Self-Diffusion in Dense Fluids

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Abstract
The time-dependent solutions to the low-order BBGKY hierarchy are examined for the case of inter-diffusion of two mechanically identical isotopes. In order to effect a closure directed at evaluation of the pair-distribution-function perturbations and the self-diffusion constant D, we invoke a dynamical superposition approximation, and a truncated expansion in inverse powers of the initial composition fluctuation wavelength. The potential feasibility of this general approach to calculation of dense-fluid transport properties is illustrated by explicit numerical calculations for the dense fluid of rigid spheres, using in addition a pair-space local equilibrium assumption. Although the resulting pair-distribution-function perturbations seem to be in accord with physical intuition, cumulative errors in the approximation sequence render the self-diffusion coefficients predicted at variance with other calculations. Systematic improvements of the present scheme are outlined.