Creeping motion of a porous approximate sphere with an impermeable core in a spherical container

Abstract

The creeping motion of a porous approximate sphere with an impermeable core at the instant it passes the center of a spherical container is discussed. The flow in the spherical container is governed by the Stokes equation. The flow inside the porous approximate sphere is governed by Brinkman’s equation. The boundary conditions used at the interface are stress jump condition for tangential stresses, continuity of the normal stresses and velocity components. The drag experienced by the porous approximate spherical particle is obtained. The wall correction factor is calculated. The variations of drag coefficient and wall correction factor are studied with respect to permeability, separation parameters, deformation parameters and stress jump coefficient.