Pulled fronts in the Cahn–Hilliard equation

Abstract

A possibility of pulling a front by a moving inhomogeneity is considered in the context of the Cahn–Hilliard equation, which is a generic model of nonequilibrium phase-separation processes. The critical (maximum) velocity of the inhomogeneity, at which it is still able to steadily drag the front, is found in an analytical approximation, using both perturbation theory and a quasiparticle description of the front. A case of steep inhomogeneities is studied in detail by means of direct simulations, showing that the analytical prediction for the critical velocity is in very good agreement with numerical results for small and moderate values of the inhomogeneity's strength. If the driving velocity exceeds the critical value, the kink is eventually destroyed. If the perturbation is strong, the simulations show that the actual critical velocity is larger than a formally extended analytical value, i.e., the kink turns out to be more robust than it is expected from the perturbative results.