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.

Figures (4)

• Figure 1: Typical flow curves of the temperature, anisotropic temperature, and viscosity for (a) $e_1>e_2$ ($(e_1, e_2)=(0.99, 0.80)$) and (b) $e_1<e_2$ ($(e_1, e_2)=(0.80, 0.95)$). Here, we have introduced the dimensionless quantities $T^*\equiv T/(mv_\mathrm{c}^2)$, $\Delta T^*\equiv \Delta T/(mv_\mathrm{c}^2)$, and $\eta^*\equiv \eta d^2/(mv_\mathrm{c}^2)$. Symbols represent results of event-driven molecular dynamics simulations.
• Figure 2: Shear-rate dependence of the viscosity exhibiting an S-shaped curve for $(e_1, e_2)=(0.80, 0.99)$. Symbols represent results of event-driven molecular dynamics simulations.
• Figure 3: Three-dimensional plot of the shear-rate dependence of the viscosity for fixed $e_2=0.99$ and varying $e_1$. The solid line connects the points at which $\partial \eta^*/\partial \dot\gamma^*$ diverges.
• Figure 4: Phase diagram in the $(e_1,e_2)$ plane indicating whether discontinuous shear thickening occurs. The shaded region corresponds to the existence of an S-shaped constitutive relation.