Transient simulations of the particle size distribution during dispersion of inorganic pigments

The purpose of this work was to develop a mathematical model capable of mapping the full particle size distribution of inorganic pigments during a dispersion process. Three kinetic mechanisms, erosion, rupture, and re-agglomeration, were investigated. For model validation, particle size distribution measurements on TiO₂ and Cu₂O pigments were used.
The best agreement between simulations and experimental data, for both the transient volume-moment mean diameter and the full particle size distribution, was obtained with only the erosion mechanism active. Furthermore, by adjusting the erosion rate constant, the model was able to simulate experimental data from the high speed disk disperser or bead mill with perturbations in the coatings formulation and dispersion parameters.
In combination with particle size measurements, the mathematical model can, for a given pigment, suggest the dominant dispersion kinetics and point at relevant process improvements. The optimal dispersion time is of particular interest.