Selected mode of dendritic growth with n-fold symmetry in the presence of a forced flow

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

Received: 26 April 2017
Accepted: 15 August 2017

Abstract

The effect of n-fold crystal symmetry is investigated for a two-dimensional stable dendritic growth in the presence of a forced convective flow. We consider dendritic growth in a one-component undercooled liquid. The theory is developed for the parabolic solid-liquid surface of dendrite growing at arbitrary growth Péclet numbers keeping in mind small anisotropies of surface energy and growth kinetics. The selection criterion determining the stable growth velocity of the dendritic tip and its stable tip diameter is found on the basis of solvability analysis. The obtained criterion includes previously developed theories of thermally and kinetically controlled dendritic growth with convection for the case of four-fold crystal symmetry. The obtained nonlinear system of equations (representing the selection criterion and undercooling balance) for the determination of dendrite tip velocity and dendrite tip diameter is analytically solved in a parametric form. These exact solutions clearly demonstrate a transition between thermally and kinetically controlled growth regimes. In addition, we show that the dendrites with larger crystal symmetry grow faster than those with smaller symmetry.