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Using the revised Enskog theory we derive equations for the thermal diffusion ratios kTi and thermal diffusion factors αij of multicomponent hard-sphere mixtures for systems in mechanical equilibrium. The first ten Enskog approximations to the thermal diffusion factor αij[N] (N=1,2,...,10) are evaluated numerically for a variety of system parameter choices appropriate to binary and ternary mixtures. We find that the first Enskog approximation does not vanish; the sequence of Enskog approximations converges most rapidly when the mass of the spheres are nearly equal. The seventh Enskog approximation was estimated to lie within about 1% of the exact value for all choices of system parameters. A comprehensive numerical study of the properties of the thermal diffusion factor for binary mixtures is given, including special mixtures such as the dusty gas, the Lorentz, quasi-Lorentz and Rayleigh gases, and isotopic mixtures. Particular emphasis is placed on showing how the properties of α12 change as the density is increased. The most striking difference between the low-density (Boltzmann) and high-density values for α12 is that the region of the mass ratio—diameter ratio plane for which α12 is either strictly positive or negative, as a function of composition, is much smaller at high densities. Also, at higher densities α12 is not a monotonic function of the mole fraction. For ternary mixtures in which two of the components are isotopes we show how the properties of the third component affect the separation of the two isotopes. [ABSTRACT FROM AUTHOR]

The equilibrium concentration autocorrelation function for an inert binary mixture is calculated by means of extended irreversible thermodynamics. The ensuing generalized transport coefficient is explicitly evaluated and the corresponding k-dependent relaxation time is also obtained. The connection with neutron scattering experiments is suggested and expressions for the dynamic structure factor and the half-width dispersion relation are given. [ABSTRACT FROM AUTHOR]

The kinetic models proposed by Garzó et al. [Phys. Fluids A 1, 380 (1989)] and Gross and Krook [Phys. Rev. 102, 593 (1956)] are used to study diffusion in uniform shear flow. The kinetic equations are solved by means of a generalized Chapman–Enskog expansion for Maxwell molecules. The main peculiarity of the method is that the successive approximations to the velocity distribution functions retain all orders in the shear rate. Two cases are considered, namely the self-diffusion and the tracer diffusion in a system under shear flow. The relevant transport properties and the distribution functions are explicitly obtained. A comparison with previous results derived from the Boltzmann equation and between both models is carried out. [ABSTRACT FROM AUTHOR]

The Boltzmann–Lorentz equation for Maxwell molecules is used to analyze the effect of mass dependence of the force law for tracer diffusion in uniform shear flow. An observed mass dependence of intermolecular forces suitable for disparate mass binary mixtures is explicitly considered. A comparison with earlier results is carried out. [ABSTRACT FROM AUTHOR]