On the creeping motion of two arbitrary-sized touching spheres in a linear shear field

Abstract

The Stokes equations describing the creeping motion of two arbitrary-sized touching spheres are solved exactly through the use of tangent-sphere coordinates. For the case of a linear shear field at infinity, explicit results covering the entire range of size ratios are presented for: (a) the forces and torques on the aggregate; (b) the hydrodynamic forces on the individual spheres comprising a freely suspended aggregate, which are in general non-zero; (c) the contribution of the pair to the bulk stress of a dilute suspension; and (d) under free suspension conditions, the velocity of any material point relative to that of the undisturbed flow.