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Related Experiment Videos

Three-dimensional effects in directional solidification in hele-shaw cells: nonlinear evolution and pattern selection

Ajaev1, Davis

  • 1Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|October 25, 2000
PubMed
Summary

Directional solidification in Hele-Shaw cells reveals that concave-down interfaces are unstable. Contact-angle conditions delay 3D pattern transitions and promote stable solutions.

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Area of Science:

  • Materials Science
  • Physics
  • Chemical Engineering

Background:

  • Directional solidification is crucial for controlling material microstructure.
  • Hele-Shaw cells provide a model system for studying interface dynamics.
  • Understanding interface stability is key to predicting material properties.

Purpose of the Study:

  • To model directional solidification of binary alloys in Hele-Shaw cells.
  • To analyze the linear and nonlinear stability of planar and non-planar interfaces.
  • To investigate the role of contact-angle conditions on pattern formation.

Main Methods:

  • Development of a long-wave nonlinear evolution equation.
  • Analytical determination of steady-state solutions and linear stability criteria.

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  • Numerical solution of the nonlinear system and weakly/strongly nonlinear analysis.

    • Main Results:

    • Concave-down interfaces are found to be more unstable than planar fronts.
    • Contact-angle conditions expand modulational instability and delay 3D pattern transitions.
    • Fully 3D steady-state solutions with larger amplitudes are found in the strongly nonlinear regime.

    Conclusions:

    • Contact-angle conditions significantly influence interface stability and pattern selection.
    • Subcritical bifurcation and secondary bifurcation to stable solutions are promoted.
    • The study provides insights into pattern formation during directional solidification.