A stochastic approach to describe the crystal size distribution dynamics in antisolvent based crystal growth processes is here introduced. Fluctuations in the process dynamics are taken into account by embedding a deterministic model into a Fokker-Planck equation, which describes the evolution in time of the particle size distribution. The deterministic model used in this application is based on the logistic model, which shows to be adequate to suit the dynamics characteristic of the growth process. Validations against experimental data are presented for the NaCl-water-ethanol antisolvent crystallization system in a bench-scale fed-batch crystallization unit. \u
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)
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