Axisymmetric motion of a slip spherical particle in the presence of a Brinkman interface with stress jump

Abstract

The axisymmetric motion of a spherical particle in the presence of a porous interface is considered in the limit of small Reynolds and capillary numbers where the interface is of negligible deformation. We consider the translation along and the rotation about an axis perpendicular to the interface. The flow through the porous medium is modeled by Brinkman equation with a tangential stress jump condition applied at the interface and a slip boundary condition is used at the surface of the particle. A semi-analytical approach based on a collocation technique is used. Due to the linearity of the present problem, the flow variables for the two flow regions are constructed by superposing basic solutions in both cylindrical and spherical coordinate systems. The collocation solutions for the normalized hydrodynamic drag force and torque acted on the particle are calculated with good convergence for various values of the separation parameter, the stress jump coefficient, viscosity ratio and the permeability parameter. The results for the normalized drag and torque coefficients are in good agreement with the available solutions in the literature for the limiting cases.