Integration through transients for inelastic hard sphere fluids

TL;DR

This paper extends the Integration Through Transients formalism to inelastic granular fluids, analyzing their rheological behavior under shear, revealing shear thinning, Bagnold scaling, and the impact of inelasticity on stress responses.

Contribution

It introduces a mode-coupling theory-based approach to compute rheological properties of dissipative granular fluids under shear, incorporating inelasticity effects.

Findings

Identification of a yield stress at the glass transition.

Observation of shear thinning and Bagnold scaling behaviors.

Stress magnitude and shear thinning range depend on inelasticity.

Abstract

We compute the rheological properties of inelastic hard spheres in steady shear flow for general shear rates and densities. Starting from the microscopic dynamics we generalise the Integration Through Transients (\textsc{itt}) formalism to a fluid of dissipative, randomly driven granular particles. The stress relaxation function is computed approximately within a mode-coupling theory---based on the physical picture, that relaxation of shear is dominated by slow structural relaxation, as the glass transition is approached. The transient build-up of stress in steady shear is thus traced back to transient density correlations which are computed self-consistently within mode-coupling theory. The glass transition is signalled by the appearance of a yield stress and a divergence of the Newtonian viscosity, characterizing linear response. For shear rates comparable to the structural relaxation time, the stress becomes independent of shear rate and we observe shear thinning, while for the largest shear rates Bagnold scaling, i.e., a quadratic increase of shear stress with shear rate, is recovered. The rheological properties are qualitatively similar for all values of $\varepsilon$, the coefficient of restitution; however, the magnitude of the stress as well as the range of shear thinning and thickening show significant dependence on the inelasticity.