Gas-surface interaction and boundary conditions for the Boltzmann equation

Stéphane Brull; Pierre Charrier; Luc Mieussens

doi:10.3934/krm.2014.7.219

Article Contents

2014, Volume 7, Issue 2: 219-251. Doi: 10.3934/krm.2014.7.219

This issue Previous Article Non-existence and non-uniqueness for multidimensional sticky particle systems Next Article Kinetic theory and numerical simulations of two-species coagulation

Gas-surface interaction and boundary conditions for the Boltzmann equation

1.
Institut de Mathématiques de Bordeaux, ENSEIRB-MATMECA, IPB, Université de Bordeaux, F-33405 Talence cedex
2.
Institut de Mathméatiques de Bordeaux, ENSEIRB-MATMECA, IPB, Université de Bordeaux, F-33405 Talence cedex

Received: April 30, 2013

Revised: January 31, 2014

Published: May 2014

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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 [10] 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 [13].

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Mathematics Subject Classification: Primary: 82C40, 76P05, 41A60, 82D05; Secondary: 74A25.

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