A new population balance model for crystal size distributions: Reversible, size-dependent growth and dissolution

A new approach to crystal growth and dissolution, based on a population balance equation (PBE) similar to models of reversible chain polymerization, describes reversible solute addition to crystal surfaces. The PBE, in combination with a mass balance for solute, can be solved for mass moments of the crystal size distribution (CSD). The first three moments provide the number, average mass, and CSD variance, which allow representation of the CSD by two-parameter, normalized statistical distributions, such as lognormal or gamma distributions. With realistic initial conditions, operating parameters, and rate coefficients, the new theory describes crystal growth, dissolution, and recrystallization (Ostwald ripening) processes. Size-dependent interfacial energy affects solubility and nucleation and determines the driving force for growth or dissolution. Because the model is reversible, the CSD evolves appropriately to equilibrium. The moment equations are readily solved and show properties consistent with observed crystal growth behavior. (C) 2001 Academic Press.