Diverging viscosity and soft granular rheology in non-Brownian suspensions

TL;DR

This study uses large-scale simulations to analyze the shear rheology of dense non-Brownian particle suspensions near jamming, revealing diverging viscosity, multiscaling behavior, and proposing a soft granular rheology model.

Contribution

It extends previous analysis of suspension rheology by two orders of magnitude, providing new insights into viscosity divergence, finite-size effects, and a novel soft granular rheology model.

Findings

Viscosity diverges with a power law at jamming

Finite-size scaling reveals a diverging correlation length

Soft particle effects modify the rheology near jamming

Abstract

We use large scale computer simulations and finite size scaling analysis to study the shear rheology of dense three-dimensional suspensions of frictionless non-Brownian particles in the vicinity of the jamming transition. We perform simulations of soft repulsive particles at constant shear rate, constant pressure, and finite system size, and study carefully the asymptotic limits of large system sizes and infinitely hard particle repulsion. Extending earlier analysis by about two orders of magnitude, we first study the asymptotic behavior of the shear viscosity in the hard particle limit. We confirm its asymptotic power law divergence at the jamming transition, but show that a precise determination of the critical density and critical exponent is difficult due to the `multiscaling' behavior of the viscosity. Additionally, finite-size scaling analysis suggests that this divergence is accompanied by a growing correlation length scale, which also diverges algebraically. We then study the effect of soft repulsion, and propose a natural extension of the standard granular rheology to account for softness effects, which we validate from simulations. Close to the jamming transition, this `soft granular rheology' offers a detailed description of the non-linear rheology of soft particles, which differs from earlier empirical scaling forms.