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Thin interface asymptotics for an energy/entropy approach to phase-field models with unequal conductivities

Thin interface asymptotics for an energy/entropy approach to phase-field models with unequal conductivities
Thin interface asymptotics for an energy/entropy approach to phase-field models with unequal conductivities
Karma and Rappel [Phys. Rev. E 57 (1998) 4342] recently developed a new sharp interface asymptotic analysis of the phase-field equations that is especially appropriate for modeling dendritic growth at low undercoolings. Their approach relieves a stringent restriction on the interface thickness that applies in the conventional asymptotic analysis, and has the added advantage that interfacial kinetic effects can also be eliminated. However, their analysis focussed on the case of equal thermal conductivities in the solid and liquid phases; when applied to a standard phase-field model with unequal conductivities, anomalous terms arise in the limiting forms of the boundary conditions for the interfacial temperature that are not present in conventional sharp interface solidification models, as discussed further by Almgren [SIAM J. Appl. Math. 59 (1999) 2086]. In this paper we apply their asymptotic methodology to a generalized phase-field model which is derived using a thermodynamically consistent approach that is based on independent entropy and internal energy gradient functionals that include double wells in both the entropy and internal energy densities. The additional degrees of freedom associated with the generalized phase-field equations can be used to eliminate the anomalous terms that arise for unequal conductivities.
phase-field model, Sharp interface analysis, thin interface analysis, dendritic growth, isothermal asymptotics
0167-2789
154-168
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.
8d7064b5-f7cd-4e54-9163-51892a9a272c

McFadden, G.B., Wheeler, A.A. and Anderson, D.M. (2000) Thin interface asymptotics for an energy/entropy approach to phase-field models with unequal conductivities. Physica D, 144 (1-2), 154-168. (doi:10.1016/S0167-2789(00)00064-6).

Record type: Article

Abstract

Karma and Rappel [Phys. Rev. E 57 (1998) 4342] recently developed a new sharp interface asymptotic analysis of the phase-field equations that is especially appropriate for modeling dendritic growth at low undercoolings. Their approach relieves a stringent restriction on the interface thickness that applies in the conventional asymptotic analysis, and has the added advantage that interfacial kinetic effects can also be eliminated. However, their analysis focussed on the case of equal thermal conductivities in the solid and liquid phases; when applied to a standard phase-field model with unequal conductivities, anomalous terms arise in the limiting forms of the boundary conditions for the interfacial temperature that are not present in conventional sharp interface solidification models, as discussed further by Almgren [SIAM J. Appl. Math. 59 (1999) 2086]. In this paper we apply their asymptotic methodology to a generalized phase-field model which is derived using a thermodynamically consistent approach that is based on independent entropy and internal energy gradient functionals that include double wells in both the entropy and internal energy densities. The additional degrees of freedom associated with the generalized phase-field equations can be used to eliminate the anomalous terms that arise for unequal conductivities.

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More information

Published date: 2000
Keywords: phase-field model, Sharp interface analysis, thin interface analysis, dendritic growth, isothermal asymptotics
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 29102
URI: http://eprints.soton.ac.uk/id/eprint/29102
ISSN: 0167-2789
PURE UUID: 50131871-fb1c-4a53-bfcb-9ddf5c56d393

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Date deposited: 18 Jul 2006
Last modified: 08 Jan 2022 09:55

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Contributors

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

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