Dynamics of Unstable Interfaces

Abstract

When a solidification front advances into a supercooled melt, its velocity is usually determined by the rate at which the latent heat diffuses away from the front.¹ In this so-called diffusion-limited regime, the interface between the solid and the molten liquid is not simply planar, but instead, it is found to adopt a complex time-dependent shape, known as a dendrite. Under carefully controlled conditions, dendrites exhibit a smooth, approximately parabolic tip, which propagates without apparent change of shape, followed by a train of oscillatory sidebranches.² In the laboratory frame, the tip propagates at a steady velocity v_tip, while the sidebranches grow away from the main body of the dendrite. As the tip advances, it generates new sidebranches behind it, so that the tip size remains constant. Thus, in the moving frame of the tip, the sidebranches are oscillatory wave-like structures, propagating down the body of the dendrite with a speed ~ v_tip