Mobilities of a Spherical Particle Straddling the Interface of a Semi-Infinite Brinkman Flow

Abstract

The motion of a spherical particle straddling the flat interface of a semi-infinite Brinkman flow is considered under the conditions of low Reynolds number and zero capillary number regime. The analysis is applied in the case of 90 deg contact angle and when the viscosity of the constituent fluid in the Brinkman region is much more than that of the adjacent fluid. Analytical expressions for the hydrodynamic scalar resistance coefficients are obtained and represented graphically as a function of the slip parameter at the surface of the particle and the permeability parameter of the porous region. The hydrodynamic mobilities are also obtained and represented in tables. The limiting cases of Stokes clear fluid and Darcy's flow are recovered.