An extension of the layer-multiple-scattering method to phononic crystals of poroelastic spheres immersed in a fluid medium is developed. The applicability of the method is demonstrated on specific examples of close-packed fcc crystals of submerged water-saturated meso- and macroporous silica microspheres. It is shown that, by varying the pore size and/or the porosity, the transmission, reflection, and absorption spectra of finite slabs of these crystals are significantly altered. Strong absorption, driven by the slow waves in the poroelastic material and enhanced by multiple scattering, leads to negligible transmittance over an extended frequency range, which might be useful for practical applications in broadband acoustic shielding. The results are analyzed by reference to relevant phononic dispersion diagrams in the viscous and inertial coupling limits, and a consistent interpretation of the underlying physics is provided.
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