Grow or perish: Dynamics of a pendant drop sliding on a thin film

Anyone who has ever painted a ceiling knows that thin coatings can destabilize into drops spontaneously under the action of gravity via the Rayleigh-Taylor instability. Once formed, these pendant drops interact with the thin film on which they lie on, producing interesting non-linear dynamics; they spontaneously move even on perfectly horizontal surfaces. Using experiments and numerical simulations we study the dynamics of such pendant drops on slightly inclined pre-wet substrates. We show that for a given film thickness, both the drop size evolution and its velocity on the substrate are highly sensitive to the inclination angle. For sufficiently large angles ($\sim 1-2$ deg), the drop shrinks and leaves a thicker film in its wake, i.e. a rivulet, while at lower angles the drop grows and depletes the thin film as it moves. Steady motion only occurs at the transition, when the drop neither grows nor shrinks.