Stokes resistance of a porous spherical particle in a spherical cavity

Abstract

The boundary effect on the asymmetrical motion of a porous spherical particle in an eccentric spherical cavity is investigated in the quasi-steady limit under creeping flow conditions. The porous particle translates and rotates in the viscous fluid, located within the spherical cavity, normal to the line connecting their centers. The fluid inside the porous particle is governed by the Brinkman equation. A tangential stress jump condition at the interface between the fluid and the porous particle is applied. A semi-analytical approach based on a collocation technique is used. Due to the linearity of the present problem, the flow variables for the clear fluid region are constructed by superposing basic solutions of two problems: the first one is the regular solution inside the cavity region in the absence of the porous particle where a first system of coordinates has its origin at the center of the cavity, while the second problem is the regular solution in the infinite region outside the spherical porous particle where a second coordinate system with its origin at the center of the porous particle is used. Numerical results displaying the resistance coefficients acting on the particle are obtained with good convergence for various values of the physical parameters of the problem. The results are tabulated and represented graphically. The findings demonstrate that the collocation results of the resistance coefficients are in good agreement with the corresponding results for the impermeable solid particle.