A new fractal modification of ultrasonic attenuation model for measuring particle size in mineral slurries

Weight percentages of different size incremental particles in a mineral slurry is integrated into the ultrasonic attenuation model to derive a relation between ultrasonic attenuation and particle sizes. However, in the inertial and scattering regimes of frequency–radius space, irregularity and aggregation of particles can results in values of ultrasonic attenuation that are significantly different from those predicted by the derived model, which is based on the assumption of separated smooth spherical particles in mineral slurries. Experimental attenuation data obtained previously from mineral slurries of iron ores particles are compared with predicted values. It is shown that there is a negligible difference between predictions and experimental data. A new modification of theoretical model for ultrasonic attenuation is derived. The theory uses ωτv or κR as a fractal scale. It requires an empirical determination of the difference between the fractal dimension of the measured mineral slurry and that of a hypothetical slurry of spheres with the same particle size distribution. The new fractal modification of ultrasonic attenuation model is found to enable better agreement with measured attenuation as a function concentration for irregular particles than the theoretical model. Moreover, the fractal approach is found to discriminate between the effects of particle irregularity and aggregation.