Extensive analysis of the applicability range of the linear kinetic approaches in the case of the pressure driven gas mixture flows

Abstract

The study of gas mixture flows through micro- and macro-channels remains a very attractive area for theorists and experimentalists worldwide, mainly due to their great practical applicability in several aspects of science and industry. The present work includes a comparative study between the linear (McCormack model) and the nonlinear (DSMC method) kinetic theories of binary gas mixture flows through channels over a wide range of the involved parameters. The results show that the McCormack model is a reliable kinetic model for predicting the gas mixture flow behavior. Specific criteria with respect to the applicability range of the linear kinetic theory of short and long capillaries are proposed. The analysis shows that the separation phenomenon remains strong even in the case of small pressure drops. The applicability range of the linear kinetic theory for binary gas mixture flows driven by large pressure drops is obtained to be smaller compared to that of single gases but still wide enough covering a wide range of pressure ratios. Furthermore, the present work shows that the long capillary theory remains a very powerful tool for studying the gas mixture flow behavior under weak and strong nonequilibrium conditions. This work provides a kinetic database of the linear kinetic data (as supplementary material), which until today is still missing from the literature, and as it is shown throughout this work, it can be used far beyond the restrictions defined by the linear kinetic theory.