Effect of Beavers–Joseph Interfacial Slip on Thermocapillary Migration of a Brinkman Porous Sphere

One might expect interfacial slip to help permeable microcarriers move; for thermocapillary propulsion, we show the opposite. For a rigid Brinkman porous sphere in a Newtonian liquid at low Reynolds and Péclet numbers, we couple exterior Stokes flow, interior Brinkman seepage, a Beavers–Joseph slip condition, and a Marangoni stress balance with a stress jump, and obtain closed-form expressions for the force-free migration velocity and the holding force. Both recover the classical bubble and viscous-drop solutions in their limits. Slip reduces both quantities monotonically, by roughly 10–70% at a unit slip coefficient and as the inverse of the slip coefficient at strong slip. However, the complete suppression of motion at extreme permeabilities (λ→0) is identified as a theoretical artifact; it reflects the breakdown of the locally flat interface assumption once the effective slip length exceeds the particle radius, rather than a verified physical prediction. The thermal conductivity ratio sets the strength of the thermal driving without altering the hydrodynamic response. An optimal permeability appears only in the presence of slip, the stress jump matters chiefly for tightly screened particles, and slip mimics a higher internal viscosity differently in velocity and force, so that measuring both could separate them. Within its idealized assumptions, the solution provides an analytic reference for numerical and experimental studies of thermally driven porous carriers.