Determination of particle size distributions from acoustic wave propagation measurements

The wave equations for the interior and exterior of the particles are ensem ble averaged and combined with an analysis by Allegra and Hawley [J. Acoust . Sec. Am. 51, 1545 (1972)] for the interaction of a single particle with t he incident wave to determine the phase speed and attenuation of sound wave s propagating through dilute slurries. The theory is shown to compare very well with the measured attenuation. The inverse problem, i.e., the problem of determining the particle size distribution given the attenuation as a fu nction of frequency, is examined using regularization techniques that have been successful for bubbly liquids. It is shown that, unlike the bubbly liq uids, the success of solving the inverse problem is limited since it depend s strongly on the nature of particles and the frequency range used in inver se calculations. (C) 1999 American Institute of Physics. [S1070-6631(99)014 05-1].