Pattern Formation and Time-Dependence in Flowing Sand
We describe three experiments characterizing the dynamics of sand flowing from a hopper. In the first experiment, we have measured time-dependence in the normal stress caused by sand flowing from a hopper in order to test recent predictions by Pitman and Schaeffer. In the second experiment, we have used fast X-ray transmission imaging techniques to follow the evolution of patterns and the propagation of fronts associated with the patterns. The patterns are seen in rough faceted sand but not in smooth sand of the same size. In mixtures of rough and smooth sand, the amplitude of the patterns vanishes smoothly as X, the mass fraction of rough sand, falls below 0.22. In the third experiment we looked for the change between mass and funnel flow. In funnel flow, the material is stagnant near the hopper walls, and the flow is typically complex; in mass flow there is smooth “laminar” flow throughout the hopper. Contrary to expectations, funnel flow was observed over a wide range of hopper opening angles θ, spanning 19° < θ < 80°. Finally, we describe cellular automata models for the flow of sand which reproduce a number of the features seen in the experiments.
KeywordsMass Flow Rate Granular Material Cellular Automaton Granular Flow Cellular Automaton Model
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