Numerical study of the shape and integral parameters of a dendrite

TL;DR

This paper numerically investigates the shape and integral parameters of dendrites during solidification, focusing on regions beyond the linear growth phase, and compares findings with experimental and theoretical results.

Contribution

It introduces a phase-field model analysis of dendrite sidebranching beyond linear theory, highlighting different growth regimes and their relation to tip radius.

Findings

Identification of two distinct sidebranching regimes

Quantitative relation between dendrite shape and tip radius

Comparison with experimental and theoretical data

Abstract

We present a numerical study of sidebranching of a solidifying dendrite by means of a phase--field model. Special attention is paid to the regions far from the tip of the dendrite, where linear theories are no longer valid. Two regions have been distinguished outside the linear region: a first one in which sidebranching is in a competition process and a second one further down where branches behave as independent of each other. The shape of the dendrite and integral parameters characterizing the whole dendrite (contour length and area of the dendrite) have been computed and related to the characteristic tip radius for both surface tension and kinetic dominated dendrites. Conclusions about the different behaviors observed and comparison with available experiments and theoretical predictions are presented.