  The physics of ice crystal growth from the liquid phase, especially in the
presence of salt, has received much less attention than the growth of snow
crystals from the vapour phase. The growth of so-called frazil ice by
solidification of a supercooled aqueous salt solution is consistent with
crystal growth in the basal plane being limited by the diffusive removal of the
latent heat of solidification from the solid--liquid interface, while being
limited by attachment kinetics in the perpendicular direction. This leads to
the formation of approximately disk-shaped crystals with a low aspect ratio of
thickness compared to radius, because radial growth is much faster than axial
growth. We calculate numerically how fast disk-shaped crystals grow in both
pure and binary melts, accounting for the comparatively slow axial growth, the
effect of dissolved solute in the fluid phase and the difference in thermal
properties between solid and fluid phases. We identify the main physical
mechanisms that control crystal growth and show that the diffusive removal of
both the latent heat released and also the salt rejected at the growing
interface are significant. Our calculations demonstrate that certain previous
parameterizations, based on scaling arguments, substantially underestimate
crystal growth rates by a factor of order 10-100 for low aspect ratio disks,
and provide a parameterization for use in models of ice crystal growth in
environmental settings.
