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Pattern formation in crystal growth under parabolic shear flow.

K Ueno1

  • 1Institute of Low Temperature Science, Hokkaido University, Sapporo 060-0819, Japan. ueno@riam.kyush-u.ac.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2003
PubMed
Summary

Crystal growth instability is stabilized by gravity and surface tension, not just Gibbs-Thomson effects. This explains icicle surface patterns, revealing key factors in crystal formation dynamics.

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Area of Science:

  • Physics
  • Materials Science
  • Fluid Dynamics

Background:

  • Crystal growth from undercooled liquids is susceptible to interface morphological instabilities.
  • Flowing liquids on inclined planes introduce shear forces that can influence crystal growth.
  • The Gibbs-Thomson effect is a known factor in stabilizing crystal interfaces.

Purpose of the Study:

  • To investigate the morphological instability of a solid-liquid interface during crystal growth under shear flow.
  • To identify stabilizing factors beyond the Gibbs-Thomson effect.
  • To explain observed surface patterns on icicles.

Main Methods:

  • Linear stability analysis was employed to study the solid-liquid interface.
  • The model incorporated shear flow, gravity, and surface tension effects.

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  • A dispersion relation was derived to analyze instability modes.

    • Main Results:

    • Gravity and surface tension act as significant restoring forces, stabilizing the solid-liquid interface on long length scales.
    • A specific long wavelength mode (approx. 1 cm) was predicted, matching observed patterns on icicles.
    • The stabilizing effect of gravity and surface tension differs from the Gibbs-Thomson effect.

    Conclusions:

    • Gravity and surface tension are crucial for stabilizing crystal growth interfaces in flowing undercooled liquids.
    • The study provides a theoretical explanation for the wavy patterns observed on icicles.
    • Understanding these stabilizing forces is important for controlling crystal morphology in various applications.