Dendritic growth at very low undercoolings

Abstract

We have performed numerical simulations of dendritic growth at very low undercoolings in two spatial dimension using a phase-field model. In this regime of growth, the dendrites present sharp corners in the tip region while the trailing region is parabolic, and the corresponding side-branching structures resemble the shape of the tip. The scaling $vρ^2\sim constant$, where $ρ$ is the tip radius of curvature from the fitting to the parabolic trailing region, still holds approximately. We find that the values of $vρ^2$ are consistent with those given by microscopic solvability theory. The sharpness of the tip region of the dendrite can be characterized in terms of the deviation $λ$ with respect to an Ivantsov parabola. We observe that this length scales as $λ\sim ρ$, consistent with experimental measurements.