The contribution of diffusion to gas microflow: An experimental study

Abstract

Moderately rarefied gas flows are clearly distinguished from viscous flow in the continuum regime and from molecular diffusion at high rarefaction. They are an intermediate of the two border cases referred to as slip flow and transition regime flow. Here, we present a new pencil-and-paper approach for modeling flows in these regimes by a superposition of convection and Fickian diffusion. It allows us to predict mass flows for helium, argon, nitrogen, and carbon dioxide in microducts with parallel walls and with slightly varying cross section. The model was validated by measurement series taken from literature and by own permeation experiments on tapered microchannels. Analytical investigation of the approach showed that the diffusive flow is proportional to the cross-sectional area at the channel entrance. Hence, the mass flow in a tapered channel is unequal in both directions when diffusion dominates due to increased rarefaction. In contrary to the common Maxwellian slip approach the superposition model describes the data reliably. From this we conclude that deviations from continuum behavior in the intermediate cannot be explained by slip flow at the walls and tangential momentum accommodation, but by Fickian diffusion. Now predictions are possible without any usage of fitted parameters such as the tangential momentum accommodation coefficient.