Transport properties in dilute gases: an approach using time-correlation functions. Part 1.—Viscosity and thermal conductivity of gases and gas mixtures in which the exchange of molecular internal energy is slow

Abstract

Equations for the viscosity and thermal conductivity are derived, using the method of time-correlation functions, for dilute single gases and gas mixtures which may contain polyatomic molecules, but in which the rate of exchange of internal molecular energy is slow. The treatment follows that of H. Mori, who showed that the assumption of an exponential form for the time-correlation functions leads to expressions for the viscosity and thermal conductivity of a single monatomic gas that are identical with those of the Chapman–Enskog first approximations. In the present analysis, time-correlation functions have to be considered in general to be sums of exponential decays which are justified on the basis of the first-collision approximation of Reissner and Steele. For many systems considered, familiar equations are obtained, e.g., Chapman–Enskog first approximations and the modified Eucken and Hirschfelder–Eucken equations. For viscosity and for the translational contribution to thermal conductivity in mixtures, however, simpler (though less correct) equations than the Chapman–Enskog approximations are obtained: in the case of thermal conductivity a new equation is derived and tested. Though less rigorous than the traditional methods, the derivations are simpler and more easily understood in physical terms (provided the expressions for the transport properties in terms of time-correlation functions are accepted as a starting point) and therefore the approach offers some advantages.