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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.

The Young's modulus of polymer thin films was measured from bulk films that are micrometers in thickness down to films having a thickness of ∼6 nm, which is less than the radius of gyration, R g . A simple, noninvasive technique in the same geometry, i.e., the wrinkling of a free-floating film on a water surface with a droplet of water on the surface of the film, was used to determine the modulus over this very large range of film thicknesses. Unlike a solid substrate, there are no in-plane stresses exerted on the film by the underlying liquid substrate except at the boundary of the film. Using recent theoretical developments in the treatment of wrinkling phenomena, we extracted the film modulus from measurements of the wrinkle length. The Young's modulus does not show any systematic change with film thickness, from the thickest bulk films down to films with a thickness of ∼R g for both PS and PMMA, although a slight increase of the Young's modulus was found for the thinnest sub-R g thick PS film.

Predicting the large-amplitude deformations of thin elastic sheets is difficult due to the complications of self-contact, geometric nonlinearities, and a multitude of low-lying energy states. We study a simple two-dimensional setting where an annular polymer sheet floating on an air-water interface is subjected to different tensions on the inner and outer rims. The sheet folds and wrinkles into many distinct morphologies that break axisymmetry. These states can be understood within a recent geometric approach for determining the gross shape of extremely bendable yet inextensible sheets by extremizing an appropriate area functional. Our analysis explains the remarkable feature that the observed buckling transitions between wrinkled and folded shapes are insensitive to the bending rigidity of the sheet.The mechanics of thin sheets at fluid interfaces is a current frontier of elasto-capillary phenomena [1]. In contrast to thicker films that balance the liquid-vapor surface tension γ by generating moderate strain [2][3][4][5] or curvature [6][7][8][9], very thin sheets strongly resist in-plane stretching but are readily curled, wrinkled, or folded under capillary forces [10,11]. In the asymptotic regimewhere B, Y are the bending and stretching moduli and R is a characteristic length, the liquid surface energy becomes the only dominant energy, rendering the elastocapillary problem into a purely geometric area minimization. This nontrivial class of "asymptotic isometries" was demonstrated in the partial wrapping of a liquid drop by an ultrathin circular sheet, where axial symmetry is spontaneously broken [12]. Our understanding of this field is still in its infancy, and many basic questions remain. What classes of gross shapes are possible, and what is the nature of the transitions between them? In general, transitions in microstructure -such as the wrinkle-fold transition in 1D systems [13][14][15] -are driven by competing energies. Are there situations in which microstructure is dictated by geometrical, rather than mechanical constraints?Here we study a simple, near-planar system which exhibits: (i) a variety of gross shapes with continuous and discontinuous transitions between them, (ii) coexistence of distinct microstructural elements, and (iii) a wrinklefold transition governed by geometric constraints. We find that purely geometric considerations determine the gross shape, which may dictate a specific microstructure. If more than one microstructure is possible, then mechanical energies may select one.Experiment.-We work in a geometry first experimentally investigated by Piñeirua et al. [16], but with much thinner films (t ∼ 100 nm) in order to probe the asymp- totic regime of Eq. (1). We spin-coat polystyrene films (E = 3.4 GPa) on glass substrates, and cut into an annular shape with radii R in and R out (Fig. 1a), where 1.2 mm < R in < 5.7 mm, and 6.5 mm < R out < 10.5 mm.The film is floated onto water in a Langmuir trough, and surfactant (perfluorododecanoic acid) is added outside the film. Surfactant concentr...

In order to provide a sound physical basis for the understanding of the formation of desiccation crack networks, an experimental study is presented addressing junction formation. Focusing on junctions, basic features of the network determining the final pattern, provides an elemental approach and imparts conceptual clarity to the rather complicated problem of the evolution of crack patterns. Using coffee-water mixtures a clear distinction between junction formation during nucleation and propagation is achieved. It is shown that for the same drying suspension, one can switch from the well-known symmetric triple junctions that are unique to the nucleation phase to propagation junctions that are purely dictated by the variations of the stress state. In the latter case, one can even manipulate the path of a propagating crack in a deterministic fashion by changing the stress state within the suspension. Clear microscopic evidence is provided for the formation of propagation junctions, and material inhomogeneity is observed to be reflected by a broad distribution of angles, in stark contrast to shrinkage cracks in homogeneous solid films.