Knudsen Layer Behaviour and Momentum Accommodation from Surface Roughness Modelling

Abstract

This work analyses the formation of the Knudsen layer in micro/nanoscale flows by linking a rough wall collision model to a continuum flow model via asymptotic matching. Expressions for the accommodation coefficients in terms of the surface characteristics are derived, allowing for boundary layer analysis of rarefied flows without the use of prior determined accommodation coefficients. This derived model, through use of the Lennard–Jones parameters for a nanoscale system, allows for a prediction of the the effective Tangential Momentum Accommodation Coefficient (TMAC) in flows against ordered nanoscale surfaces.

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

“…21,22 This work focuses on an 3D extension of the LSR model, a statistical model applicable to rare flows, which has been shown to admit a slip relation asymptotically. 19 To begin this work, first we will recap some points made of the LSR model of the tangential momentum accommodation coefficient (TMAC) for fluid interactions with nanoscale materials. In this analysis, we characterize the effect of particle-boundary interactions solely by the TMAC and describe the average fraction of a particle's tangential momentum which is lost to the wall per collision.…”

“…Vice versa, for larger s, the corrugation of the surface is increased and the surface is termed as "rougher." In the prior work, 19 the model considers a single 2D cross section of such a wall, which is shown in Fig. 1.…”

“…It may be seen from Eq. ( 4) that enforcing H ¼ R leads to a high effective roughness value, approaching s 1=2 for most light gases interacting with Reproduced with permission from 19 .…”

“…As stated before, this model will only consider the free-molecular regime, and not any viscous effects that were present in the Knudsen layer which included in the prior work. 19 To generalize a 3D system, we introduce a 2D surface at which collision occurs. We take this surface to lie along the x À y plane in standard Cartesian coordinates.…”

“…This model was investigated through a kinetic approach in a prior work by the authors. 19 Here, this model is extended and applied to the problem of gas separation, with a focus on binary gas mixtures containing diatomic hydrogen.…”