(310a) A Microdynamic Basis for Nonlinear Particle Breakage in Dry Milling

In the modeling of milling process, it is generally assumed that the specific breakage rate for a given particle is dependent on its size, materials properties, and the stressing conditions, but not by the presence of dissimilar sized particles in the milling environment. An abundance of experimental evidence contradicts this assumption finding that the milling environment characterized by the instantaneous particle size distribution (PSD) may affect particle breakage behavior. The occurrence of an environmental dependent specific breakage rate has been observed in particle bed compression tests and various wet and dry milling devices including ball mills. The phenomenon known as “cushioning” or “decelerated breakage” is most commonly observed in which the specific breakage rate of coarse particle is reduced in the presence of fine particles resulting in a slower rate of breakage although an increased rate of breakage known as acceleration has also been observed in some milling environments. Experimental studies have also shown that fine particles in the presence of coarser particles may also be subjected to accelerated breakage. Such breakage behavior can be attributed to mechanical interparticle interactions resulting in force and stress transmission dependent upon the granular composition; however, forces and stresses within powder beds cannot easily be measured. 

As a major novelty, this study adapts a multi-scale modeling approach and utilizes a particle-scale breakage model, DEM for interparticle interactions at the ensemble scale (microdynamic information) combined with a non-linear PBM to explore the origin and influence of non-linear breakage kinetics in dry milling processes. To this end, this study uses DEM to simulate impact tests of unconfined particle beds which are intended to reproduce the conditions likely to be found in a ball mill.  Mono, binary, ternary, and polydispersed particle beds were simulated to elucidate the effects of their composition on the specific breakage rate.  First, a non-linear PBM framework for batch milling processes, which accounts for mechanical interparticle interactions through a phenomenological effectiveness factor, is presented.  The effectiveness factor is then defined mechanistically via a particle-scale breakage model for use in DEM simulations.  Particle-scale dynamics obtained from DEM simulations combined with the mechanistic effectiveness factor show that vastly different mechanical interactions present in various mixtures of coarse–fines lead to marked deviations in the effectiveness factor, signifying a substantial deviation from the traditional first-order breakage hypothesis. The aforementioned experimentally observed deceleration and acceleration effects have been successfully delineated via the effectiveness factor determined from the DEM simulations. The analysis of impact energy rate, different types of collisions, and normal force distributions has enabled us to explain the origin of these prevailing non-linear effects.  In addition, the phenomenological effectiveness factor was also assessed and found to accurately describe the influence of particle bed composition on non-linear effects in binary particle beds as well as predict the behavior in ternary and polydispersed particle beds. This insight supports the phenomenological effectiveness factor’s use within the non-linear PBM framework for the simulation of dry milling processes.  Overall, this study provides mechanistic insight and particle-scale understanding of the effects of the granular composition on the non-linear particle breakage in dry milling processes.