Modeling thermophoretic transport of a colloidal particle in porous media with planar wall constraints

Abstract

The quasisteady thermophoretic motion of a spherical colloidal particle in a porous medium adjacent to an impermeable plane wall is analyzed. A constant temperature gradient, directed inward and normal to the wall, is applied. The Brinkman equation is used to model the porous medium. The governing energy and momentum equations are solved analytically, supplemented by a numerical collocation method, under the assumptions of small Péclet and Reynolds numbers. A small Knudsen number justifies the use of a continuum model incorporating slip and temperature jump conditions. Numerical results for the normalized thermophoretic velocity show good convergence across a range of relevant parameters and are presented in both graphical and tabular formats. The findings indicate that the planar surface, along with thermal, slip, and permeability parameters, significantly affects the normalized thermophoretic velocity. These results are compared with existing data from the literature for corresponding limiting cases. The study suggests potential applications in targeted drug delivery, where thermally guided particle transport through porous biological tissues is essential.