Dispersion of viscous liquids by turbulent flow in a static mixer

Abstract

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...

Statistical description of the bubble cloud resulting from the injection of air into a turbulent water jet

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Modeling interfacial area transport in multi-fluid systems

“…In addition, the equilibrium phase fraction for the experimental data varied from 0.001 to 0.00057 (Berkman, 1988) and this could potentially cause some variance.…”

“…Berkman (Berkman, 1988) extended these correlations by examining the effects of viscosity and hydrodynamic conditions on drop size distributions produced by a Kenics mixer. He found a slight dependence on hydrodynamic conditions for Re > 12,000 and a measurable dependence on viscosity, when viscosity is greater than 20 cp.…”

“…Middleman used Kolmogoroff theory to obtain a semiempirical relationship to describe the equilibrium sauter mean drop diameter. Because this approach assumes that the drop is acted upon only by inertial subrange eddies opposed by surface tension, Berkman (1988) extended the correlation to regions where the disruptive force was balanced by both viscous and surface tension forces by examining fluids with a range of viscosities and surface tensions in a Kenics static mixer.…”

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“…The most investigated mixer for liquid-liquid dispersion in turbulent flow in the literature is the classical Kenics helical mixer (Middleman, 1974;Chen and Libby, 1978;Haas, 1987;Berkman and Calabrese, 1988;Yamamoto, 2007). Emulsification, using the Sulzer SMX mixer, has been studied not only in laminar flow (Legrand et al, 2001;Das et al, 2005;Liu et al, 2005;Rama Rao et al, 2007;Fradette et al, 2007;Gingras et al, 2007) but also in turbulent regime (Streiff et al, 1997).…”