Slow Migration of Brine Inclusions in First-Year Sea Ice

Abstract

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.