Interest in the interaction of acoustic waves with particulate mixtures has a long history—dating back to the work of Rayleigh in the 19th century. This interest has intensified over the last fifteen years as advances in electronics and instrumentation science have brought the possibility of using ultrasound to characterize colloidal mixtures both in the laboratory and in-process, and in both of these contexts a small number of instruments are currently in use. The characterization of colloidal mixtures by ultrasound requires a formal theoretical basis which relates the properties of the mixture, particularly the dispersed phase particle size distribution (PSD), to the complex wavenumber governing propagation. The number of theoretical treatments is vast, having evolved over more than a century. This paper is intended to provide a review of these developments in a form which will enable new researchers in the field to climb a very steep learning curve in a relatively short time. We discuss definitions and production techniques for colloidal mixtures and the basic physical phenomena underlying wave propagation through them. We identify two approaches to the propagation problem—scattering and coupled-phase; these are treated both separately and comparatively, particularly in relation to limitations that arise when the concentration of particles is high and the basic theories break down. We introduce the basic method for the measurement of PSD and show how dynamic effects such as flocculation and crystallization can be observed and modelled. The core of all ultrasonic characterization procedures is the physical measurement of the ultrasonic wave attenuation coefficient and phase velocity as functions of frequency; here we discuss these techniques on the basis that what is observable or measurable about a colloid depends on both its physical properties and the frequency bandwidth available for measurement. This paper concludes with our view on future developments of measurement technique and theoretical treatments.

https://iopscience.iop.org/article/10.1088/0034-4885/68/7/R01/pdf

Ultrasound techniques for characterizing colloidal dispersions

Theory of Resonance Scattering

An operational definition of backscattering cross section is developed for the wideband reception of finite echoes. This is supported by relative measurements on a set of copper spheres by each of four echo sounders operating at frequencies from 38 to 120 kHz. Experiential and theoretical arguments are advanced for the superiority of commercial, electrical–grade copper in the application. An optimization problem for determining the sphere size is then formulated, and solved for the case of calibration of a 38 kHz echo sounder by a sphere of the described material. The solution: that the copper sphere diameter be 60.00 mm, is tested through a variety of measurements. These demonstrate an accuracy of 0.1 dB. The further exercise of theory indicates the feasibility of precision calibration of diverse hydroacoustic equipment by copper spheres over most of the kilohertz frequency range.

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Optimizing copper spheres for precision calibration of hydroacoustic equipment

Multifrequency acoustic scattering experiments were carried out in the laboratory using a free, turbulent water jet carrying solid particles in suspension. A crossed‐beam geometry was used, in which the axis of the jet was perpendicular, or nearly so, to the direction of the incident sound. The suspended particles were either natural sand grains or lead‐glass beads, 100–500 μm in diameter. The results, based on measurements made simultaneously at 1, 2.25, and 5 MHz, include backscatter and attenuation as a function of suspended sediment concentration, measurements of the total scattering and backscattering cross sections of natural sand grains and glass beads as a function of frequency and particle size, and two‐point correlation measurements of the fluctuations in apparent suspended sediment concentration. The lead‐glass bead cross sections exhibit both the resonance and diffraction extrema expected of solid spherical scatterers; the sand cross sections do not and, for acoustic wavelengths comparable to ...

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Sound scattering from a particle‐laden, turbulent jet

Formulations for the scattering properties of suspended sandy sediments for use in the application of acoustics to sediment transport processes

Measurements are made of the acoustic reflected pressure from aluminum and tungsten‐carbide spheres for ka values between 5 and 20. Only the farfield monostatic case is considered. Experimental values are compared to a harmonic‐wave solution. Excellent agreement is observed when the wave speeds in the sphere material are adjusted by an amount smaller than the known uncertainty in the wave‐speed values in the solids. The position of rapid changes in the reflection solution with ka is found to be very sensitive to shear‐wave speed and insensitive to longitudinal‐wave speed. The sensitivity to ambient temperature of the position of a selected minimum in the reflection solution is examined computationally for an aluminum sphere. A shift in the value of ka at which a minimum is calculated is also observed experimentally. Long pulses are used to approximate steady‐state conditions and agreement with the steady‐state theory shows that this approximation is adequate.

Acoustic reflection from elastic spheres. I. Steady‐state signals

Curves relating the reflected acoustic pressures to frequency for a rigid sphere and spheroid and for elastic spheres of aluminum, brass, and tungsten carbide in water are obtained. Experimental measurements using single short acoustic pulseforms are compared with theory. Excellent agreement is obtained for the limited ranges of ka over which the experiments were done. Only the case of monostatic reflection is considered.

Acoustic reflection from elastic spheres and rigid spheres and spheroids. II. Transient analysis

The behavior of the solution to acoustic backscattering by elastic spheres in water expressed as a form function vs ka, relative to the normal modes of vibration of solid homogeneous elastic spheres is examined. Specific free modes of vibration are identified with significant changes in form function. The solution for spheres of tungsten carbide, aluminum, and brass are considered for values of ka as high as 28. Minima in the form function usually occur at or near frequencies at which sphere resonances occur. Form functions are examined which are computed from mixing rigid and elastic terms in the waveharmonic series. In this way it is possible to see the effect of an isolated mode of vibration on the form function that describes the backscattering. Calculated resonance widths as well as observed pulse decay times allow determination of analytical and experimental Q’s of isolated resonances.Subject Classification: [43]20.30, [43]20.60, [43]20.50; [43]40.20.

Relationship between acoustic reflection and vibrational modes of elastic spheres

The monostatic reflection from a lucite sphere in water is measured and compared with the exact classical scattering theory. Experimental results do not agree with theory which neglects absorption, in direct contrast to the excellent agreement found when metal spheres are used as targets. The theory is modified to include the effects of absorption of shear and compressional waves in lucite, and agreement between experiment and the modified theory is demonstrated.Subject Classification: 20.30, 20.15.

Richard H. Vogt

Papers

Acoustic reflection from elastic spheres. I. Steady‐state signals

Acoustic reflection from elastic spheres and rigid spheres and spheroids. II. Transient analysis

Relationship between acoustic reflection and vibrational modes of elastic spheres

Monostatic reflection of a plane wave from an absorbing sphere

Erratum: Monostatic reflection of a plane wave from an absorbing sphere [J. Acoust. Soc. Am. 57, 558–561 (1975)]