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A multifractal method describing the fine-scale structure of turbulence, including its intermittency, is applied to derive the drop breakage functions for drops whose diameter falls within the inertial subrange of turbulence, including effects of the viscosity of the dispersed phase. The model predicts well the transient drop size distributions of dispersions undergoing breakage at long stirring times. Concepts of quasi-stable and asymptotically stable drop sizes are presented and discussed in relation to the exponent on the Weber number. The functions for drop break-up in the viscous subrange are proposed and discussed.On applique une mCthode multifractale dCcrivant la structure fine de la turbulence, incluant son intermittence, afin de calculer les fonctions de rupture des gouttes B partir de gouttes dont le diamttre correspond au sous-domaine inertiel de turbulence, incluant les effets de la viscositt de la phase disperske. Le modtle prtdit convenablement les distributions de tailles de gouttes transitoires des dispersions subissant une rupture h des temps de mClange longs. Des concepts de tailles de gouttes quasi stables et asymptotiquement stables sont prtsentts et examints par rapport h l'exposant du nombre de Weber. Les fonctions pour la rupture des gouttes dans le sous-domaine visqueux sont proposCes et analystes.Keywords: breakage, intermittency, multifractal distribution, transient drop size distribution, turbulence.drop, suspended in a continuous phase, breaks up if the A local instantaneous stresses generated by turbulent motions in the continuous phase exceed the stabilizing forces due to the interfacial tension and the drop viscosity. In the present paper the authors are interested in the phenomenon of turbulent dispersion of droplets for some practical as well as theoretical reasons. Liquid-liquid dispersions are of importance to industry, as they are involved with many engineering operations including extraction, chemical reaction, emulsion and suspension polymerization etc. From the theoretical point of view, investigation of relations between turbulence and droplet breakage can help to understand the question, how the fluid mechanical forces induced by turbulence cause drop break-up. Understanding of this phenomenon should enable construction of the mathematical models able to predict the transient drop size distributions and the diameter of the largest stable drops. The droplet size distribution and its rate of evolution are determined by the processes of drop breakage and coalescence. In this paper we are interested in drop break-up, hence we shall confine our considerations to experimental conditions under which drop sizes are not influenced by coalescence. To this end one should consider low concentrations of the dispersed phase and, possibly, a soluble dispersant in an aqueous phase.The phenomenon of drop dispersion has been a subject of many studies starting from the fundamental papers by Kolmogorov (1949) and Hinze (1955). In these studies the fine-scale turbulence is interpreted by using...

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The effect of bulk fluid motion on aggregation of small particles subject to interaction forces of the DVLO type is investigated In particular, the convection-diffusion equation for the probability of finding two particles at a given relative position is solved numerically for the case of an axisymmetrical linear flow field, which approximates a turbulent flow field. The effect of bulk motion is shown to be important particularly in the case of thick double layers, where a critical size exists above which aggregation exhibits a self-accelerating behavior, that is, the aggregation rate constant increases with particle size. On the other hand, systems with thin double layers appear to be almost unaffected by shear. An approximate criterion for distinguishing between these two cases is presented