Eur. Phys. J. E (2005) 17: 189-198
https://doi.org/10.1140/epje/i2004-10139-4

Regular Articles

The bubble cloud as an N-degree of freedom harmonic oscillator

Laboratoire Matière et Systèmes Complexes, Université Denis Diderot - Paris 7 and CNRS UMR 7057, 140 rue de Lourmel, 75015, Paris, France

^* e-mail: valentin.leroy@loa.espci.fr,

Received: 15 October 2004
Accepted: 30 March 2005
Published online: 6 May 2005

Abstract

The dynamics of a two-dimensional N-bubble static cloud is investigated and shown to be well described by an N-degree of freedom harmonic oscillator model, at least at low enough frequencies. Eigenmodes and eigenfrequencies are calculated and compared with experimental results obtained with an assembly of bubbles caught up under a net in a water tank. Accordance is found to be excellent in the frequency range of validity of the model, the limits of which are discussed. An interpretation of the low-frequency branch of Foldy’s dispersion relation in bubbly liquids is suggested in terms of “bubble waves” in a quasi-incompressible medium.