Multimode multiple scattering in disordered systems of spherical scatterers

We will consider the propagation of ultrasound in nano/microparticle suspensions consisting of disordered (randomly distributed) solid particles in a viscous liquid or other soft viscoelastic material. Understanding the complex wave propagation in such systems is important, both from the point of view of characterising soft materials – for biological tissues, or for industrial process monitoring e.g. in pharma and food – and for the design of metamaterials where enhanced absorption may be desirable – for example for stealth coatings. An important and interesting characteristic of these systems is the existence of two wavenumbers of very different magnitudes in the continuous phase – for the compressional and shear modes. For typical liquids at MHz frequencies, and with colloidal particles, the dimensionless compressional wavenumber (based on particle size) may be small whereas the dimensionless shear wavenumber can range from small to large and is always much larger than the dimensionless compressional wavenumber. In addition, we have another length scale that affects the multiple scattering, i.e. the interparticle separation; its effects are usually accounted for through the concentration or number density but it may be helpful to consider these effects in terms of additional dimensionless wavenumbers relating to the interparticle distance. Recently, a new formulation for the effective wavenumber arising from multiple scattering in a multi-mode media was published (Luppe, Conoir Valier-Brasier, Wave Motion 115 (2022) 103082). In this presentation, we will show analytical asymptotic results obtained from the model at long compressional wavelength (low frequency), but arbitrary shear wavelength for these soft media, highlighting the dominant wave-conversion and correlation contributions. We will show numerical results to validate the approximations made for this system and compare with experimental data. Although it is common to consider that structure has minimal effect at long wavelength, in these dual-wave-mode systems the particle correlations are seen to have a significant effect because of the influence of the small shear wavelength.