Kinetic theory analysis for temperature and density fields of a slightly rarefied binary gas mixture over a solid wall

Abstract

Temperature and number density fields of a binary gas mixture over a plane solid wall kept at a constant temperature have been studied analytically on the basis of the linearized version of the Boltzmann equation of BGK type subject to the boundary condition of Maxwell’s type (specular-diffusive reflection). An analysis within the Knudsen layer in the vicinity of the wall has been carried out by solving the set of equations accurately, which has enabled us to obtain the distributions of the temperature and number density explicitly over the entire flow field. Fictitious gas mixtures have been taken up, in addition to the mixtures of real gases such as helium–neon, helium–argon, neon–argon and so on, in order to see the effects of the molecular mass ratio, the concentration ratio and the accommodation coefficients of the component gases on the temperature and number density fields by suppressing the effects associated with the transport coefficients. The macroscopic jump coefficients in temperature at the wall have also been given for making a comparison with the other results available. The comparison with the theoretical results by other authors for a helium–argon mixture case shows a reasonably good agreement. The experimental data, however, seem to be too large compared with the present results, which may partly be attributable to some ambiguities in the definitions of some quantities involved in the experiment.