Enhanced flow rate by the concentration mechanism of Tetris particles when discharged from a hopper with an obstacle

• Published in: arXiv.org
• Main Authors: Guo-Jie, Jason Gao, Fu-Ling, Yang, Holcomb, Michael C, Blawzdziewicz, Jerzy
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 13.05.2021
• Subjects: Convergence; Discharge; Flow velocity; Local flow; Particle acceleration; Physics - Soft Condensed Matter; Two dimensional models; Waiting rooms
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2003.01898

We apply a holistic 2D Tetris-like model, where particles move based on prescribed rules, to investigate the flow rate enhancement from a hopper. This phenomenon was originally reported in the literature as a feature of placing an obstacle at an optimal location near the exit of a hopper discharging athermal granular particles under gravity. We find that this phenomenon is limited to a system of sufficiently many particles. In addition to the waiting room effect, another mechanism able to explain and create the flow rate enhancement is the concentration mechanism of particles on their way to reaching the hopper exit after passing the obstacle. We elucidate the concentration mechanism by decomposing the flow rate into its constituent variables: the local area packing fraction \(\phi_l^E\) and the averaged particle velocity \(v_y^E\) at the hopper exit. In comparison to the case without an obstacle, our results show that an optimally placed obstacle can create a net flow rate enhancement of relatively weakly driven particles, caused by the exit-bottleneck coupling if \(\phi_l^E > \phi_o^c\), where \(\phi_o^c\) is a characteristic area packing fraction marking a transition from fast to slow flow regimes of Tetris particles. Utilizing the concentration mechanism by artificially guiding particles into the central sparse space under the obstacle or narrowing the hopper exit angle under the obstacle, we can create a man-made flow rate peak of relatively strongly-driven particles that initially exhibit no flow rate peak. Additionally, the enhanced flow rate can be maximized by an optimal obstacle shape, particle acceleration rate towards the hopper exit, or exit geometry of the hopper.