Resonant interactions in bouncing droplet chains

Lauren Barnes; Giuseppe Pucci; Anand U. Oza

doi:10.5802/crmeca.30

Bouncing drops, memory

Resonant interactions in bouncing droplet chains

Lauren Barnes ¹ ; Giuseppe Pucci ² ; Anand U. Oza ³

¹ Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA
² Université de Rennes 1, CNRS, IPR (Institut de Physique de Rennes) UMR 6251, F-35000 Rennes, France
³ Department of Mathematical Sciences & Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, New Jersey 07102, USA

Comptes Rendus. Mécanique, Volume 348 (2020) no. 6-7, pp. 573-589.

Résumé

In a pioneering series of experiments, Yves Couder, Emmanuel Fort and coworkers demonstrated that droplets bouncing on the surface of a vertically vibrating fluid bath exhibit phenomena reminiscent of those observed in the microscopic quantum realm. Inspired by this discovery, we here conduct a theoretical and numerical investigation into the structure and dynamics of one-dimensional chains of bouncing droplets. We demonstrate that such chains undergo an oscillatory instability as the system’s wave-induced memory is increased progressively. The predicted oscillation frequency compares well with previously reported experimental data. We then investigate the resonant oscillations excited in the chain when the drop at one end is subjected to periodic forcing in the horizontal direction. At relatively high memory, the drops may oscillate with an amplitude larger than that prescribed, suggesting that the drops effectively extract energy from the collective wave field. We also find that dynamic stabilization of new bouncing states can be achieved by forcing the chain at high frequency. Generally, our work provides insight into the collective behavior of particles interacting through long-range and temporally nonlocal forces.

Supplementary Materials:
Supplementary material for this article is supplied as a separate file:

crmeca-30-suppl.pdf

Publié le : 2020-11-16

DOI : 10.5802/crmeca.30

Mots clés : Pilot-wave hydrodynamics, Walking droplets, Nonlinear dynamics, Drop interactions, Collective dynamics, Non-equilibrium systems

Affiliations des auteurs :

Lauren Barnes ¹ ; Giuseppe Pucci ² ; Anand U. Oza ³

¹ Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA
² Université de Rennes 1, CNRS, IPR (Institut de Physique de Rennes) UMR 6251, F-35000 Rennes, France
³ Department of Mathematical Sciences & Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, New Jersey 07102, USA

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Resonant interactions in bouncing droplet chains},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {573--589},
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Lauren Barnes; Giuseppe Pucci; Anand U. Oza. Resonant interactions in bouncing droplet chains. Comptes Rendus. Mécanique, Volume 348 (2020) no. 6-7, pp. 573-589. doi : 10.5802/crmeca.30. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.30/

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