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 rho(s) and rho(l) of the solid and 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 rho(s)/rho(l) increases, we observe a decrease of the tip velocity, 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 circular germ, is slightly anticipated by the flow effects.