The boundary integral theory for slow and rapid curved solid/liquid interfaces propagating into binary systems

Area of Science:

• Materials Science
• Computational Physics
• Chemical Engineering

Background:

• Solidification processes are crucial in materials science and crystal growth.
• Understanding interface propagation under thermo-solutal conditions is complex.
• Existing models often simplify local equilibrium or non-equilibrium effects.

Purpose of the Study:

• To develop a unified boundary integral method for solid/liquid interface propagation.
• To incorporate both local equilibrium and non-equilibrium solidification conditions.
• To derive and analyze thermo-solutal selection criteria for dendritic growth.

Main Methods:

• Boundary integral method applied to thermo-solutal Stefan-type models.
• Derivation of a unified integro-differential equation for curved interfaces.
• Analysis of quasi-stationary Ivantsov and Horvay-Cahn solutions.
• Computational modeling of crystal growth in binary mixtures.

Main Results:

• A unified equation encompassing steady-state solidification is derived.
• Quasi-stationary solutions predict paraboloidal and elliptical crystal shapes.
• Dendritic tip morphology is described as spherical (isotropic) or deformed spherical (anisotropic).
• A thermo-solutal selection criterion for quasi-stationary dendrite growth is established.

Conclusions:

• The boundary integral method effectively models complex solidification phenomena.
• Selected crystal structures (dendritic, fractal, planar) can be obtained through computational modeling.
• The study provides insights into the selection of growth modes based on Péclet numbers and anisotropy.