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dc.contributor.authorBush, John W. M.
dc.contributor.authorMolacek, Jan
dc.date.accessioned2013-09-12T18:11:32Z
dc.date.available2013-09-12T18:11:32Z
dc.date.issued2013-06
dc.date.submitted2013-04
dc.identifier.issn0022-1120
dc.identifier.issn1469-7645
dc.identifier.urihttp://hdl.handle.net/1721.1/80417
dc.description.abstractWe present the results of a combined experimental and theoretical investigation of droplets walking on a vertically vibrating fluid bath. Several walking states are reported, including pure resonant walkers that bounce with precisely half the driving frequency, limping states, wherein a short contact occurs between two longer ones, and irregular chaotic walking. It is possible for several states to arise for the same parameter combination, including high- and low-energy resonant walking states. The extent of the walking regime is shown to be crucially dependent on the stability of the bouncing states. In order to estimate the resistive forces acting on the drop during impact, we measure the tangential coefficient of restitution of drops impacting a quiescent bath. We then analyse the spatio-temporal evolution of the standing waves created by the drop impact and obtain approximations to their form in the small-drop and long-time limits. By combining theoretical descriptions of the horizontal and vertical drop dynamics and the associated wave field, we develop a theoretical model for the walking drops that allows us to rationalize the limited extent of the walking regimes. The critical requirement for walking is that the drop achieves resonance with its guiding wave field. We also rationalize the observed dependence of the walking speed on system parameters: while the walking speed is generally an increasing function of the driving acceleration, exceptions arise due to possible switching between different vertical bouncing modes. Special focus is given to elucidating the critical role of impact phase on the walking dynamics. The model predictions are shown to compare favourably with previous and new experimental data. Our results form the basis of the first rational hydrodynamic pilot-wave theory.en_US
dc.language.isoen_US
dc.publisherCambridge University Pressen_US
dc.relation.isversionofhttp://dx.doi.org/10.1017/jfm.2013.280en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceMIT web domainen_US
dc.titleDrops walking on a vibrating bath: towards a hydrodynamic pilot-wave theoryen_US
dc.typeArticleen_US
dc.identifier.citationMolacek, Jan, and John W. M. Bush. “Drops walking on a vibrating bath: towards a hydrodynamic pilot-wave theory.” Journal of Fluid Mechanics 727 (July 28, 2013): 612-647.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.mitauthorMolacek, Janen_US
dc.contributor.mitauthorBush, John W. M.en_US
dc.relation.journalJournal of Fluid Mechanicsen_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsMoláček, Jan; Bush, John W. M.en_US
dc.identifier.orcidhttps://orcid.org/0000-0002-7936-7256
mit.licensePUBLISHER_POLICYen_US


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