Dynamic evolution of PSD modelled using an Ornstein-Uhlenbeck process approach

In this paper a new stochastic approach for the description of antisolvent crystal growth processes is presented. In this approach, the trajectory of crystals mean size is modeled as a Gompertz equation and the time evolution of the Particle Size Distribution (PSD) is modeled as a Fokker-Planck equation. In the new formulation the problem is reformulated as an Ornstein Uhlenbeck process and using Fourier transformation an analytical solution is then obtained to describe the time evolution of the PSD as function of the model parameters. Validations against experimental data are provided for the NaCl-water-ethanol antisolvent crystallization system.