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

Kazuo Aoki (1, 1) , Vincent Giovangigli (2) , Shingo Kosuge (3)

1 NCKU - National Cheng Kung University
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 Institute for Liberal Arts and Sciences [Kyoto]

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.

Domaines: Physique mathématique [math-ph]

Kazuo Aoki, Vincent Giovangigli, Shingo Kosuge. Boundary conditions for the Boltzmann equation from gas-surface interaction kinetic models. Physical Review E , 2022, 106 (3), ⟨10.1103/physreve.106.035306⟩. ⟨hal-03841964⟩