A qualitative comparison between population balances and stochastic models for non-isothermal antisolvent crystallization processes

The goal of the present work is to model the crystal growth processes mediated by both antisolvent feed and temperature variations through the time evolution of the Particle Size Distribution (PSD). The study is carried out by exploiting two different approaches. In the first approach a Population Balance Equation (PBE) model is devised, where crystal nucleation and growth phenomena are developed taking into account rigorous first principle assumptions. The second approach is based on a phenomenological stochastic formulation leading to a global Fokker-Planck Equation (FPE) governed by a limited number of parameters, describing the time evolution of the probability density function representing the crystal PSD. Validations against experimental data are presented for the NaCl-water-ethanol ternary system. The pros and cons of both approaches are discussed.