Faraday instability in floating drops out of equilibrium: Motion and self-propulsion from wave radiation stress

• We study the Faraday instability in floating drops out of equilibrium.
• Non-equilibrium occurs when wave radiation pressure exceeds capillarity.
• We model drop self-propulsion via the wave radiation stress.

Instabilities in fluids are usually studied in domains with fixed boundaries or free to grow in space. In the Faraday instability, a liquid undergoing vertical oscillation is unstable to surface waves. Recently, a novel situation has been explored in which Faraday waves are triggered in floating drops that behave as deformable domains. A mutual adaptation between wave pattern and drop shape occurs, that leads either to equilibrium or out-of-equilibrium behaviors depending on the magnitude of wave radiation pressure over capillary pressure at the drop boundary. Here we investigate experimentally the out-of-equilibrium system, in which the radiation pressure exceeds the capillary response. The drop is abruptly deformed by the waves and possibly splits in fragments that have complex dynamics. These dynamics are explained by the radiation stress exerted by Faraday waves at boundaries. In particular, a simple model is able to predict the limit speed of self-propulsion of croissant-shaped drops.