Effect of Beavers–Joseph Interfacial Slip on Thermocapillary Migration of a Brinkman Porous Sphere
- 1Institute of Basic and Applied Science, College of Engineering, Arab Academy for Science, Technology and Maritime Transport, Alexandria 21974, Egypt
- 2Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21568, Egypt
- 3Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Abstract
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.
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BibTeX
@article{sayed2026effect,
title = {{Effect of Beavers–Joseph Interfacial Slip on Thermocapillary Migration of a Brinkman Porous Sphere}},
author = {Mohamed El Sayed and Ahmed Saeed Ibrahim Aamer and Baraa A. Ahmed and Osman Osman and Samar A. Mahrous},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14193563},
url = {https://www.mdpi.com/2227-7390/14/19/3563},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Effect of Beavers–Joseph Interfacial Slip on Thermocapillary Migration of a Brinkman Porous Sphere
AU - Mohamed El Sayed
AU - Ahmed Saeed Ibrahim Aamer
AU - Baraa A. Ahmed
AU - Osman Osman
AU - Samar A. Mahrous
PY - 2026
DA - 2026/10/01
JO - Mathematics
DO - 10.3390/math14193563
UR - https://www.mdpi.com/2227-7390/14/19/3563
AB - 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.
SN - 2227-7390
ER -