Boundary effect on slow motion of a composite sphere perpendicular to two parallel impermeable plates

Abstract

The boundary effect on the perpendicular motion of a composite sphere towards a plane wall or between two parallel plates is investigated under the creeping flow conditions. The composite particle consists of a solid core and a porous shell. No restriction is placed on the shell thickness relative to the core size. The fluid flow inside the porous layer is governed by the Brinkman equation. A boundary collocation method is used to analyze the general case where the shell thickness and separation distance between the particle and the wall can be arbitrary. A lubrication theory is also employed to examine the special case of a particle with a thin permeable layer in near contact with a single plane. A good agreement between the results from both methods is attained. It is found that the hydrodynamic effect of the boundaries on the drag force experienced by a composite sphere or a porous one is weaker than that by a solid particle. While the drag force of a porous particle having a low to moderate permeability is a monotonic, decreasing function of the separation distance, a weak maximum drag may occur for a sphere with a very high permeability at a certain distance from the wall. This behavior agrees qualitatively with what Payatakes and Dassios (1987, Chemical Engineering Communications, 58, 119-138) and Burganos, Michalopoulou, Dassios and Payatakes (1992, Chemical Engineering Science, 117, 85-88) discovered using Darcy's law. (C) 2000 Elsevier Science Ltd. All rights reserved.