Viscous and thermal velocity slip coefficients via the linearized Boltzmann equation with ab initio potential

Abstract

The viscous and thermal velocity slip coefficients of various monatomic gases are computed via the linearized classical Boltzmann equation, with ab initio potential, subject to Maxwell and Cercignani–Lampis boundary conditions. Both classical and quantum interatomic interactions are considered. Comparisons with hard sphere and Lennard–Jones potentials, as well as the linearized Shakhov model are performed. The produced database is dense, covers the whole range of the accommodation coefficients and is of high accuracy. Using symbolic regression, very accurate closed form expressions of the slip coefficients, easily implemented in the future computational and experimental works, are deduced. The thermal slip coefficient depends, much more than the viscous one, on the intermolecular potential. For example, in the case of diffuse scattering, the relative differences in the viscous slip coefficient data between HS and AI potentials are less than 4%, whilst the corresponding ones in the thermal slip coefficient data are about 6% for He, reaching 15% for Xe. Quantum effects are considered for He, at temperatures 1–104 K to deduce that deviations from the classical behaviour are not important in the viscous slip coefficient, but they become important in the thermal slip coefficient, where the differences between the classical and quantum approaches reach 15% at 1 K. The computational effort of solving the linearized Boltzmann equation with ab initio and Lennard–Jones potentials is the same. Since ab initio potentials do not contain any adjustable parameters, it is recommended to use them at any temperature.

Numerical Study of Rarefied Gas Flow in Diverging Channels of Finite Length at Various Pressure Ratios

“…The system of the two kinetic Equations ( 4) and (5) in conjunction with the moments (6) and the boundary conditions ( 7)-( 9) is solved by applying the Discrete Velocity Method (DVM). The deterministic DVM method is nowadays considered the widely accepted numerical technique by the research community for solving kinetic equations and describing heat, mass, and momentum transfer phenomena in the whole range of gas rarefaction (e.g., [52][53][54][55][56][57][58][59][60]). The literature survey is very extensive, and for this reason, only a brief description of the method is provided here, focusing on the numerical details concerning the present flow problem.…”