Growth from a hypercooled melt near absolute stability

The stability of a solid-liquid interface in a hypercooled melt is studied, taking into account attachment kinetics, surface energy, and surface energy in the heat balance. There is a basic-state solution with the planar interface moving at constant speed. Linear-stability theory gives a long-wave absolute-stability limit. Near this point a string model is introduced in which a thermal-boundary-layer approximation is used and an evolution equation for the interface is obtained. In a limiting case this interface equation reduces to a Kuromoto-Sivashinsky equation. Comparison with experimental and numerical results are discussed, and a conceptual picture of unconstrained growth for all undercoolings is addressed.