Titanium dioxide breakage in a bead mill: a process parameter influence and a coupled CFD–population balance model construction

This work presents experimental and modeling studies of a high-speed bead mill. In the experimental part, the influence of key process parameters such as rotation speed, bead size, and powder concentration was investigated. The results showed that both deagglomeration and deaggregation occur during bead milling. This phenomenon was confirmed using TEM–EDX analysis. The evolution of particle size distribution over time revealed that erosion is the dominant mechanism governing the deaggregation process. Moreover, increasing the powder concentration resulted in a reduced breakage rate, which may be attributed to the increased viscosity, leading to greater drag forces acting on the beads. Experiments with different bead sizes showed that while the final particle size was similar, smaller beads led to a faster particle size reduction. This observation supports the conclusion that collision frequency is a key parameter controlling the breakage process in a bead mill. In the modeling part, Computational Fluid Dynamics (CFD) methods were employed, the Eulerian granular multiphase model was applied to simulate bead motion inside the milling chamber. Based on the CFD results, a Population Balance (PB) model was developed to predict particle size evolution. The PB equations were solved using the Quadrature Method of Moments (QMOM). The model predictions showed good agreement with the experimental data. Furthermore, CFD simulations were used to verify that collision frequency governs the breakage rate. The simulations were used to determine the required fill level of smaller beads that would maintain the same collision frequency as the system with larger beads used in the experiments. The results confirmed that maintaining the same collision frequency results in a similar breakage rate. • The milling process leads to deagglomeration and deaggregation of TiO 2 powders. • The presented CFD-population balance model can predict changes in particle size. • Collision frequency is a parameter that controls the rate of particle breakage.