Formal Kinetic Theory of Transport Phenomena in Polyatomic Gas Mixtures

Abstract

A rigorous formal kinetic theory of multicomponent polyatomic gas mixtures is derived. The methods are essentially a combination of those used by Chapman and Enskog for monatomic gases (as extended to multicomponent mixtures by Curtiss and Hirschfelder), and those used by Wang Chang and Uhlenbeck for a single polyatomic gas for the case where the equilibration between internal and translational degrees of freedom is easy. The calculations correspond to the first approximation in the classical Chapman—Enskog theory. Expressions are derived for the coefficients of shear viscosity, volume viscosity (which is proportional to a relaxation time), ordinary diffusion, translational and internal thermal conductivity, and thermal diffusion. Although the results are rather formal, a number of useful conclusions about the effects of inelastic collisions can be drawn without the necessity of detailed calculations. For instance, it is comparatively simple to show that inelastic collisions have very little effect on shear viscosity and ordinary diffusion, but probably seriously affect thermal conductivity and thermal diffusion. The Hirschfelder—Eucken formula for the thermal conductivity of polyatomic gas mixtures appears as a limiting case of the present formulas. A number of other conclusions and implications of the present formulas are also discussed.