A Stochastic Formulation for the Prediction of PSD in Crystallization Processes: Comparative Assessment of Alternative Model Formulations

A stochastic formulation for the description of antisolvent mediated crystal growth processes is discussed. In the proposed approach the crystal size growth dynamics is driven by a deterministic growth factor coupled to a stochastic component. The evolution in time of the particle size distribution is then described in terms of a Fokker-Planck equation. In this formulation the specific form of the stochastic model leads to different shapes for the probability density function. I this work we investigate and assess comparatively the performance of the FPE approach to model the crystal size distribution based on different expressions for the stochastic component. In particular, we consider the Langevin equation with a multiplicative noise term that depends on the crystal size (time and space). It is shown and corroborated via experimentation that the best stochastic model is given by the Geometric Brownian Motion (GBM). Excellent quantitative agreement between experiments and the predictions from the FPE-GBM model were obtained for a range of conditions. Validations against experimental data are presented for the NaCl-water-ethanol anti-solvent crystallization system.