Relaxation Times and Rheology in Dense Athermal Suspensions

We study the jamming transition in a model of elastic particles under shear at zero temperature. The key quantity is the relaxation time $\tau$ which is obtained by stopping the shearing and letting energy and pressure decay to zero. At many different densities and initial shear rates we do several such relaxations to determine the average $\tau$. We establish that $\tau$ diverges with the same exponent as the viscosity and determine another exponent from the relation between $\tau$ and the coordination number. Though most of the simulations are done for the model with dissipation due to the motion of particles relative to an affinely shearing substrate (the RD$_0$ model), we also examine the CD$_0$ model, where the dissipation is instead due to velocity differences of disks in contact, and confirm that the above-mentioned exponent is the same for these two models. We also consider finite size effects on both $\tau$ and the coordination number.