A multiscale DEM-PBM approach for a continuous comilling process using a mechanistically developed breakage kernel

The population balance approach (PBM) is generally used in the literature to simulate a milling process. The formulation of a breakage kernel to represent particle breakage phenomenon is an important part of the model. This study proposes a methodology to estimate parameters of a breakage kernel that captures material property dependent particle level dynamics through discrete element method (DEM) simulations of a comill process. The DEM model takes into account a threshold impact energy that if exceeded, results in granule breakage. The impact energy distribution data for various size classes and impellor speeds is obtained from DEM. Comill experiments at various impeller speeds result in different observed size distributions and other process variables such as hold up amount, and time required for process to reach steady state. An iterative algorithm is proposed that uses mechanistic information from DEM and process variables from experiments to calibrate the breakage kernel through which material specific kernel parameters are estimated. A multi-scale modeling framework utilizing DEM, PBM as well as experimental data is developed. The framework is implemented to estimate material specific properties using milling experimental data at various impeller speeds. The milled particle size distribution predicted from the model with parameters estimated using this framework, demonstrated excellent agreement with experimental results.