Discontinuous change of viscosity in a sheared granular gas with velocity-dependent restitution

TL;DR

This paper models the shear viscosity of a granular gas with velocity-dependent restitution, revealing a discontinuous transition between low- and high-shear regimes due to kinetic effects.

Contribution

It introduces a kinetic theory-based explanation for viscosity discontinuity in sheared granular gases with velocity-dependent restitution.

Findings

Viscosity exhibits an S-shaped dependence on shear rate.

A discontinuous change in viscosity occurs between low- and high-shear regimes.

Transition arises purely from kinetic effects, not friction or jamming.

Abstract

We investigate the rheology of a sheared granular gas composed of hard spheres with a velocity-dependent restitution coefficient. Using kinetic theory, we derive the shear viscosity and show that it exhibits an S-shaped dependence on the shear rate when the restitution coefficient switches between two values depending on the collision velocity. As a result, a discontinuous change of viscosity emerges between low- and high-shear regimes, both characterized by Bagnold-type scaling. While the phenomenology resembles the Wyart-Cates scenario for dense suspensions, the present transition arises purely from kinetic effects without frictional contacts or jamming.