Density functional approach to nonlinear rheology

We present a density-functional–based closure of the pair Smoluchowski equation for Brownian particles under shear flow. Given an equilibrium free-energy functional as input, the theory provides first-principles predictions for the flow-distorted pair correlation function and associated rheological quantities over a wide range of volume fractions and flow rates. Taking two-dimensional hard disks under shear flow as an illustrative model, we calculate the pair correlation function, viscosity and normal-stress difference under both steady and start-up shear.