Molecular mass effect on the flow of a thermal binary gas mixture in a circular micro channel

Abstract

Micro metric channels are present in a wide range of applications. For instance, micro filters are used in high-tech industry to detect biological or chemical entities as well as in daily-use objects. In order to describe the gas flows in the micro channels involved in these tools, Bird’s DSMC method is frequently used. This method is efficient but it requires a large computation time to obtain a flow description [1, 2]. Consequently, it is of main interest to develop alternative asymptotic models in order to predict these flows more quickly. The purpose of this communication is to model the flow of a mixture of two compressible gases in circular micro pipes with a wall temperature depending on the longitudinal space variable. This work deals with flows at low Mach numbers and at low to moderate Knudsen numbers that correspond to the slip-flow regime. Under these assumptions, it is suitable to use the usual macroscopic balance laws of mass, momentum and energy (Navier-Stokes-Fourier equations) with additional coupling terms in the momentum and energy equations [3, 4, 5, 6]. The results of this asymptotic modeling are compared to DSMC simulations in the same configuration. The effects of the molecular weights is investigated.