Relationship between the flow rate and the packing fraction in the choke area of the two-dimensional granular flow.

Two-dimensional granular flow in a channel with small exit is studied by both experiments and simulations. We first observe the time variation of the transition from dilute flow state to dense flow state by both experiments and simulations. Then we obtain a relationship between the local flow rate and the local packing fraction in the choke area by use of molecular dynamics simulations. The relationship is a continuous function rather than a discontinuous one. The flow rate has a maximum at a moderate packing fraction and the packing fraction is terminated at high value with negative slope. According to the relationship, four flow states--i.e., stable dilute flow state, metastable dilute flow state, unstable dense flow state, and stable dense flow state--are defined for fixed inflow rate. The discontinuities and the complex time variation behavior occurring in the transition between dilute and dense flow states can be attributed to the abrupt variation through unstable flow state.