Journal
JOURNAL OF FLUID MECHANICS
Volume 778, Issue -, Pages -Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2015.386
Keywords
capillary waves; drops; Faraday waves
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Funding
- Royal Society Wolfson award
- Brazilian National Petroleum Agency (ANP) through the program COMPETRO [PRH32]
- CNPq [(PQ-1B) 301949/2007-7]
- FAPERJ Cientistas do Nosso Estado project [102.917/2011]
- CAPES(ESN) [4156/13-7]
- NSF [CMMI-1333242]
- MIT-Brazil Program
- CNPq-Science Without Borders award [402300/2012-2, 402178/2012-2]
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [1333242] Funding Source: National Science Foundation
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A millimetric droplet bouncing on the surface of a vibrating fluid bath can self-propel by virtue of a resonant interaction with its own wave field. This system represents the first known example of a pilot-wave system of the form envisaged by Louis de Broglie in his double-solution pilot-wave theory. We here develop a fluid model of pilot-wave hydrodynamics by coupling recent models of the droplet's bouncing dynamics with a more realistic model of weakly viscous quasi-potential wave generation and evolution. The resulting model is the first to capture a number of features reported in experiment, including the rapid transient wave generated during impact, the Doppler effect and walker-walker interactions.
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