Theoretical and experimental investigation of the shapes formed by floating droplets excited with Faraday waves

When the Faraday instability is induced in floating droplets in a viscous bath, a wave radiation pressure is exerted on the droplet boundary, causing it to evolve until a new equilibrium shape is reached. Different shapes are obtained by varying the forcing amplitude and frequency, though the system is highly hysteretic. We develop a theoretical model for the time evolution of the droplet boundary through the separation of timescales, with a strong agreement between the predicted equilibrium profiles and experimental observations.