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Sharp interface limits of phase-field models.

K R Elder1, M Grant, N Provatas

  • 1Department of Physics, Oakland University, Rochester, Michigan 48309-4487, USA. elder@oakland.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2001
PubMed
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Continuum phase-field models describe interface motion in materials science phenomena. Using the projection operator method, we derive sharp-interface equations from diffuse-interface models, unifying key physical conditions.

Area of Science:

  • Materials Science
  • Computational Physics
  • Chemical Engineering

Background:

  • Continuum phase-field models are widely used to simulate interface dynamics.
  • These models often feature diffuse interfaces, complicating direct comparison with sharp-interface theories.
  • Phenomena include order-disorder transitions, spinodal decomposition, dendritic growth, and alloy solidification.

Purpose of the Study:

  • To develop a general framework for deriving sharp-interface equations from diffuse-interface phase-field models.
  • To establish the conditions under which phase-field models yield sharp-interface behavior.
  • To unify various sharp-interface equations within a single theoretical approach.

Main Methods:

  • Application of the projection operator method to phase-field models.

Related Experiment Videos

  • Derivation of sharp-interface equations in the limit of small interface width (xi).
  • Analysis of phase-field equations in the limits xi(kappa)<<1 and xi(v)/D<<1.

    • Main Results:

    • A general set of sharp-interface equations is derived from diffuse-interface phase-field models.
    • The derived equations incorporate fundamental physical conditions like the Gibbs-Thomson effect.
    • The framework unifies the Allen-Cahn and Kardar-Parisi-Zhang equations.

    Conclusions:

    • The projection operator method effectively bridges diffuse-interface phase-field models and sharp-interface descriptions.
    • This work provides a unified theoretical basis for understanding interface dynamics across various materials phenomena.
    • The derived sharp-interface equations offer a powerful tool for accurate simulations and theoretical analysis.