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

TL;DR

This paper analyzes the late-stage coarsening behavior of the Cahn-Hilliard equation with an order-parameter-dependent mobility, revealing a generalized Lifshitz-Slyozov scaling law and explicit domain-size distribution for a specific case.

Contribution

It derives a new scaling law for domain growth with mobility dependence and explicitly determines the domain-size distribution for the case lpha=1.

Findings

Mean domain size grows as t^{1/(3+lpha)}

Domain-size distribution explicitly obtained for lpha=1

Coarsening occurs via subdiffusive transport despite absence of bulk diffusion

Abstract

The coarsening dynamics of the Cahn-Hilliard equation with order-parameter dependent mobility, $\lambda(\phi) \propto (1-\phi^2)^\alpha$, 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 $\alpha>0$, the mean domain size is found to grow as $<R > \propto t^{1/(3+\alpha)}$, due to subdiffusive transport of the order parameter through the majority phase. The domain-size distribution is determined explicitly for the physically relevant case $\alpha = 1$.