Three-dimensional numerical simulation of drops suspended in Poiseuille flow at non-zero Reynolds numbers

Abstract

A finite difference/front tracking method is used to study the motion of three-dimensional deformable drops suspended in plane Poiseuille flow at non-zero Reynolds numbers. A parallel version of the code was used to study the behavior of suspension on a reasonable grid resolution (128×128×128 grids). The viscosity and density of drops are assumed to be equal to that of the suspending medium. The effect of Capillary number, the Reynolds number, and volume fraction are studied in detail. It is found that drops with small deformation behave like rigid particles and migrate to an equilibrium position about half way between the wall and the centerline (the Segre-Silberberg effect). However, for highly deformable drops there is a tendency for drops to migrate to the middle of the channel, and the maximum concentration occurs at the centerline. The concentration profile obtained across the channel is in agreement with that measured by Kowalewski (T. A. Kowalewski, “Concentration and velocity measurement in the flow of droplet suspensions through a tube,” Exp. Fluids 2, 213 (1984)) experimentally for viscosity ratios less than or equal to one. The effective viscosity of suspension decreases with Capillary number in agreement with the creeping flow limit. Also, the effective viscosity increases with the Reynolds number of the flow.