Characterization and modeling of a sub-micron milling process limited by agglomeration phenomena

The objective of this work was to characterize a sub-micron grinding process in a wet ball mill including the agglomeration of fines inside the grinding chamber. To do so a population balance model has been developed. A Dynomill ball mill was used and the grinding medium consisted of zirconium oxide beads. The product under investigation was poorly water-soluble. The particle size distribution of the initial powder ranged from 1 to 100 um. Laser diffraction was used to analyze the particle size distribution.During grinding the average particle diameter of a particulate product is reduced to a minimum value. These grinding experiments showed that for a specific product this minimum value is a fixed constant within the range of tested operating conditions. This minimum average particle diameter could be influenced by modification of the particle surface properties with surface active agents.The minimum mass mean particle diameter is a result of grinding and simultaneous agglomeration of broken particles. To build a representative model, a dynamic population balance model was developed. The crystallite size as measured with X-Ray diffraction was chosen as the minimum achievable particle size by grinding. Simulations showed that the applied population balance model is an adequate tool to forecast the evolution of the particle size reduction process and the time required to reach the final product specifications.The product could be defined as “very brittle” using the approach from Kwade et al. (1996b) and Stadler et al. (1990). The shear induced by the translation movements of the grinding medium beads was thus enough to break the particles.The median particle size of the broken particles (x50) was plotted as function of the number of stress events (SN) in the mill. This number of stress events was calculated for one initial product particle. That is the representative number of stresses that needs to be applied on an initial particle to break it into fractions with the desired fine particle size. SN is proportional to the number of media contacts and their frequency, and the probability that a media contact leads to particle breakage. That frequency of media contact is defined as the angular rotation speed (ω) of the mill corrected by an efficiency factor (γF). The stress number SN is characteristic of the ground product.The efficiency factor γF describes the efficiency with which the impellor transfers its energy to the grinding medium. γF was a function of the mill design and more specifically the impellor shape. Factor γF is taken as the surface of the impellor in contact with the grinding media.This approach leads to a general representation of the grinding profile of the studied product in a stirred media mill.