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 corotating 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-disk friction and disk-disk friction are critical for inducing counterrotation.
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We are grateful to Tadashi Tokieda for introducing us to this phenomenon. This work was supported by the NSF (DMR-1420570). M.H.-C. and J.P.R. were supported by US Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics Program under Award No. DE-SC0012296. M.H.-C. and J.P.R. thank Leif Ristroph for procuring tabletop experimental materials. S.M.R. and M.H.-C. acknowledge support from the Alfred P. Sloan Foundation.
© 2019 American Physical Society.