The Enskog theory for multicomponent mixtures. IV. Thermal diffusion

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Abstract
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.

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