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Kinetic and Related Models (KRM)
 

Gas-surface interaction and boundary conditions for the Boltzmann equation

Pages: 219 - 251, Volume 7, Issue 2, June 2014      doi:10.3934/krm.2014.7.219

 
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Stéphane Brull - Institut de Mathématiques de Bordeaux, ENSEIRB-MATMECA, IPB, Université de Bordeaux, F-33405 Talence cedex, France (email)
Pierre Charrier - Institut de Mathméatiques de Bordeaux, ENSEIRB-MATMECA, IPB, Université de Bordeaux, F-33405 Talence cedex, France (email)
Luc Mieussens - Institut de Mathématiques de Bordeaux, ENSEIRB-MATMECA, IPB, Université de Bordeaux, F-33405 Talence cedex, France (email)

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].

Keywords:  Kinetic theory, nanoflows, surface diffusion.
Mathematics Subject Classification:  Primary: 82C40, 76P05, 41A60, 82D05; Secondary: 74A25.

Received: May 2013;      Revised: February 2014;      Available Online: March 2014.

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