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Interface closure in the root region of steady deep-cellular growth in directional solidification

  • J.-J. XU (a1) (a2) and Y.-Q. CHEN (a3)

Abstract

The present paper investigates the mechanism of interface closure in the root region of the solutions for steady deep-cellular growth. This phenomenon is determined by a transcendentally small factor beyond all orders. It is found that the root region comprises three inner-inner regions; the inner system in the root region has a simple turning point, whose presence generates the so-called trapped-waves mechanism, which is responsible for the interface closure at the bottom of root. The quantization condition derived from the trapped-waves mechanism yields the eigenvalue that determines the location of interface closure and its dependence on the interfacial energy and other physical parameters.

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Keywords

Interface closure in the root region of steady deep-cellular growth in directional solidification

  • J.-J. XU (a1) (a2) and Y.-Q. CHEN (a3)

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