Transport theory of binary mixture with one trace component of disparate mass

We present a simple method for calculating transport coefficients for binary hard-sphere mixtures with one trace component of extreme mass disparity (Lorentz and Rayleigh mixtures). The results that we obtain by using the Chapman–Enskog method are exact on the Enskog-theory level. In such mixtures we can expand the solute–solvent collision integral in powers of the mass ratio and thereby reduce it to a differential form, from which we can in principle calculate directly the solute–particle velocity moments of various orders relevant to the fluxes instead of determining its distribution function. Here we mainly concern ourselves with determination of the transport coefficients in the Lorentz and Rayleigh limits, including the solvent contribution for the case of shear viscosity, bulk viscosity, and thermal conductivity. We give a brief analysis of these quantities in both limits and compare with the results of the lowest Sonine-polynomial approximation.