Geometric frustration induces the transition between rotation and counterrotation in swirled granular media

TL;DR

This study explores how geometric frustration caused by frictional interactions in dense swirled granular media leads to a transition from co-rotation to counterrotation of the particle cluster, combining experimental and numerical approaches.

Contribution

It reveals the role of frictional effects and geometric frustration in inducing the rotation transition, providing new insights into granular flow behavior.

Findings

Counterrotation occurs at high particle densities due to frictional geometric frustration.

Friction between particles and container wall is critical for the transition.

Numerical simulations confirm the importance of wall-disc and disc-disc friction.

Abstract

Granular material in a swirled container exhibits a curious transition as the number of particles is increased: at low densities the particle cluster rotates in the same direction as the swirling motion of the container, while at high densities it rotates in the opposite direction. We investigate this phenomenon experimentally and numerically using a co-rotating reference frame in which the system reaches a statistical steady-state. In this steady-state the particles form a cluster whose translational degrees of freedom are stationary, while the individual particles constantly circulate around the cluster's center of mass, similar to a ball rolling along the wall within a rotating drum. We show that the transition to counterrotation is friction-dependent. At high particle densities, frictional effects result in geometric frustration which prevents particles from cooperatively rolling and spinning. Consequently, the particle cluster rolls like a rigid body with no-slip conditions on the container wall, which necessarily counterrotates around its own axis. Numerical simulations verify that both wall-disc friction and disc-disc friction are critical for inducing counterrotation.