Application of particle fracture energy distributions to ball milling kinetics

In the classical application of the population balance method to ball mills, little effort is made to isolate the influence of the strength of the particles on grinding kinetics. This practice greatly reduces the usefulness of the population balance method as a design tool. In fact, it is difficult to predict the effect of the strength of the particles on the selection and breakage functions, especially for the larger particle sizes, where abnormal breakage behavior can be usually observed. A significant part of this limitation lays in the fact that the particles are characterized only by size. In this context, a kinetic model for ball milling, which incorporates size and fracture energy as descriptive variables, was developed. The interaction between the facture energies, which characterize the strength of the particles, and the absorbed impact energies, which characterize the motion of the ball charge, can be described by the proposed bi-variate grinding kinetics. Thus, the model is prepared to simulate the effect of preferential breakage of the weaker particles in a narrow size interval and the resulting non-first-order breakage. The model was fitted with success to batch grinding data where abnormal breakage was detected.