A generalized stochastic modelling approach for crystal size distribution in antisolvent crystallization operations

A generalized formulation for the development of stochastic models to predict the crystal size distribution (CSD) in antisolvent crystallization processes is proposed. Exploiting the result of the noise induced dynamic in stochastic processes, new results are provided to represent the CSD as function of the operational parameters. The generalized formulation enables the full description of the CSD using nonlinear drift term in conjunction with multiplicative noise, i.e., state dependent diffusion. For the first time a deterministic nonlinear differential equation to represent the mean and most probable size (mode) time evolution as function of the model parameters is provided. Furthermore, the analytical solution of the asymptotic probability distribution of the CSD can also be obtained. Finally, a global model formulation is finally presented by defining relationships between the model parameters and the operating conditions. Experimental results and validations are provided using the ternary system of NaCl, water, and ethanol.