  We derive a thermodynamically consistent model for phase change in sea ice by
adding salt to the framework introduced by Penrose and Fife. Taking the salt
entropy relative to the liquid water molar fraction provides a transparent
mechanism for salt rejection under ice formation. We identify slow varying
coordinates, including salt density relative to liquid water 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
under-determined and the leading order system is closed by imposing local
conservation of salt under interface perturbation. The quasi-steady system
determines interface motion as balance of curvature, temperature gradient, and
salt 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
inclusion sizes is a key component of sea ice albedo which factors into global
climate models.
