A Tetris-like Model Showing a Universal Enhanced Flow Rate of a Hopper Discharging Hard Discs Through an Adjustable Inclusion

TL;DR

This paper introduces a Tetris-like model to explain the universal phenomenon of enhanced flow rate in hopper systems with an inclusion, revealing that local effects can be understood without Newtonian physics.

Contribution

The model demonstrates that a simple probabilistic approach can reproduce the enhanced flow rate effect, offering a new fundamental understanding of hopper flow dynamics.

Findings

The model reproduces the enhanced flow rate observed experimentally.

A moderate response time and flow rate difference explain the local effect.

The approach does not rely on Newtonian dynamics, highlighting a probabilistic mechanism.

Abstract

In the literature, placing an inclusion near the orifice of a hopper, containing disc particles, has been experimentally and numerically reported to locally enhance the gravity-driven hopper flow rate. Moreover, the peaked flow rate can happen regardless of the interparticle friction, the inclusion geometry, or the disc dispersity. To reveal the fundamental reason causing this local effect, we propose a Tetris-like model that sequentially moves one disc particle at a time towards the hopper orifice. A Gaussian displacement function that independently controls a disc's movement in the horizontal or vertical direction, and the algorithm of the model accepts a movement as long as it creates no overlap between objects in the system. Our model creates an artificial steady probability-driven hopper flow without knowing the Newtonian dynamics which allows interparticle collaborative motion. Under specific conditions, we reproduce the enhanced flow rate and show that a moderate response time of the system and a flow rate difference between its value around the inclusion and its maximum without an inclusion are sufficient to explain this local effect with no Newton's laws involved.