A New Crystal Nucleation Theory for Continuous Precipitation of Silver Halides

Abstract

A new steady state theory of crystallization in the continuous stirred tank reactor (CSTR), or mixed-suspension mixed-product-removal (MSMPR), system was developed based on a dynamic balance between growth and nucleation. The present model was (but is not) limited to nonseeded systems with homogeneous nucleation, diffusion controlled growth, and a nucleation model previously confirmed for such systems in controlled double-jet batch precipitations. No assumptions of size-dependent growth were needed. The model predicts the correlation of the average crystal size with residence time, solubility, and temperature of the system and enables calculation of the supersaturation ratio, the maximum growth rate, the ratio of nucleation to growth, the ratio of average to critical crystal size, and the size of the nasent nuclei. The model predicts that the average crystal size is independent of reactant addition rate and suspension density. The average crystal size is a nonlinear function of the residence time where the crystal size has a positive value at zero residence time (plug–flow condition). Results of continuous precipitations of silver chloride confirm the predictions of the model. The ratio of the fraction of the input stream used for nucleation and crystal growth was calculated from the experimental results to decrease from 4.79 to 0.12, and the size of the nascent crystals to increase from 0.194 to 0.221 mm between 0.5- and 5.0-min residence time. The ratio of average to critical crystal size was determined to 5.73*103 (1.02 to1.09), the supersaturation ratio to 12.2 (0.54, average crystal size L = 0.5 μm ), the supersaturation to 8.2*10−8 (12.7*10−9mol/l, L = 0.5 μm), and the maximum growth rate to 4.68 A/s (1.20 to 4.25). The data in the brackets are for equivalent batch precipitations. The experiments indicate that the width of the crystal size distribution increased with suspension density and was independent of reactant addition rate. While the present model was developed for homogeneous nucleation, diffusion limited growth, and unseeded systems, it may be modified to model seeded systems, systems containing ripening agents or growth restrainers, and systems where growth and nucleation are kinetically, heterogeneously, or otherwise controlled.