Exact Solutions for Anisotropic Coarsening in the Dilute Limit

We study the influence of anisotropy on coarsening dynamics via two dilute coarsening models: Lifshitz-Slyozov theory for locally conserved order parameter dynamics, and Wagner theory for the globally conserved analog. We adopt a perturbative approach to analyze the effect of surface tension anisotropy on drop shapes and the scaled drop size distribution. In both models we find that coarsening solutions exhibit growth laws that are unchanged from the isotropic theories, $L\sim t^{1/3}$ and $L\sim t^{1/2}$ respectively, and drop shapes that are in general nonspherical and non-Wulffian. We also determine that the drop size distribution varies from the isotropic case.