AOKI, Kazuo; CHARRIER, Pierre; DEGOND, Pierre

doi:10.3934/krm.2011.4.53

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AOKI, Kazuo
Department of Mechanical Engineering and Science, Graduate School of Engineering

CHARRIER, Pierre
Institut de Mathématiques de Bordeaux [IMB]

DEGOND, Pierre
Department of Mathematics [Imperial College London]

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Kinetic and Relared Models. 2011-03, vol. 4, n° 1, p. 53

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In last years a great interest was brought to molecular transport problems at nanoscales, such as surface di usion or molecular ows 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 di usion coe cient. In this paper we revisit these works to derive the kinetic and di usion 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.< Leer menos

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Kinetic theory

nanoflows

surface diffusion

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A HIERARCHY OF MODELS RELATED TO NANOFLOWS AND SURFACE DIFFUSION

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