Granular Flows in a Rotating Drum: the Scaling Law between Velocity and Thickness of the Flow

TL;DR

This study investigates how the velocity of granular flow in a rotating drum relates to flow thickness, revealing that the scaling law exponent varies with system geometry, challenging previous assumptions of a constant velocity gradient.

Contribution

It introduces a variable scaling law between flow velocity and thickness in rotating drums, showing dependence on system size ratios and geometry, which was not previously understood.

Findings

The velocity-thickness relationship follows a power law with an exponent that varies with size ratio.

Exponents greater than 1 occur at small size ratios due to saturation effects.

The flow's velocity gradient is not constant and depends on system geometry.

Abstract

The flow of dry granular material in a half-filled rotating drum is studied. The thickness of the flowing zone is measured for several rotation speeds, drum sizes and beads sizes (size ratio between drum and beads ranging from 47 to 7400). Varying the rotation speed, a scaling law linking mean velocity vs thickness of the flow, $v\sim h^m$, is deduced for each couple (beads, drum). The obtained exponent $m$ is not always equal to 1, value previously reported in a drum, but varies with the geometry of the system. For small size ratios, exponents higher than 1 are obtained due to a saturation of the flowing zone thickness. The exponent of the power law decreases with the size ratio, leading to exponents lower than 1 for high size ratios. These exponents imply that the velocity gradient of a dry granular flow in a rotating drum is not constant. More fundamentally, these results show that the flow of a granular material in a rotating drum is very sensible to the geometry, and that the deduction of the ``rheology'' of a granular medium flowing in such a geometry is not obvious.