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Dendrite tips as elliptical paraboloids.

D V Alexandrov1, E A Titova2, P K Galenko1,3

  • 1Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Ekaterinburg 620000, Russia.

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|August 3, 2021
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Summary
This summary is machine-generated.

This study explores dendrite growth, focusing on elliptical paraboloid shapes. A new theory explains their steady-state growth, differing from axisymmetric models and validated with ice crystal data.

Keywords:
crystal growthdendrite tipselliptical paraboloids

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Area of Science:

  • Materials Science
  • Physics
  • Crystallography

Background:

  • Dendrite growth is crucial in materials science and solidification processes.
  • Understanding steady-state growth modes is key to controlling material properties.
  • Previous models often simplified dendrite tip morphology.

Purpose of the Study:

  • To review and develop theories for steady-state dendrite growth.
  • To analyze the tip shape, temperature, and concentration fields around dendrites.
  • To derive a hydrodynamic solution for viscous fluid flow against dendrite tips.

Main Methods:

  • Analysis of elliptical paraboloid dendrite tip shapes.
  • Description of temperature and solute concentration distributions.
  • Development of a hydrodynamic solution for fluid flow.
  • Derivation of nonlinear equations for growth velocity and radii of curvature.

Main Results:

  • Elliptical paraboloid morphology yields different analytical solutions compared to axisymmetric shapes.
  • A system of nonlinear equations for stationary growth velocity and radii of curvature was derived.
  • The developed theory shows good agreement with experimental data for D2O and H2O ice crystals.

Conclusions:

  • The elliptical paraboloid model provides a more accurate description of dendrite tip morphology.
  • The derived theory enhances understanding of the physics governing dendrite growth.
  • This work offers a refined theoretical framework for studying solidification phenomena.