Mathematical modeling validation of experimental brine droplet freeze desalination with phase change under natural free convection

•A mathematical model for cooling and purifying NaCl using natural convection.•Validation of model with real experiments.•The model predicts temperature patterns across various sizes and salinities.•Enables dynamic profiles for brine cooling research.•This model offers electrolyte effects on brine droplet cooling to be studied. Freeze desalination (FD) emerges as an innovative and eco-friendly approach to water purification, utilizing sub-zero temperatures to crystallize and segregate salts and impurities from brine. This study presents a novel comprehensive mathematical model that describes all cooling stages and ice purification processes within saline water droplet freezing under natural free convection. This model integrates conjugated heat and mass transfer to represent the entirety of the process. Thorough validation is conducted by comparing the predictions of theenergy balance kinetic model with experimental data.The model successfully replicates experimental temperature and phase change patterns across various conditions, including cooling temperatures (−15 °C to −40 °C), brine concentrations (8–70 g/L), and droplet volumes (3–9 μL). Significantly, the model accurately captures experimental temperatures at all stages and predicts durations of solid–liquid phase equilibrium, ranging from 40 to over 100 s depending on experimental conditions.This derived and validated model extends its applicability beyond freeze desalination, demonstrating its potential in freeze concentration of beverage and medicinal product as well as wastewater treatment. The proposed system allows for dynamic salinity/impurity and temperature profiles, variation in droplet radii, groundbreaking droplet freezing in ambient conditions research. Advanced modeling and experiments can further test the model's adaptability to a boarder range of electrolyte solutions and external stimuli, improving its predictive abilities.