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.