Density Functional approach to Nonlinear Rheology

TL;DR

This paper introduces a density functional approach to predict the rheological behavior of Brownian particles under shear flow, providing first-principles calculations of flow-induced structural and stress responses.

Contribution

It develops a novel density functional closure for the pair Smoluchowski equation, enabling accurate predictions of rheology from equilibrium free energy functionals.

Findings

Calculated pair correlation functions under shear.

Predicted viscosity and normal stress differences.

Validated approach for two-dimensional hard-disks.

Abstract

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.