Correlation functions in Couette flow from group theory and molecular dynamics

Abstract

We describe group theory statistical mechanics, GTSM, which enables us to predict new non-vanishing time correlation functions in fluids at steady state subjected to planar couette flow. These are by symmetry trivially zero at equilibrium. An ensemble average is treated using the rules of group theory in the laboratory XYZ frame and in the molecule-fixed xyz frame of the point group character tables. In this paper we determine the effect of couette flow on a range of ensemble averages by establishing the symmetry of the strain rate tensor in terms of the irreducible representations of the Rh (3) rotation reflection group in the XYZ frame. This symmetry, D (0) g + D (1) g + D (2) g , is the same as the pressure tensor, P and consists of an antisymmetric vorticity term, D (1) g and a symmetric strain rate component of symmetry D (0) g + D (2) g . This allows non-zero ensemble averages of the same symmetry in the XYZ frame. Depending on the number of off-diagonal elements in the strain rate tensor, up to six new off-diagonal elements of microscopic time-autocorrelation functions of type, <A(0)A T (t> appear by GTSM in the XYZ frame. We confirm this theory for monatomic fluids using molecular dynamics computer simulation. The SLLOD equations of motion for couette dvx /dZ flow were implemented. We calculated non-vanishing peculiar quantity autocorrelation functions, ACF, of the generic form, <v α(0)v β(t)>, <v α(0)R β(t)> (R is the position of a molecule) and <P αβ(0)P γδ(t)> for the Lennard-Jones fluid. The new correlation functions are highly structured and generally have a finite negative value at t = 0. They can exhibit time reversal dissymmetry, especially at low density.