Axisymmetric creeping flow past a porous prolate spheroidal particle using the Brinkman model

Abstract

A boundary-value solution to axisymmetric creeping flow past and through a porous prolate spheroidal particle is presented. The Brinkman model for the flow inside the porous medium and the Stokes model for the free-flow region in their stream function formulations are used. As boundary conditions, continuity of velocity, pressure and tangential stresses across the interface are employed. A mainly analytical procedure for calculating the required eigenvalues and eigenfunctions for the porous region part of the solution is proposed. The coefficients of the convergent series expansions of the general solutions for the stream functions, and thus for the velocity, pressure, vorticity and stress fields, both for the flow inside and outside the porous particle, can be calculated to any desired degree of accuracy as the solution of a truncated algebraic system of linear equations, once the eigenvalues to the Brinkman equation for a given focal distance and permeability have been computed. The drag force experienced by the porous particle is then given as a function of only one of these coefficients. Streamline-pattern and drag-force dependence on permeability and focal distance are presented and discussed.