Critical Scaling of Shear Viscosity at the Jamming Transition

Abstract

We carry out numerical simulations to study transport behavior about the jamming transition of a model granular material in two dimensions at zero temperature. Shear viscosity $\ensuremath{\eta}$ is computed as a function of particle volume density $\ensuremath{\rho}$ and applied shear stress $\ensuremath{\sigma}$, for diffusively moving particles with a soft core interaction. We find an excellent scaling collapse of our data as a function of the scaling variable $\ensuremath{\sigma}/|{\ensuremath{\rho}}_{c}\ensuremath{-}\ensuremath{\rho}{|}^{\ensuremath{\Delta}}$, where ${\ensuremath{\rho}}_{c}$ is the critical density at $\ensuremath{\sigma}=0$ (``point $J$''), and $\ensuremath{\Delta}$ is the crossover scaling critical exponent. We define a correlation length $\ensuremath{\xi}$ from velocity correlations in the driven steady state and show that it diverges at point $J$. Our results support the assertion that jamming is a true second-order critical phenomenon.