Diffusion-limited solidification with anisotropy and sidebranching
Dendritic solidification emerges from diffusion-limited growth with a solid-liquid interface governed by the Gibbs-Thomson condition: T_interface = T_melt(1 − d₀κ) where d₀ is the capillary length and κ is local curvature. Anisotropy selects the growth direction (6-fold for ice), and the Mullins-Sekerka instability amplifies sidebranches. Ivantsov's solution gives tip velocity V ~ Δ² (undercooling squared).