Advection flow effects in the growth of a free dendrite

The growth of a free dendrite into a supercooled liquid is simulated through a modified version of the phase-field model, which takes into account the advection flow due to the different densities ρ s and ρ l of the solidand liquid phases. The intensity of the flow is maximal at the dendrite tip and decays far from the surface of the crystal. At fixed undercooling, as the density ratio p, /ρ l increases, we observe a decrease of the tip volocity, while the tip radius increases. The Peclet number is shifted with respect to the pure diffusive value. The onset of the morphological instability, which is responsible for the origin of the dendrite from a growing circuler gean, is slightly anticipated by the flow effects.