Development and validation of a semi-analytical framework for droplet freezing with heterogeneous nucleation and non-linear interface kinetics

Abstract

We present a novel, semi-analytical framework which accurately predicts every stage of droplet freezing. Supercooling degree of the freezing droplet is computed by coupling the 1-D transient heat conduction equation in spherical coordinates with a modified heterogeneous nucleation model. The coupling connects atomic-scale thermodynamic properties with bulk thermophysical properties and yields interesting insights into the freezing process. The study also develops a novel dendritic growth model for crystal propagation that takes into account the effects of non-linear interface kinetics and surface curvature. This non-equilibrium phase-change formulation during the recalescence stage is coupled with quasi-steady phase change approximation using perturbation series for equilibrium freezing stage to yield an accurate closed form solution of freezing dynamics. The temperature curves, nucleation rates, dendritic growth velocities and mass fraction evolution from the model are validated or verified with the available experimental or numerical data in the literature. The analytical framework developed is a reduced-order freezing model that is fast to compute and yields accurate results. The framework presented can be useful as a subgrid model for high-fidelity crystal growth and spray freezing simulations.