Boundary conditions for the Boltzmann equation from gas-surface interaction kinetic models

Abstract

Boundary conditions for the Boltzmann equation are investigated on the basis of a kinetic model for gassurface interactions. The model takes into account gas and physisorbed molecules interacting with a surface potential and colliding with phonons. The potential field is generated by fixed crystal molecules, and the interaction with phonons represents the fluctuating part of the surface. The interaction layer is assumed to be thinner than the mean free path of the gas and physisorbed molecules, and the phonons are assumed to be at equilibrium. The asymptotic kinetic equation for the inner physisorbate layer is derived and used to investigate gas distribution boundary conditions. To be more specific, a model of the boundary condition for the Boltzmann equation is derived on the basis of an approximate iterative solution of the kinetic equation for the physisorbate layer, and the quality of the model is assessed by detailed numerical simulations, which also clarify the behavior of the molecules in the layer.

Impact of surface physisorption on gas scattering dynamics

“…Despite the many studies devoted to gas–surface interactions, relatively little attention has been paid to the development of SKs that incorporate adsorption (Kuščer 1978; Borman, Krylov & Prosyanov 1988; Aoki & Giovangigli 2019; Brancher et al. 2020; Aoki & Giovangigli 2021; Aoki, Giovangigli & Kosuge 2022). Yet, experimental, theoretical and numerical evidence clearly indicates that neglecting the presence of adsorbed molecules oversimplifies the scattering dynamics and introduces inaccuracies in the resulting prediction of fluid flow.…”

“…In particular, while we propose an SK to capture the overall effects of adsorption, previous studies have attempted to derive models from first principles. For example, Borman et al (1988) proposed a kinetic equation to study the dynamics of gas molecules in a potential field generated by surface atoms, with molecule-phonon collisions accounting for fluctuations, and this approach has recently been extended to include adsorption and chemical reactions on crystal surfaces (Aoki & Giovangigli 2019Aoki et al 2022). Despite its ability to precisely capture the intricate physics of adsorption, this kinetic equation-based modelling is computationally demanding and not suitable for engineering simulations.…”