Rheology of inelastic hard spheres at finite density and shear rate

TL;DR

This paper develops a kinetic theory for inelastic hard spheres to predict complex rheological behaviors like shear thinning and thickening at finite densities and shear rates, including flow curves and yield stress.

Contribution

It introduces a first-principles kinetic theory that accurately predicts granular fluid rheology near the glass transition, covering various flow regimes.

Findings

Predicted viscosity and Bagnold coefficient at relevant parameters.

Derived flow curves relating shear stress and shear rate.

Provided predictions for yield stress in granular flows.

Abstract

Considering a granular fluid of inelastic smooth hard spheres we discuss the conditions delineating the rheological regimes comprising Newtonian, Bagnoldian, shear thinning, and shear thickening behavior. Developing a kinetic theory, valid at finite shear rates and densities around the glass transition density, we predict the viscosity and Bagnold coefficient at practically relevant values of the control parameters. The determination of full flow curves relating the shear stress $\sigma$ to the shear rate $\dot\gamma$, and predictions of the yield stress complete our discussion of granular rheology derived from first principles.