Computational studies of coarsening rates for the Cahn-Hilliard equation with phase-dependent diffusion mobility

We study computationally coarsening rates of the Cahn-Hilliard equation with a smooth double-well potential, and with phase-dependent diffusion mobilities. The latter is a feature of many materials systems and makes accurate numerical simulations challenging. Our numerical simulations confirm earlier theoretical predictions on the coarsening dynamics based on asymptotic analysis. We demonstrate that the numerical solutions are consistent with the physical Gibbs-Thomson effect, even if the mobility is degenerate in one or both phases. For the two-sided degenerate mobility, we report computational results showing that the coarsening rate is on the order of l∼ct1/4, independent of the volume fraction of each phase. For the one-sided degenerate mobility, that is non-degenerate in the positive phase but degenerate in the negative phase, we illustrate that the coarsening rate depends on the volume fraction of the positive phase. For large positive volume fractions, the coarsening rate is on the order of l∼ct1/3 and for small positive volume fractions, the coarsening rate becomes l∼ct1/4.