Phase diagram for inertial granular flows

Flows of hard granular materials depend strongly on the interparticle friction coefficient mu(p) and on the inertial number I, which characterizes proximity to the jamming transition where flow stops. Guided by numerical simulations, we derive the phase diagram of dense inertial flow of spherical particles, finding three regimes for 10(-4) less than or similar to I less than or similar to 10(-1): frictionless, frictional sliding, and rolling. These are distinguished by the dominant means of energy dissipation, changing from collisional to sliding friction, and back to collisional, as mu(p) increases from zero at constant I. The three regimes differ in their kinetics and rheology; in particular, the velocity fluctuations and the stress ratio both display nonmonotonic behavior with mu(p), corresponding to transitions between the three regimes of flow. We rationalize the phase boundaries between these regimes, show that energy balance yields scaling relations between microscopic properties in each of them, and derive the strain scale atwhich particles lose memory of their velocity. For the frictional sliding regime most relevant experimentally, we find for I >= 10(-2.5) that the growth of the macroscopic friction mu(I) with I is induced by an increase of collisional dissipation. This implies in that range that mu(I) - mu(0) similar to I1-2b, where b approximate to 0.2 is an exponent that characterizes both the dimensionless velocity fluctuations L similar to I-b and the density of sliding contacts chi similar to I-b.