Réflexion cohérente et incohérente d'une onde acoustique plane harmonique par un rideau de bulles stratifié plan

A mathematical and numerical model is presented for the prediction of the coherent and incoherent acoustic reflexion coefficients for bubble layers in a liquid medium, excited by a harmonic pressure farfield. The layer is plane infinite, and looks like a random stratified system, where bubble position and size obey a statistical distribution, that depends on immersion only. The bubbles are assumed to be spherical at rest. No hypothesis is made about the layer's thickness, neither on the process of bubbles interaction and scattering. All linear bubble deformations and multiple scattering are considered, as well as thermal conduction in the bubbles. The geometrical configuration leads us to use a mathematical transformation of the acoustic integral equation, that «delocalizes» the observation in a plane parallel to the layer and introduces natural collective contributions of bubbles at each immersion, without any physical approximation. After this transformation, coherent and incoherent acoustic pressure are obtained in the form of an integral equation over the thickness of the layer. We present the general model, the mathematical formulation and numerical results. We show the link between our results and Foldy's formalism, when only monopolar diffusion is considered