In crystallization, the mean crystal size is governed by thetotal number of crystals sharing the total mass produced in theprocess. In reaction crystallization, it is believed that asignificant part of the crystals is formed during the localcontacts between reactant solutions close to the feed point. Inthe ultimate stage of the mixing processes, small vorticesbring the reactant solutions into contact in a lamellarstructure of thin fluid films which are strained. The aim ofthe present work is to analyse the local solute concentrationgradients that develop during the life time of the smallestvortex as well as the crystal size distribution that may begenerated as a result of crystal nucleation and growth in thevortex. The investigation has been carried out by mathematicalmodelling of the physical situation in the locally occurringlamellar structure of reactant solution films. The chemicalreaction is assumedto be instantaneous, and the subsequentcrystallization to be fast and to occur via the formation of asparingly soluble solute molecule.
Three models of increasing complexity have been developed.All models consider mass transfer and instantaneous reaction instrained fluid reactant films. Model I assumes that thegeometry of the fluid films is semi-infinite. In model II, alamellar structure of finite reactant films is considered. Themost complex model, model III, is an extension of model IItaking also the crystallization phenomena intoconsideration.
The effects on the locally occurring crystallization ofdifferent parameters such as reactant concentrations,diffusivities, specific local energy dissipation rate andcrystallization kinetics are examined. Simulations of model IIIshow that the mean size and number concentration generallyincrease with decreasing specific local energy dissipationrate. The simulations also suggest that the size of thecrystals leaving the vortex is often governed by the growthrate and not by nucleation and mass constraints, and that themean size may be larger than the limiting size for Ostvaldripening in the bulk. The size distribution is usually quitenarrow. The range of total crystal number concentration is ofthe same order of magnitude as that reported in the literature.The neglect of the detailed conditions at the feed point inreaction crystallization of a molecular compound may not bejustified.
It is found that due to the very non-linear dependence ofnucleation rate on supersaturation, the maximum supersaturationoccurring in the vortex correlates well with the total numberconcentration of crystals formed during the local contact. Themaximum product concentration depends in a complex way on thediffusivities, reactant concentrations, film thicknesses anddegree of consumption. However, the results show that themaximum product concentration during a local contact can beestimated by either of the two simpler models, even thoughneither of these models considers crystallization. Model IIestimates the maximum product concentration at negligibleconsumption and model I at a high degree of consumption.
Based on calculations using models I and II of the behaviourof the maximum product concentration, recommendations arepresented for how to choose reactant concentrations in batchand semi-batch reaction crystallization processes in order tominimise the locally occurring maximum product concentration.In addition, a new methodology for carrying out semi-batchreaction crystallization processes is suggested: the"programmed feed concentration" concept. By starting with a lowfeed reactant concentration and then continuously increasingit, the local supersaturation is lowered considerably,especially during start up of the process.
Keywords:Reaction crystallization, Precipitation,Micromixing, Modelling, Programmed feed concentration
Stockholm: Kemiteknik , 1999. , 70 p.