Stress distribution and analysis in a vertical stirred mill: A multiscale analysis

This study investigates media-scale stress distribution, flow structure, and energy transmission in a laboratory-scale vertical stirred mill using the Discrete Element Method (DEM). The DEM model was coupled with a hydrodynamic lubrication-force correction to represent near-contact viscous resistance between grinding media. Particle-scale DEM outputs, including positions, velocities, and contact forces, were converted into continuum fields of solid fraction, velocity, contact stress, kinetic stress, pressure, and shear stress using a Gaussian coarse-graining method. The DEM-predicted power draw was validated against experimentally measured shaft torque at 300 rpm, showing good agreement with a power-draw error of approximately 5.72%. A coarse-graining-width sensitivity analysis and a comparison with simple bin averaging were also performed to demonstrate the robustness and added value of the coarse-grained fields. The results show that stress transmission is highly heterogeneous: the dominant contact pressure and contact shear stress are concentrated in the dense outer lower bed between the stirrer pins and the vessel wall, while the shaft-adjacent core remains more weakly stressed and primarily contributes to recirculation. Contact stresses dominate kinetic stresses over most of the bed, indicating that frictional and abrasive stressing are the primary media-scale energy-transfer mechanisms under the studied conditions. These findings show that stirred-mill optimization should focus on controlling the internal stressing architecture of the media bed rather than simply increasing rotational speed. The study provides a validated DEM-to-continuum stress-mapping framework for identifying active grinding zones, weakly mobilized regions, and operating or design variables relevant to improved energy efficiency. The results should be interpreted as media-scale flow and stress maps under lubrication-corrected DEM conditions, rather than as a complete slurry-grinding or breakage prediction.