Ostwald Ripening in Thin Film Equations

Fourth order thin film equations can have late stage dynamics that are analogous to the classical Cahn–Hilliard equation. We undertake a systematic asymptotic analysis of a class of equations that describe partial wetting with a stable precursor film introduced by intermolecular interactions. The limit of small precursor film thickness is considered, leading to explicit expressions for the late stage dynamics of droplets. Our main finding is that exchange of mass between droplets characteristic of traditional Ostwald ripening is a subdominant effect over a wide range of kinetic exponents. Instead, droplets migrate in response to variations of the precursor film. Timescales for these processes are computed using an effective medium approximation to the reduced free boundary problem, and dynamic scaling in the reduced system is demonstrated.