Gas-surface interaction and boundary conditions for the Boltzmann equation

TL;DR

This paper derives boundary conditions for the Boltzmann equation by modeling gas-surface interactions with a kinetic surface layer, extending to nanoscale roughness and ensuring classical properties of scattering kernels.

Contribution

It introduces a systematic derivation of boundary conditions from a kinetic surface model, including effects of nanoscale roughness, for the Boltzmann equation.

Findings

Derived boundary conditions from a kinetic surface model.

Extended boundary conditions to nanoscale rough surfaces.

Proved scattering kernels satisfy classical properties.

Abstract

In this paper we revisit the derivation of boundary conditions for the Boltzmann Equation. The interaction between the wall atoms and the gas molecules within a thin surface layer is described by a kinetic equation introduced in [9] and used in [1]. This equation includes a Vlasov term and a linear molecule-phonon collision term and is coupled with the Boltzmann equation describing the evolution of the gas in the bulk flow. Boundary conditions are formally derived from this model by using classical tools of kinetic theory such as scaling and systematic asymptotic expansion. In a first step this method is applied to the simplified case of a flat wall. Then it is extented to walls with nanoscale roughness allowing to obtain more complex scattering patterns related to the morphology of the wall. It is proved that the obtained scattering kernels satisfy the classical imposed properties of non-negativeness, normalization and reciprocity introduced by Cercignani [11].