Intuitively we expect that two volumes of the same liquid brought into contact will merge. But, let a droplet fall onto a vertically oscillating bath of the same fluid and, under the right conditions, it can be made to bounce indefinitely. The dynamics of such 'bouncing' droplets can be complex, displaying multiperiodicity and period-doubling transitions to chaos, as Tristan Gilet and John Bush show (Phys. Rev. Lett. 102, 014501; 2009).

Credit: ISTOCKPHOTO

The study of the curious behaviour of bouncing droplets is not new — it's been around for more than a century — but only recently has the richness of its dynamics been revealed. For instance, a droplet can 'walk', due to the coupling between its bouncing self and the surface wave it generates on the bath; such self-propelled droplets have even shown diffraction and interference phenomena when passing through one or two slits limiting the transverse extent of their wave, prompting analogies to particle interference effects on the quantum scale.

The experiments performed by Gilet and Bush are conceptually simple: a submillimetre droplet of a glycerol−water−soap mixture is released onto a thin film of soap, which is driven by a sinusoidal force field tuned to counteract the energy dissipated on the droplet's impact on the film. From carefully compiled video images, spatiotemporal diagrams reveal a variety of more or less complex periodic bouncing states, as well as chaotic behaviour.

Taking advantage of the fact that the soap film behaves like a linear spring, with an effective spring constant depending on the surface tension, the authors have developed a force-balance equation that describes the experimental findings well. Further numerical analyses in terms of iterative maps and bifurcation diagrams show that the system in fact exhibits all the features of a classic, low-dimensional, chaotic oscillator.