A drop on a floating sheet: boundary conditions, topography and formation of wrinkles

The radial wrinkle pattern generated by a liquid drop on a floating elastic sheet has stimulated a number of advances in the understanding of wrinkle patterns in ultrathin sheets. A puzzle associated with the spatial extent of this simple, highly symmetric pattern has only recently been resolved, but several other basic aspects of the pattern remain unexplained. Our previous experiments have studied the extent and wavenumber of the pattern via 2-dimensional images. In the current study we report a full 3-dimensional topographical characterization of this archetypical problem, and of its counterpart, a bubble beneath a sheet. In addition to measurements of the wrinkle amplitude, these studies reveal the elastic deformation and the resulting wrinkle pattern beneath the drop. We also show that the flat boundary condition at the contact line of the drop is achieved by a cascade of wrinkles on both sides of the boundary. Finally, we report studies by high-speed video imaging of the propagation of the wrinkle pattern, with the unexpected result that the wavenumber is established early in the development of the pattern, before it has reached its full spatial extent.