Eur. Phys. J. Special Topics 229, 2891–2897 (2020)
https://doi.org/10.1140/epjst/e2020-000100-4

Regular Article

Selection constants in the theory of stable dendritic growth

¹ Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Lenin Avenue 51, Ekaterinburg 620000, Russia
² Friedrich-Schiller-Universität-Jena, Physikalisch-Astronomische Fakultät, 07743 Jena, Germany

^a e-mail: ekatitova@mail.ru

Received: 30 May 2020
Accepted: 14 September 2020
Published online: 19 November 2020

Abstract

A stationary growth of the dendritic tip having the tip shape of an elliptical paraboloid in a binary liquid is considered. A method for constructing a selection criterion that allows one to obtain the growth rate and two radii of the dendritic tip as functions of undercooling is proposed. Selection constants are found theoretically for the n-fold crystalline symmetry. The theory is in good agreement with experimental data obtained on water and water solution previously described in literature.