Steady planar Couette flow of rarefied binary gaseous mixture based on kinetic modeling

Abstract

The planar Couette flow of binary gaseous mixtures is studied on the basis of the kinetic model introduced by Kosuge (2009). The calculations were carried out for a wide range of the gas rarefaction, various values of the mole fraction and for two values of the wall speed corresponding to linear and non-linear Couette flow configurations. The kinetic model shear stress, number density, temperature and the mole fraction have been found to be in very good agreement with corresponding ones obtained by the DSMC method. However, the difference in the velocity profiles obtained by the Kosuge model and the DSMC method can be large, especially near the free molecular regime. Also, very good agreement between the Kosuge model results and the Chapman–Enskog solutions is observed. Moreover, the influence of the intermolecular potential is investigated by comparing the results of the Hard-Sphere model with those for a Realistic potential. It was shown that the shear stress significantly depends on the intermolecular potential when the wall speed is large. Finally, applying the equivalent single gas approach it is deduced that this concept can be applied in binary gas mixture Couette flows at any pressure when the molecular mass ratio approaches unity, but only at high pressure when the ratio is large. • The Couette flow problem is solved on the basis of the Kosuge model. • Very good agreement between Kosuge model and the DSMC method has been provided for the shear stress, number density, temperature and the mole fraction. • The differences in the velocity distributions of the individual species can be large. • The influence of the intermolecular potential is investigated. • The validity of the equivalent single gas approach is analyzed.