Onset of sidebranching in directional solidification

Blas Echebarria, Alain Karma, and Sebastian Gurevich
Phys. Rev. E 81, 021608 – Published 26 February 2010

Abstract

We use a computationally efficient phase-field formulation [B. Echebarria et al., Phys. Rev. E 70, 061604 (2004)] to investigate the origin and dynamics of sidebranching in directional solidification for realistic parameters of a dilute alloy previously studied experimentally [M. Gorgelin and A. Pocheau, Phys. Rev. E 57, 3189 (1998)]. Sidebranching is found to result either from noise amplification or from deterministic oscillations that exist both in two dimensions and in a three-dimensional thin-sample geometry. The oscillatory branch of growth solutions bifurcates subcritically from the main steady-state branch of solutions and exists over a finite range of large array spacings. In contrast, noise-induced sidebranching is associated with a smooth transition where the sidebranching amplitude increases exponentially with spacing up to nonlinear saturation due to the overlap of diffusion fields from neighboring cells, as observed experimentally. In the latter case where sidebranching is noise-induced, we find that increasing the externally imposed thermal gradient reduces the onset velocity and wavelength of sidebranching, as also observed experimentally. We show that this counterintuitive effect is due to tip blunting with increasing thermal gradient that promotes noise amplification in the tip region.

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  • Received 23 December 2009

DOI:https://doi.org/10.1103/PhysRevE.81.021608

©2010 American Physical Society

Authors & Affiliations

Blas Echebarria

  • Departament de Física Aplicada, Universitat Politècnica de Catalunya, Av. Dr. Marañón 44-50, 08028 Barcelona, Spain

Alain Karma and Sebastian Gurevich

  • Department of Physics and Center for Interdisciplinary Research on Complex Systems, Northeastern University, Boston, Massachusetts 02115, USA

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Vol. 81, Iss. 2 — February 2010

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