Dendritic growth at very low undercoolings

TL;DR

This study uses phase-field simulations to analyze dendritic growth at very low undercoolings, revealing sharp tip corners, parabolic trailing regions, and scaling laws consistent with microscopic solvability theory.

Contribution

It provides new insights into dendritic morphology and scaling behavior at low undercoolings through detailed numerical simulations.

Findings

Sharp dendrite tips with corners observed

Scaling law vρ^2 ≈ constant holds

Tip sharpness characterized by deviation λ scales with ρ

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 $v\rho^2\sim constant$, where $\rho$ is the tip radius of curvature from the fitting to the parabolic trailing region, still holds approximately. We find that the values of $v\rho^2$ 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 $\lambda$ with respect to an Ivantsov parabola. We observe that this length scales as $\lambda \sim \rho$, consistent with experimental measurements.