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

Arlemark, E.J. and Reese, J.M. (2009) Investigating the effect of solid boundaries on the gas molecular mean-free-path. In: 7th International Conference on Nanochannels, Microchannels and Minichannels, ICNMM2009, 2009-06-22 - 2009-06-24.

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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.