Solidification of a supercooled liquid in a narrow channel

We simulate solidification in a narrow channel through the use of a phase-f ield model with an adaptive grid. In different regimes, we find that the so lid can grow in fingerlike steady-state shapes, or become unstable, exhibit ing unsteady growth. At low melt undercoolings. we find good agreement betw een our results, theoretical predictions, and experiment. For high undercoo lings. we report evidence for a new stable steady-state finger shape which exists in experimentally accessible ranges for typical materials.