A hierarchy of models related to nanoflows and surface diffusion

Kazuo Aoki (1) , Pierre Charrier (2) , Pierre Degond (3)

1 Department of Mechanical Engineering and Science
2 IMB - Institut de Mathématiques de Bordeaux
3 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Domaines: Equations aux dérivées partielles [math.AP]

Kazuo Aoki, Pierre Charrier, Pierre Degond. A hierarchy of models related to nanoflows and surface diffusion. Kinetic and Related Models , 2011, 4, pp.53-85. ⟨hal-00529590⟩