Theory for the rheology of dense non-Brownian suspensions: divergence of viscosities and $\mu$-$J$ rheology

TL;DR

This paper develops a microscopic theory for dense non-Brownian suspensions, accurately describing the divergence of viscosities and the rheological behavior near the jamming transition, including critical scaling laws.

Contribution

It introduces a systematic microscopic framework that captures the critical behavior of pressure and shear stress near the jamming point in dense suspensions.

Findings

Derives divergence of viscosities as ^{-2} near jamming

Describes the - rheology and stress ratio  in terms of the viscous number J

Provides a unified theoretical description matching experimental observations

Abstract

A systematic microscopic theory for the rheology of dense non-Brownian suspensions characterized by the volume fraction $\varphi$ is developed. The theory successfully derives the critical behavior in the vicinity of the jamming point (volume fraction $\varphi_{J}$), for both the pressure $P$ and the shear stress $\sigma_{xy}$, i.e. $P \sim \sigma_{xy} \sim \dot\gamma \eta_0 \delta\varphi^{-2}$, where $\dot\gamma$ is the shear rate, $\eta_0$ is the shear viscosity of the solvent, and $\delta\varphi = \varphi_J - \varphi > 0$ is the distance from the jamming point. It also successfully describes the behavior of the stress ratio $\mu = \sigma_{xy}/P$ with respect to the viscous number $J=\dot\gamma\eta_{0}/P$.