Gradient flows ostensibly have dynamics that (1) result from the decrease of energy and (2) do not exhibit oscillations. Neither of these statements is true for limits of singularly perturbed systems, however. This talk illustrates these points in the context of liquid film evolution.

Energy-driven coarsening processes arise as the late-stage dynamics of many problems. Two examples are the spinodal decomposition of binary mixtures and the dewetting of an unstable film of viscous liquid. The first case gives rise to Ostwald ripening, where large particles grow at the expense of smaller ones by exchanging material. Migration of the particles as a result of the ambient mass flux is a slower process and is usually ignored. In contrast, the nearly singular kinetics associated with the hydrodynamics of liquid films makes the role of migration significant. We discuss this phenomenon from both a variational and a perturbation theory point of view.

The effects of gravity or hoop stress can also lead to migration, but for different reasons. Interaction of droplets or fluid ridges is shown to give rise to a system which produces neighbor-neighbor repulsion and oscillatory dynamics.