Gravito-capillary pinning of pendant droplets under wet uneven surfaces

Pendant drops spontaneously appear on the underside of wet surfaces through the Rayleigh-Taylor instability. These droplets have no contact line, they are connected to a thin liquid film with which they exchange liquid and are thus mobile: any perturbation will set them in motion. Here, using experiments, numerical simulations, and theory I show that pendant drops sliding under a slightly tilted wet substrate can pin on topographic defects, despite their lack of contact line. Instead, this pinning force has a gravito-capillary origin: liquid has to moves up or down and the interface has to deforms for the drop the pass the defect. I propose a semi-analytical model for arbitrary substrate topographies that matches the pinning force observed experimentally and numerically, without any fitting parameter. I finally demonstrate how to harness this pinning force to guide pendant drops on complex paths.