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Calculation of Mass Transfer Coefficients in a Crystal Growth Chamber through Heat Transfer Measurements

The growth rate of a crystal in a supersaturated solution is limited by both reaction kinetics and the local concentration of solute. If the local mass transfer coefficient is too low, concentration of solute at the crystal-solution interface will drop below saturation, leading to a defect in the growing crystal. Here, mass transfer coefficients are calculated for a rotating crystal growing in a supersaturated solution of potassium di-hydrogen phosphate (KDP) in water. Since mass transfer is difficult to measure directly, the instantaneous distribution of the heat transfer coefficient on a heated scale model crystal in water is measured using temperature-sensitive paint (TSP). To the authors' knowledge this is the first use of TSP to measure temperature distributions in water. The corresponding mass transfer coefficient is then calculated using the Chilton-Colburn analogy. Measurements were made for three crystal sizes at two running conditions each. Running conditions include periodic reversals of rotation direction. Heat transfer coefficients were found to vary significantly both across the crystal faces and over the course of a rotation cycle, but not from one face to another. Mean heat transfer coefficients increased with both crystal size and rotation rate. Additional experiments show that continuous rotation of the crystal results in about a 40% lower heat transfer compared to rotation with periodic reversals. The continuous rotation case also shows a cyclic variation in heat transfer coefficient of about 15%, with a period of about 72 times the rotation period. Calculated mass transfer coefficients were broadly in line with expectations from the full-scale crystal growth experiments.