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We find analytical solutions to the Cahn-Hilliard equation for the dynamicsof an interface in a system with a conserved order parameter (Model B). We showthat, although steady-state solutions of Model B are unphysical in thefar-field, they shed light on the local dynamics of an interface. Exactsolutions are given for a particular class of order-parameter potentials, andan expandable integral equation is derived for the general case. As well asrevealing some generic properties of interfaces moving under condensation orevaporation, the formalism is used to investigate two distinct modes ofinterface propagation in systems with a metastable potential well. Given asufficient transient increase in the flux of material onto a condensationnucleus, the normal motion of the interface can be disrupted by interfacialunbinding, leading to growth of a macroscopic amount of a metastable phase.Comment: 23 pages, Latex, eps

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