Self-diffusion and relative diffusion processes in liquids: microdynamic and hydrodynamic points of view

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Abstract
A microdynamic theory for the self-diffusion coefficient, which involves a wave-number-dependent viscosity, eta (q), is successfully tested on a hard-sphere system. The models the authors introduce for eta (q) are adapted to the Lennard-Jones fluid. New molecular dynamics data for the relative diffusion coefficient, in which the initial separation of two particles appears as an additional degree of freedom, are reported for this fluid. A systematic investigation of near-neighbour pairs shows (i) clear evidence of effects that slow their relative motion and (ii) that the relative diffusion coefficient varies remarkably smoothly with separation. The theory is extended to interpret the results and it is shown that the expressions for both types of diffusion coefficient take a form that is strongly reminiscent of a hydrodynamic treatment. This, the authors suggest, is why hydrodynamic theories (e.g. the Stokes-Einstein equation for the self-diffusion coefficient, and the Oseen approach to relative diffusion) appear to be applicable even at an atomic level. They emphasise, instead, the essentially microscopic nature of the diffusion process in monatomic liquids.