Diffusive Evolution of Stable and Metastable Phases I: Local Dynamics of Interfaces

TL;DR

This paper analytically investigates the local dynamics of interfaces in systems with conserved order parameters, revealing how transient flux increases can cause metastable phase growth through interface unbinding.

Contribution

It provides exact solutions and a formalism for understanding interface behavior in the Cahn-Hilliard model, especially under conditions leading to metastable phase growth.

Findings

Exact solutions for specific potentials elucidate interface dynamics.

Transient flux increases can induce metastable phase growth.

Interface unbinding can disrupt normal interface motion.

Abstract

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.