Numerical Study of the Cahn-Hilliard Equation in Three Dimensions

Abstract

We present results of the first numerical study of the Cahn-Hilliard equation in three dimensions. We study the asymptotic time dependence of the characteristic domain size $R(t)$, as well as the scaling of the pair correlation function and the structure factor. The results indicate that dynamical scaling holds at sufficiently late times and that the data for $R(t)$ are consistent with a Lifshitz-Slyozov growth law $R(t)\ensuremath{\sim}{t}^{\frac{1}{3}}$.