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Improved model for the U-tube granular instability: Analytical solution and delayed coupling

Abstract:

Abstract The U-tube granular instability is understood as a tendency to increase of the height difference Δh between the granular material in both branches of a vertically vibrated U-tube. Δh has been reported to increase exponentially with time for a certain range of experimental parameters. A simple model based on a cyclic fluid/solid response of the granular material has been used to explain the dependence of the exponential growth rate γ with the maximum dimensionless acceleration Γ of vibration, at least within a certain range of applicability. We introduce an analytic solution of the model and use it to discuss the effect of several parameters on γ. The original model could not pbkp_redict an abrupt decrease of γ observed at large Γ. In this work we show how considering a Γ dependent delayed coupling between the granular material and the vibrating tube allows the model to describe the rapid decrease of γ seen at large Γ and provides a new perspective to understand this behavior.