Growth from a hypercooled melt near absolute stability

We study the stability of a solid-liquid interface in a hypercooled melt, 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 we introduce a string model in which we use a thermal-boundary-layer approximation and obtain an evolution equation for the interface. 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.