Inclusion and Surface Adsorption of Impurities

The thermodynamic distribution coefficient fe,.q characterizes the maximum purity achievable by crystallization it is a substance-spedfic parameter. Under real process conditions, the amount of impurities incorporated in the crystallized material usually exceeds the amount predicted from thermodynamics. This arises from different factors related to nonequilibrium, that is, kinetically controlled growth processes that commonly occur in technical crystallization processes. 

In real crystallization processes (e.g., in industrial-scale crystallizers), the level of impurities incorporated in the target product is often strongly related to 

The rejection of impurities by the growing crystal leads to an enrichment of the impurities at the interface that is decreased by both diffusion and convection. 

To account for deviation from thermodynamics, under real conditions an effective distribution coefficient ke F is defined (Equation 7.3). The equation is similar to Equation 7.2, but the effective distribution coefficient results from parameters measured under real crystallization conditions. That is, the parameters Xir,ip s as the impurity content in the solid phase and ximp.i, as the impurity content in the liquid phase are values obtained from the separation process performed. In contrast, the parameters in Equation 7.2 are directly related to the phase diagram. Thus, the effective distribution coefficient also comprises the influence of the crystallization kinetics, in particular the crystal growth rate and mass transfer limitations. 

Burton et al. [4, 5] introduced an expression that quantitatively relates the effective distribution coefficient keff to the thermodynamic distribution coefficient keq (Equation 7.4)  

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