Kinetic theory of inhomogeneous fluid: Tracer diffusion

Abstract

Enskog’s kinetic theory of dense hard sphere fluids, modified to allow long-ranged attractive interactions in a mean field sense, is used to derive the friction and tracer diffusion coefficient tensors for strongly inhomogeneous fluid. The kinetic equation yields the exact Yvon–Born–Green equations for the density distributions at equilibrium. Resulting formulas for the friction and diffusion coefficients are similar to the Enskog formulas for homogeneous fluid except that in inhomogeneous fluid they are tensors and they are computed as local averages of the product of the local density and pair correlation function. With a suitable closure approximation for the pair correlation function, such as that introduced by Fischer, the theory provides for the first time a tractable, unified approximation for computing density distributions and tracer diffusion coefficients in fluids in interfacial regions, microporous solids, and external fields.