Image system for Stokes-flow singularity between two parallel planar walls

Abstract

Using a recently developed image representation for Stokes flow in a half-space bounded by a planar wall [Cichocki and Jones, Physica A 258, 273 (1998)], the image system is constructed for the flow field produced by a force multipole in the space bounded by two parallel walls. The image singularities are expressed in terms of products of double-reflection matrices, and the expansion is simplified using symmetries of the double-reflection operation. Our analysis yields recurrence relations for the strengths of the image multipoles. The relations are solved explicitly, and a complete image system is obtained for an arbitrary source-force multipole. Applications of our image representation for evaluating the hydrodynamic friction and mobility matrices of particles interacting with two parallel planar walls are indicated.