The fluid trampoline: droplets bouncing on a soap film Citation

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We present the results of a combined experimental and theoretical investigation of droplets falling onto a horizontal soap film. Both static and vertically vibrated soap films are considered. In the static case, a variety of behaviours were observed, including bouncing, crossing and partial coalescence. A quasi-static description of the soap film shape yields a force–displacement relation that provides excellent agreement with experiment, and allows us to model the film as a nonlinear spring. This approach yields an accurate criterion for the transition between droplet bouncing and crossing. Moreover, it allows us to rationalize the observed constancy of the contact time and scaling for the coefficient of restitution in the bouncing states. On the vibrating film, a variety of bouncing behaviours were observed, including simple and complex periodic states, multi-periodicity and chaos. A simple theoretical model is developed that captures the essential physics of the bouncing process, reproducing all observed bouncing states. The model enables us to rationalize the observed coexistence of multiple periodic bouncing states by considering the dependence of the energy transferred to the droplet on the phase of impact. Quantitative agreement between model and experiment is deduced for simple periodic modes, and qualitative agreement for more complex periodic and chaotic bouncing states. Analytical solutions are deduced in the limit of weak forcing and dissipation, yielding insight into the contact time and periodicity of the bouncing states. 1. Introduction A remarkable series of experiments has recently been conducted by Couder and co-workers. First, they demonstrated that a droplet is able to bounce indefinitely without coalescing on the surface of a vertically vibrated liquid bath (Couder et al. 2005a). In certain regimes, a bouncing droplet moves laterally through its interaction with its own wave field (Couder et al. 2005b;Protì ere et al. 2005;Protì ere, Boudaoud & Couder 2006). As the droplet thus walks across the surface, its wave field probes the surroundings, detecting solid obstacles that may be used to guide the droplets. When many such walkers are present, they may interact to form stable orbits or lattice structures (Lieber et al. 2007). More surprising yet, when a droplet passes