Characterization of particle size distribution in slurries using ultrasonic attenuation spectroscopy: Addressing challenges of unknown physical properties

Abstract Ultrasonic attenuation spectroscopy (UAS) has many advantages in online in-process characterization of particle size distribution (PSD) in slurries. It can be applied to systems with relatively high solid concentration and wide particle size range from nanometres to millimetres sized particles. The model used by a UAS instrument to estimate the PSD from an attenuation spectrum requires some physical properties of both the liquid and solid phases to be known. For instance, the most popular UAS model, the Epstein–Carhart and Allegra–Hawley (ECAH) model, requires fourteen physical properties. Therefore, applications where all or some of the required physical properties are unknown or difficult to measure, such as crystallization, pose a major challenge to its use. In this work, a procedure for estimating the unknown physical properties is proposed. This is done by iteratively learning the unknown physical properties to minimise the difference between the measured attenuation spectra and that predicted by the ECAH model. One of the main challenges of this procedure is the presence of multiple local minima but these can be eliminated by a combination of a global optimisation algorithm the use of multiple particle size distributions and solid concentrations. The procedure was validated using Silica and Titania standard reference materials, and applied to the estimation of the relevant physical properties of saturated aqueous solution of SrCl2.6H2O and Sr(OH)2.8H2O. The properties thus obtained was used for acoustic monitoring of the real-time evolution of PSD during the batch cooling crystallization of SrCl2.6H2O in water.