Effective viscosity of a concentrated suspension of composite porous spherical particles

Abstract

We present an analytical study of the effective viscosity of concentrated suspension of porous spherical particles with a rigid core, under the creeping flow conditions. It is assumed that the individual particle is surrounded by a hypothetical fluid envelope. This model is popularly known as cell model, which takes into account the interaction of neighboring particles. The flow fields inside the free flow region and porous region are governed by Stokes equation and Brinkman equation together with mass conservation, respectively. The effective viscosity of the suspension depends on various parameters such as, radii of the fluid envelope and porous particle, permeability of the porous particle and further on the type of boundary condition at the outer cell, volume fraction etc. Various limiting cases are obtained and compared with earlier existing results in literature both theoretical and experimental.