Granular flow in a rotating drum: Experiments and theory

Abstract:

Erosion at the base of a debris flow fundamentally controls how large the flow will become and how far it will travel. Experimental observations of this important phenomenon are rather limited, and this lack has led theoretical treatments to making ad hoc assumptions about the basal process. In light of this, we carried out a combination of laboratory experiments and theoretical analysis of granular flow in a rotating drum, a canonical example of steady grain motion in which entrainment rates can be precisely controlled. Our main result is that basal sediment is entrained as the velocity profile adjusts to imbalance in the flow of kinetic energy.

Our experimental apparatus consisted of a 40cm-diameter drum, 4cm-deep, half-filled with 2.3mm grains. Rotation rates varied from 1-70 rpm. We varied the effective scale by varying effective gravity from 1g to 70g on a geotechnical centrifuge. The field of grain motion was recorded using high-speed video and mapped using particle tracking velocimetry. In tandem we developed a depth-averaged theory using balance equations for mass, momentum and kinetic energy. We assumed a linearized GDR Midi granular rheology [da Cruz, 2005] and a Coulomb friction law along the sidewalls [Jop et al., 2005]. A scaling analysis of our equations yields a dimensionless “entrainment number” En, which neatly parametrizes the flow geometry in the drum for a wide range of variables, e.g., rotation rate and effective gravity. At low En, the flow profile is planar and kinetic energy is balanced locally in the flow layer. At high En, the flow profile is sigmoidal (yin-yang shaped) and the kinetic energy is dominated by longitudinal, streamwise transfer. We observe different scaling behavior under each of these flow regimes, e.g., between En and kinetic energy, surface slope and flow depth. Our theory correctly predicts their scaling exponents and the value of En at which the regime transition takes place. We are also able to make corrections for Coriolis and dilation effects that improve the match between theory and experiment.