Rheology and scaling behavior of cascading granular flows in rotating drums

Mixing, agglomerating, and milling of granular materials within a rotating drum is often performed in the cascading flow regime; however, the scaling behavior of these industrial applications remains poorly understood. It involves both centrifugal forces and an inertial surface flow with a curved profile. By means of discrete element simulations, we investigate the rheology of cascading flows in rotating drums as a function of drum size, rotation speed, and filling degree. We find that the surface profile, described by the ratio between the steepest descent slope and an average slope, is strongly correlated with flow variables such as active layer thickness, contact force variability, and wall slip. We show that the flow variables cannot be scaled by Froude number alone but are instead nicely scaled by a dimensionless parameter that combines the Froude number with other system parameters. This scaling works even for small drums and low filling degrees where finite-size effects prevail and the slippage of particles at the drum wall considerably affects the cascading flow at the free surface. The observed correlation between this parameter and contact force fluctuations suggests that it may also be a relevant upscaling parameter for milling and agglomeration in rotating drums.