Faxen's laws of a composite sphere under creeping flow conditions

Abstract

Under creeping flow conditions, Faxen's laws are derived for a composite sphere comprising a solid core covered by a permeable layer of arbitrary thickness. The derivations are carried out by applying reciprocal theorem in combination with fluid velocity and pressure distributions in certain simple flow as a comparison field. In this regard, the fluid velocity disturbances caused by a composite sphere subject to a simple shear flow and a rotational flow are solved individually. In the limiting case where the solid core vanishes, the resulting Faxen expressions for the drag force, torque, and stresslet compare very well with the existing Faxen's law for a porous sphere. It is found that when the porous layer is thick enough and its permeability is sufficiently low, the hydrodynamic behavior of a composite sphere can be approximated by that of a porous particle with equal permeability. This can be explained by the fact that the fluid cannot penetrate deeply into a porous layer of low permeability to flow through the pores near the core surface, and thereby the fluid can hardly feel the resistance from the core surface.