Heterarchical modelling of comminution for rotary mills: part II—particle crushing with segregation and mixing

In granular media, the crushing of individual particles is influenced by the number of contacts with neighbouring particles. This well-known phenomenon of “cushioning” shields the individual particles from crushing when the number of contacts is high. However, in open systems that involve extensive granular flow and bulk motion, like those found in industrial mills, the neighbouring particles continually exchange positions due to segregation and mixing, thereby altering the number of neighbouring contacts and their sizes, affecting the crushing of individual particles. Therefore, a critical challenge for properly modelling comminution in such systems lies in tracking the fluxes of the various particle size classes. Here, we explore the physics that governs the mechanisms of segregation and mixing within the multiscale heterarchical modelling paradigm. Building upon the framework developed in Part I, which integrated the heterarchical aspects of the physics of crushing along streamlines, we further account for segregation and mixing, and demonstrate their impact on the comminution efficiency of autogenous grinding mills. In particular, segregation is shown to greatly enhance the extent of particle crushing within the mill. Accordingly, we posit that this mechanism cannot be ignored. In summary, the new model sheds light on previously obscured dynamics within industrial mills, as well as enables the field to predict the time evolution of the particle size distribution at any point in the mill domain. This modelling capability opens the doors to new developments for estimating and improving milling efficiencies.