Ind. Eng. Chem. Res. 1990,29, 1300-1306
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SEPARATIONS Minimum Impeller Speeds for Complete Dispersion of Non-Newtonian Liquid-Liquid Systems in Baffled Vessels A. H. P.Skelland* and J e f f r e y S.Kanel School of Chemical Engineering, The Georgia Institute of Technology, Atlanta, Georgia 30332
The minimum impeller speed needed to completely disperse a Newtonian fluid in a pseudoplastic continuous phase was accurately predicted by the Skelland and Ramsay correlation (eq 12). The overall absolute deviation was 8.9% for 120 runs when Vermeulen e t al.’s viscosity expression was combined with Metzner and Otto’s definition of apparent viscosity, pA,in place of pc. The variables included four pseudoplastic fluids with flow behavior indices between 0.52 and 0.83, three 4 values (0.5, 0.33, 0.167), and four common impeller types in a baffled vessel. Liquid-liquid dispersions occur commonly in industry. Often one of the liquid phases is non-Newtonian, as in liquid-liquid extraction for the recovery of antibiotics from fermentation broths and in emulsion polymerization. In such contactors, the immiscible liquids are mixed by an impeller rotating at a speed sufficient to ensure complete dispersion. Previous studies on such minimum impeller speeds are summarized in Table I. Differences are noted in exponents on several variables among these correlations; for example, exponents on D, po and u vary significantly from one expression to another. The relation by Skelland and Ramsay (1987) (eqs 9-13) is based on 251 runs of their own, 35 by van Heuven and Beek (1971),and 195 by Skelland and Seksaria (1978). The variables included 5 common types of impellers, 2 generating axial flow and 3 radial flow in 4 locations, fluid properties in 11 systems, 3 tank diameters, 3 impeller diameters, liquid height, and volume fraction of the dispersed phase. Fluid properties included a 31-fold range of dispersed-phase viscosity, pd [shown by Calabrese et al. (1986a,b)and Wang and Calabrese (1986) to be important in determining the drop size and hence Nmi,],a 400-fold range of continuous-phase “viscosity”, p A (including the present data), a 7-fold range of interfacial tension, u, and a 14.5-fold range of density difference, Ap. Concerning the use of pM and pM (eqs 10 and 11)in eqs 9, 12, and 13, Hong and Lee (1985) have proved that “continuous” reduction in the mean drop size occurs in an agitated liquid-liquid dispersion, until a state of equilibrium is reached at which the drop breakage rate equals the drop coalescence rate. This continual generation of new interface, together with the maintenance of shearing flow and the overcoming of gravitational effects, necessitates a steady rate of consumption and dissipation of energy (i.e., power consumption) by the vessel contents. But power consumption in agitated liquid-liquid systems has been shown by Laity and Treybal(l957) to be best characterized in terms of pM and pM, the latter having been introduced by Miller and Mann (1944). Since the same phenomena (namely shearing flow with drop breakage and coalescence, plus the overcoming of gravitational effects) are involved in determining “in, pM and pM were also used-with success-in its correlation as eq 9. The latter expression 0888-5885/90/ 2629- 13OO$Q2.50/0
emerged from the use of dimensional analysis and statistical techniques in correlating all the above variables in a total of 481 runs with a mean absolute deviation of 12.7%. The physical significance and previous relevant application of the various groups involved (eq 12) is further described in the original paper. No literature guidance exists, to the authors’ knowledge, on the correlation of power consumption and related phenomena in agitated liquid-liquid systems when the continuous phase is non-Newtonian. Thus it was decided to formulate pM following Vermeulen et al. (1955) and Laity and Treybal (1957), but with the pc component of pM replaced by pA,the latter having been established for correlation of power consumption in the agitation of single-phase, non-Newtonian systems by Metzner et al. (1957, 1960,1961). The efficacy of this approach must be judged by the results to follow. The present work concerns the contribution of nonNewtonian effects in the continuous phase to Nmh. Since non-Newtonian behavior relates to bulk flow undergoing shear, and not to interfacial phenomena (asshown by the constancy of u in our Table 111),the previously determined effect of u should hold without change here, as confirmed later by the results. Metzner and Otto (1957) and Magnusson (1952), while studying single-phase, non-Newtonian power requirements, proposed that an average shear rate, (duldy),, exists within an agitated vessel. A corresponding apparent viscosity, p A , of the non-Newtonian fluid would equal the viscosity of a Newtonian fluid agitated under identical conditions in the laminar region with the same power input. Metzner and Otto further assumed a linear relation exists between the average shear rate and the rotational speed of the impeller (du / dy)A = k8N (14) This assumption was verified by Metzner and Taylor (1960) when studying local shear rates, power dissipation rates, and fluid velocities in various regions of a baffled vessel for both Newtonian and nowNewtonian systems. Metzner et al. (1961), while investigating agitation of viscous Newtonian and non-Newtonian fluids, recommended a value for K, of 11 f 5 for most fluids. They also noted that a 30% change in k , yields only a 12% variation 0 1990 American Chemical Society
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