Brine-ice sandwich with disparate diffusion scales ($ϵ{\lambda }_a\sim \frac{1}{4}[\sqrt{\pi }-\sqrt{\pi +8/S}]$)

For an ice layer between freshwater and cold brine, set $ϵ=\sqrt{D/\kappa }$ and use solutal similarity positions $a=2{\lambda }_a\sqrt{Dt}$, $b=2{\lambda }_b\sqrt{Dt}$. A linear ice temperature, two Stefan conditions and interfacial salt conservation determine both negative interface constants. As $ϵ\to 0$ with fixed latent-to-sensible heat ratio $S$, ${\lambda }_b=O(1)$ but ${\lambda }_a=O({ϵ}^{-1})$. Freezing above occurs over the thermal diffusion scale, while dilution-driven melting below has the much shorter solutal scale.