Lifshitz-Slyozov scaling for late-stage coarsening with an order-parameter-dependent mobility.

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 $ \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 $\alpha = 1$.