Microscopic origin of frictional rheology in dense suspensions: correlations in force space

TL;DR

This paper introduces a microscopic statistical framework based on force correlations in dense suspensions to predict macroscopic rheological behavior, including Discontinuous Shear Thickening, aligning well with simulations and experiments.

Contribution

It develops a novel force-space correlation approach to connect microscopic interactions with macroscopic rheology in dense suspensions.

Findings

Force anisotropy varies with shear stress and packing fraction.

The theory predicts a DST flow diagram consistent with simulations.

The model captures qualitative features of shear thickening behavior.

Abstract

We develop a statistical framework for the rheology of dense, non-Brownian suspensions, based on correlations in a space representing forces, which is dual to position space. Working with the ensemble of steady state configurations obtained from simulations of suspensions in two dimensions, we find that the anisotropy of the pair correlation function in force space changes with confining shear stress ($\sigma_{xy}$) and packing fraction ($\phi$). Using these microscopic correlations, we build a statistical theory for the macroscopic friction coefficient: the anisotropy of the stress tensor, $\mu = \sigma_{xy}/P$. We find that $\mu$ decreases (i) as $\phi$ is increased and (ii) as $\sigma_{xy}$ is increased. Using a new constitutive relation between $\mu$ and viscosity for dense suspensions that generalizes the rate-independent one, we show that our theory predicts a Discontinuous Shear Thickening (DST) flow diagram that is in good agreement with numerical simulations, and the qualitative features of $\mu$ that lead to the generic flow diagram of a DST fluid observed in experiments.