Lifshitz-Slyozov Scaling For Late-Stage Coarsening With An Order-Parameter-Dependent Mobility

Abstract

The coarsening dynamics of the Cahn-Hilliard equation with order-parameter dependent mobility, $λ(ϕ) \propto (1-ϕ^2)^α$, is addressed at zero temperature in the Lifshitz-Slyozov limit where the minority phase occupies a vanishingly small volume fraction. Despite the absence of bulk diffusion for $α>0$, the mean domain size is found to grow as $<R > \propto t^{1/(3+α)}$, due to subdiffusive transport of the order parameter through the majority phase. The domain-size distribution is determined explicitly for the physically relevant case $α= 1$.