We explore the effects of polydispersity in 3D heterogeneous media consisting of scattering species (e.g., droplets, particles) in viscous liquids using a multiple scattering formulation to define effective speed and attenuation spectra. We adopt a published formulation [A. L. Gower, M. J. A. Smith, W. J. Parnell, and I. D. Abrahams, in Proceedings of the Royal Society of America (2018), p. 474] that rigorously extends multiple scattering theory to multi-component systems and show that in the long wavelength region it is consistent with a previous heuristic methodology applied to polydisperse scatterers. We investigate cases of a monomodal size distribution of finite width, and multi-modal size distributions with similar species. Further, systems of mixed scatterer species (i.e., different types of scatterer) with different sizes and distributions are considered. We will discuss the implications for inversion of ultrasonic spectra to determine particle size distributions and for the design of materials with targeted properties by varying composition (concentrations of different scatterer species) and scatterer properties.
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