Model of heap formation in vibrated gravitational suspensions

Hiroyuki Ebata, Masaki Sano

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In vertically vibrated dense suspensions, several localized structures have been discovered, such as heaps, stable holes, expanding holes, and replicating holes. Because an inclined free fluid surface is difficult to maintain because of gravitational pressure, the mechanism of those structures is not understood intuitively. In this paper, as a candidate for the driving mechanism, we focus on the boundary condition on a solid wall: the slip-nonslip switching boundary condition in synchronization with vertical vibration. By applying the lubrication approximation, we derived the time evolution equation of the fluid thickness from the Oldroyd-B fluid model. In our model we show that the initially flat fluid layer becomes unstable in a subcritical manner, and heaps and convectional flow appear. The obtained results are consistent with those observed experimentally. We also find that heaps climb a slope when the bottom is slightly inclined. We show that viscoelasticity enhances heap formation and climbing of a heap on the slope.

Original languageEnglish
Article number053016
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number5
Publication statusPublished - Nov 23 2015

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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