The University of Southampton
University of Southampton Institutional Repository

A phase-field model with convection: sharp-interface asymptotics

Anderson, D.M., Wheeler, A.A. and McFadden, G.B. (2001) A phase-field model with convection: sharp-interface asymptotics Physica D: Nonlinear Phenomena, 151, (2-4), pp. 305-331. (doi:10.1016/S0167-2789(01)00229-9).

Record type: Article


We have previously developed a phase-field model of solidification that includes convection in the melt [Physica D 135 (2000) 175]. 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.

Full text not available from this repository.

More information

Published date: 2001
Keywords: phase-field, convection, solidification, sharp-interface analysis
Organisations: Applied Mathematics


Local EPrints ID: 29106
ISSN: 0167-2789
PURE UUID: 00b7b3fe-bff9-4c8a-8e7d-9af25f0e8055

Catalogue record

Date deposited: 10 May 2006
Last modified: 17 Jul 2017 15:59

Export record



Author: D.M. Anderson
Author: A.A. Wheeler
Author: G.B. McFadden

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton:

ePrints Soton supports OAI 2.0 with a base URL of

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.