Development of a multi-stage model for freezing of a suspended binary solution droplet

The importance of developing spray freeze-drying technology for extending the shelf life of biological and pharmaceutical materials has never been greater, given the increasing food shortage and the strong demand for pharma processes. In particular, the optimal thermal design and application of spray freeze-drying technologies now depend on the estimation of nucleation behavior for droplet solidification (especially the droplets of binary mixtures). Although earlier nucleation models could estimate the nucleation rate and temperature of solidifying droplets, few considered extreme environmental factors, such as extremely low ambient temperatures below -60 degrees C. To ensure the preservation and storage of biological and pharmaceutical products, such as vaccines and protein drugs, these conditions are essential. Hence, developing an accurate and trustworthy mathematical framework for simulating nucleation is paramount. In this study, a multi-stage, hybrid analytical-numerical model for droplet solidification is developed while coupled with a gradient-based optimization algorithm. Specifically, the five-stage solidification of binary mixtures is simulated (including supercooling of liquid, nucleation, recalescence, equilibrium freezing, and subcooling of solid), which captures the dynamic behaviors of temperature and composition or solute concentration during phase change. The heterogeneous nucleation of a binary-mixture droplet in a frigid environment is predicted and validated against a series of experiments on single suspended droplets at a wide range of ambient temperatures between -20 and -160 degrees C. The freezing curves of different solute concentrations are also validated against experimental data. It is found that significant variations in interfacial tension lead to abrupt changes in nucleation temperature for extremely cold environments. Further, the effects of the concentration, contact angle, droplet size, and heat transfer coefficient are investigated.