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

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.