Variational formulation of a quantitative phase-field model for nonisothermal solidification in a multicomponent...

Area of Science:

• Materials Science
• Thermodynamics
• Computational Modeling

Background:

• Quantitative phase-field models are crucial for simulating alloy solidification.
• Existing models often lack accuracy in handling asymmetric diffusion and cross-coupling effects.

Purpose of the Study:

• To present a variational formulation for nonisothermal multicomponent alloy solidification.
• To incorporate two-sided asymmetric diffusion and naturally derive cross-coupling terms.
• To develop a numerically efficient nonvariational form of the model.

Main Methods:

• Deriving diffusion fluxes from functional derivatives of total entropy.
• Enforcing local equilibrium conditions between phases.
• Asymptotic analysis to validate against free-boundary problems.
• Developing a nonvariational approach for enhanced numerical performance.

Main Results:

• Naturally arising cross-coupling terms, including an antitrapping current.
• Interface diffusivities of tensor form.
• Exact reproduction of the free-boundary problem in the thin-interface limit.
• Fast convergence in numerical tests for binary alloys.

Conclusions:

• The variational model accurately captures complex diffusion phenomena in alloy solidification.
• The nonvariational form ensures high numerical efficiency and wide applicability.
• This formulation advances the simulation of materials processing with asymmetric diffusion.