A New Conceptual Model for Ball Milling

The population balance concept has provided a useful framework for the description of the operating behavior of the ball mill. This approach finds expression in the so-called selection breakage function model for batch and continuous mills. This model produces very good descriptions of the size distribution of the products from ball milling operations and the model is very useful for the description of batch and continuous mills and, when combined with models for classifiers and other unit operations, provides a solid basis for flowsheet simulation procedures. The breakage and selection function model is essentially descriptive and not predictive because the parameters in the model cannot as yet be related to the fundamental material properties of the material that is broken and to the fracture mechanics that govern the comminution of brittle particulate material during the rapid impact and compression events that occur with high frequency in a ball mill. The population balance approach smears over the individual processes and regards the ball mill as a continuum with breakage occurring continuously in time and space. New experimental techniques, particularly the adaptation of the Hopkinson bar as the ultrafast load cell (UFLC) to the problem of observing the extremely rapid impact fracture of particulate solids, have made it possible to make accurate and consistent measurements of particle strength, particle fracture energy and the single-impact breakage function. These quantitative measurements have been incorporated into a new conceptual model for the description of the ball mill. The model is based on identifying all events that give rise to particle breakage, and using the fundamental experimental data obtained on the UFLC and other single-particle fracture tests, the probabilities of these events can be independently determined. The distribution of impact energies that occur in the ball mill has been established by discrete element simulation of the media motion. The probabilistic description of the individual fracture events and the distribution of impact energies are combined to make a priori predictions of ball mill performance under a variety of operating conditions. The new model is used to calculate the selection and breakage functions for quartz in a small batch mill.