Investigating the effect of solid boundaries on the gas molecular mean-free-path

A key parameter for micro-gas-flows, the mean free path, is investigated in this paper. The mean free path is used in various models for predicting micro gas flows, both in the governing equations and their boundary conditions. The conventional definition of the mean free path is based on the assumption that only binary collisions occur and is commonly described using the macroscopic quantities density, viscosity and temperature. In this paper we compare the prediction by this definition of the mean free paths for helium, neon and argon gases under standard temperature and pressure conditions, with the mean free paths achieved by measurements of individual molecules using the numerical simulation technique of molecular dynamics. Our simulation using molecular dynamics consists of a cube with six periodic boundary conditions, allowing us to simulate an unconfined gas “package”. Although, the size of this package is important, since its impact on computational cost is considerable, it is also important to have enough simulated molecules to average data from. We find that the molecular dynamics method using 20520 simulated molecules yields results that are within 1% accuracy from the conventional definition of the mean free paths for neon and argon and within 2.5% for helium. We can also conclude that the normal approximation of only considering binary collisions is seemingly adequate for these gases under standard temperature and pressure conditions. We introduce a single planar wall and two parallel planar walls to the simulated gas of neon and record the mean free paths at various distances to the walls. It is found that the mean free paths affected by molecular collisions with the walls corresponds well with theoretical models up to Knudsen numbers of 0.2

An extension to the Navier-Stokes-Fourier equations by considering molecular collisions with boundaries

In this paper we propose a model for micro gas flows consisting of the Navier-Stokes-Fourier equations (NSF) extended by a description of molecular collisions with solid boundaries and discontinuous velocity slip and temperature jump boundary conditions. By considering the molecular collisions with the solid boundaries in gas flows we capture some of the near wall effects that the conventional NSF with linear stress/strain-rate and heat-flux/ temperature-gradient relationships seem to be unable to describe. The model that we propose incorporates the molecular collisions with solid boundaries as an extension to the conventional definition of the average travelling distance of molecules before experiencing intermolecular collisions (the mean free path). By considering both of these types of collisions we obtain an effective mean free path expression, which varies with distance to surfaces. The effective mean free path is proposed to be used to obtain new definitions of effective viscosity and effective thermal conductivity, which will extend the applicability of NSF equations to higher Knudsen numbers. We show results of simple flow cases that are solved using this extended NSF model and discuss limitations to the model due to various assumptions. We also mention interesting ideas for further development of the model based on a more detailed gas description

A Navier-Stokes model incorporating the effects of near-wall molecular collisions with applications to micro gas flows

We propose a model for describing surface effects on micro gas flows. This model consists of the Navier-Stokes equations (NS) with discontinuous velocity slip boundary conditions and a description of a geometry-dependent and effective viscosity due to special consideration of the molecular collisions with solid boundaries. By extending NS with an effective viscosity we obtain a non-linear stress/strain-rate relationship which captures some of the near-wall effects that the conventional NS are unable to describe. We show results of NS extended by using our effective viscosity applied with Maxwell's boundary condition as well as a second order boundary condition achieved by partly incorporating higher order methods, the Maxwell-Burnett boundary condition proposed by Lockerby et al. (2004). With this proposed model the simple isothermal planar channel case of 2D Poiseuille flow is solved. The results of our proposed model are compared with the conventional NS using similar boundary conditions, the BGK-method and experiments. On the one hand it is seen that our extended NS model yields results that are asymptotic to the results of conventional NS for large flow scales. On the other hand, when comparing results on the micro scale, we see that our extended NS model yields results that are closer to the results of the BGK-method and the experiments than the conventional NS. Our extended NS-model shows signs of capturing the physics of the flow to a certain rarefaction degree where it does not predict the mass flow minimum shown by the BGK-method and the experiments

Molecular dynamics simulation of classical thermosize effects

We present the first molecular dynamics simulations of classical thermosize effects for realistic molecular conditions and flows. The classical thermosize effect is the chemical potential difference induced between two different-sized channels that have different fluid transport processes. It can be generated by applying a temperature gradient within the different-sized domains, and in this article the system investigated is a combination of a microchannel and a nanochannel. Our molecular dynamics results are compared with a theoretical calculation of the induced chemical potential difference, and this yields useful new insight into diffusive transport in nonequilibrium gas flows