Multiple scattering by cylinders randomly located in a fluid: Effective properties

Abstract

We consider the interface between a homogeneous fluid and that same fluid with a random distribution of n0 cylinders per square meter inside. A harmonic plane wave, frequency v and wavenumber k, is incident upon that boundary under incidence angle α. The reflection coefficient obtained with the Fikioris and Waterman approach is expanded into powers of n0/K2 up to order 2, using Linton and Martin's expansion of the wavenumber of the coherent wave. This coefficient is then compared to that obtained when a homogeneous viscous fluid replaces the random medium. When the two reflection coefficients are equal, the random fluid is acoustically equivalent to the viscous one, which is called in that case the effective fluid. The coherent wave in the random medium is thus described as the acoustic mode in the effective fluid. Equating the two reflection coefficients provides expressions for the effective properties of the random medium: mass density ρeff, and coefficient of dilatation viscosity ρeff, as the shear viscosity is set to zero. Both depend on α and v, unless low frequencies only are considered, in which case the dependence on α vanishes.