a1 Group for Research and Applications in Statistical Physics, Department of Physics, University of Liege, 4000 Liege, Belgium
a2 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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.
(Received March 08 2008)
(Revised December 04 2008)