Self-preserving size spectra of comminuted particles

Abstract

Three pertinent aspects associated with grinding of brittle solids, namely, grinding kinetics, particle-size distributions and energy-size reduction relationships have been unified in the framework of a phenomenological model of particle-size reduction. It is shown, and verified with experimental data, that the particle-size spectra eventually acquire a self-preserving character when plotted on a reduced-size scale and the scaling factor varies with time as in the Walker general energy-size reduction equation. Specialization of parameters in the derived similarity distribution equation leads to a number of well known empirical particle-size distribution expressions including the Rosin-Rammler-Bennet equation. Plots of the similarity distributions for some representative values of the rate and breakage functions are presented.