Second order in the gradients effects in a dilute binary mixture

Abstract

A study is made to compute relevant transport properties for a dilute binary mixture of inert gases to second order in the gradients without explicitly solving the Boltzmann equation to that order. This is done with the Chapman-Enskog method, seeking to express such quantities in terms of the solution to first order. The pressure tensor and the velocity of diffusion are two quantities which allow for this computation. In the particular case when the sum of the particle densities of the mixture (n A, n B) is constant, one finds that in order to keep the Chapman-Enskog method mathematically consistent, it is necessary that the divergence of the mass velocity be position independent. Finally, we consider the case of swarms of charged particles and study the prediction of the method in the Navier-Stokes and Burnett regimes for diffusion phenomena. In the latter case, the results are restricted to electrons in a gas.