Dilute Limit Coarsening with an Anisotropic Surface Tension

TL;DR

This paper studies how weak anisotropic surface tension affects late-stage dilute phase separation, showing that while growth laws remain, drop shapes and size distributions deviate from isotropic predictions, breaking morphological universality.

Contribution

It provides a perturbative analysis of anisotropic effects on coarsening, explicitly deriving nonequilibrium drop shapes and modified size distributions.

Findings

Drop shapes depend on scaled size and deviate from equilibrium shapes.

Growth law remains as t^{1/3} despite anisotropy.

Drop size distribution is altered at second order in anisotropy.

Abstract

We investigate the impact of an anisotropic surface tension on the late-stage dilute phase separation dynamics, revisiting the seminal Lifshitz-Slyozov (LS) theory, which traditionally relies on the assumption of isotropic surface tension. Using a perturbative treatment for weak anisotropy, we demonstrate that although the characteristic $t^{1/3}$ drop growth law remains unchanged, the anisotropy causes a significant breakdown of morphological universality. Specifically, we calculate explicitly a one-parameter family of nonequilibrium drop shapes that depend on the scaled drop size. These shapes are close to the equilibrium Wulff shape, but the smaller drops are more spherical and the larger drops have an enhanced anisotropy in comparison to the Wulff shape. We also demonstrate that the the drop size distribution is modified from the isotropic LS distribution at second order in the anisotropy strength.