Micro- and nanostructured ceramic materials have received increasing attention in light of the attainable mechanical properties of the resulting components, parts, and products. Stirred ball mill grinding is an important process in reducing the size of ceramic micro- and/or nanoparticles to a desirable range to be used as a constituent for micro- and nanostructured materials. In this study, the time change of particle size of titanium dioxide $TiO2$ micro- and nanoparticles in the stirred ball mill grinding process is characterized with a fracture mechanics analysis combined with a population balance model. The approach provides both the mean and the statistical distribution of particle sizes produced by ball grinding. It also yields an estimate for the amount of time necessary to achieve a desired particle size. The model examines the effects of process parameters, including the grinding speed, the viscosity of the suspending fluid, and the concentration of the feed as input variables. Experiments performed with $TiO2$ suspended in ethylene glycol are used for comparison to model predictions for validation. The results show that the initial particle-size reduction rate is relatively high, however, as the particle size decreases, the time required for further reduction increases significantly. Good agreement exists between the model predictions and the experimental results in the context of micro- and nanoparticle-size reduction trends.

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