Shear instabilities in granular flows

Benjamin J. Glasser & Troy Shinbrot
Rutgers University
& David J. Goldfarb
Schering-Plough Research Institute

Unstable waves have long been studied in fluid shear layers. These waves affect transport in the atmosphere and oceans as well as slipstream stability behind ships, planes, and heat transfer devices. Corresponding instabilities in granular flows have not previously been documented , despite the importance of these flows in geophysical and industrial systems.

In recent experiments, we have found that breaking waves can form at the interface between two streams of identical grains downstream of a splitter plate. The waves appear to be a manifestation of a competition between shear and extensional strains in the flowing granular bed that can be described in terms of the dimensionless group:

where dy/dx is the slope of an initial small disturbance, and the remaining terms are the shear rate in the numerator, and a dispersive term and the elongational rate in the denominator.

The experiments are performed in an inclined chute, where two streams of identical grains are directed down the chute past a splitter plate, as shown in the schematic at the right. The evolving instability shown in the schematic is superimposed from an actual experiment -- here the red grains travel more slowly than the blue ones.

 

The appearance of the granular breaking waves can be quite variable, ranging from a weak tendril to a large overhanging 'tongue'. Some examples of these breaking waves are shown below in overhead snapshots of a chute in which grains travel from left to right. The upper grains travel more rapidly than the lower grains. We emphasize that in all experiments, all grains are identical except for color: this is an intrinsic instability associated with the mechanism of transmission of shear in granular streams.

For a 1.8 MB quicktime movie of this phenomenon, with apologies to Stevie Wonder, see this link.

For a 9 MB .avi movie of this phenomenon, with further apologies to Stevie Wonder, see this link.