Abstract
The thermal and the chemical phase-field models for free growth in a two-dimensional channel are both studied in their one-sided version for which diffusion only occurs in the liquid. We compare the steady state fingers obtained in our phase-field simulations with the results of boundary integral techniques available in the literature. The excellent agreement found between both methods provides a valuable benchmark of the one-sided thin-interface phase model which makes use of an antitrapping current. Coexistence of several steady states predicted by the Green's function calculations is also recovered. The dynamical stability of two competing modes (symmetric and asymmetric finger) is studied and the extension of their respective basins of attraction is evaluated. General implications of our results for a large class of isotropic systems are discussed.
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