Kingery and Goodnow (1963) distinguish between gravity drainage of salt, brine expulsion by pressure buildup, and the movement of brine pockets towards higher temperatures. A temperature gradient in the ice requires a concentration gradient in the brine pocket, and any process that disturbs this thermodynamic equilibrium leads to freezing at the colder end of a pocket and melting at the warmer end, so that the brine migrates towards higher temperatures. Two possible processes re-distributing salt concentrations in the brine are molecular diffusion and buoyancy-driven convection. The experimental evidence to date points to molecular diffusion driving brine pocket migration (Hoekstra et al, 1965 and Seidensticker, 1966). The velocities associated with this are too small to produce significant heat flows.
Hoekstra et al (1965) measure brine pocket velocities in the
laboratory, finding them to scale linearly with temperature gradient,
with values about 5 
m hr 
at a temperature gradient of
20 
C m , two orders of magnitude too small to produce
significant heat fluxes. Larger (isolated) brine pockets, which might
be subject to convective internal flow and higher migration
velocities, were observed to break down into smaller pockets in their
experiments.
Also, brine pocket velocities were observed to be practically independent of whether the temperature gradient was imposed in the same direction as gravity, or in the opposite direction. The work of Seidensticker (1966) shows that molecular diffusion of salt, together with a careful treatment of thermal conductivity, accounts nicely for the brine pocket velocities obtained in these experiments.