Reactive Crystallization with a Solid Reactant

Consider a liquid feed stream containing reactant species A entering an MSMPR crystallizer at a volumetric flow rate F. A solid reactant B is also charged continuously at a molar flow rate W. The solid reactant B dissolves, and reacts with A in the liquid phase in the presence of an inert solvent S. The reaction rate can be generally given as a function of the concentrations of the reactant species, t (c). An amount of product P in excess of the solubility limit precipitates out of the solution as a solid product. 

The material balances for the reactant and product species Balance for species A 

7 7 Development of Reactive Crystallization Processes Solid phase 

Cp is the concentration of the dissolved solute in the bulk of the liquid, Cp is the concentration of the solute at the liquid-crystal interface, and Cp is the solubility. Note that the nucleation rate (Jn) and the linear growth rate (G) have been transformed into molar units by using appropriate multiplying factors. It should be emphasized that, while these equations capture the phenomena under consideration, to be correct, they should be expressed in terms of activities in stead of concentrations. 

Examination of Eqs. (12) to (16) reveals five distinct rate steps dissolution of B the reaction between A and B the generation of P nuclei in the liquid phase the mass transfer of dissolved P to the growing P crystals and the surface integration of the solute P into the crystal lattice (i.e., the crystal growth step). The relative importance of each of these steps can be characterized by a dimensionless number. For a reaction which is second order overall, and for nucleation and growth kinetics which can be represented by conventional power law expressions, we have 

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