Regensburg 2013 – scientific programme

Parts | Days | Selection | Search | Updates | Downloads | Help

DY: Fachverband Dynamik und Statistische Physik

DY 16: Pattern Formation

DY 16.3: Talk

Wednesday, March 13, 2013, 10:15–10:30, H46

Selection theory of free crystal growth in convective systems — •Martin von Kurnatowski and Klaus Kassner — Otto-von-Guericke-University Magdeburg, Department of Theoretical Physics, Universitätsplatz 2, 39106 Magdeburg

The liquid-solid-interface of a crystal growing freely in its undercooled melt forms dendritic patterns. Understanding these patterns is crucial for controlling the material properties of solid substances such as metals. In the simplest models, the growth is governed by heat transport. Neglecting surface tension, one obtains a so-called Stefan problem having a parabolic solution. This zeroth-order problem does not lead to the selection of values for important system parameters that are experimentally fully determined. Capillary effects at the two-phase boundary constitute a singular perturbation selecting the length scale of the pattern.

Solution methods are usually based on the use of Green’s functions [1]. However, with convection this method is normally not applicable due to the nonlinearity of the field equations. Density changes at the phase transition are a possible cause for convection. A potential flow and a Stokes flow are two simple approximations for the flow velocity field. This contribution focuses on the latter but more extended results have also been obtained. To approach the nonlinearities analytically, we use asymptotic decomposition as a powerful extension to the standard method. It yields an eigenvalue equation to be solved numerically.
[1] E. A. Brener and V. I. Melnikov, Adv. Phys. 40, p. 53-97 (1991)