Population Balance Modeling and Mechanistic Analysis of Inorganic Pigment Dispersion in a High-Speed Disk Disperser and a Vertical Bead Mill

Abstract

The purpose of the present work was to develop a mathematical model describing the dispersion of agglomerates in inorganic pigment concentrates. Three potential mechanisms, i.e., surface erosion, rupture, and re-agglomeration, were included in the population balance analysis. For model validation, measurements of transient agglomerate size distributions of TiO2 and Cu2O pigments in a high-speed disk disperser and a vertical bead mill were applied. When taking into account the erosion mechanism only, assigning values to pigment-specific parameters, and allowing for a single adjustable parameter (i.e., an erosion rate constant), a very good agreement between simulations and experimental data was found at all values of time. Conversely, rupture and re-agglomeration did not even provide a qualitative agreement. In comparison with earlier work on organic pigments, surface erosion appears to be the central mechanism in pigment dispersion, even though the rate dependency of the agglomerate diameter was expressed by exponents of, respectively, 2 and 3 for organic and inorganic particles. In summary, the population balance model provides a quantitative description of the dispersion process, which can be used for the optimization of energy consumption and dispersion time. Furthermore, potential dispersion limitations, such as the degree of presence of non-dispersible particle aggregates in the pigment concentrate, can be evaluated.