Slow migration of brine inclusions in first-year sea ice

We derive a thermodynamically consistent model for liquid-solid phase change in sea ice by incorporating a phase sensitive scalar to a classical framework of liquid-solid phase change. The entropy of the scalar is taken relative to the liquid molar fraction which induces a chemotactic behavior. This provides a transparent mechanism for the rejection of the scalar under formation of the solid phase. We identify slow varying coordinates, including the scalar density relative to liquid molarity weighted by latent heat, and use multiscale analysis to derive a quasi-equilibrium Stefan-type problem via a sharp interface scaling. The singular limit is underdetermined, and the leading order system is closed by imposing local conservation of the scalar under interface perturbation. The quasi-steady system determines interface motion as balance of curvature, temperature gradient, and scalar density. We resolve this numerically for axisymmetric surfaces and show that the thermal gradients typical of arctic sea ice can have a decisive impact on the mode of pinch-off of cylindrical brine inclusions and on the size distribution of the resultant spherical shapes. The density and distribution of these inclusion sizes is a key component of sea ice albedo which factors into global climate models.