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Free rings of bouncing droplets: stability and dynamics

Published online by Cambridge University Press:  05 October 2020

Miles M. P. Couchman Open the ORCID record for Miles M. P. Couchman [Opens in a new window]  and
John W. M. Bush Open the ORCID record for John W. M. Bush [Opens in a new window]
Miles M. P. Couchman
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA02139, USA
John W. M. Bush*
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA02139, USA
*
†Email address for correspondence: bush@math.mit.edu
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Abstract

We present the results of a combined experimental and theoretical investigation of the stability of rings of millimetric droplets bouncing on the surface of a vibrating liquid bath. As the bath's vibrational acceleration is increased progressively, droplet rings are found to destabilize into a rich variety of dynamical states including steady rotational motion, periodic radial or azimuthal oscillations and azimuthal travelling waves. The instability observed is dependent on the ring's initial radius and drop number, and whether the drops are bouncing in- or out-of-phase relative to their neighbours. As the vibrational acceleration is further increased, more exotic dynamics emerges, including quasi-periodic motion and rearrangement into regular polygonal structures. Linear stability analysis and simulation of the rings based on the theoretical model of Couchman et al. (J. Fluid Mech., vol. 871, 2019, pp. 212–243) largely reproduce the observed behaviour. We demonstrate that the wave amplitude beneath each drop has a significant influence on the stability of the multi-droplet structures: the system seeks to minimize the mean wave amplitude beneath the drops at impact. Our work provides insight into the complex interactions and collective motions that arise in bouncing-droplet aggregates.

JFM classification

Drops and Bubbles: Drops Waves/Free-surface Flows: Faraday waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 903 , 25 November 2020 , A49
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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