Boundary-layer formulation of dendritic growth: Existence of a family of steady-state needle solutions

We develop a systematic boundary-layer-type formalism for diffusion-controlled dendritic growth, which yields an expression for the shape of steady-state needle solutions valid at large undercoolings. Both physical and analytical considerations suggest the general existence of a continuous family of steady-state needlelike solutions of the heat-flow equations. Simple modifications of the boundary-layer model of Ben-Jacob et al. exhibit this behavior.