Saline Stefan problem

A saline Stefan problem couples a heat equation, a solute diffusion equation, a Stefan condition, solute conservation, and a concentration-dependent liquidus at a moving solid-liquid boundary. Different thermal and solutal diffusivities produce nested boundary layers.

For a planar ice-ocean interface with no fluid motion, similarity places the boundary at $a(t)=2\lambda \sqrt{Dt}$. The sign of $\lambda$ distinguishes ice growth from ablation, while rejected salt during growth can cause constitutional supercooling in the adjacent ocean.