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A phase-field model of solidification with convection

A phase-field model of solidification with convection
A phase-field model of solidification with convection
We develop a phase-field model for the solidification of a pure material that includes convection in the liquid phase. The model permits the interface to have an anisotropic surface energy, and allows a quasi-incompressible thermodynamic description in which the densities in the solid and liquid phases may each be uniform. The solid phase is modeled as an extremely viscous liquid, and the formalism of irreversible thermodynamics is employed to derive the governing equations. We investigate the behavior of our model in two important simple situations corresponding to the solidification of a planar interface at constant velocity: density change flow and a shear flow. In the former case we obtain a non-equilibrium form of the Clausius–Clapeyron equation and investigate its behavior by both a direct numerical integration of the governing equations, and an asymptotic analysis corresponding to a small density difference between the two phases. In the case of a parallel shear flow we are able to obtain an exact solution which allows us to investigate its behavior in the sharp interface limit, and for large values of the viscosity ratio.
phase-field, convection, solidification, diffuse interface
0167-2789
175-194
Anderson, D.M.
8d7064b5-f7cd-4e54-9163-51892a9a272c
McFadden, G.B.
56b0d29e-1cfb-4775-96d1-d32d50ea08d2
Wheeler, A.A.
eb831100-6e51-4674-878a-a2936ad04d73
Anderson, D.M.
8d7064b5-f7cd-4e54-9163-51892a9a272c
McFadden, G.B.
56b0d29e-1cfb-4775-96d1-d32d50ea08d2
Wheeler, A.A.
eb831100-6e51-4674-878a-a2936ad04d73

Anderson, D.M., McFadden, G.B. and Wheeler, A.A. (2000) A phase-field model of solidification with convection. Physica D: Nonlinear Phenomena, 135 (1-2), 175-194. (doi:10.1016/S0167-2789(99)00109-8).

Record type: Article

Abstract

We develop a phase-field model for the solidification of a pure material that includes convection in the liquid phase. The model permits the interface to have an anisotropic surface energy, and allows a quasi-incompressible thermodynamic description in which the densities in the solid and liquid phases may each be uniform. The solid phase is modeled as an extremely viscous liquid, and the formalism of irreversible thermodynamics is employed to derive the governing equations. We investigate the behavior of our model in two important simple situations corresponding to the solidification of a planar interface at constant velocity: density change flow and a shear flow. In the former case we obtain a non-equilibrium form of the Clausius–Clapeyron equation and investigate its behavior by both a direct numerical integration of the governing equations, and an asymptotic analysis corresponding to a small density difference between the two phases. In the case of a parallel shear flow we are able to obtain an exact solution which allows us to investigate its behavior in the sharp interface limit, and for large values of the viscosity ratio.

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More information

Published date: 2000
Keywords: phase-field, convection, solidification, diffuse interface
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 29104
URI: http://eprints.soton.ac.uk/id/eprint/29104
ISSN: 0167-2789
PURE UUID: 109c7766-3cbc-447e-8f31-9e41c2b3c319

Catalogue record

Date deposited: 18 Jul 2006
Last modified: 15 Jul 2019 19:09

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Contributors

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

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