SYMBOLIC REGRESSION MODELS FOR NUCLEATION KINETICS IN CRYSTALLIZATION PROCESSES

Crystallization is a key process for the separation and purification of products, with extensive applications in industries such as pharmaceuticals and fine chemicals. Traditionally, the kinetics of crystallization are mathematically described using empirical rates for each phenomenon, with less emphasis on developing physically representative models that account for non-equilibrium thermodynamics. The primary challenge in building reliable predictive models for nucleation lies in capturing the complex interplay between molecular-scale phenomena, such as critical nucleus formation, and macroscopic thermodynamic variables while also considering the stochastic fluctuations and non-equilibrium conditions inherent in the process. Symbolic regression offers a promising approach by revealing explicit mathematical relationships between key variables. This allows for the discovery of simplified, interpretable models that capture underlying physical principles without the need for predefined equations. In this study, we propose applying symbolic regression models to analyze the nucleation of potassium sulfate crystals and acetaminophen crystallization data. Moments of the crystal size distribution (CSD) were used as statistical parameters to describe the crystal population in suspension. The identified mathematical models describe the nucleation rate as the time derivative of the zero-order moment, which relates to the number of crystals in suspension. These models express the nucleation rate as functions of variables such as supersaturation, temperature, species concentration, and first- to third-order moments of the CSD. The resulting equations provide accurate models for the evolution of the zero-order moment, aiding in nucleation prediction and supporting implementations of nucleation control and crystal size control strategies.