The low Reynolds number motion of a porous particle near a plane interface

The aim of this paper is to develop a 3D numerical model for the problem of a porous body, moving both parallel with and toward (perpendicular to) a plane interface between two similar fluids. The ratio of the viscosity of the fluids at the interface will be altered to test the validity of the technique. This is based upon an integral equation formulation, the external flow being represented in terms of the Stokes integral representation formula and the internal flow by means of the Brinkman integral representation formula. To avoid discretisation at the interface and the inevitable truncation errors, the corresponding Green function needed to satisfy the matching condition at the interface (image system) is used in the Stokes integral representation formulae instead of the free-space Green function (fundamental singular solution; Stokeslet). It is important to note here that the Brinkman formulation is chosen over the more traditional Darcy solution because of its all-round effectiveness and lack of analytical restrictions. Numerical results are presented for the different flow configurations, both parallel with and perpendicular to the interface, around a porous sphere, in which the accuracy of the method is shown. (C) 1996 by Elsevier Science Inc.