Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

A Phase-Field Model With Convection: Sharp-Interface Asymptotics

Published

Author(s)

D M. Anderson, Geoffrey B. McFadden, A A. Wheeler

Abstract

We have previously developed a phase-field model of solidification that includes convection in the melt. This model represents the two phases as viscous liquids, where the putative solid phase has a viscosity much larger than the liquid phase. The object of this paper is to examine in detail a simplified version of the governing equations for this phase-field model in the sharp-interface limit to derive the interfacial conditions of the associated free-boundary problem.The importance of this analysis is that it reveals the underlying physical mechanisms built into the phase-field model in the context of a free-boundary problem and, in turn, provides a further validation of the model. In equilibrium we recover the standard interfacial conditions including the Young-Laplace and Clausius--Clapeyron equations that relate the temperature to the pressures in the two bulk phases, the interface curvature and material parameters. In nonequilibrium we identify boundary conditions associated with classical hydrodynamics, such as the normal mass flux condition, the no-slip condition and stress balances. We also identify the heat flux balance condition which is modified to account for the flow, interface curvature and density difference between the bulk phases. The interface temperature satisfies a nonequilibrium version of the Clausius--Clapeyron relation which includes the effects of curvature, attachment kinetics and viscous dissipation.
Citation
Physica D-Nonlinear Phenomena
Volume
151
Issue
No. 2-4

Keywords

`phase-field, convection, sharp-interface analysis, solidification

Citation

Anderson, D. , McFadden, G. and Wheeler, A. (2001), A Phase-Field Model With Convection: Sharp-Interface Asymptotics, Physica D-Nonlinear Phenomena (Accessed June 12, 2024)

Issues

If you have any questions about this publication or are having problems accessing it, please contact reflib@nist.gov.

Created April 30, 2001, Updated October 12, 2021