Numerical study of particle motion pattern in a rotating wavy tumbler based on angular momentum analysis

This work uses the hard-sphere model to simulate the particle motion pattern in a two-dimensional rotating tumbler with a sine-wave boundary. Based on the angular momentum analysis, the present work investigates the intrinsic effects of boundary configuration of tumblers, e.g. the wave number and the boundary amplitude, on the motion pattern of the particles separately. It is found that the particle motion pattern depends on the configuration of the tumbler significantly. There are two collision patterns, namely the primary and secondary patterns. The former pattern dominates when the boundary is composed of low wave numbers or small boundary amplitudes, whereas the latter pattern dominates when the boundary is composed of high wave numbers or large boundary amplitudes. The primary collision pattern is beneficial for the bulk motion of tumbling of the particle clusters, whereas the secondary pattern suppresses it. The interpretation for the different mechanisms of collision pattern indicates the existence of different regions, which is either positive or negative to the tumbling motion. It provides some guiding information for engineering application, such as the design of tumblers for efficient mixing.