A hierarchy of models related to nanoflows and surface diffusion

Kazuo Aoki; Pierre Charrier; Pierre Degond

doi:10.3934/krm.2011.4.53

Article Contents

2011, Volume 4, Issue 1: 53-85. Doi: 10.3934/krm.2011.4.53

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A hierarchy of models related to nanoflows and surface diffusion

1.
Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto 606-8501
2.
Institut de Mathméatiques de Bordeaux, ENSEIRB-MATMECA, IPB, Université de Bordeaux, F-33405 Talence cedex
3.
1-Université de Toulouse; UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, F-31062 Toulouse

Received: September 2010

Revised: October 2010

Published: March 2011

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Abstract

In last years a great interest was brought to molecular transport problems at nanoscales, such as surface diffusion or molecular flows in nano or sub-nano-channels. In a series of papers V. D. Borman, S. Y. Krylov, A. V. Prosyanov and J. J. M. Beenakker proposed to use kinetic theory in order to analyze the mechanisms that determine mobility of molecules in nanoscale channels. This approach proved to be remarkably useful to give new insight on these issues, such as density dependence of the diffusion coefficient. In this paper we revisit these works to derive the kinetic and diffusion models introduced by V. D. Borman, S. Y. Krylov, A. V. Prosyanov and J. J. M. Beenakker by using classical tools of kinetic theory such as scaling and systematic asymptotic analysis. Some results are extended to less restrictive hypothesis.

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

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