Model-based analysis of the effect of particle and impact geometry on attrition of brittle material

Secondary nucleation by attrition frequently occurs in industrial crystallizers. By collisions with the impeller or with the crystallizer walls, small fragments of larger crystals get chipped off, which serve as secondary nuclei. Gahn and Mersmann (Chem. Eng. Sci., 54(9), 1999, Part A: 1273-1282, Part B: 1283-1292) presented a mechanistic modeling approach to predict the attrition behavior of crystals on the basis of measurable material properties. Their model is based on several assumptions to facilitate an analytical derivation. One of these assumptions is that the crystal corner is hit by a target, such that the target surface is perpendicular to the central axis of the corner. In this contribution their principal modeling approach is extended to a more general formulation allowing impact angle and opening angle of the corner to be variable. The results show that there is a large dependence of the resulting attrition volume on the geometric conditions. The model is evaluated for platonic solids with fictitious material properties to investigate the general effect of geometry. For a selection of crystalline species (ammonium sulphate, potassium nitrate, potash alum, tartaric acid, citric acid), detailed crystal shapes have been used to predict the attrition volume for defined single crystal impact experiments. Comparing the model predictions to the experimental results showed that predictiveness can be improved by considering a detailed impact and crystal geometry.