Transitional granular flow in a spinning bucket at high frequencies

Abstract

A large-scale three-dimensional simulation study of dense granular media was performed to investigate the flow dynamics of grains in a spinning bucket at high frequencies. The time intermittency in the high energy releases by grains was observed which was speculated to be a signature of a chaotic dynamics for the flowing grains. By utilizing the results obtained from simulations, a theory was developed for dense flows of dry, cohesionless, coarse, monodispersed spherical particle aggregates that exhibit viscous-like behavior. Using a continuum approach, the hydrodynamic equations are presented and an expression for viscosity is obtained which provides a liquid-like character at low shear rates and a gaseous-like behavior at high shear rates. The theory is utilized to predict the flow dynamics of grains spinning at high frequencies in a cylindrical bucket, which appears to be a simple geometry useful for testing and for comparing theories of granular materials. The model results were found to be consistent with experimentally observed surface phenomena across a wide range of rotation rates, including the development of a depression near the axis of rotation at high rotation rates and the formation of a cusp in the central section of the bucket at lower rotation rates. The comparison of the computed and experimental surface shapes suggests that the theory may lead to a renewed interpretation of many previously unexplained hydrodynamic phenomena that are observed in spinning buckets.