Thermophoresis of a spherical particle straddling a flat interface in a Brinkman medium at a 90° contact angle

Abstract

This study investigates the quasi-steady axisymmetric thermophoretic motion of a spherical particle partially submerged at the flat interface of a semi-infinite Brinkman medium. The analysis is conducted under the assumptions of small Reynolds and Péclet numbers, while the capillary number is considered sufficiently small to preserve the flatness of the interface. The specific case of a $90°$ contact angle with the flat surface is examined. To avoid singularities at the contact line, the Knudsen number is assumed to lie within the slip-flow regime. Analytical expressions are derived for the thermophoretic velocity and force acting on the half-submerged particle. Graphical results illustrate the influence of parameters such as Fourier thermal conductivity ratio, Knudsen number, medium permeability, frictional slip, and thermal stress slip. Furthermore, the limiting behavior corresponding to thermophoresis in a classical viscous fluid is discussed. Since the present solution is exact, the case of a $90°$ contact angle also serves as a benchmark for validating numerical solutions at other contact angles. The findings are relevant to applications involving particle manipulation at fluid–porous interfaces, such as targeted drug delivery across biological membranes, pollutant transport at soil–air boundaries, and the design of microfluidic systems for controlled colloidal assembly.