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.

Collision integrals (transport cross sections) for atomic and molecular interactions of importance in high-temperature air are calculated based on accurate force laws which have recently become available. The tabulations include the collision integrals for diffusion, viscosity, and thermal conductivity, and the collision integral ratios A*, B*, and C* needed for mixture calculations, and cover the range from 1000° to 15 000°K for the major interactions N–N, O–O, N–O, N–N2, O–O2, O–N2, N2–N2, O2–O2, and N2–O2. Average potential energy functions, but no collision integrals, are given for the minor interactions O–NO, O2–NO, N2–NO, and NO–NO. The calculations all refer to atoms and molecules in their ground states only. Calculational errors are estimated to be about 5% over the temperature range, but may occasionally rise as high as 10%. The relative magnitudes of the average collision integrals are discussed briefly for their bearing on the qualitative behavior of the corresponding gas mixtures, and on the assessment of the errors involved in some approximations commonly used in calculations of transport properties of air.

Transport properties of dissociating nitrogen and dissociating oxygen have been calculated from 1000° to 10 000°K with the assumption of no ionization or electronic excitation, using rigorous kinetic-theory formulas. The transport coefficients at each temperature are tabulated as a function of composition. The transport properties of the mixtures exhibit no special unusual features (unlike hydrogen). Various approximate formulas for the calculation of transport properties of mixtures have been checked against the results of the rigorous calculations, and give agreement to about 5%. A few checks of the calculations against experimental diffusion coefficients, viscosities, and thermal conductivities are possible, and the agreement seems reasonable.

The rough-sphere model is investigated in some detail from the point of view of the formal kinetic theory of polyatomic molecules developed by Wang Chang and Uhlenbeck, and by Taxman. The purpose is to clarify the sources of some discrepancies between the known results for the transport properties of a rough-sphere gas and the results recently obtained by Mason and Monchick in an approximate treatment of the formal kinetic theory, in which the corrections for inelastic collisions are given in terms of relaxation times. It is found that the deviations of the transport coefficients of rough spheres from those of smooth spheres can be understood in first approximation as the result of two effects: an enhancement of the backward and sideward scattering of rough spheres over that for smooth spheres, and an apparent resonant exchange of internal energy when two rough spheres collide. Since these effects are, for the most part, peculiar to rough spheres, it is concluded that the deviations found between the rough-sphere model and the approximate theory are not to be expected for real molecules.

The composition dependence of the thermal-diffusion factor αT of a dust–gas mixture is derived. In the case of monatomic gas, (αT)−1 is shown to vary linearly with mole fraction, but nonlinear contributions arise in the case of a polyatomic gas as a result of inelastic gas–gas collisions. Application of the result to a description of thermal transpiration in terms of the “dusty-gas” model yields a correction to the previously derived equation for thermal transpiration and may have a significant effect on the determination of rotational collision numbers from thermal transpiration measurements.