Slow motion of a porous spherical particle with a rigid core in a spherical fluid cavity

Abstract

We present an analytical study of viscous flow past a porous spherical particle composed of a rigid core inside. We consider that this particle is located inside a spherical fluid cavity filled with incompressible Newtonian fluid, under the creeping flow conditions. The governing equations inside the fluid region and the porous region are governed by Stokes equation and Brinkman equation respectively, supplemented with the corresponding mass conservation. Hydrodynamic drag and torque exerted by the fluid on particle are obtained which are later used to obtain the translational and rotational mobility of the particle inside the spherical cavity. In general the presence of cavity wall retards the particle movement as a result the mobility parameter becomes smaller than unity. The boundary effect is more pronounced when the separation distance between the particle surface and the cavity wall is less. Various limiting cases are obtained which agree with earlier existing results.