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 deter mining the growth of dendrites: even without interfacial anisotropy th ere exists a certain critical value of the supercooling Delta above wh ich the governing equations admit steady state solutions and the dendr ites advance with constant velocity. In the range considered, for fixe d supercooling the growth velocity is a decreasing function of the cha nnel width. When the anisotropy parameter gamma is not too low, the co mputed dendrite tip radius rho and growth velocity upsilon are consist ent with the dependence rho(2) upsilon proportional to gamma(-7/4), va lid for a free dendrite. On the other hand, for vanishing anisotropy t he channel constraint is sufficient to determine a steady growth regim e. The present results, taking into account the kinetic undercooling e ffect and the fully unsteady dynamics of the process, represent an imp rovement over existing studies based on approximate free boundary mode ls.