The resistance and mobility functions of two equal spheres in low-Reynolds-number flow

Abstract

The resistance and mobility functions which completely characterize the linear relations between the force, torque, and stresslet and the translational and rotational velocities of two spheres in low-Reynolds-number flow have been calculated using a boundary collocation technique. The ambient velocity field is assumed to be a superposition of a uniform stream and a linear (vorticity and rate-of-strain) field. This is the first compilation of accurate expressions for the entire set of functions. The calculations are in agreement with earlier results for all functions for which such results are available. The technique is successful at all sphere–sphere separations except at the almost-touching (gaps of less than 0.005 of the sphere diameter) configuration. New results for the stresslet functions have been used to determine Batchelor and Green’s [J. Fluid Mech. 56, 401 (1972)] order c2 coefficient in the bulk stress (7.1 instead of their 7.6). The two-sphere functions have also been used to determine the motion of a rigid dumbbell in a linear field. We also show that certain functions have extrema.