Size-dependent torque scaling and flow-field evolution in vertical planetary mixing of high-solid non-Newtonian particulate slurries

This study establishes a torque-scaling framework for high-solid-loading non-Newtonian particulate slurries in vertical planetary mixing, enabling torque prediction across mixer sizes by coupling multiphase flow evolution with concentration-dependent rheology. Combining an experimentally determined frictional-ignition threshold, mixture multiphase simulations, and dimensional analysis, the framework predicts angular velocity limits and corresponding torques for geometrically similar mixers under a continuum-pressure approximation. The frictional-ignition threshold is measured experimentally and introduced into a local hazard intensity parameter defined by extrusion pressure and shear rate. The mixing process is modeled using the mixture model with concentration-dependent non-Newtonian rheology, while dimensional analysis establishes similarity relationships among angular velocity, scale, torque, and ignition threshold. Results show that high-solid-loading regions initially agglomerate and stratify, then are progressively broken up, dispersed, and homogenized by blade-induced entrainment, shear, and extrusion. Homogenization is positively correlated with torque. The twin-blade intermeshing region is identified as the dominant hazardous zone owing to coexisting strong extrusion and high shear. Geometrically similar mixers follow consistent dimensionless relationships, while the characteristic radius shifts the safety boundary and determines scale-dependent limits under the baseline assumption. The predicted maximum safe characteristic angular velocities and corresponding torques are 503.9 s−1 and 4.21 × 104 N m for the approximately 2000 liter mixer, and 520.0 s−1 and 42.4 N m for the 5 liter mixer. For the 5 liter mixer, at the predicted limiting angular velocity, the dimensional analysis predictions differ from the computational fluid dynamics results by 17.2% in torque and 1.5% in the local hazard parameter.