Effective dynamic constitutive parameters of acoustic metamaterials with random microstructure

A multiple scattering analysis in a non-viscous fluid is developed 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 uses suitable pair-correlation functions to account for the essential features 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 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 for testing ideas in silico in the 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. (paper)