Effect of permeability of Brinkman flow on thermophoresis of a particle in a spherical cavity

This article investigates the effect of permeability of a Brinkman medium on the thermophoresis for the quasi-steady translational motion of a spherical particle located at the center of a spherical cavity filled with a porous medium under a prescribed temperature gradient. The Knudsen number is assumed to be small so that the fluid flow through a porous medium is described by a continuum model with a temperature jump, a thermal creep, and a viscous slip and thermal stress at the solid surfaces of the particle and cavity. An analytic expression for the thermophoretic velocity of the confined particle is obtained for various values of the Brinkman number characterizing the permeability of the medium, the thermal properties of the porous medium and particle and the particle-to-cavity radius ratio. Limiting cases of Stokes and Darcy's flows are discussed. (C) 2019 Published by Elsevier Masson SAS.