Fraction of clogging configurations sampled by granular hopper flow

TL;DR

This study quantifies the likelihood of clogging in granular hopper flow, showing it depends on aperture geometry and can be modeled as a Poisson process with no sharp transition, applicable across different configurations.

Contribution

It introduces a method to measure clogging probability based on discharged mass, revealing a universal exponential decay model and the absence of a sharp clogging transition.

Findings

Clogging probability depends on aperture geometry and orientation.

Data fits an exponential decay model based on hole width and system dimensionality.

All hoppers have a nonzero probability to clog, with no sharp transition.

Abstract

We measure the fraction $F$ of flowing grain configurations that precede a clog, based on the average mass discharged between clogging events for various aperture geometries. By tilting the hopper, we demonstrate that $F$ is a function of the hole area projected in the direction of the exiting grain velocity. By varying the length of slits, we demonstrate that grains clog in the same manner as if they were flowing out of a set of smaller independent circular openings. The collapsed data for $F$ can be fit to a decay that is exponential in hole width raised to the power of the system dimensionality. This is consistent with a simple model in which individual grains near the hole have a large but constant probability to precede a clog. Such a picture implies that there is no sharp clogging transition, and that all hoppers have a nonzero probability to clog. See Supplemental Material for models of clogging as a discrete Poisson process, and for resulting alternative measures of l based on the standard deviation of the discharge mass distribution.