Quantitative characterization of hydrophobic agglomeration at different mixing intensities using a copula-based probabilistic modeling approach

The agglomeration of small poorly wetted alumina particles in a stirred tank is investigated. For different experimental conditions, two bivariate probability densities for the area-equivalent diameter and aspect ratio of primary particles and agglomerates, respectively, are determined, using 2D image data from an inline camera system. Throughout each experiment, these densities do not change since the geometries of primary particles are unaffected by the experimental conditions, while large agglomerates fragment into multiple smaller ones, which results in an equilibrium state regarding the distribution of agglomerate descriptors. Mixtures of these densities are used to model the contents of the stirred tank at each time step of the experiments. Analytical functions, whose parameters characterize the agglomeration dynamics, are fitted to the time-dependent weights of these mixtures. This enables a quantitative comparison of agglomeration processes, highlighting the impact of mixing intensity on the joint distribution of agglomerate descriptors.