Stokes–Einstein relations for a square-well fluid

A Stokes–Einstein relation, relating the shear viscosity η to the self-diffusion coefficient D, is constructed for a classical fluid subject to an effective two-body intermolecular force, derived from a square-well potential, undergoing dynamics as described by a Smoluchowski equation for pair diffusion. The time correlation functions for η and 1∕D are separated into contributions from delta function, hard-sphere forces, and from delta function, square-well soft forces. Furthermore, D is separated into its two- and three-body time correlation functions, and η into its two- to four-body terms. D shows activated diffusion, as in Arrhenius behavior, and on the level of two-body dynamics, the Dη product adheres to the Stokes–Einstein relation, subject to a small correction for potential softness. Three-body time correlation functions increase D, whereas three- and four-body correlation functions in η are partially offsetting. The deviation of Dη product from the Stokes–Einstein law arises from the three-body ...