Modeling Growth Rate Dispersion in Industrial Crystallizers

The phenomenon of healing appears to be a plausible explanation for the growth rate dispersion observed in many industrial crystallizers. In this paper a growth model is postulated, which describes the healing of plastically deformed attrition fragments. The rate of healing is assumed to be inversely proportional to the initial strain and to the rate of change of either the length, the area, or the volume of the crystal. The validity of the proposed model is verified by the simulation of growth of the smallest crystals (L0) in time in a growth experiment for specific combinations of the model parameters. In addition, the applicability of the proposed model is evaluated through simulations of steady state experimental data obtained in a 75‐liter Draft Tube (DT) crystallizer. It is concluded that the proposed model is able to fit reasonably well the experimental crystal size distribution. The model predicts the existence of a ‘dead time’ during which attrition fragments with large initial strain do not grow and which may last several residence times. Healing appears to be a plausible explanation for the growth rate dispersion observed in many industrial crystallizers. However, for some relaxation functions the stress appears to be not monotonously decreasing with size which contradicts the assumption that lattice strain decreases upon crystal outgrow. Therefore, an alternative growth model is proposed and analyzed, which considers healing of the plastically deformed surfaces of the attrition fragments.