The shape of dendritic tips

Abstract

The present article is focused on the shapes of dendritic tips occurring in undercooled binary systems in the absence of convection. A circular/globular shape appears in limiting cases of small and large Péclet numbers. A parabolic/paraboloidal shape describes the tip regions of dendrites whereas a fractional power law defines a shape behind their tips in the case of low/moderate Péclet number. The parabolic/paraboloidal and fractional power law shapes are sewed together in the present work to describe the dendritic shape in a broader region adjacent to the dendritic tip. Such a generalized law is in good agreement with the parabolic/paraboloidal and fractional power laws of dendritic shapes. A special case of the angled dendrite is considered and analysed in addition. The obtained results are compared with previous experimental data and the results of numerical simulations on dendritic growth. © 2020 The Author(s) Published by the Royal Society. All rights reserved.Russian Science Foundation, RSF: 16-11-10095Competing interests. We declare we have no competing interests. Funding. Authors thank Efim Brener and Mathis Plapp for the fruitful discussions. This work was supported by the Russian Science Foundation (grant no. 16-11-10095)