An ellipsoidal droplet model for dilute emulsions: application to complex mixing flows

A compact droplet model and numerical simulation are used to examine the behavior of multiphase fluids in complex mixing flows. The two-dimensional, time-periodic fluid between eccentric cylinders is used as a prototypical chaotic mixing flow. The multiphase fluid is a dilute dispersion of Newtonian droplets in a Newtonian matrix. The droplets are assumed to be much smaller than the mixer dimensions, and to have no interfacial tension, a situation for which there is an exact, yet compact, model for droplet deformation. We examine the spatial distribution of droplet stretching, as well as global stretching statistics, for a variety of droplet-to-matrix viscosity ratios. Chaotic flows are able to stretch high-viscosity droplets (which cannot be stretched in simple shear flow), and many features of the stretching statistics follow the "universal" laws for chaotic mixing of passive fluids.