The aim of this paper is to present a unified approach to the calculation of the complex wavenumber for a randomly distributed ensemble of homogeneous isotropic spheres suspended in a homogeneous isotropic continuum. Three classical formulations of the diffraction problem for a compression wave incident on a single particle are reviewed; the first is for liquid particles in a liquid continuum (Epstein and Carhart), the second for solid or liquid particles in a liquid continuum (Allegra and Hawley), and the third for solid particles in a solid continuum (Ying and Truell). Equivalences between these formulations are demonstrated and it is shown that the Allegra and Hawley formulation can be adapted to provide a basis for calculation in all three regimes. The complex wavenumber that results from an ensemble of such scatterers is treated using the formulations of Foldy (simple forward scattering), Waterman and Truell, and Lloyd and Berry (multiple scattering). The analysis is extended to provide an approximation for the case of a distribution of particle sizes in the mixture. A number of experimental measurements using a broadband spectrometric technique (reported elsewhere) to obtain the attenuation coefficient and phase velocity as functions of frequency are presented for various mixtures of differing contrasts in physical properties between phases in order to provide a comparison with theory. The materials used were aqueous suspensions of polystyrene spheres, silica spheres, iron spheres, pigment (AHR), droplets of 1-bromohexadecane, and a suspension of talc particles in a cured epoxy resin.

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Absorption of ultrasound in adhesive materials is significant in forming ultrasonic signals obtained in nondestructive evaluation (NDE) procedures, and may also have diagnostic value in the evaluation of adhesive materials themselves. This paper investigates the effects of filler particles in adhesive polymers on ultrasonic compression wave absorption and phase velocity dispersion as functions of frequency. Wave propagation is affected by relaxations in the continuous polymer phase as well as by scattering at filler particles. The complex compression wave number for the composite material is derived on the basis of conventional theories of scattering in randomly distributed fields of particles, together with a formulation of the particle diffraction problem based on a combination of the cases for solid particles in solid continua and solid particles in liquid continua first proposed by Ying and Truell, and Allegra and Hawley, respectively. Experiments are described which demonstrate the effects of relaxations and scattering on absorption and phase velocity as functions of frequency in an epoxy material containing a mineral filler. Good agreement is obtained between theory and experiment.

Ultrasound is beginning to be used to characterize many types of industrial two-phase dispersions, both suspensions and emulsions. It also has great potential as a process-monitoring tool alongside the well-established techniques of conductivity, pH, optical turbidity, tomography, and so forth. This paper describes a small volume test cell that has been developed to ultrasonically monitor the batch crystallization of a hydrated salt from saturated solution. The interaction of low-power, low-frequency (2− 7 MHz) ultrasound with a two-phase dispersion is discussed, and a series of experiments are outlined that have been carried out on a crystallizing 24% w/w (anhydrous) solution of copper(II) sulfate. The nucleation and growth of the crystals have been successfully monitored ultrasonically. Crystal size distributions of the final crystallized product have been obtained using light scattering and are used to model the effects that crystallization has on the ultrasonic data. It is shown that the Allegra and Hawley model of ultrasonic propagation in a two-phase dispersion, in a form modified to account for time dependent changes in the continuous phase, gives reasonable correlation with experimental data.