J. W. Mullin

Interpretation of crystallization induction periods

The crystallization induction period tind, is interpreted as the sum of the time for critical nucleus formation, tn, and growth to detectable size, tg. Expressions describing the dependence of tind on supersaturation are derived for the cases tn ⪢ tg, tn ≈ tg, and tn ⪡ tg, taking into account different possible nucleation and growth mechanisms, and their validity is assessed on the basis of experimental evidence. From the dependence of the induction period on solution supersaturation it is possible to deduce whether the new phase appearance is governed either by nucleation (or nucleation followed by growth) or by growth alone. In specific cases the dependence can also reveal the controlling mechanisms of nucleation and/or growth. Non-steady-state nucleation is not significant in the precipitation of inorganic electrolytes from aqueous solutions, except in special cases.

Programmed cooling crystallization of potassium sulphate solutions

Abstract The crystal size distribution from a batch cooling crystallizer is predicted by the numerical solution of a mathematical model which uses empirical kinetics of nucleation and crystal growth. The predictions clearly point out the potential advantages of controlled cooling at a constant nucleation rate for improving the product crystal size over that obtained by either natural or linear cooling. Experimental runs following programmed cooling curves for seeded potassium sulphate solutions showed reasonable agreement with the theoretical predictions. A size dispersion of the crystals was observed which contributes to a slight deviation from theory. Nevertheless, controlled cooling significantly reduced the quantity of nuclei formed and improved the product crystal size distribution.

Expressions of supersaturation in crystallization studies

Abstract The driving force for crystallization in a binary system is considered from the thermodynamic viewpoint. Exact relationships, derived for particular cases, are compared with commonly used expressions of supersaturation calculated from solution concentrations. Errors incurred when activity coefficient ratios are ignored are evaluated. The need to incorporate the number of ions, into which a molecule dissociates, in the expressions of supersaturation for electrolyte solutions is emphasized. Examples are given for the crystallization of several inorganic salts from aqueous solution.

Batch crystallization and solid-liquid separation of potassium sulphate

Influence de la forme physique des cristaux de sulfate de potassium produits dans des cristalliseurs discontinus de laboratoire soit par refroidissement, soit par precipitation, sur les caracteristiques de la separation solide-liquide. Le controle des conditions operatoires ameliore la distribution granulometrique des cristaux dans les deux cas et accroit considerablement la permeabilite des precipites

Crystallization kinetics of ammonium sulphate

Abstract Nucleation and growth rates of ammonium sulphate in aqueous solution are measured by several different techniques and comparisons are made. Traces of Cr 3+ suppress both nucleation and growth and modify the crystal habit.

The periodic behaviour of continuous crystallizers

Abstract A mathematical model of a continuous stirred crystallizer is presented which demonstrates that periodic changes of supersaturation, solid phase content, crystal size and production rate can readily occur, and that under certain conditions the steady state may not be established. These theoretical considerations help to explain the results from a pilot-plant study.

Expressions of supersaturation for systems containing hydrates, partially dissociated electrolytes and mixtures of electrolytes

Abstract The crystallization of hydrates and partially dissociated salts from aqueous solution is analysed from the thermodynamic viewpoint and exact expression

The mass transfer driving force for high mass flux

Abstract For the dissolution of single spheres of moderately soluble electrolytes, mass transfer data can be correlated by an equation of the type It is shown that the correlation constant φ is approximately the same for the four different electrolyte-water systems studied and is approximately equal to the value obtained by Rowe for heat and low mass flux mass transfer, provided the driving force is defined by the relationship Any other choice of driving force would, for these systems, lead to different φ values for each system, all markedly different from that obtained for low mass flux.

Some effects of chromium (III) on the crystallization of potassium sulphate

Abstract Significant effects of traces (up to 10 ppm) of chromium(III) on crystal growth and nucleation kinetics, crystal habit and attrition of potassium sulphate are reported. Heterogeneous nucleation is reduced by the presence of Cr(III) and crystal habit is also modified, in some cases substantially. The action of Cr(III) is strongly affected by solution pH and the presence of Cl − . With both impurities present in neutral solutions both growth and secondary nucleation rates pass through a maximum prior to inhibition. Cl − enhances the effect of Cr(III) on micro-attrition during stirring but has a moderating effect on macro-attrition in well-agitated slurries. These characteristics are assessed in terms of the interaction between the formation of chromium aqua- and chloro-complex ions, solution pH and the mechanism of crystallization process.

The effect of a receding interface and concentration-dependent physical properties on dissolution mass transfer rates

Abstract The differential equations governing dissolution mass transfer rates through a laminar boundary layer are derived, taking into account the mass flux and solute interface recession. These equations are solved for the general case of concentration-dependent physical properties and particular solutions are compared to experimental results from the dissolution of five solids. reasonable agreement is obtained, significantly better than with other theoretical predictions.