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Extended computation of ultrasonic wavenumber in
particulate dispersions

Extended computation of ultrasonic wavenumber in
particulate dispersions Thumbnail


Methods to characterize dispersions in terms of concentration, sizes and size distribution of suspended particles promise significant commercial and industrial utility. Ultrasonic spectroscopy offers practical advantages over existing, mostly off-line, non-ultrasonic
methods. A necessary function of a spectrometer would be the correlation of experimental with modelled ultrasonic spectra. These are derived from the complex ultrasonic
wavenumber. There are a number of mathematical models to calculate the propagation wavenumber of ultrasound in a dispersion. Of these, that of Epstein & Carhart, extended by Allegra & Hawley and known as the ECAH model, offers the best compromise of inclusion of all significant loss mechanisms and ability to model a wide range of combinations of continuous and dispersed phase materials, frequencies, concentrations and particle sizes. Use
of the ECAH model and some associated multiple scattering models in ultrasonic spectroscopy are evaluated and compared to experimental data. Although mathematically
related, attenuation and phase velocity spectra are shown separately to contain information that might uniquely characterize a dispersion. Truncating the summation of the ultrasonic scattering wavenumber at low orders of its convergent infinite series solution is demonstrated to result sometimes in serious error. The orders required for limits of convergence for a variety of materials, frequencies and particle sizes are listed and analyzed.
A relationship between the required order, frequency, particle size and compressive wave velocity in the continuous phase is established. Difficulties computing higher orders are examined and a solution, based on the work of Amos, developed. Also shown are modifications to the formulation of the ECAH model that substantially extend the limits of particle size and frequency that can be modelled without computational instability.
Sensitivity of output to errors in temperature and values of physical properties of a modelled dispersion is examined and quantified. Spectral features that are indicators of concentration, size and size distribution of particles, that could be exploited in an on-line instrument to characterize dispersions, are identified and described.

Publication Date Dec 1, 1998


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