History-dependent deformation of a rotated granular pile governed by granular friction

TL;DR

This study investigates how the deformation of a granular pile under rotation depends on its deformation history, revealing that the granular friction coefficient increases with rotation but does not fully recover after rotation decreases.

Contribution

It provides experimental evidence of the history-dependent behavior of granular friction in rotating granular piles and models this behavior through force balance analysis.

Findings

Granular friction coefficient increases with rotation rate.

Friction coefficient does not fully recover after decreasing rotation.

Force balance model explains part of the history dependence.

Abstract

We experimentally examined the history dependence of the rotation-induced granular deformation. As an initial state, we prepared a quasi-two-dimensional granular pile whose apex is at the rotational axis and its initial inclination is at the angle of repose. The rotation rate was increased from $0$ to $620$~(rpm) and then decreased back to $0$. During the rotation, deformation of the rotated granular pile was captured by a camera. From the acquired image data, granular friction coefficient $\mu$ was measured as a function of the ratio between centrifugal force and gravity, $\Gamma$. To systematically evaluate the variation of $\mu$ both in the increasing (spinning up) and decreasing (spinning down) rotation-rate regimes, surface profiles of the deformed granular piles were fitted to a model considering the force balance among gravity, friction, and centrifugal force at the surface. We found that $\mu$ value grows in the increasing $\Gamma$ regime. However, when $\Gamma$ was reduced, $\mu$ cannot recover its initial value. A part of the history-dependent behaviors of the rotated granular pile can be understood by the force balance model.