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

Steady-state solid-liquid interfaces allow both analytic description as sharp-interface profiles, and numerical simulation via phase-field modeling as stationary diffuse-interface microstructures. Profiles for sharp interfaces reveal their exact shapes and allow identification of the thermodynamic origin of all interfacial capillary fields, including distributions of curvature, thermochemical potential, gradients, fluxes, and surface Laplacians. By contrast, simulated diffuse interface images allow thermodynamic evolution and measurement of interfacial temperatures and fluxes. Quantitative results using both approaches verify these capillary fields and their divergent heat flow, to provide insights into interface energy balances, dynamic pattern formation, and novel methods for microstructure control. The microgravity environment of low-Earth orbit was proven useful in past studies of solidification phenomena. We suggest that NASA's ISS National Lab can uniquely accommodate aspects of experimental research needed to explore these novel topics.