J. Mydlarz

Growth and dissolution kinetics of potassium sulphate crystals in aqueous 2-propanol solutions

Abstract Measured growth and dissolution rates of potassium sulphate crystals in aqueous 2-propanol solutions within a batch agitated vessel are reported. The data are compared to predictions from theoretical models of mass transfer and surface integration kinetics and the thermodynamics of the solid/solution interface. Addition of the organic solvent reduces the volume diffusion rate during dissolution with a corresponding reduction in the overall crystall growth rate. Surface integration kinetics, however, pass through a weak maximum at low concentrations of the second solvent consistent with enhanced surface nucleation. At higher concentration solute—solvent interaction appear to dominate indicating increased surface entropy and absorption. This reduces the integration rate below that of the pure system, thereby creating a further decrease in the overall crystal growth rate.

On numerical computation of size-dependent crystal growth rates

A comparison of current methods for the estimation of crystal growth rates in continuous MSMPR crystallizers exhibiting both linear and non-linear log population density distributions is presented Direct fitting of population density data using an exponential two-parameter model is examined in detail. This method is shown to give an excellent estimation of growth rates during MSMPR crystallization both for systems which obey, and those which violate, McCabes ΔL law. Potential errors in growth rate estimation arising from numerical integration of discrete sieve test type data are highlighted.

ON MODELLING THE SIZE-DEPENDENT GROWTH RATE OF POTASSIUM SULPHATE IN AN MSMPR CRYSTALLIZER

A revised empirical two parameter size-dependent growth rate model is proposed and illustrated for the analysis of potassium sulphate MSMPR population density and cumulative number oversize data. It is shown to have superior curve fitting properties to former methods and models tested and improved consistency in the prediction of the growth rate of large crystals.

On the estimation of size-dependent crystal growth rate functions in MSMPR crystallizers

Abstract A three-parameter exponential size-dependent crystal growth rate function G(L) = G m {1 − exp[− a ( L + c )]} is proposed. The model has been examined in detail for the direct determination of size-dependent crystal growth rates from the population density data of continuous mixed-suspension mixed-product-removal (MSMPR) crystallizers using two sets of realistic data, both for systems which hold and which violate McCabes Δ L law respectively. It is shown that direct fitting of differential population density data using the proposed model gives an improved estimation of effective crystal growth rates over the whole size range during MSMPR crystallization compared with previous models tested.

An assessment of MSMPR crystallization kinetics data for systems modelled by size-dependent crystal growth rate functions

Abstract A comparison of methods proposed for the determination of crystallization kinetics from the crystal size distribution in continuous mixed-suspension, mixed-product-removal (MSMPR) crystallizers is presented for several systems exhibiting size-dependent crystal growth rates reported in the literature. Wide variations in inferred kinetic parameters are obtained depending on the analytical method adopted, leading to uncertainty in their utility. Direct fitting of differential population density data using exponential size-dependent growth models, however, gives an improved estimation of growth rates over the whole size range and leads to higher zero-size crystal growth and nucleation rates in comparison with other models tested.

CRYSTAL GROWTH EFFECTIVENESS FACTORS FOR POTASSIUM SULPHATE IN AQUEOUS ORGANIC SOLVENT SOLUTIONS

Abstract Previously reported potassium sulphate crystal growth rate data in two mixed solvent systems viz. aqueous 2-propanol and aqueous propanone solutions within batch and continuous MSMPR agitated vessels respectively are re-analysed in terms of the surface integration effectiveness factor. In both cases, the effectiveness factor generally decreases with increasing concentration of the organic precipitants indicating increased diffusion control. At 2-propanol concentrations x =0.10 w/w and supersaturations σ>0.05, however, a local minimum in the effectiveness factor is detected indicating a change in mechanism consistent with an earlier kinetic analysis. These results demonstrate that the concept of effectiveness factors can be conveniently used to quantify the effect of solvents on the growth of potassium sulphate crystals.