Viscoelastic ECAH: Scattering analysis of spherical particles in suspension with viscoelasticity

Ultrasonic scattering method is a promising technique to evaluate the particle size distribution and/or the elastic properties of particle suspended in liquid. Among the wide variety of scattering theories, the ECAH theory proposed by Epstein-Carhart-Allegra-Hawley is one of the most relevant acoustic scattering theories to reproduce the ultrasonic spectroscopy data for the particle suspensions. However, the original theory assumes that the shear contribution is provided for either elastic solid or viscous liquid. Thus, the viscoelastic effect of particle to the frequency spectra of the attenuation coefficient and the phase velocity has gained less attention and is not fully understood yet. In order to minimize the number of unknown parameters for the analysis of viscoelastic suspensions, we employed the multiple echo-reflection ultrasonic spectroscopy (MERUS) technique, which allowed us to determine the material properties, prior to the complicated scattering analysis. In this study, we prepared the particle suspensions of poly(methyl methacrylate) (PMMA), bisphenol-A polycarbonate (PC) and cross-linked poly(dimethyl siloxane) (PDMS) and the acoustic spectra were measured by the ultrasonic spectroscopy. Then, we demonstrated the effect of the particle viscosity on the spectra by using the viscoelastic ECAH model at the wavelength comparable with the particle size.