Shear-induced rigidity and diffusivity in dense frictional suspensions

Dense suspensions often exhibit a dramatic response to large external deformation. Recent work has related this behavior to the transition from an unconstrained lubricated state to a constrained frictional state. Here, we use numerical simulations to study the flow behavior and shear-induced diffusion of frictional non-Brownian spheres in two dimensions under simple shear flow. To build up the full rate or stress dependence, our focus is on the frictional and frictionless rate-independent states. We analyze the collective motion of particles using both diffusivity and rigid cluster size (extracted using the non-affine velocity correlations). We find that close to jamming, the collective motion of particles increases rapidly and becomes system size. Further, we demonstrate a Stokes-Einstien-type relation correlating diffusivity and viscosity, which we find to depend on high or low friction, with μ=0.1 being the rough demarcation. For low friction, the system transitions from D ∼ η to D ∼ η^1/3 power law. On the other hand, for high friction, the relation is always D ∼ η1/3. These relations cannot be explained using the distance from the jamming point. Finally, we show that varying rolling friction does not affect the power laws.