What do dry granular flows tell us about dense non-Brownian suspension rheology?

Recent years have seen significant progress in our understanding of the rheology of dry granular materials. A scale invariance of equations of motion in the rigid grain limit has helped identifying dimensionless quantities which govern flow. After a review of recent results on dry granular materials, we show how this same dimensional analysis carries over to the case of dense, non-Brownian suspensions. Our review is based on compiled data from various sets of numerical simulations, using both molecular and contact dynamics. It covers the breakdown of kinetic theory, which arises when contact forces dominate collisional forces in inertial flows, and the approach to dense flows up to the quasi-static limit. We show that simple invariance arguments permit to clarify the conditions of occurrence of viscous and inertial scaling in suspensions, and show in particular that both may occur in dense flows even in the presence of significant contact forces, up to the jamming limit. Some implications of the properties of steady uniform quasistatic granular flow under constant pressure for very dense suspensions near the maximum concentration are also discussed.