A Deterministic Mechanism for Side-branching in Dendritic Growth

In this paper, we suggest a deterministic mechanism for the generation and development of sidebranches in dendritic growth. We investigated the existence of such a mechanism for Gibbs-Thomson-Herring (GTH [1]) anisotropic capillary boundary condition recently in our previous work [2] . Here, we focus our study on the GTH anisotropic kinetic boundary condition. We develop and apply accurate boundary integral methods in 2D and 3D, in which a time and space rescaling scheme, capable of separating the dynamics of growth from those of morphology change, is implemented. Numerical results reveal that under anisotropic kinetic boundary conditions, a non-monotone temperature distribution forms on the interface that leads to oscillations of the scaled tip velocity. This dynamical process works like a limit cycle that generates a sequence of protuberances near the tip. These protuberances propagate away from the tip and develop into side-branches at later times. Unlike the conventional noise-amplification theory [3], the generation and development of side-branches is intrinsic and occurs solely under the influence of GTH boundary condition. keyword: dendrites, side-branching, solidification, boundary integral.