Critical Scaling of Shear Viscosity at the Jamming Transition

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 \eta is computed as a function of particle volume density \rho and applied shear stress \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 \sigma/|\rho_c-\rho|^\Delta, where \rho_c is the critical density at \sigma=0 ("point J"), and \Delta is the crossover scaling critical exponent. Our results show that jamming is a true critical phenomenon, extending to driven steady states along the non-equilibrium \sigma axis of the \rho-\sigma phase diagram.