Abstract. In this paper we focus on the application of the constructal theory in predicting the dendritic solid structure. First we analyse the marginal stability criterion from the perspective of the constructal principle. Having as a guiding principle the constructal law we have shown that among the whole range of possible dendrite tip radiuses predicted by the stability analysis the dendrite tip will choose the smallest one, that is a radius equal with the smallest perturbation wavelength leading to instabilities. We identify as well the existence of a competition between the diffusion controlled growth and the dendritic growth. Second, we develop a model for the secondary arm spacing. We identify a competition between the lateral diffusion controlled growth of a needle and the dendritic growth of lateral secondary arms. By analysing this competition we are able to characterize the sidebranching mechanism and to finally compute the secondary arm spacing. The result is in good agreement with the experimental results. Finally, the primary arm spacing is analysed from the perspective of the constructal law. The constructal law predicts that the only way the columnar tips can optimize the solidification process is to minimize the spacing between two adjacent tips, namely λ₁. By quantifying the two mechanisms responsible for the selection of λ₁, the dendrite division and the dendrite overgrown mechanisms, we were finally able to obtain a model for the primary arm spacing. This model is also validated against various experimental data.

Print publication: Issue 24 (21 December 2006)
Received 16 July 2006, in final form 23 October 2006
Published 1 December 2006