A hierarchy of models related to nanoflows and surface diffusion

TL;DR

This paper revisits and extends kinetic models for nanoflows and surface diffusion, providing a systematic derivation and broader applicability of the models used to understand molecular transport at nanoscale.

Contribution

It offers a rigorous derivation of existing kinetic and diffusion models for nanoflows using classical kinetic theory methods, extending their validity.

Findings

Derived kinetic and diffusion models using asymptotic analysis

Extended models to less restrictive assumptions

Provided deeper insight into nanoscale molecular mobility

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.