Waveguides for walking droplets

Abstract

When gently placing a droplet onto a vertically vibrated bath, a drop can bounce without coalescing. Upon increasing the forcing acceleration, the droplet is propelled by the wave it generates and becomes a walker with a well defined speed. We investigate the confinement of a walker in different rectangular cavities, used as waveguides for the Faraday waves emitted by successive droplet bounces. By studying the walker velocities, we discover that 1d confinement is optimal for narrow channels of width of $D \simeq 1.5 \lambda_F $. We also propose an analogy with waveguide models based on the observation of the Faraday instability within the channels.