Sharp interface limit of a two-time scale phase field model of a binary mixture

Area of Science:

• Materials Science and Engineering
• Thermodynamics and Physical Chemistry
• Computational Materials Science

Background:

• Phase field methodology offers analytical flexibility and thermodynamic consistency for studying phase equilibria and transformations.
• Hyperbolic phase field models are crucial for analyzing both slow and fast phase transformations.
• Understanding solidification processes, especially in metastable liquids and binary mixtures, is vital for materials design.

Purpose of the Study:

• To review hyperbolic phase field models applicable to slow and fast phase transformations.
• To analyze the reduction of diffuse interfaces to sharp interfaces using solidification of metastable liquid as an example.
• To investigate non-equilibrium effects and the transition between diffusion-limited and diffusionless solidification.

Main Methods:

• Asymptotic analysis of hyperbolic phase field models for binary mixtures with diffuse interfaces.
• Mapping hyperbolic phase field models to the hyperbolic Stefan problem in the sharp interface limit.
• Utilizing common tangent construction to analyze non-equilibrium phenomena.

Main Results:

• The hyperbolic phase field model can be accurately mapped to the hyperbolic Stefan problem under sharp interface conditions.
• Non-equilibrium effects, such as solute trapping, can be analyzed using this framework.
• The complete transition from diffusion-limited to diffusionless solidification at finite interface velocities is elucidated.

Conclusions:

• Hyperbolic phase field models provide a robust framework for analyzing complex solidification phenomena, including non-equilibrium effects.
• The sharp interface limit offers a valuable simplification for theoretical and computational analysis.
• The findings align with and provide theoretical underpinnings for experimental observations in solidification science.