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ARTICLE

A Deterministic Mechanism for Side-branching in Dendritic Growth

Shuwang Li¹, Xiangrong Li¹, John Lowengrub^1,2, Martin Glicksman³

1 Department of Mathematics, University of California atIrvine, Irvine CA 92697
2 Corresponding author. Department of Chemical Engineering and Material Science, University of California atIrvine, Irvine CA 92697
3 Department of Material Science and Engineering, University of Florida, Gainesville, FL 32611

Fluid Dynamics & Materials Processing 2008, 4(1), 27-42. https://doi.org/10.3970/fdmp.2008.004.027

Abstract

In this paper, we suggest a deterministic mechanism for the generation and development of side-branches in dendritic growth. The present authors investigated recently [Glicksman, Lowengrub, and Li (2006)] the existence of such a deterministic branching mechanism induced through the Gibbs-Thomson-Herring (GTH [Herring (1951)]) anisotropic capillary boundary condition. In this paper, we focus our study on an anisotropic kinetic boundary condition. We develop and apply accurate boundary integral methods in 2D and 3D, in which a time and space rescaling scheme is implemented, that are capable of separating the dynamics of growth from those of morphology change. Numerical results reveal that under anisotropic kinetic boundary conditions a non-monotone temperature distribution forms on the interface near the tip that leads to oscillations of the scaled tip velocity. This dynamical process resembles a limit cycle that generates a sequence of time-periodic 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 [Pieters and Langer (1986)], the generation and development of side-branches is intrinsic, and occurs solely under the deterministic influence of the anisotropic kinetic boundary condition.

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Keywords

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