  We analyze the early phase of brine entrapment in sea ice, using a phase
field model. This model for a first-order phase transition couples
non-conserved order parameter kinetics to salt diffusion. The evolution
equations are derived from a Landau-Ginzburg order parameter gradient dynamics
together with salinity conservation. The numerical solution of model equations
by an exponential time differencing scheme describes the time evolution of
phase separation between liquid water with high salinity and the ice phase with
low salinity. The numerical solution in one and two dimensions indicates the
formation of one dominant wavelength which sets the length scale of short-time
frozen structures. A stability analysis provides the phase diagram in terms of
two Landau parameters. It is distinguished an uniform ice phase, a homogeneous
liquid saline water solution and a phase where solidification structures can be
formed. The Landau parameters are extracted from the supercooling and
superheating as well as the freezing point temperature of water. With the help
of realistic parameters the distribution of brine inclusions is calculated and
found in agreement with the measured samples. The size of the ice domains
separating regions of concentrated seawater depends on salinity and temperature
and corresponds to the size of sea ice platelets obtained from a morphological
stability analysis for the solidification of salt water.
