A model for heap formation in vibrated gravitational suspensions


Various surface instabilities are found in vertically vibrated dense suspensions, such as heaping, stable holes, expanding holes and replicating holes. All of these phenomena are counterintuitive because a steady surface deformation remains in the fluid. In general, an inclined free fluid surface is difficult to maintain because surface deformation is suppressed by gravity. The mechanisms of these instabilities are still unclear and it is important to identify the rheological feature that is crucial for such surface instabilities.
We propose a model of heaping induced by a boundary condition on a solid wall [1]. We found that a flat fluid layer becomes unstable and form heaps when we impose a boundary condition that shows slip / non-slip switching in synchronization with vertical vibration. The obtained onset acceleration, bifurcation type and flow of the heaps are consistent with those observed experimentally. Furthermore, we found that heaps can drift and climb a slope when the bottom is slightly inclined. This result indicates that our model can be applied to the migration of localized structures.

[1] H. Ebata and M. Sano, EPL, 100, 14001 (2012)

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