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

A phase-field model with convection: sharp-interface asymptotics
A phase-field model with convection: sharp-interface asymptotics
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.
phase-field, convection, solidification, sharp-interface analysis
0167-2789
305-331
Anderson, D.M.
8d7064b5-f7cd-4e54-9163-51892a9a272c
Wheeler, A.A.
eb831100-6e51-4674-878a-a2936ad04d73
McFadden, G.B.
56b0d29e-1cfb-4775-96d1-d32d50ea08d2
Anderson, D.M.
8d7064b5-f7cd-4e54-9163-51892a9a272c
Wheeler, A.A.
eb831100-6e51-4674-878a-a2936ad04d73
McFadden, G.B.
56b0d29e-1cfb-4775-96d1-d32d50ea08d2

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

Record type: Article

Abstract

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.

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More information

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

Identifiers

Local EPrints ID: 29106
URI: http://eprints.soton.ac.uk/id/eprint/29106
ISSN: 0167-2789
PURE UUID: 00b7b3fe-bff9-4c8a-8e7d-9af25f0e8055

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Date deposited: 10 May 2006
Last modified: 15 Mar 2024 07:28

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Contributors

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

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