Behavior of pressure and viscosity at high densities for two-dimensional hard and soft granular materials

Abstract

The pressure and viscosity in two-dimensional sheared granular assemblies are investigated numerically for varying disks' toughness, degree of polydispersity and coefficient of normal restitution. In the rigid, elastic limit of monodisperse systems, the viscosity is approximately inverse proportional to the area fraction difference from φη ≃ 0.7, but the pressure is still finite at φη. On the other hand, in moderately soft, dissipative and polydisperse systems, we confirm the recent theoretical prediction that both scaled pressure (divided by the kinetic temperature T) and scaled viscosity (divided by √T) diverge at the same density, i.e., the jamming transition point φj> φη, with the critical exponents -2 and -3, respectively. Furthermore, we observe that the critical region of the jamming transition disappears as the restitution coefficient approaches unity, i.e. for vanishing dissipation. In order to understand the conflict between these two different predictions on the divergence of the pressure and viscosity, the transition from soft to near-rigid particles is studied in detail and the dimensionless control parameters are defined as ratios of various time-scales. We introduce a dimensionless number, i.e. the ratio of dissipation rate and shear rate, that can identify the crossover from the scaling of very hard, i.e. rigid disks, in the collisional regime, to the scaling in the soft, jamming regime with multiple contacts.