Rarefaction Effects on Gas Mixing in Micro- and Nanoscales

Abstract

We present the rarefaction effects on diffusive mass transport in micro- and nanoscales using the results of direct simulation Monte Carlo DSMC method. Unlike the previous investigations, the momentum and heat contributions are eliminated from the computations via uniform velocity, pressure, and temperature field considerations. The effects of global Knudsen number on the diffusion phenomenon are studied for the same Peclet number and a unique mixer shape. The results indicate that there is considerable weakening in diffusion mechanism for high Knudsen number cases. As a result, the non-dimensional diffusive mass fluxes would decrease and the non-dimensional mixing length would increase as the Knudsen number increases. The effective diffusion coefficient is calculated throughout the mixer using the diffusive mass fluxes and the species mass fraction gradients. It is observed that the effective diffusion coefficient can vary considerably as a result of local rarefaction variations. It reaches to the lowest value at the point of confluence, where the maximum mass fraction gradient magnitude would occur for the species. Moving away from this point, the local rarefaction effects would weaken and the effective diffusion coefficient would reinforce subsequently. All the presented results indicate that there would be a convergent to a limiting behavior, which corresponds to the continuum mass diffusion case. Despite this, the local rarefaction level decreases continuously. Unfortunately, because of a considerable increase in the statistical fluctuations at very low rarefaction levels, the simulations do not provide reliable results in the limit of continuum regime.