Diffusive behavior in walking droplets

Fluid droplets walking on a vibrating fluid bath have been observed to display deterministic diffusion. We present an experimental and theoretical investigation of such droplets. In our experiments a droplet is placed into an annular region on a vibrating fluid bath. The droplet motion becomes increasingly diffusive as the bath vibration is intensified above the Faraday wave threshold. This is also captured in our hydrodynamic – kinematic models, which shows close agreement between theory and experiments. Since the model can be studied at a much higher spatio-temporal resolutions than experiments, we use the model to numerically investigate bifurcations and chaotic dynamics suggested by experiments. Finally, we briefly discuss the possibility of model reduction to mitigate computational costs.