Geometry dependence of the clogging transition in tilted hoppers

TL;DR

This study explores how the geometry and grain shape influence the clogging transition in tilted hoppers, revealing that critical aperture size diverges with tilt angle and varies with grain and aperture shape.

Contribution

It provides a detailed phase diagram showing the dependence of the clogging transition on hopper tilt, aperture shape, and grain type, highlighting the geometry's role in clogging behavior.

Findings

Critical aperture size diverges at tilt angles near the angle of repose.

Shape of the clogging transition is consistent across grain types for circular holes.

Growth rate of critical hole size with tilt angle varies for slit apertures depending on grain shape.

Abstract

We report the effect of system geometry on the clogging of granular material flowing out of flat-bottomed hoppers with variable aperture size D. For such systems, there exists a critical aperture size Dc at which there is a divergence in the time for a flow to clog. To better understand the origins of Dc, we perturb the system by tilting the hopper an angle Q and mapping out a clogging phase diagram as a function of Q and D. The clogging transition demarcates the boundary between the freely-flowing (large D, small Q) and clogging (small D, large Q) regimes. We investigate how the system geometry affects Dc by mapping out this phase diagram for hoppers with either a circular hole or a rectangular narrow slit. Additionally, we vary the grain shape, investigating smooth spheres (glass beads), compact angular grains (beach sand), disk-like grains (lentils), and rod-like grains (rice). We find that the value of Dc grows with increasing Q, diverging at pi-Qr where Qr is the angle of repose. For circular apertures, the shape of the clogging transition is the same for all grain types. However, this is not the case for the narrow slit apertures, where the rate of growth of the critical hole size with tilt angle depends on the material.