Asymptotic modelling of thermal binary gas flows in circular micro-channels

Abstract

Many industrial and medical tools include micro-metric channels. These are found, for example, in micro-filters. The DSMC methods are commonly used to compute gas flows in these sub-millimeter-sized channels. Nevertheless, these statistical methods are expensive in computation time (Bird in Gas dynamics and the direct simulation of gas flows. Clarendon Press, Oxford, 1994; Aktas et al. in J Microelectromech Syst 10:538–549, 2001). Consequently, the development of alternative methods, with lower computation cost, is an approach of main interest. This paper focuses on binary gas mixture flows with low Mach numbers and low to moderate Knudsen numbers. In a phenomenological point of view, this case corresponds to the slip regime. An asymptotic model for two compressible gases is presented in the case of axisymmetric flows in circular micro-pipes. This model is derived from a BGK-type model for the mixture. Its results are compared to DSMC simulations, and the impact on the flow of the mass flow rates, the wall temperature and the molecular weights are discussed.