Theory of dynamic pair correlation functions for nonequilibrium dense fluids

Abstract

We present an integral equation for the dynamic pair correlation function for nonequilibrium dense simple fluids. The integral equation reduces to the well known Percus-Yevick integral equation or the hypernetted chain equation for the equilibrium pair correlation function for dense simple fluids, as the nonequilibrium fluxes vanish and the system approaches equilibrium. The integral equation is derived from the nonequilibrium Kirkwood hierarchy generated from the nonequilibrium canonical distribution function, which in a thermodynamically consistent manner solves the generalized Boltzmann equation for dense simple fluids. In this theory, the equilibrium theory of fluid structures is an integral part of the nonequilibrium theory presented. The integral equation is applied to study the nonequilibrium effects induced by shearing a non-Newtonian fluid. In the high shear-rate regime the structure factors break into diffraction-like patterns, which indicate that the fluid organizes into a local structure. The nonequilibrium effects also show a plateau behavior in the non-Newtonian regime in a qualitative agreement with the experimental observation on a non-Newtonian fluid - for example, a suspension of ciliated silica spheres.