Contact Percolation in Dense Granular Flow

Steady-state rheology of spheres are studied in the dense flow regime with three-dimensional molecular dynamics simulations in two different geometries: Simple shear flow and gravity-driven chute flow. The same set of constitutive equations, which are only a function of the local dimensionless strain rate, $I$, are found to characterize bulk macroscopic observables such as density, internal Coulomb coefficient and scaled velocity fluctuations in both cases. A transition has been identified at a finite (non-universal) value of $I=I_{c}$, corresponding to the percolation transition of the instantaneous contact network. For $I \quad < \quad I_{c}$, an infinite contact network spans the system. The flow dilates and the internal Coulomb coefficient increases with increasing $I$. For $I > \quad I_{c}$, the instantaneous contact network is broken into finite clusters. The system dilates further with increasing $I$ while the internal Coulomb coefficient becomes independent of $I$, resulting in a maximum tilt angle for steady chute flow. Scaled velocity fluctuations exhibit power-law dependence on $I$ on both sides of $I_{c}$, with a minimum at the transition. The transition is distinct from the ``jamming'' transition at $I$ = 0 associated with the \textit{rigidity} percolation of the contact network.