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

The Faraday instability has been extensively studied in bounded containers but only recently has research on this phenomenon in flexible domains been conducted. Here, we study floating liquid droplets with Faraday waves excited on their surface, which undergo a slow time evolution toward a stable noncircular shape. We develop a theoretical model for the evolution of the boundary of the droplet, thus allowing us to simulate its full transient motion toward steady state. By changing the forcing frequency and amplitude of our system, we observe a variety of stable droplet shapes. We experimentally measure the geometrical properties of these droplets and conditions under which different shapes are stable, which match our theoretical predictions well. Interesting transient behavior such as hysteresis is also discussed, where the final droplet shape depends on its previous shape. Finally, we touch upon droplets that do not reach a steady state shape, instead oscillating periodically in time or rotating at a constant angular velocity.