Axisymmetric motion of multiple composite spheres: Solid core with permeable shell, under creeping flow conditions

Abstract

The axisymmetric creeping motion of multiple composite spheres is analyzed to investigate the hydrodynamic interactions among these particles. A composite particle referred to in this paper is a spherical solid core covered with a permeable shell, whose thickness can be arbitrary. The Stokes equation and the Brinkman equation are used to describe the flow fields outside and inside the particle, respectively. For two identical composite spheres with thin porous layers in near contact, a lubrication analysis is employed to examine their relative motion. Analytic expressions for the pressure and the drag force are obtained for the layers having high permeability. For general cases, a boundary collocation method is applied to numerically solve for the unknown coefficients in the series solutions for the flow behavior of the multiple particles. The resulting drag forces are in good agreement with the predictions from the lubrication analysis and the reflection method. In general, the strength of hydrodynamic interaction among composite particles lies between the values among permeable particles with the same permeabilities and among solid particles. The hydrodynamic behavior for composite spheres may be approximated by that for permeable spheres when the porous layer is sufficiently thick, depending on the permeability. When the particles undergo relative motion, the drag increases with decreasing distance between them. However, the drag on the particle with larger size or lower permeability may reach a minimum at a certain distance for a chain of dissimilar particles, rather than in contact, when they translate at the same velocity. © 1998 American Institute of Physics.