Mobility functions for two unequal viscous drops in Stokes flow. I. Axisymmetric motions

Abstract

Analytical results are obtained for mobility functions which describe the hydrodynamic interactions between two unequal viscous drops. It is assumed that the surface tension is sufficiently high so that the drops retain a spherical shape. Exact solutions are introduced for the velocity images for Stokeslets and higher‐order Stokes singularities near a viscous drop 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.