Kinetic Theory of Nonspherical Molecules. III

Abstract

The kinetic theory of nonspherical molecules has been extended to multicomponent mixtures. The treatment is based on a set of generalized Boltzmann equations analogous to that used in the treatment of a pure gas, which are solved by a perturbation method similar to that of Chapman and Enskog. The transport coefficients are obtained in terms of a set of multidimensional integrals which depend on the dynamics of collisions of nonspherical molecules. These integrals are related to the ``bracket'' integrals of Chapman and Cowling and are generalizations of similar integrals which appear in the treatment of a pure gas of non-spherical molecules. These integrals are reduced to four-dimensional integrals, the integrands of which depend only on the geometry of the molecules, and the integrations are carried out over the surfaces of the two molecules. As an example, the final integrations are carried out for the spherocylindrical model. The coefficients of diffusion, thermal diffusion, shear and bulk viscosity, and thermal conductivity for a binary system are obtained in terms of two parameters characteristic of the shape and mass distribution of each molecule. The coefficient of self-diffusion is used to compare the thermal conductivity of a pure gas with that given by a modified form of the Eucken approximation.