Sound propagation in a monodisperse bubble cloud: From the crystal to the glass |
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Authors: | M Devaud T Hocquet and V Leroy |
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Institution: | 1.Laboratoire Matière et Systèmes Complexes (MSC),UMR 7057 (CNRS) et Université Paris Diderot,PARIS CEDEX 13,France;2.Université Pierre et Marie Curie,PARIS CEDEX 05,France |
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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. |
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Keywords: | |
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