Stochastic Approach for the Prediction of PSD in Crystallization Processes: Formulation and Comparative Assessment of Different Stochastic Models

Abstract

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 (PSD) is then described in terms of a Fokker−Planck equation. In 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 investigate the one-dimensional Fokker−Planck equation with a nonlinear diffusion coefficient to represent the crystal growth process. Validations against experimental data are presented for the NaCl−water−ethanol antisolvent crystallization system. It is shown that the stochastic model better suited to describe the experiments is given by the Geometric Brownian Motion (GBM), which gives an excellent agreement, with the experiments for a wide range of process conditions (i.e., antisolvent feed rate).