Selection theory of free dendritic growth in a potential flow
Martin von Kurnatowski, Thomas Grillenbeck, Klaus Kassner
TL;DR
This paper extends the Kruskal-Segur approach with Zauderer decomposition to analyze free dendritic growth in potential flow, enabling more rigorous solutions to complex nonlinear growth problems.
Contribution
It introduces a novel combination of methods to improve the mathematical analysis of dendritic growth in fluid flows, surpassing previous approximations.
Findings
Method successfully applied to 2D crystal growth in potential flow
Achieves more rigorous solutions than earlier simplified models
Extends analytical capabilities to complex nonlinear growth problems
Abstract
The Kruskal-Segur approach to selection theory in diffusion-limited or Laplacian growth is extended via combination with the Zauderer decomposition scheme. This way nonlinear bulk equations become tractable. To demonstrate the method, we apply it to two-dimensional crystal growth in a potential flow. We omit the simplifying approximations used in a preliminary calculation for the same system [T. Fischaleck, K. Kassner, EPL 81, 54004 (2008)], thus exhibiting the capability of the method to extend mathematical rigor to more complex problems than hitherto accessible.
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