Karma and Rappel (1) recently developed a new sharp interface asymptotic analysis211u001eof the phase-field equations that is especially appropriate for modeling 211u001edendritic growth at low undercoolings. Their approach relieves a stringent 211u001erestriction on the interface thickness that applies in the conventional 211u001easymptotic analysis, and has the added advantage that interfacial kinetic effects 211u001ecan also be eliminated. However, their analysis focused on the case of equal 211u001ethermal conductivities, in the solid and liquid phases; when applied to a 211u001estandard phase-field model with unequal conductivities, anomalous terms arise in 211u001ethe limiting forms of the boundary conditions for the interfacial temperature 211u001ethat are not present in conventional sharp-interface solidification models, as 211u001ediscussed further by Almgren (2). In this paper we apply their asymptotic 211u001emethodology to a generalized phase-field model which is derived using a 211u001ethermodynamically consistent approach that is based on independent entropy and 211u001einternal energy gradient functionals that include double wells in both the 211u001eentropy and internal energy densities.
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