ < 0.25. Chen and Libby (1978) dispersed kerosene and mineral oil in water in a Kenics mixer. They correlated mean drop size data, empirically, in terms of Weber number and viscosity ratio. A single drop size distribution was reported. Al Taweel and Walker (1983) measured mean drop size for dilute dispersions of kerosene in water in two different configurations of a Lightnin "In-liner" mixer. The systematically varied energy dissipation rate (average velocity) and the number of mixer elements (residence time). They reported the number of elements required to achieve equilibriu...