A Stochastic Model for Nucleation in the Boundary Layer during Solvent Freeze-Concentration

Nucleation kinetics, induction times, and metastable zone widths are often modeled in quiescent, quasi-steady, and/or spatially uniform concentration fields. However, freezing an aqueous solution can concentrate the solute and effectively increase the supersaturation. During the freezing process, a boundary layer of giant supersaturation develops ahead of the moving ice front. We develop stochastic models of nucleation in the boundary layer when the growing ice perfectly excludes the solute for a one-dimensional system. The models make three simplifying assumptions: quasi-stationary nucleation kinetics, nuclei that are small compared to the boundary layer thickness, and a constant solvent crystallization growth velocity. Whether heterogeneous on the ice surface, or homogeneous in the boundary layer, the models suggest that nucleation is dramatically accelerated by the growing ice. For methane hydrates, which form at conditions similar to that of ice, induction times for hydrate nucleation can be reduced by as much as 10105 times because of the moving supersaturation zone.