Migration of a Liquid Zone through a Solid: Part II

Abstract

The migration of slab, cylindrical, and spherical zones of liquid through a solid under the influence of an electric field has been analyzed theoretically. The absolute magnitude of the migration velocity has been predicted to be directly proportional to the macroscopic potential gradient E*; the relative migration rates for these zone shapes was found to be in the order slab>cylinder>sphere for ζS>ζL and in the reverse order for ζS<ζL (ζ=dielectric constant, S=solid, L=liquid). An analytical expression has been developed for the zone migration velocity in terms of (i) the effective ionic mobility of the solvent atoms U, (ii) the Peltier coefficient at the solid—melt interface SPL, (iii) the imposed macroscopic field gradient E* and temperature gradient G*, (iv) the zone size l, and (v) the atomic kinetics of the freezing and melting processes. It was determined that the zone could migrate either up or down the potential gradient E* depending on the magnitude and sign of U, SPL, and G*.