Migration of a porous spherical particle in the presence of a non-deformable interface

Abstract

Semi-analytical solutions are obtained for a porous spherical particle moving in the presence of an interface separating two immiscible Newtonian fluids. The motion of the particle is considered for the following two cases: (a) quasi-steady translation perpendicular to the interface and (b) steady rotation about a diameter perpendicular to the interface. The porous medium within the particle is governed by the Brinkman equation with a tangential stress jump condition. The Capillary number is assumed to be small, which leads to negligible interface deformation. Using both cylindrical and spherical coordinates, general solutions for the Newtonian and Brinkman regions are constructed from basic solutions. Conditions are first satisfied at the bounding interface, followed by the application of the Fourier–Bessel transforms; then comes the application of the boundary conditions at the surface of the porous particle, which is handled by a collocation technique. The aim of this paper is to study and determine the effect of the bounding interface and the permeability of the Brinkman region on the drag force and torque acting on the porous particle. The drag force and torque coefficients are calculated with good convergence as functions of the dimensionless clearance distance between the porous particle and the bounding interface for the entire range of the dimensionless hydraulic permeability of the Brinkman medium, the stress jump factor, and the viscosity ratio between the fluid containing the particle and the fluid below the interface. Our collocation results are in good agreement with the available solutions in the literature for the limiting cases. The present study has potential applications in the fields of biomedical and industrial processes, such as the biophysics of membranes and porous agglomerates.