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Physica D 144 (2000) 154168 Thin interface asymptotics for an energy/entropy approach to
 

Summary: Physica D 144 (2000) 154­168
Thin interface asymptotics for an energy/entropy approach to
phase-field models with unequal conductivities
G.B. McFaddena,, A.A. Wheelerb, D.M. Andersonc
a National Institute of Standards and Technology, Room 365, Building 820, 100 Bureau Drive, Stop 8910, Gaithersburg, MD 20899-8910, USA
b Faculty of Mathematical Studies, University of Southampton, Southampton SO17 1BJ, UK
c Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA
Received 4 October 1999; accepted 8 March 2000
Communicated by H. Müller-Krumbhaar
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

  

Source: Anderson, Daniel M. - Department of Mathematical Sciences, George Mason University

 

Collections: Mathematics