Fragmentation with abrasion and cleavage: Analytical results

Abrasion and abrasion/cleavage processes are modeled via fragmentation theory. An analytical solution to the evolution of the particle size distribution in an abrasion-dominated process is presented. This solution to the fragmentation equation cannot be described by the usual self-similar form; nevertheless, it allows for the prediction of the mass fraction of unbroken material. Fitting to available data is discussed. Also considered are processes including simultaneous abrasion and cleavage. An analytical solution shows that the distribution diverges from the self-similar form as the average size approaches zero. It is concluded that these types of processes should be scaled with the weight average size, not the number average size.