Granular discharge and clogging for tilted hoppers

TL;DR

This study investigates how the flow of spherical glass beads through tilted hoppers depends on tilt angle and hole size, revealing relationships with clogging behavior and flow cessation.

Contribution

It provides a systematic analysis of discharge rates and clogging conditions for tilted hoppers, extending understanding of granular flow dynamics.

Findings

Discharge rate follows Beverloo relation with larger cutoff for vertical holes.

Flux decreases linearly with cosine of tilt angle for large holes.

Flow ceases abruptly at certain tilt angles depending on hole size.

Abstract

We measure the flux of spherical glass beads through a hole as a systematic function of both tilt angle and hole diameter, for two different size beads. The discharge increases with hole diameter in accord with the Beverloo relation for both horizontal and vertical holes, but in the latter case with a larger small-hole cutoff. For large holes the flux decreases linearly in cosine of the tilt angle, vanishing smoothly somewhat below the angle of repose. For small holes it vanishes abruptly at a smaller angle. The conditions for zero flux are discussed in the context of a {\it clogging phase diagram} of flow state vs tilt angle and ratio of hole to grain size.