Breaking Morphological Universality: Anisotropy in Lifshitz-Slyozov Coarsening

We investigate late-stage phase separation dynamics by extending the classic Lifshitz-Slyozov (LS) theory, which traditionally assumes isotropic surface tension, to the case of an anisotropic surface tension. LS theory provides an exact solution for dilute systems, predicting the characteristic t^1/3 droplet growth law and a universal scaling function for the size distribution; however, previous work has largely assumed isotropic surface tension, leaving open questions about the role of anisotropy. We generalize the LS framework by deriving and utilizing the anisotropic Gibbs-Thomson relation and then solving the Dirichlet problem for the chemical potential using a perturbative approach to first order in anisotropy. Contrary to the assertion made by Lifshitz and Slyozov that anisotropy would not affect the dilute limit dynamics, we obtain a one-parameter family of nonequilibrium drop shapes that depend on the scaled drop size. Furthermore, we provide evidence that the size distribution itself is altered to second order, a modification that occurs even though the characteristic t^1/3 droplet growth law remains unchanged.