Thin Interface Asymptotics for an Energy/Entropy Approach to Phase-Field Models with Unequal Conductivities

Published

September 1, 1999

Author(s)

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

Abstract

Karma and Rappel (1) 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 (2). 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 chosen to eliminate the anomalous terms that arise for unequal conductivities.

Citation

- 6377

Report Number

6377

Volume

144

Issue

No. 1-2

Pub Type

NIST Pubs

Download Paper

https://doi.org/10.6028/NIST.IR.6377

Keywords

dendritic growth, isothermal asymptotics, phase-field model, sharp interface analysis, thin interface analysis

Citation

McFadden, G. , Wheeler, A. and Anderson, D. (1999), Thin Interface Asymptotics for an Energy/Entropy Approach to Phase-Field Models with Unequal Conductivities, - 6377, National Institute of Standards and Technology, Gaithersburg, MD, [online], https://doi.org/10.6028/NIST.IR.6377 (Accessed March 13, 2025)