Effect of finite boundaries on the Stokes resistance of an arbitrary particle Part 2. Asymmetrical orientations

Abstract

A general treatment is given of the first-order effects of wall proximity on the increased resistance to translational motions of a rigid particle of arbitrary shape settling in the Stokes régime. The analysis generalizes a previous treatment (Brenner 1962) to the case where the principal axes of resistance of the particle may have any orientation relative to the principal axes of the bounding walls. It is shown that, to the first order in the ratio of particle-to-boundary dimensions, the increased resistance of the particle can be represented by a symmetric, second-rank tensor (dyadic) whose value is independent of particle shape and orientation.