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.