Thermal transpiration in molecular gas

The thermal transpiration of molecular gas is investigated based on the model of Wu et al. ["A kinetic model of the Boltzmann equation for non-vibrating polyatomic gases,"J. Fluid Mech. 763, 24-50 (2015)], which is solved by a synthetic iterative scheme efficiently and accurately. A detailed investigation of the thermal slip coefficient, Knudsen layer function, mass flow rate for molecular gas interacting with the inverse power-law potential is performed. It is found that (i) the thermal slip coefficient and Knudsen layer function increase with the viscosity index determined by the intermolecular potential. Therefore, at small Knudsen number, gas with a larger viscosity index has a larger mass flow rate; however, at late transition and free molecular flow regimes, this is reversed. (ii) The thermal slip coefficient is a linear function of the accommodation coefficient in Maxwell's diffuse-specular boundary condition, while its variation with the tangential momentum accommodation coefficient is complicated in Cercignani-Lampis's boundary condition. (iii) The ratio of the thermal slip coefficients between monatomic and molecular gases is roughly the ratio of their translational Eucken factors, thus, molecular gas always has a lower normalized mass flow rate than monatomic gas. (iv) In the transition flow regime, the translational Eucken factor continues to affect the mass flow rate of thermal transpiration, but in the free molecular flow regime, the mass flow rate converges to that of monatomic gas. Based on these results, accommodation coefficients were extracted from thermal transpiration experiments of air and carbon dioxide, which are found to be 0.9 and 0.85, respectively, rather than unity used in the literature. The methodology and data presented in this paper are useful, e.g., in the pressure correction of capacitance diaphragm gauge when measuring low gas pressures.