Stationary bubble formation and cavity collapse in wedge-shaped hoppers

TL;DR

This study investigates the dynamic behaviors of granular materials in a wedge-shaped hopper, revealing novel bubbling and cavity regimes, with theories explaining their physical conditions, which could aid in mixing processes.

Contribution

It introduces and explains two new dynamic regimes in granular flow within wedge-shaped hoppers, supported by simple theoretical models.

Findings

Bubbles of nearly equal size form at regular intervals in the bubbling regime.

A cavity grows and suddenly collapses in the cavity regime.

The regimes depend on stability and clogging conditions of the granular layer.

Abstract

The hourglass is one of the apparatuses familiar to everyone, but reveals intriguing behaviors peculiar to granular materials, and many issues are remained to be explored. In this study, we examined the dynamics of falling sand in a special form of hourglass, i.e., a wedge-shaped hopper, when a suspended granular layer is stabilized to a certain degree. As a result, we found remarkably different dynamic regimes of bubbling and cavity. In the bubbling regime, bubbles of nearly equal size are created in the sand at a regular time interval. In the cavity regime, a cavity grows as sand beads fall before a sudden collapse of the cavity. Bubbling found here is quite visible to a level never discussed in the physics literature and the cavity regime is a novel phase, which is neither continuous, intermittent nor completely blocked phase. We elucidate the physical conditions necessary for the bubbling and cavity regimes and develop simple theories for the regimes to successfully explain the observed phenomena by considering the stability of a suspended granular layer and clogging of granular flow at the outlet of the hopper. The bubbling and cavity regimes could be useful for mixing a fluid with granular materials.