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

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.