Understanding the local flow rate peak of a hopper discharging discs through an obstacle using a Tetris-like model

摘要

Placing a round obstacle above the orifice of a flat hopper discharging uniform frictional discs has been experimentally and numerically shown in the literature to create a local peak in the gravity-driven hopper flow rate. Using frictionless molecular dynamics simulations, we show that the local peak is unrelated to the interparticle friction, the particle dispersity, and the obstacle geometry. We then construct a probabilistic Tetris-like model, where particles update their positions according to prescribed rules rather than in response to forces, and show that Newtonian dynamics is also not responsible for the local peak. Finally, we propose that the local peak is caused by an interplay between the flow rate around the obstacle, greater than the maximum when the hopper contains no obstacle, and a slow response time, allowing the overflowing particles to achieve a higher local area packing fraction by converging well upon reaching the hopper orifice.