Surface Laplacian of interfacial thermochemical potential: its role in solid-liquid pattern formation

Area of Science:

• Materials Science
• Thermodynamics
• Computational Modeling

Background:

• Steady-state solid-liquid interfaces can be described analytically (sharp-interface) or numerically (phase-field modeling).
• Sharp interfaces provide exact shapes and thermodynamic origins of interfacial capillary fields.
• Diffuse interfaces allow for the study of thermodynamic evolution and measurement of interfacial properties.

Purpose of the Study:

• To analytically and numerically investigate steady-state solid-liquid interfaces.
• To identify the thermodynamic origin of interfacial capillary fields.
• To explore novel methods for microstructure control and understand interface energy balances.

Main Methods:

• Analytic description of sharp-interface profiles.
• Numerical simulation using phase-field modeling for diffuse interfaces.
• Quantitative verification of capillary fields and heat flow.

Main Results:

• Sharp interfaces reveal exact shapes and thermodynamic origins of capillary fields (curvature, thermochemical potential, gradients, fluxes, surface Laplacians).
• Diffuse interface simulations enable measurement of interfacial temperatures and fluxes.
• Verified capillary fields and divergent heat flow provide insights into interface energy balances and pattern formation.

Conclusions:

• Both sharp-interface and phase-field models offer complementary insights into solid-liquid interfaces.
• Understanding interfacial capillary fields is crucial for controlling microstructures.
• The microgravity environment of the ISS National Lab is proposed for future experimental research on these topics.