In classical models, an interface between two fluids is treated as infinitely thin, or sharp, and is endowed with properties such as surface tension. Diffuse-interface theories replace this sharp interface with continuous variations of an order parameter such as density in a way consistent with microscopic theories of the interface. The diffuse-interface, or phase-field, approach has been used extensively by researchers in ACMD and MSEL to describe phase transitions such as solidification. The present work describes a similar approach, used to model the motion of a fluid/fluid system. Surface tension effects, for example, are incorporated into the model through a modified stress tensor in the classical Navier-Stokes equations. The diffuse-interface model recovers in the asymptotic limit of vanishing interface thickness the governing equations and the associated boundary conditions used in the sharp-interface formulation. The diffuse-interface approach is illustrated by modeling internal gravity waves, which have been observed experimentally (Robert Berg, CSTL) in xenon near its critical point. Internal gravity wave frequencies have been computed numerically and compared with the existing experimental data and sharp-interface model predictions.
This work, in conjunction with previous and current NIST research on phase-field models of solidification, will provide the underpinnings for the development of more detailed phase-field models which couple solidification with fluid motion.