Asymptotic modeling of the axisymmetric flow of a thermal binary gas mixture in a circular micro-channel

Abstract

Sub-millimeter-sized channels are present in many medical and industrial tools such as micro-filters. In order to describe the gas flows in these micro-channels, the DSMC methods are frequently used but a large computation time is usually required to obtain the solutions [1, 2]. Consequently, it is of main interest to develop alternative methods to describe these flows. In this contribution, we are interested in flows at low Mach numbers and with low to moderate Knudsen numbers so that the flow is in the slip regime. We propose an asymptotic model for the axisymmetric flow of a mixture of two compressible gases in circular microchannels with a temperature gradient at the wall. The model is obtained from the Navier-Stokes-Fourier equations. The results of the model are compared to DSMC simulations and the influence of the temperature gradient which is present along the walls is investigated.