Free surface pumping via an undulating carpet

Undulating boundaries that pass traveling waves is one popular strategy nature has adopted to transport liquids across different length scales. While our understanding of symmetry breaking due to non-reciprocal wave motion has greatly extended in the last few decades, relatively little is known about the effects of having a fluid-fluid interface near the undulating boundary. Inspired by unusual feeding strategies of apple snails near a free surface, we demonstrate large-scale pumping of a thin liquid near the liquid-air interface driven by a two-dimensional undulating boundary. The presence of the free surface eliminates the imposition of the pressure build-up as the usual pumping strategy, and the shape of the free surface becomes part of the unknown. Our experiments with a simple robotic undulator show that the pumping rate has a counterintuitive dependence on the wave speed of surface undulations. We rationalize the experimental observations with a 2D thin-film mathematical model that reproduces key features of the experiments.