Modified log-normal particle size distribution in acoustic spectroscopy

Abstract

The modified log-normal distribution is a smooth continuous distribution depending on four parameters: median size, standard deviation, minimum size and maximum size. This distribution introduced by Kottler [J. Franklin Inst. 250 (1950) 339] and Irani [J. Phys. Chem. 63 (1959) 1603] gives an opportunity to restrict the particle size range. This distribution is asymmetrical on the logarithmic scale of particle sizes. The modified log-normal distribution is especially useful for acoustic spectroscopy because sound attenuation is very sensitive to the presence of large particles. Particles with size above 3 μm cause significant scattering losses. As a result, sound attenuation spectra show a sharp growth within a sound frequency range 10–100 MHz when large particles are present. The high sensitivity to large particles is a very useful feature of acoustic spectroscopy allowing one to detect these particles. This feature requires a special approach allowing the characterization of large particles with a high accuracy. Regular log-normal distribution tends to overestimate the fraction of large particles and underestimate the median size. Experimental tests have been performed with silicon particles dispersed in water. The particle size distribution has been measured independently by X-ray sedimentation and by an acoustic spectrometer. This test shows that the log-normal distribution provided by the acoustic spectrometer deviates from the sedimentation data. Implementation of the modified log-normal distribution resolves this discrepancy.