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

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.