The Stokes resistance of an arbitrary particle—II: An extension

Abstract

A previous attempt [1] to characterize the intrinsic hydrodynamic resistance of rigid particles to translational and rotational motions in Stokes flow, via two fundamental symmetric tensors, has been found to be adequate only for particles whose geometric form lacks skewness. More general bodies are found to be screw-like in behaviour and require, for a complete specification of their hydrodynamic resistance, a third fundamental tensor—the Coupling Tensor. A general study is made of the properties of this non-symmetric, second-rank tensor. Under certain circumstances its existence is shown to impart a permanent spinning motion to particles settling through a fluid at small Reynolds numbers. A dyadic-matrix method is developed by means of which one may also characterize the intrinsic Stokesian resistance of multiparticle systems comprised of particles of any shape in any configuration.