Orbiting pairs of walking droplets: Dynamics and stability

Anand U. Oza; Emmanuel Siéfert; Daniel M. Harris; Jan Moláček; John W.M. Bush

doi:10.1103/PhysRevFluids.2.053601

Orbiting pairs of walking droplets: Dynamics and stability

Anand U. Oza, Emmanuel Siéfert, Daniel M. Harris, Jan Moláček, John W.M. Bush

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

A decade ago, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)]PRLTAO0031-900710.1103/PhysRevLett.97.154101 discovered that a millimetric droplet sustained on the surface of a vibrating fluid bath may self-propel through a resonant interaction with its own wave field. We here present the results of a combined experimental and theoretical investigation of the interactions of such walking droplets. Specifically, we delimit experimentally the different regimes for an orbiting pair of identical walkers and extend the theoretical model of Oza [J. Fluid Mech. 737, 552 (2013)]JFLSA70022-112010.1017/jfm.2013.581 in order to rationalize our observations. A quantitative comparison between experiment and theory highlights the importance of spatial damping of the wave field. Our results also indicate that walkers adapt their impact phase according to the local wave height, an effect that stabilizes orbiting bound states.

Original language	English (US)
Article number	053601
Journal	Physical Review Fluids
Volume	2
Issue number	5
DOIs	https://doi.org/10.1103/PhysRevFluids.2.053601
State	Published - May 2017
Externally published	Yes

All Science Journal Classification (ASJC) codes

Computational Mechanics
Modeling and Simulation
Fluid Flow and Transfer Processes

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10.1103/PhysRevFluids.2.053601

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title = "Orbiting pairs of walking droplets: Dynamics and stability",

abstract = "A decade ago, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)]PRLTAO0031-900710.1103/PhysRevLett.97.154101 discovered that a millimetric droplet sustained on the surface of a vibrating fluid bath may self-propel through a resonant interaction with its own wave field. We here present the results of a combined experimental and theoretical investigation of the interactions of such walking droplets. Specifically, we delimit experimentally the different regimes for an orbiting pair of identical walkers and extend the theoretical model of Oza [J. Fluid Mech. 737, 552 (2013)]JFLSA70022-112010.1017/jfm.2013.581 in order to rationalize our observations. A quantitative comparison between experiment and theory highlights the importance of spatial damping of the wave field. Our results also indicate that walkers adapt their impact phase according to the local wave height, an effect that stabilizes orbiting bound states.",

author = "Oza, {Anand U.} and Emmanuel Si{\'e}fert and Harris, {Daniel M.} and Jan Mol{\'a}{\v c}ek and Bush, {John W.M.}",

note = "Funding Information: J.B. gratefully acknowledges the financial support of the NSF through grants CMMI-1333242 and DMS-1614043, the MIT-Brazil Program and the CNPq-Science Without Borders Program. A.O. acknowledges the support of the NSF Mathematical Sciences Postdoctoral Research Fellowship. Funding Information: The authors gratefully acknowledge Ruben Rosales, Giuseppe Pucci, Pedro S{\'a}enz, and Juncal Arbelaiz for valuable conversations and assistance. J.B. gratefully acknowledges the financial support of the NSF through grants CMMI-1333242 and DMS-1614043, the MIT-Brazil Program and the CNPq-Science Without Borders Program. A.O. acknowledges the support of the NSF Mathematical Sciences Postdoctoral Research Fellowship. Publisher Copyright: {\textcopyright} 2017 American Physical Society.",

year = "2017",

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doi = "10.1103/PhysRevFluids.2.053601",

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N1 - Funding Information: J.B. gratefully acknowledges the financial support of the NSF through grants CMMI-1333242 and DMS-1614043, the MIT-Brazil Program and the CNPq-Science Without Borders Program. A.O. acknowledges the support of the NSF Mathematical Sciences Postdoctoral Research Fellowship. Funding Information: The authors gratefully acknowledge Ruben Rosales, Giuseppe Pucci, Pedro Sáenz, and Juncal Arbelaiz for valuable conversations and assistance. J.B. gratefully acknowledges the financial support of the NSF through grants CMMI-1333242 and DMS-1614043, the MIT-Brazil Program and the CNPq-Science Without Borders Program. A.O. acknowledges the support of the NSF Mathematical Sciences Postdoctoral Research Fellowship. Publisher Copyright: © 2017 American Physical Society.

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Orbiting pairs of walking droplets: Dynamics and stability

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