Numerical simulation of open-circuit continuous mills using a non-linear population balance framework: Incorporation of non-first-order effects

Population balance modeling has been used as a tool for simulating, optimizing, and designing various particulate processes, including milling. A fundamental tenet of the traditional models for milling processes is the first-order breakage kinetics. Ample data obtained from batch milling studies show that this assumption is not necessarily valid for certain milling systems. In the present theoretical investigation, an attempt has been made to incorporate these experimentally observed non-first-order effects into continuous mill models within the context of a novel non-linear population balance framework. In view of two idealized flow regimes, i.e., perfect mixing and plug-flow, continuous mills operating in the open-circuit mode are numerically simulated. The simulations indicate that not only does the product size distribution depend on the degree of mixedness in a continuous mill, but also on the non-first-order effects arising from multi-particle interactions.