On cellular instability in the solidification of a dilute binary alloy

Abstract In the solidification of a dilute binary alloy, a planar solid-liquid interface is often found to be unstable, spontaneously assuming a cellular structure. If the solute rejection coefficient is close to unity, then, near the stability threshold, the characteristic cell size may significantly exceed the diffusional width of the solidification zone. This situation enables one to derive an asymptotic nonlinear equation which directly describes the dynamics of the onset and stabilization of cellular structure: ƒ τ +▿ 4 +▿[(2−ƒ)▿+αƒ=0 .