Theoretical and experimental study of the influence of the particle size distribution on acoustic wave properties of strongly inhomogeneous media.

The ultrasonic method is particularly suitable to characterize diffusive media, as acoustic properties (velocity and attenuation) are related to the properties and concentrations of the homogeneous phase and scatterers. Thus, ultrasonic characterization can be useful in the study of sedimentation or flocculation processes, in concentration measurements, and granulometry evaluation. Many models have been developed for media where particles are very small compared to the incident wavelength. When the diameter of the particles is close to the wavelength, multiple-scattering theories have to be used to describe the propagation of waves. In this paper, the case where the ratio of wavelength to scatterer size is around unity is studied. First, the particle size distribution is taken into account in two types of multiple-scattering theories based on the effective field approximation or on the quasicrystalline approximation and theoretical results are produced. The T-matrix formalism has been used to calculate the amplitude of the wave scattered by a single sphere. The calculation of the complex wave number in the effective medium has been implemented, using in particular the Percus-Yevick equation as a spatial pair-correlation function between scatterers, and a normal particle-size distribution. The influence of these parameters is discussed. Finally, attenuation and phase velocity measurements are performed in moving suspensions of acrylic spheres in ethylene glycol, at various concentrations and for different particle-size distributions. A good agreement between the theoretical results and the measurements is found for both velocity and attenuation. These results show that the size distribution is a critical parameter to understand velocity and attenuation behavior as function of frequency and volume fraction.