Milling is an important unit operation in the production of raw materials, specialty chemicals, and value-added products. Population balance models (PBMs) have been used as a quantitative tool to model the evolution of particle size distribution (PSD) during milling processes. Most PBMs used in the last 70 years assumed the linearity of the breakage rate, i.e., first-order breakage kinetics. In this presentation, I will present some fundamental experimental studies that provide strong evidence for the emergence of non-linear breakage: deviations from first-order breakage kinetics, significant impact of initial PSD on the breakage kinetics, anomalies in binary breakage tests, etc. The non-linear breakage appears to be prevalent in dense milling systems such as in dry ball mills where enduring mechanical multi-particle interactions occur among particles. Then, I will give highlights from recent theoretical developments that address this complex phenomenon of non-linear particle breakage. The traditional linear PBM, the time-variant PBM, and the non-linear functional model  have been critically analyzed in view of experimental data. Extensive numerical simulations of dry ball milling systems [2,3] and particle bed breakage experiments  suggest that the non-linear functional model can serve as a unified framework by which non-linear particle breakage in a multitude of comminution systems can be systematically studied and quantified at the process length scale. Finally, the presentation will highlight recent efforts in exploring the origin of non-linear breakage
 via multi-scale DEMâPBM models and how to best use such models judiciously to predict the evolution of PSD in non-linear milling processes .
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