Shear Reversal in Dense Suspensions: The Challenge to Fabric Evolution Models from Simulation Data

TL;DR

This study tests the validity of fabric evolution models for dense suspensions under shear reversal using simulations, revealing that second-rank fabric tensors are insufficient to capture microstructural dynamics, suggesting the need for higher-rank tensor models.

Contribution

The paper provides a rigorous simulation-based evaluation of fabric evolution models, demonstrating their limitations and proposing the necessity of incorporating higher-rank tensors for accurate microstructural descriptions.

Findings

Second-rank fabric tensors inadequately describe microstructure during shear reversal.

Observed microstructural distributions are four-lobed, not two-lobed as assumed by simple models.

Closure models involving higher-rank tensors may better capture the microstructural evolution.

Abstract

Despite the industrial importance of dense suspensions of hard particles, few constitutive models for them have been proposed or tested. Most of these are effectively "fabric evolution models" (FEMs) based on a stress rule connecting the bulk stress to a rank-2 microstructural fabric tensor Q and a closed time-evolution equation for Q. In dense suspensions most of the stress comes from short-ranged pairwise steric or lubrication interactions at near-contacts, so a natural choice for Q is the deviatoric 2nd moment of the distribution P(p) of the near-contact orientations p. Here we test directly whether a closed time-evolution equation for such a Q can exist for inertialess non-Brownian hard spheres in a Newtonian solvent. We perform extensive numerical simulations for the evolution of P(p) under shear reversal, providing a stringent test for FEMs. We consider a generic class of these as defined by Hand (1962) constrained only by frame indifference. Motivated by the small microstructural anisotropy in the dense regime, we start with linear models and successively consider increasingly nonlinear ones. Based on these results we suggest that no closed FEM properly describes the dynamics of Q under reversal. We attribute this to the fact that Q gives a poor description of the microstructure during large parts of the microstructural evolution following shear reversal. Specifically, the truncation of P(p) at 2nd spherical harmonic level describes two-lobed distributions of near-contact orientations, whereas on reversal we observe distributions that are markedly four-lobed; moreover dP/dt (p) has oblique axes, not collinear with those of Q in the shear plane. This structure likely precludes any adequate closure at second-rank level. Instead, our numerical data suggest that closures involving the coupled evolution of both a fabric tensor and a fourth-rank tensor might be reasonably accurate.