Rarefied gas flow of binary mixtures through long channels with triangular and trapezoidal cross sections

Abstract

The flow of binary gas mixtures through long micro-channels with triangular and trapezoidal cross sections is investigated in the whole range of the Knudsen number. The flow is driven by pressure and concentration gradients. The McCormack kinetic model is utilized to simulate the rarefied flow of the gas mixture, and the kinetic equations are solved by an upgraded discrete velocity algorithm. The kinetic dimensionless flow rates are tabulated for selected noble gas mixtures flowing through micro-channels etched by KOH in silicon (triangular and trapezoidal channels with acute angle of 54.74°). Furthermore, the complete procedure to obtain the mass flow rate for a gas mixture flowing through a channel, based on the dimensionless kinetic results, which are valid in each cross section of the channel, is presented. The study includes the effect of the separation phenomenon. It is shown that gas separation may change significantly the estimated mass flow rate. The presented methodology can be used for engineering purposes and for the accurate comparison with experimental results.