Some identities and relations for transport coefficients of dense fluids

Abstract

The transport coefficients appearing in the dense fluid kinetic theory by the author are cast in the forms of time correlation functions suitable for numerical simulation methods. The Einstein relation for the diffusion coefficient and friction constant is found to follow exactly from the collision integral for the diffusion coefficient in the dense fluid kinetic theory. By assuming that the momentum and the force (or configuration) relax at different rates in the dilute and dense regimes of density, it is shown that the self-diffusion coefficient and the viscosity have two different relations, i.e., the one predicted by the mean free path theory and the Stokes–Einstein-type relation. The intrinsic viscosity of a polymer solution is shown to scale like mν/2a, where ν is an index and ma is the molecular weight, if the momentum relaxation time of the polymer scales like (∼(l−2a))ν/2 with ∼(l−2a) denoting the mean square end-to-end distance. If ν=1, the scaling follows Flory’s prediction for instrinsic viscosity.