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 p 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/vertical bar p(c) - p vertical bar(Delta), where p(c) is the critical density at sigma = 0 (point J''), and Delta is the crossover scaling critical exponent. We define a correlation length 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.