Spreading and retraction as a function of drop size

We simulate the spreading and retraction of a two-dimensional drop over a thin film in the small slope limit for drop heights ranging from a few nanometers to hundreds of nanometers. Drop motion is initiated by an impulsive change in surface wettability expressed in terms of disjoining pressure. Owing to the presence of the film, these simulations require no closure condition at the 'apparent' contact line. Rather, we study the relationships that emerge between the apparent contact line velocity and dynamic contact angles. The disjoining pressure that we study includes stabilizing van der Waals interactions and destabilizing acid-base interactions. Changes in wetting conditions that promote spreading place the thin film surrounding the drop out of equilibrium; the drop spreads as the film thickens to its new equilibrium value. Changes in wetting conditions that promote retraction can either place the thin film out of equilibrium in a stable regime, or they can place the thin film in a spinodally unstable regime. We study drop rearrangement as a function of drop scale for these three cases. Small drops, with heights on the same order as the film thickness, are strongly influenced by disjoining pressure gradients everywhere beneath them. Larger drops, with heights at least an order of magnitude greater than the film thickness, have disjoining pressure gradients isolated near the apparent contact line at all times. For these larger drops, after initial dynamics, macroscopic behavior is recovered; drops move in agreement with Tanner's law. However, dynamics associated with the thin film can play a leading role in the ensuing drop response even after Tanner's law emerges. In particular, when drops retract over spinodally unstable films, retraction occurs in three regimes. Rims form near the apparent contact line over time scales comparable to the time scale for the instability. The rim geometry can be characterized in terms of spinodal film thicknesses. The rims then propagate toward the bulk drop. Finally, the rim disappears and the drop assumes a cap-like shape. Tanner's law is obeyed during the latter two regimes. Attempts to simulate drop rearrangements disregarding the thin film dynamics before Tanner's law manifests can lead to erroneous outcomes, as shown in simulations of drop retraction on a solid surface with an imposed Navier slip length.