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ERIC Number: EJ819230
Record Type: Journal
Publication Date: 2008-Nov
Pages: 23
Abstractor: As Provided
Reference Count: 24
ISBN: N/A
ISSN: ISSN-0143-0807
The Minnaert Bubble: An Acoustic Approach
Devaud, Martin; Hocquet, Thierry; Bacri, Jean-Claude; Leroy, Valentin
European Journal of Physics, v29 n6 p1263-1285 Nov 2008
We propose an "ab initio" introduction to the well-known Minnaert pulsating bubble at graduate level. After a brief recall of the standard stuff, we begin with a detailed discussion of the radial movements of an air bubble in water. This discussion is managed from an acoustic point of view, and using the Lagrangian rather than the Eulerian variables. In unbounded water, the air-water system has a continuum of "eigenmodes", some of them correspond to regular Fabry-Perot "resonances". A singular resonance, the lowest one, is shown to coincide with that of Minnaert. In bounded water, the eigenmodes spectrum is discrete, with a finite fundamental frequency. A spectacular quasi-locking of the latter occurs if it happens to exceed the Minnaert frequency, which provides an unforeseen one-bubble alternative version of the famous "hot chocolate effect". In the (low) frequency domain in which sound propagation inside the bubble reduces to a simple "breathing" (i.e. inflation/deflation), the light air bubble can be "dressed" by the outer water pressure forces, and is turned into the heavy Minnaert bubble. Thanks to this unexpected renormalization process, we demonstrate that the Minnaert bubble definitely behaves like a true harmonic oscillator of the spring-bob type, but with a damping term and a forcing term in apparent disagreement with those commonly admitted in the literature. Finally, we underline the double role played by the water. In order to tell the water motion associated with water compressibility (i.e. the sound) from the simple incompressible accompaniment of the bubble breathing, we introduce a new picture analogous to the electromagnetic radiative picture in Coulomb gauge, which naturally leads us to split the water displacement in an instantaneous and a retarded part. The Minnaert renormalized mass of the dressed bubble is then automatically recovered. (Contains 3 figures and 2 footnotes.)
Institute of Physics Publishing. The Public Ledger Building Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106. Tel: 215-627-0880; Fax: 215-627-0879; e-mail: info@ioppubusa.com; Web site: http://www.iop.org/EJ/journal/EJP
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: Students; Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A