Stochastic models of free-molecular nanopore flows

Abstract

In gas transport systems of the nanoscale, fluid–surface interactions become the main forces governing the evolution of the flow state. In ideal nanoscale systems, such as atomically smooth carbon nanotubes, the characteristic lengths reduce to such an extent that the non-equilibrium entrance region comprises a large proportion of the domain. In this regime, the added effective resistance induced by the non-equilibrium entrance region becomes large enough that classical effusion models break down. The mechanisms behind the resistance in this regime are still poorly understood. A stochastic model of interfacial resistance is developed here, which allows for the determination of the effective diffusion coefficient via a novel finite-difference solution. We use this method to model free-molecular gas flow through long nanotubes, showing that such non-equilibrium effects may be present in systems of length scales currently within manufacturing capabilities. Finally, this model is used to discuss gas separation through aligned carbon nanotube arrays, with a focus on the effect of membrane length on the separation of a H2–CH4 mixture.

On the increased interfacial resistance of hydrogen in carbon nanotube arrays and its effect on gas mixture separation

“…Since this work has discussed both considerations in wall spacing and geometry which lowers the TMAC estimate developed prior significantly, we will now investigate the use of this altered model with the free-molecular Fokker-Planck model utilized in another prior work. 28 In the Fokker-Planck model of free-molecular flows, the particle distribution, f , in a thin, non-tortuous nanopore, is governed by the Kramers-Chandrasekhar (or Klein-Kramers) equation, which reads…”