Relaxation of a Free-Molecular Gas to Equilibrium Caused by Interaction with Vessel Wall

Tetsuro Tsuji 1 Kazuo Aoki 1 François Golse 2, 3
1 Department of Mechanical Engineering and Science
2 LJLL - Laboratoire Jacques-Louis Lions
3 CMLS - Centre de Mathématiques Laurent Schwartz
Abstract : A free-molecular gas contained in a static vessel with a uniform temperature is considered. The approach of the velocity distribution function of the gas molecules from a given initial distribution to the uniform equilibrium state at rest is investigated numerically under the diffuse reflection boundary condition. This relaxation is caused by the interaction of gas molecules with the vessel wall. It is shown that, for a spherical vessel, the velocity distribution function approaches the final uniform equilibrium distribution in such a way that their difference decreases in proportion to an inverse power of time. This is slower than the known result for a rarefied gas with molecular collisions.
Keywords : Free-molecular gas Approach to equilibrium Diffuse reflection Kinetic theory of gases
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Journal articles
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https://hal-polytechnique.archives-ouvertes.fr/hal-00767550
Contributor : François Golse <>
Submitted on : Thursday, December 20, 2012 - 9:00:52 AM
Last modification on : Wednesday, March 27, 2019 - 4:10:22 PM

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Tetsuro Tsuji, Kazuo Aoki, François Golse. Relaxation of a Free-Molecular Gas to Equilibrium Caused by Interaction with Vessel Wall. Journal of Statistical Physics, Springer Verlag, 2010, 140 (3), pp.518-543. ⟨10.1007/s10955-010-9997-5⟩. ⟨hal-00767550⟩

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