Modelling of crystal growth in multicomponent solutions

The crystal growth model was derived from Maxwell-Stefan equations for the diffusioncontrolled growth regime. As a model system, the ternary potassium dihydrogen phosphate (crystallizing substance)-water (solvent)-urea (foreign substance) system was employed. The thermodynamic model for the present system was successfully derived by the Pitzer method and allowed calculating activity coefficients of each component. The resulting activity-based driving force on each component and other solution properties; mass transfer coefficient, concentration of each component and solution density, were introduced to the Maxwell-Stefan equations. The crystal growth rates were successively determined by solving the Maxwell-Stefan equations. The model was evaluated from single crystal growth measurements. The urea concentrations, supersaturation level and solution velocity were varied. The results showed that experimental and predicted growth rates are in acceptable agreements.