Theory of transport in dilute solutions, suspensions, and pure fluids. I. Translational diffusion

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Abstract
We develop a microscopic theory of transport for dilute suspensions and solutions in which the dynamics of the solute–solvent (i.e., tagged particle–fluid particle) collision is treated on a level of the Enskog approximation, appropriately modified by the presence of the solvent sea, which is described hydrodynamically. The treatment of the solvent as a continuum using appropriate generalized boundary conditions gives rise to an effective solute–solvent core radius as well as an effective solute–solvent reduced mass. In this paper, we consider translational diffusion of the solute particle of arbitrary size and mass. We derive an analytically simple expression for the coefficient of diffusion, which yields the correct hydrodynamic limit (Stokes–Einstein law). Our expression for self‐diffusion DS (diffusion of a tagged particle in a fluid of identical particles) is in excellent agreement with molecular‐dynamical results, showing both an increase over the Enskog value DSE at low fluid density as well as a quite precipitous drop at liquid densities (the enhanced caging effect). Our result turns out to be in close agreement with the Stokes–Einstein law for a wide range of solute particle sizes provided the solvent is at liquid density.