Note on the direct calculation of mobility functions for two equal-sized spheres in Stokes flow

Abstract

A simple, direct method is presented for the calculation of mobility functions for the translational and rotational velocities and stresslets of two equal-sized spheres in unbounded low-Reynolds-number flow when the ambient velocity field is a superposition of a uniform stream, a vorticity and a rate-of-strain field. Our numerical procedure furnishes accurate values for touching spheres and coefficients for the near-field asymptotic expansions. The singular behaviour of the mobility functions is clarified. These results have been used to determine accurately the coefficient of the O(c2) term in the expression for the bulk stress in a suspension of spheres (6.95c2 instead of 7.6c2).