Kinetic Theory of Moderately Dense Rigid Sphere Fluids. III. The Formulation and Solution of the Transport Equation for Binary Mixtures

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Abstract
The theory of the moderately dense rigid sphere fluid is extended to mixtures. The modified Boltzmann equation is derived from the Liouville equation using the technique of time smoothing. The solution of the Boltzmann equation is given in terms of bracket integrals and the entropy production formulated in terms of the perturbation to the distribution function. The bracket integrals are not explicitly evaluated in this paper but a first order result valid for a mixture of spheres of equal diameters gives for the leading term of the diffusion coefficient D=D0/g0(2)(σ) with D0 the dilute gas diffusion coefficient, and g0(2)(σ) the pair correlation function evaluated at contact. This leading term is in agreement with the corresponding leading terms for the thermal conductivity and shear viscosity of a one component hard sphere fluid, which also differ from the dilute gas coefficients by the factor [g0(2)(σ)]—1. The results quoted in this abstract are the leading terms and do not include all contributions of order v—1.