Diffusive evolution of stable and metastable phases. I. Local dynamics of interfaces

We find analytical solutions to the Cahn-Hilliard equation for the dynamics of an interface in a system with a conserved order parameter (model $B)$. We show that, although steady-state solutions of model $B$ are unphysical in the far field, they shed light on the local dynamics of an interface. Exact solutions are given for a particular class of order-parameter potentials and an expandable integral equation is derived for the general case. As well as revealing some generic properties of interfaces moving under condensation or evaporation, the formalism is used to investigate two distinct modes of interface propagation in systems with a metastable potential well. Given a sufficient transient increase in the flux of material onto a condensation nucleus, the normal motion of the interface can be disrupted by interfacial unbinding, leading to growth of a macroscopic amount of a metastable phase.