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

TL;DR

This study numerically investigates the pressure and viscosity behavior in two-dimensional sheared granular materials, revealing how dissipation, particle softness, and polydispersity influence the approach to jamming and the divergence of rheological properties.

Contribution

It provides new insights into the transition from hard to soft particles and the conditions under which pressure and viscosity diverge at the jamming transition.

Findings

Viscosity inversely proportional to area fraction difference near rigid limit.

Both scaled pressure and viscosity diverge at the jamming point with exponents -2 and -3.

Critical jamming behavior diminishes as dissipation approaches zero.

Abstract

The pressure and the viscosity in two-dimensional sheared granular assemblies are investigated numerically. The behavior of both pressure and viscosity is smoothly changing qualitatively when starting from a mono-disperse hard-disk system without dissipation and moving towards a system of (i) poly-disperse, (ii) soft particles with (iii) considerable dissipation. In the rigid, elastic limit of mono-disperse systems, the viscosity is approximately inverse proportional to the area fraction difference from $\phi_{\eta} \simeq 0.7$, but the pressure is still finite at $\phi_{\eta}$. In moderately soft, dissipative and poly-disperse systems, on the other hand, we confirm the recent theoretical prediction that both scaled pressure (divided by the kinetic temperature $T$) and scaled viscosity (divided by $\sqrt{T}$) diverge at the same density, i.e., the jamming transition point $\phi_J > \phi_\eta$, with the exponents -2 and -3, respectively. Furthermore, we observe that the critical region of the jamming transition becomes invisible 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 the viscosity, the transition from soft to hard 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 to the scaling in the soft, jamming regime.