Eur. Phys. J. E (2010) 32: 13-23
https://doi.org/10.1140/epje/i2010-10588-0

Regular Article

Sound propagation in a monodisperse bubble cloud: From the crystal to the glass

¹ Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 (CNRS) et Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, 75205, PARIS CEDEX 13, France
² Université Pierre et Marie Curie, 4 place Jussieu, 75252, PARIS CEDEX 05, France

^* e-mail: martin.devaud@univ-paris-diderot.fr
^** e-mail: Thierry.Hocquet@upmc.fr

Received: 19 October 2009
Revised: 19 March 2010
Accepted: 9 April 2010
Published online: 20 May 2010

Abstract

We present a theoretical study of the propagation of a monochromatic pressure wave in an unbounded monodisperse bubbly liquid. We begin with the case of a regular bubble array --a bubble crystal-- for which we derive a dispersion relation. In order to interpret the different branches of this relation, we introduce a formalism, the radiative picture, which is the adaptation to acoustics of the standard splitting of the electric field in an electrostatic and a radiative part in Coulomb gauge. In the case of an irregular or completely random array --a bubble glass-- and at wavelengths large compared to the size of the bubble array spatial inhomogeneities, the difference between order and disorder is not felt by the pressure wave: a dispersion relation still holds, coinciding with that of a bubble crystal with the same bubble size and air volume fraction at the centre of its first Brillouin zone. This relation is discussed and compared to that obtained by Foldy in the framework of his multiscattering approach.