Spatial Patterns and Shock Waves in Granular Flows

Harry L Swinney, University of Texas at Austin

Collections of particles are poured, mixed, and separated in many industrial processes, yet granular media remain less well understood than fluids and solids. Vertically oscillating granular layers provide a test bed for theory and modeling of granular dynamics. Experiments on oscillating granular layers reveal a variety of spatial patterns that emerge spontaneously for different container accelerations and frequencies: stripes, squares, hexagons, spirals, and oscillons (localized structures). In granular flows shock waves form easily because the sound speed in a granular gas is typically only a few cm/sec. Molecular dynamics simulations agree well with observations of patterns and shock waves, but only if the particle collision operator includes particle friction. Hydrodynamic theory is on shaky ground for granular media because particle mean free paths are typically comparable to the distances over which the macroscopic fields change, but in some cases hydrodynamic theory works rather well. In summary, a comparison of experiment, molecular dynamics simulations, and hydrodynamic theory yields insights into granular dynamics and indicates shortcomings of existing theory.

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