Batch crystallization supersaturation balance

In a batch crystallizer supersaturation can be achieved by cooling, evaporation of solvent, or both combined if Ac /AT) > 0. If orrly one component crystalUzes, the mass balance for this component is (suspension derrsity nij = p - [Pg.436]

Tavare and Garside ( ) developed a method to employ the time evolution of the CSD in a seeded isothermal batch crystallizer to estimate both growth and nucleation kinetics. In this method, a distinction is made between the seed (S) crystals and those which have nucleated (N crystals). The moment transformation of the population balance model is used to represent the N crystals. A supersaturation balance is written in terms of both the N and S crystals. Experimental size distribution data is used along with a parameter estimation technique to obtain the kinetic constants. The parameter estimation involves a Laplace transform of the experimentally determined size distribution data followed a linear least square analysis. Depending on the form of the nucleation equation employed four, six or eight parameters will be estimated. A nonlinear method of parameter estimation employing desupersaturation curve data has been developed by Witkowki et al (S5). 

An early attempt to establish an optimum cooling curve for batch cooling crystallization (Mullin and Nyvlt, 1971) considered a controlled operation at constant supersaturation, and used a calculation method based on a supersaturation balance in which nuclei were generated in a sequence of discrete time steps. 

A supersaturation balance on a batch cooling crystallizer gives... 

As stated above, control of the crystallization or precipitation process is essential to obtain crystals of biochemical compounds having appropriate properties. The phenomena, techniques, and analysis discussed in many of the previous chapters solubility and supersaturation, nucleation and growth kinetics, population balance methods, batch and continuous crystallizers, and factors governing crystal purity, habit and morphology are all relevant to the discussion of the crystallization of pharmaceuticals. We shall analyze the crystallization/precipitation of biomolecules in terms of these concepts. 

---