Phase-field model for dendritic growth in a channel

We present a phase-field description of dendritic growth in a channel. We observe that both the anisotropic solid-liquid interfacial tension and the geometrical constraint imposed by the channel concur in determining the growth of dendrites: even without interfacial anisotropy there exists a certain critical value of the supercooling Delta above which the governing equations admit steady state solutions and the dendrites advance with constant velocity. In the range considered, for fixed supercooling the growth velocity is a decreasing function of the channel width. When the anisotropy parameter gamma is not too low, the computed dendrite tip radius rho and growth velocity upsilon are consistent with the dependence rho(2) upsilon proportional to gamma(-7/4), valid for a free dendrite. On the other hand, for vanishing anisotropy the channel constraint is sufficient to determine a steady growth regime. The present results, taking into account the kinetic undercooling effect and the fully unsteady dynamics of the process, represent an improvement over existing studies based on approximate free boundary models.