Journal of Statistical Physics

, Volume 140, Issue 3, pp 518–543 | Cite as

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

  • Tetsuro Tsuji
  • Kazuo AokiEmail author
  • François Golse


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.


Free-molecular gas Approach to equilibrium Diffuse reflection Kinetic theory of gases 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mechanical Engineering and ScienceKyoto UniversityKyotoJapan
  2. 2.Department of Mechanical Engineering and Science and Advanced Research Institute of Fluid Science and EngineeringKyoto UniversityKyotoJapan
  3. 3.Centre de Mathématiques Laurent SchwartzÉcole PolytechniquePalaiseau cedexFrance

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