Dynamic effective properties of a random configuration of cylinders in a fluid

Francine Luppé (1) , Jean-Marc Conoir (2) , Pascal Pareige (1)

1 LOMC - Laboratoire Ondes et Milieux Complexes
2 DALEMBERT - Institut Jean Le Rond d'Alembert

The dynamic effective properties of a random medium consisting in a uniform concentration of cylindrical scatterers in an ideal fluid are looked for, with special focus on low frequencies. The effective medium is described as an isotropic viscous fluid whose mass density and dilation viscosity depend on frequency, and whose shear viscosity is nil. An explicit expression of the reflection coefficient of a harmonic plane wave incident upon the interface between the ideal fluid and the random medium may be obtained at low frequency, using the Fikioris and Waterman's approach, in two ways. In the first one, the low frequency assumption is introduced from the very beginning, while in the second one, the same hypotheses than those used by Linton et al. [J. Acoust. Soc. Am. 117 6, 2005] to calculate the effective wavenumber are used first, and, then, the low frequency assumption. In both cases, comparison of this reflection coefficient with that at the interface between the ideal fluid and the effective viscous fluid provides the effective density, which, coupled to the effective wavenumber, provides the effective dilatation viscosity. In the first case, the effective parameters found are identical to those found by Mei et al. [Phys. Rev. B 76, 2007] in a different way, while in the second case they are expressed in terms of form functions of the cylinders that reduce at low frequency to those found by Martin et al. [J. Acous. Soc. Am. 128, 2010]. PACS no. 43.20.Fn, 43.35.Bf

Domaines: Sciences de l'ingénieur [physics]; Acoustique [physics.class-ph]

Francine Luppé, Jean-Marc Conoir, Pascal Pareige. Dynamic effective properties of a random configuration of cylinders in a fluid. Forum Acusticum, 2011, Aalborg, Denmark. ⟨hal-02163673⟩