Dense granular flows: two-particle argument accounts for friction-like constitutive law with threshold

A scalar constitutive law is obtained for dense granular flows, both in the inertial regime where the grain inertia dominates, and in the viscous regime. Considering a pair of grains rather than a single grain, the classical arguments yield a constitutive law that exhibits a flow threshold expressed as a finite effective friction at flow onset. The value of the threshold is not predicted. The resulting law seems to be compatible with existing data, provided the saturation at high velocity (collisional regime) is added empirically. The law is not exactly the same in both regimes, which seems to indicate that there is no “universal” law.