Scaling law for velocity profiles of surface granular flows observed in rotating cylinders

Surface flows of granular materials over an erodible bed occur in industrial and natural systems, e.g., granular material processed using tumbling mixers and sediment transport at river beds. In laboratory studies, such granular flows can be generated conveniently using well-controlled rotating cylinders. To describe the flow profile, several scaling considerations have been reported in the literature. However, none of them is generally applicable to experimental observations. In this study, we propose to scale velocity profiles using the maximum surface velocity and a characteristic flow depth at which the flow velocity reduces to one half of the maximum surface velocity. This scaling is further explained using a simple viscosity model, which is developed by assuming that the apparent viscosity is inversely proportional to the local velocity. The analysis presented in this study is applicable only for velocity profiles measured at the centre of quasi-two-dimensional rotating cylinders half-filled with monosize, spherical particles.