On the origin of non-linear breakage kinetics in dry milling

While population balance models (PBMs) have described the impact of mechanical interparticle interactions on the specific breakage rate in dry milling processes through a phenomenological effectiveness factor, such models lack particle-scale information and thus a mechanistic basis. In this study, a mechanistic effectiveness factor of the non-linear PBM was derived and calculated by coupling a particle-scale breakage model with interparticle interactions obtained from discrete element method (DEM) simulations of a grinding ball impacting an unconfined particle bed. Mono, binary, ternary, and polydispersed particle beds were simulated to determine the effects of granular composition on breakage kinetics. The effectiveness factor obtained from the DEM simulations shows a reduction in the specific breakage rate for coarse particles in binary mixtures. The origin of this phenomenon, commonly known as cushioning or decelerated breakage in dry milling processes, was explained by the DEM simulations: fine particles in a particle bed increase mechanical energy loss, and reduce and distribute interparticle forces thereby inhibiting the breakage of the coarse component. On the other hand, the specific breakage rate of fine particles increased due to contacts associated with coarse particles. Such phenomenon, known as acceleration, was shown to be less significant, but should be considered in future attempts to accurately quantify non-linear breakage kinetics in the modeling of dry milling processes. The phenomenological effectiveness factor was also assessed and found to accurately describe the impact of mechanical interparticle interactions in binary particle beds as well as predict the non-linear breakage behavior in ternary and polydispersed particle beds. Aside from gaining particle-scale insight into non-linear breakage kinetics, the above findings provide the guidelines for the usage of non-linear PBM framework and are expected to improve the design, control, and optimization of dry milling processes that exhibit non-linear breakage kinetics.