Critical behavior of the viscous to inertial shear thickening transition in dense non-Brownian suspensions

Dense non-Brownian suspensions exhibit a transition with increasing shear rate, wherein their shear viscosity changes from a constant value at low shear rates to a linearly increasing function of the shear rate when particle inertia becomes important. Experiments on the shear rheology of frictionless non-Brownian suspensions have revealed the shear rate for the transition to sensitively depend on the suspension volume fraction. In this work, we use Discrete Element Method (DEM) simulations to show that the transitional shear rate is indeed sensitive to the volume fraction of the suspension and that it goes to zero as we approach the jamming volume fraction of the suspension. We rationalize that the reduction in the transitional shear rate arises from the growing length scale of the microstructure as one approaches the jamming volume fraction. This allows the development of a scaling framework that yields a collapse of the rheological data across a broad range of volume fractions and shear rates. We confirm this physical mechanism by extracting an estimate of the microstructural length scale and showcasing its role in triggering the viscous to inertial transition.