Mobility functions for two unequal viscous drops in Stokes flow. II. Asymmetric motions

Abstract

Analytical results are obtained for mobility functions that describe the hydrodynamic interactions for transverse motions of two unequal viscous drops. In conjunction with the results of an earlier paper on axisymmetric motions, the motion induced by external forces in an arbitrary direction, i.e., the solution of the general mobility problem, is thus obtained. In the problem of interest, the drops are small and the surface tension is sufficiently high so that the drops retain a spherical shape. Exact solutions for the velocity images for Stokeslets and higher-order Stokes singularities near a viscous drop are introduced and then these image solutions are used to generate expressions valid for all two-sphere geometries except those for which the gap is much smaller than the diameter of the smaller drop. For rigid spheres, these results are used to obtain a closed-form expression for the Stokes–Einstein Brownian diffusion coefficient.