Axisymmetric creeping flow past a porous approximate sphere with an impermeable core

Abstract

The creeping flow of an incompressible viscous liquid past and through a porous approximate sphere with an impermeable core is considered. The flow in the free-fluid region outside the sphere is governed by the Stokes equation. The flow inside the porous sphere is governed by Brinkman’s model. The boundary conditions used at the porous-liquid interface of the clear fluid and porous region are continuity of the velocity, continuity of the pressure and Ochoa-Tapia and Whitaker's stress jump condition. On the surface of the impermeable core no slip condition is used. An exact solution for the problem is obtained. An expression for the drag on the porous approximate spherical particle is obtained. A comparison is made with our earlier results on the particle with the fluid core. The variation of drag is studied with respect to permeability and stress jump coefficient. It is observed that the stress jump condition, characterized by a stress jump coefficient, has a significant influence on the drag acting on a particle.