Eur. Phys. J. Special Topics 229, 2899–2909 (2020)
https://doi.org/10.1140/epjst/e2020-000045-2

Regular Article

Non-axisymmetric growth of dendrite with arbitrary symmetry in two and three dimensions: sharp interface model vs phase-field model

¹ Department of Theoretical and Mathematical Physics, Ural Mathematical Center, Ural Federal University, Lenin Avenue, 51, Ekaterinburg 620000, Russia
² Friedrich-Schiller-Universität-Jena, Physikalisch-Astronomische Fakultät, 07743 Jena, Germany
³ Centre for Numerical Modelling and Process Analysis, University of Greenwich, Old Royal Naval College, Park Row, London SE10 9LS, UK
⁴ GPM, CNRS-UMR 6634, University of Rouen Normandy, 76801 Saint Étienne Du Rouvray, France

^a e-mail: gilles.demange@univ-rouen.fr

Received: 21 March 2020
Accepted: 9 September 2020
Published online: 19 November 2020

Abstract

The growth of a free dendrite having a non-axisymmetric morphology with arbitrary symmetry in a pure substance is considered with the interfacial effect of anisotropy and in the absence of convective flow. A stable mode of thermal dendritic growth with the n-fold crystal symmetry is formulated using the solvability theory. A complete set of nonlinear equations, consisting of the undercooling balance condition and the selection criterion, is derived. Theoretical predictions are compared with phase field modeling data in two and three dimensional geometry obtained for ice dendrites growing in pure water.