Understanding the Local Flow Rate Peak of a Hopper Discharging Discs through an Obstacle Using a Tetris-like Model

TL;DR

This study investigates the cause of a local peak in hopper flow rate caused by an obstacle, using simulations and a Tetris-like model to show that the peak is due to flow dynamics and response time, not friction or geometry.

Contribution

The paper introduces a probabilistic Tetris-like model to explain the flow rate peak, demonstrating that it is unrelated to interparticle friction, particle dispersity, or obstacle geometry.

Findings

Flow rate peak is independent of interparticle friction.

Flow rate peak is unaffected by obstacle geometry.

Flow rate peak results from flow dynamics and response time.

Abstract

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 (MD) 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 are 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 converge well upon reaching the hopper orifice.