Enhanced Scale-Up of Rotor-Stator Wet Milling Using Population Balance Modeling with a Novel Exponential Shear-Activated Kernel

Abstract Wet milling is a critical operation in drug substance manufacturing, enabling control of the particle size distribution of active pharmaceutical ingredients. Scaling up of the wet milling process usually involves equipment change. Due to material availability limitations during the early stage of development, there is a limited opportunity to experimentally determine optimal operating conditions for scale-up equipment. As a result, model-based approaches are essential for a reliable transition from the laboratory to commercial production. Existing population balance modeling (PBM) frameworks have enabled model-aided scale-up but typically employ empirical linear relationships between the breakage rate and the shear number, limiting their mechanistic interpretability and cross-scale robustness. This study presents an enhanced PBM kernel formulation that introduces an exponential dependence of the breakage rate on the shear number, reflecting a stress-activated mechanism analogous to barrier-crossing kinetics observed in material deformation and fracture. The proposed kernel retains the structure of the conventional PBM while embedding physical meaning into the shear dependence. Using experimental data from laboratory- and pilot-scale wet mills, the model successfully predicts clinical-scale performance without empirical refitting, demonstrating improved predictive capability. The exponential shear-activated formulation strengthens the physical foundation of the PBM-based scale-up and provides a more generalizable framework for wet milling process design. In addition, a model credibility and regulatory validation framework is proposed to support the regulatory acceptance of model-based digital design approaches for pharmaceutical manufacturing processes.