Modeling of Carbon Black Fragmentation During High‐Intensity Dry Mixing Using the Population Balance Equation and the Discrete Element Method

A complex interaction between the process design and the properties of carbon black (CB) during dry mixing of cathode material influences the microstructure and thus the performance of the Li-ion battery. The description of these interactions by means of a coupling of the mixing process simulation and the fragmentation of CB is the focus of this work. The discrete element method provides information about the frequency and intensity of the stress. The change of the CB size distribution is done by the population balance equation. The material strength as well as the fracture behavior are represented with simple models. The calibration of the model parameters is performed using the Nelder–Mead algorithm. The calibrated models provide good agreement with the measurements of the size distributions from experimental investigations. Transfer of the calibrated parameters to other process settings is possible and provides good agreement in some cases. Recalibration of the fracture behavior improves the accuracy of the model so that it can be used as a predictive tool.