Free surface waves in wall-bounded
granular flows
Stephen L. Conway, Troy Shinbrot , and Benjamin
J. Glasser
Department
of Chemical & Biochemical Engineering,
David J. Goldfarb
Schering-Plough
Research Institute
Phys. Rev Lett. 90 (7) 074301-1-4, 2003
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Improved insight into mechanisms of granular flow has clear significance for countless solids transport and mixing processes, and for describing catastrophic geophysical events. Newly discovered free-surface waves have been shown to occur when a granular stream impinges on an inclined plane with vertical sidewalls. This has relevance to material conveyance in industrial chutes, and serves as a metaphor for free surface flows, such as the flow inside tumbling blenders. Past work in similar simplified flow geometries has yielded details of stress development and ensuing granular flow, and can help probe shear-induced mixing processes, as well as accompanying behavior such as segregation and jamming. Free-stream instabilities have been revealed before in chutes and in unbounded avalanches on inclined planes. The understanding gained echoes that from earlier studies of analogous fluid systems, such as boundary layer instabilities in channel flow past flat plates. We have extended the analogy by investigation of sheared granular flow near walls, which has associated implications for heat and mass transfer mechanisms. The chevron-shaped traveling waves spontaneously develop at inclinations close to the angle of repose for both steady and accelerating flows. Two distinct regimes are characterized by internal angle and frequency variations. Experimental measurements and Particle Image Velocimetry (PIV) analysis indicates that subsurface circulation driven by velocity gradients near frictional walls plays a central role in the pattern formation mechanism, suggesting that the wave generation is controlled by the granular analog of a fluid boundary layer. |
(a)
(b) (c)
(d)
(e)
(f)
Chevron waves viewed from above, at various chute
inclinations. Flow is from top to bottom, where the top edge of the frame is
30 cm downstream of the impingement area. Snapshots capture the entire width
of the acrylic chute (7.6 cm), which is 107 cm long, with grounded aluminum
flashing fitted into the bottom to minimize static. The steel hopper is
elevated 8 cm above the chute, and also grounded. q = a)
33.6º, b) 31.8º, c) 28.7º, d) 24.7º, e) 24.2º, f)
23.5º, measured with a digital level (±0.1º). Material mass
flow = 281±2 g/s, tapped density 1.35 kg/m3.
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Quicktime Video of this phenomena (17MB)
For more information see: Physical Review Letters 90 (7)
074301-1-4, 2003