The movement of a sphere in front of a plane at low Reynolds number

Abstract

The general solution is given for the perturbation velocity due to a rigid sphere placed in an arbitrary flow, and for the perturbation velocity due to an infinite plane in a flow caused by an arbitrary distribution of discontinuities. The method of successive reflections is then applied to find an approximation for the torque and force experienced by a sphere placed in an arbitrary flow in front of a rigid plane. Very small Reynolds number is assumed throughout.