Effective dynamic constitutive parameters of acoustic metamaterials with random microstructure

A multiple scattering analysis in a non-viscous fluid is developped in order to predict the effective constitutive parameters of certain suspensions of disordered particles or bubbles. The analysis is based on an effective field approach, and employs suitable pair-correlation functions in order to account for the essential feautures of densely distributed particles. The effective medium that is equivalent to the original suspension of particles is a medium with space and time dispersion, and hence, its parameters are functions of the frequency of the incident acoustic wave. Under the quasi-crystalline approximation, novel expressions are presented for the effective constitutive parameters, which are valid at any frequency and wavelength. The emerging possibility of designing fluid-particle mixtures to form acoustic metamaterials is discussed. Our theory provides a convenient tool to test ideas in silico in search for new metamaterials with specific desired properties. An important conclusion of the proposed approach is that negative constitutive parameters can also be achieved by using suspensions of particles with random microstructures with properties similar to those shown in periodic arrays of microstructures.