Influence of positional correlations on the propagation of waves in a complex medium with polydisperse resonant scatterers

TL;DR

This study investigates how positional correlations among resonant scatterers like bubbles affect wave propagation in complex media, revealing that correlations significantly influence effective medium properties and require models beyond the Independent Scattering Approximation.

Contribution

The paper introduces a self-consistent model accounting for polydisperse positional correlations, improving predictions of wave behavior in resonant scatterer media over traditional methods.

Findings

Discrepancies between experimental data and ISA are explained by scatterer correlations.

A polydisperse correlation model better fits experimental results.

Positional correlations depend on scatterer size and influence wave transport.

Abstract

We present experimental results on a model system for studying wave propagation in a complex medium exhibiting low frequency resonances. These experiments enable us to investigate a fundamental question that is relevant for many materials, such as metamaterials, where low-frequency scattering resonances strongly influence the effective medium properties. This question concerns the effect of correlations in the positions of the scatterers on the coupling between their resonances, and hence on wave transport through the medium. To examine this question experimentally, we measure the effective medium wave number of acoustic waves in a sample made of bubbles embedded in an elastic matrix over a frequency range that includes the resonance frequency of the bubbles. The effective medium is highly dispersive, showing peaks in the attenuation and the phase velocity as functions of the frequency, which cannot be accurately described using the Independent Scattering Approximation (ISA). This discrepancy may be explained by the effects of the positional correlations of the scatterers, which we show to be dependent on the size of the scatterers. We propose a self-consistent approach for taking this "polydisperse correlation" into account and show that our model better describes the experimental results than the ISA.