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Slip-flow theory for thermo-osmosis based on a kinetic model with near-wall potential

Tetsuro Tsuji*, Koichiro Takita, and Satoshi Taguchi

  • *Contact author: tsuji.tetsuro.7x@kyoto-u.ac.jp
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Phys. Rev. Fluids 10, 114202 – Published 12 November, 2025

DOI: https://doi.org/10.1103/zpzj-ngrh

Abstract

In this paper, thermal-slip coefficients in slip boundary conditions of the Stokes equation are derived using the generalized slip-flow theory, with special interest in the role of near-wall potential in micro- and nanoscale flows. As the model of fluids and fluid-solid interaction, we employ the model Boltzmann equation for dilute gases and the diffuse-reflection boundaries with near-wall potential, respectively. It is found that, when the mean free path of gas molecules and the effective range of potential are of the same order of magnitude, the thermal-slip boundary condition can be derived in the near-continuum limit. In the derived slip-flow theory, the thermal-slip coefficient and the boundary-layer corrections (i.e., Knudsen-layer corrections) are determined by solving the kinetic boundary-layer problems (i.e., Knudsen-layer problems) that include external- force terms and inhomogeneous terms both driven by the potential. As an application of the slip-flow theory, thermo-osmosis between two parallel plates with uniform temperature gradients is analyzed. The results of the slip-flow theory are validated by comparing them with those of the direct numerical analysis of the same problem. Furthermore, it is found that thermo-osmosis and thermal slip on the plates are significantly affected by the features of the near-wall potential; even the gas-flow direction can be reversed when the near-wall potential is repulsive. Such a flow reversal is qualitatively similar to thermo-osmosis in liquids reported in existing molecular dynamics simulation.

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Phys. Rev. Fluids 10, 114202– Published 12 November, 2025
  • Received 25 June 2025
  • Revised 3 September 2025
  • Accepted 16 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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