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While important research has been focused on developing surfaces that do not wet, some textures with high-wetting resistance are familiar in other applications in which the opposite is needed. A multivalued surface, common in most fabrics or meshes, allows the invading gas-liquid interface to support relatively high imposed pressures and plays a key role in producing topographic elements that avoid wetting. Here we study experimentally and theoretically the critical pressure needed to move a liquid through a network of pores and show that, for small aperture size, wetting and leaking are typical first-order transitions, with a singular behavior at the omniphobic/omniphilic limit (θc = π/2).

Natural surfaces excel in self-renewal and preventing bio-fouling, while synthetic materials placed in contact with complex fluids quickly foul1,2. We present a novel biophysics-inspired mechanism3,4 for surface renewal using actuating surface topography, generated by wrinkling. We calculate a critical surface curvature, given by an intrinsic characteristic length scale of the fouling layer that accounts for its effective flexural or bending stiffness and adhesion energy, beyond which surface renewal occurs. The effective bending stiffness includes the elasticity and thickness of the fouling patch, but also the boundary layer depth of the imposed wrinkled topography. The analytical scaling laws are validated using finite-element simulations and physical experiments. Our data span over five orders of magnitude in critical curvatures and are well normalized by the analytically calculated scaling. Moreover, our numerics suggests an energy-release mechanism whereby stored elastic energy in the fouling layer drives surface renewal. The strategy is broadly applicable to any surface with tunable topography and fouling layers with elastic response.

The buckling and wrinkling of thin films has recently seen a surge of interest among physicists, biologists, mathematicians, and engineers. This activity has been triggered by the growing interest in developing technologies at ever-decreasing scales and the resulting necessity to control the mechanics of tiny structures, as well as by the realization that morphogenetic processes, such as the tissue-shaping instabilities occurring in animal epithelia or plant leaves, often emerge from mechanical instabilities of cell sheets. Although the most basic buckling instability of uniaxially compressed plates was understood by Euler more than two centuries ago, recent experiments on nanometrically thin (ultrathin) films have shown significant deviations from predictions of standard buckling theory. Motivated by this puzzle, we introduce here a theoretical model that allows for a systematic analysis of wrinkling in sheets far from their instability threshold. We focus on the simplest extension of Euler buckling that exhibits wrinkles of finite length—a sheet under axisymmetric tensile loads. The first study of this geometry, which is attributed to Lamé, allows us to construct a phase diagram that demonstrates the dramatic variation of wrinkling patterns from near-threshold to far-from-threshold conditions. Theoretical arguments and comparison to experiments show that the thinner the sheet is, the smaller is the compressive load above which the far-from-threshold regime emerges. This observation emphasizes the relevance of our analysis for nanomechanics applications.

We derive a set of non-linear amplitude equations that predicts the presence of nonlinear patterns in a vertically oscillated one dimensional viscous fluid layer.

A piece of paper coiled up in a tube hugs the wall in order to minimize its elastic energy. However, a moment's observation shows that the paper fails to make complete contact near its ends. Here, we show that the detached region in the inner part of the coil touches down the tube wall in an angle that is independent of the system size, thickness and stiffness of the surface. This angle is universal for any coiled sheet whose unstressed state is initially flat. Our results show how the shape and stress distribution for this detached region define the geometry and mechanical equilibrium for the rest of the sheet. In particular, we find scaling relations to describe the structure of the outer part of the coil, in contact with the tube wall, as a function of the number of times the sheet is coiled, N .

We derive an exact equation which is nonlocal in time for the linear evolution of the surface of a viscous fluid, and show that this equation becomes local and of second order in an interesting limit. We use our local equation to study Faraday's instability in a strongly dissipative regime and find a new scenario which is the analog of the Rayleigh-Taylor instability. Analytic and numerical calculations are presented for the threshold of the forcing and for the most unstable mode with impressive agreement with experiments and numerical work on the exact Navier-Stokes equations.

The wrinkled geometry of thin films is known to vary appreciably as the applied stresses exceed their buckling threshold. Here we derive and analyze a minimal, nonperturbative set of equations that captures the continuous evolution of radial wrinkles in the simplest axisymmetric geometry from threshold to the far-from-threshold limit, where the compressive stress collapses. This description of the growth of wrinkles is different from the traditional post-buckling approach and is expected to be valid for highly bendable sheets. Numerical analysis of our model predicts two surprising results. First, the number of wrinkles scales anomalously with the thickness of the sheet and the exerted load, in apparent contradiction with previous predictions. Second, there exists an invariant quantity that characterizes the mutual variation of the amplitude and number of wrinkles from threshold to the far-from-threshold regime.

The wrinkling of thin elastic sheets occurs over a range of length scales, from the fine scale patterns in substrates on which cells crawl to the coarse wrinkles seen in clothes. Motivated by the wrinkling of a stretched elastic sheet, we deduce a general theory of wrinkling, valid far from the onset of the instability, using elementary geometry and the physics of bending and stretching. Our main result is a set of simple scaling laws; the wavelength of the wrinkles lambda approximately K(-1/4), where K is the stiffness due to an "elastic substrate" effect with a multitude of origins, and the amplitude of the wrinkle A approximately lambda. These could form the basis of a highly sensitive quantitative wrinkling assay for the mechanical characterization of thin solid membranes.

We consider a layer of viscous incompressible fluid on a plate which can be vibrated vertically and we derive an equation which is non local in time for the linear evolution of the deformation of the surface in contact with the atmosphere. The equation is used to study the decay of a deformation of the surface. We characterize an interesting regime of high viscosity where the equation becomes local and we use it to study Faraday's instability. A new scenario is found for low frequency of the forcing. Key words : viscous fluid, Faraday's instability, lubrication regime., Cerda Enrique, Tirapegui Enrique. On the linear evolution of the surface of a viscous incompressible fluid. In: Bulletin de la Classe des sciences, tome 7, n°7-12, 1996. pp. 301-320.

Controlling the fracture propagation in a film is an important element in the design of better packaging seals that must resist handling and yet provide a tearing mechanism for easy opening. Here we show that under simple initial setup conditions a divergent tear can be obtained that follows the path of a logarithmic spiral over two decades in length scale. We study the general rules leading to the “spiral growth” of a tear and connect its geometry to the specific material properties of the film.

A thin fibre or sheet curled into a circular container has a detached region whose shape and force ratios are independent of material properties and container radius. We compute this shape and compare it with experiments. The discrete forces acting at either end of the detached region have a ratio that depends only on the length of the fibre or sheet relative to the circle radius. We calculate this force ratio in three regimes of circle radius.