A mean free path approach to the micro/nanochannel gas flows

Jianfei Xie

doi:10.1186/s42774-020-00035-w

Abstract

We investigate the gas flows near to solid surfaces in terms of the local spatial variation in the molecular mean free path (MFP). Molecular dynamics (MD) is the appropriate scientific tool for obtaining molecularly-accurate dynamic information in micro and nano-scale gas flows, and has been used to evaluate the molecular mean free path of gases. In the calibration procedure, the viscosity of a gas in the homogeneous case can be recovered in our MD simulations and reach good agreement with the theoretical prediction and data from NIST. In surface-bounded gas flows, if the collisions between gas molecules and walls are counted, a spatially-varying mean free path is presented, and for the first time we have observed that the distribution of the free paths deviates from the exponential one and spikes appear in their distributions at larger Kn, i.e. in the transition flow regime. Based on elementary kinetic theory, the effective viscosity of the gas derived from the mean free path has been incorporated into the framework of the continuum-fluid dynamics equations, and micro-Couette flows are performed to demonstrate this potential application.

Highlights

The Knudsen number (Kn) is usually adopted to quantify the deviation from the continuum behaviour in gas flows, i.e. the traditional index of the degree of rarefaction, and is defined as the ratio of the molecular mean free path (MFP) of gases to the characteristic dimension of the flow
The gas viscosity has been calculated for temperatures ranging from 273 K to 473 K at a pressure of 1 atm, and the results are shown in Table 1; the viscosities obtained in our molecular dynamics (MD) simulations reach good agreement with the theoretical prediction of a Lennard-Jones (LJ) fluid [36, 37] as well as with the data for argon from National Institute of Science and Technology (NIST, http://webbook.nist.gov/chemistry/fluid/ )
The collision simulations) or roughly linear relationship exists in explored gas temperatures diameters predicted based on Eq (6) significantly differ from the one obtained in MD: the change of collision diameter as the gas temperature is insignificant in MD simulations; but in both hard-sphere gas and LJ fluids the molecular diameter significantly depends on the gas temperature indicating a variable hard-sphere (VHS) model that is commonly used in kinetic theory

Summary

Introduction

The Knudsen number (Kn) is usually adopted to quantify the deviation from the continuum behaviour in gas flows, i.e. the traditional index of the degree of rarefaction, and is defined as the ratio of the molecular mean free path (MFP) of gases to the characteristic dimension of the flow. Various researchers had proposed several different scaling functions for the rarefied gas flows: wall function [6], Kn-dependent functions [8], power-law scaling [9], and recently developed double power series [10, 11] These scaling functions come from the curve-fitting of kinetic theory or the direct simulation Monte Carlo (DSMC) calculations, and can provide the effective gas viscosity, which varies as a function of the normal wall distance. The novelty of this paper is to explore the potential of a molecular MFP-based scaling constitutive relation, which can be incorporated into the framework of continuum-based fluid dynamics equations to capture the effects that deviate from the equilibrium state such as the Knudsen layer in near-wall regions.

Assessment of MFP

Direct evaluation

Results and discussion

Conclusion