Dynamic transition in conveyor belt driven granular flow
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We consider the flow of disks of diameter d driven by a conveyor belt of dynamic friction coefficient μ through an aperture on a flat barrier. The flow rate presents two distinct regimes. At low belt velocities v the flow rate is proportional to v and to the aperture width A. However, beyond a critical velocity, the flow rate becomes independent of v and proportional to (A − kd)3/2 in correspondence with a two-dimensional Beverloo scaling. In this high-velocity regime we also show that the flow rate is proportional to μ1/2. We discuss that these contrasting behaviors arise from the competition between two characteristic time scales: the typical time a disk takes to stop on the belt after detaching from the granular pack and the time it takes to reach the aperture.
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