Gravity-driven granular flow from a wedge-shaped hopper: Analysis of the exit region

We present results of experimental measurements and discrete element method simulations for granular flow in the exit region of a quasi-two-dimensional (2D) wedge-shaped hopper with glass front and back walls. The results are important from a practical viewpoint, since the mass flow rate from hoppers, widely used in industry, is determined primarily by the flow in this region. Experiments and simulations, which closely match the experiments, show that the acceleration of particles is about 20% larger than the acceleration due to gravity (g) near the exit. Simulations are carried out for a 3D hopper in which the front and back walls are replaced by a periodic boundary. In this case, the effect is larger with the maximum acceleration equal to 1.75g. The larger than gravity acceleration is shown to be a consequence of the large normal stress gradient near the exit plane. A theoretical analysis for the flow and stress distribution in the hopper is presented, predictions of which match simulation results. The theory is used to derive an expression for the mass flow rate.