Parameters and scalings for dry and immersed granular flowing layers in rotating tumblers.

The scaling properties of the continuous flowing layer in a quasi-2D circular tumbler half filled with a granular material are studied experimentally in the presence of three different interstitial fluids (air, water, and glycerine). In the dry case, the dimensionless flowing layer thickness δ(0)/d scales with the dimensionless flow rate Q(dry)(*) = Q/(dsqrt[gd]), where Q is the flow rate, d is the particle diameter, and g is the acceleration due to gravity, in agreement with previous studies. However, unlike previous studies, we show that the exponent for the power-law relation between the two depends on the range of Q(dry)(*) Meanwhile, the angle of repose increases linearly with Q(dry)(*). In the immersed case, the interstitial fluid changes the relevant time scales, which can be accommodated by considering the fluid properties. The result is that there are two different expressions for the dimensionless flow rate in the immersed flow; one corresponding to a free fall regime for a large Stokes number, and one corresponding to a viscous regime at small Stokes number. On this basis, a single dimensionless flow rate that incorporates both buoyancy and viscous friction is proposed. The effect of side walls is also investigated. For dry flows and those immersed in water, the thickness of the flowing layer decreases while the slope of the free surface increases as the gap separating the walls becomes smaller. For immersed granular flows with glycerine as the interstitial fluid, however, the ratio of the thickness of the flowing layer to the bead diameter is independent of the distance the between the side walls because viscous effects dominate.