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Faraday instability in floating liquid lenses: the spontaneous mutual adaptation due to radiation pressure

Published online by Cambridge University Press:  14 May 2013

G. Pucci ,
M. Ben Amar  and
Y. Couder
G. Pucci*
Affiliation:
Matière et Systèmes Complexes, Université Paris Diderot–Paris 7, CNRS–UMR 7057, Bâtiment Condorcet, 75013 Paris, France
M. Ben Amar
Affiliation:
Laboratoire de Physique Statistique, Ecole Normale Supérieure, UPMC Univ. Paris 6, Université Paris Diderot–Paris 7, CNRS–UMR 8550, 24 rue Lhomond, 75005 Paris, France
Y. Couder
Affiliation:
Matière et Systèmes Complexes, Université Paris Diderot–Paris 7, CNRS–UMR 7057, Bâtiment Condorcet, 75013 Paris, France
*
†Email address for correspondence: giuseppepucci@gmail.com
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Abstract

Fluid dynamics instabilities are usually investigated in two types of situations, either confined in cells with fixed boundaries, or free to grow in open space. In this article we study the Faraday instability triggered in a floating liquid lens. This is an intermediate situation in which a hydrodynamical instability develops in a domain with flexible boundaries. The instability is observed to be initially disordered with fluctuations of both the wave field and the lens boundaries. However, a slow dynamics takes place, leading to a mutual adaptation so that a steady regime is reached with a stable wave field in a stable lens contour. The most recurrent equilibrium lens shape is elongated with the Faraday wave vector along the main axis. In this self-organized situation an equilibrium is reached between the radiation pressure exerted by Faraday waves on the borders and their capillary response. The elongated shape is obtained theoretically as the exact solution of a Riccati equation with a unique control parameter and compared with the experiment.

JFM classification

Drops and Bubbles: Drops Waves/Free-surface Flows: Faraday waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 725 , 25 June 2013 , pp. 402 - 427
Copyright
©2013 Cambridge University Press 

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