Objects that float at the interface between a liquid and a gas interact because of interfacial deformation and the effect of gravity. We highlight the crucial role of buoyancy in this interaction, which, for small particles, prevails over the capillary suction that is often assumed to be the dominant effect. We emphasize this point using a simple classroom demonstration, and then derive the physical conditions leading to mutual attraction or repulsion. We also quantify the force of interaction in some particular instances and present a simple dynamical model of this interaction. The results obtained from this model are then validated by comparison to experimental results for the mutual attraction of two identical spherical particles. We conclude by looking at some of the applications of the effect that can be found in the natural and manmade worlds.I.

PACS. 62.20.Dc -Elasticity, elastic constants. PACS. 68.03.-g -Gas-liquid and vacuum-liquid interfaces. PACS. 46.32.+x -Static buckling and instability.Abstract. -We study the collective behaviour of a close packed monolayer of non-Brownian particles at a fluid-liquid interface. Such a particle raft forms a two-dimensional elastic solid and can support anisotropic stresses and strains, e.g. it buckles in uniaxial compression and cracks in tension. We characterise this solid in terms of a Young's modulus and Poisson ratio derived from simple theoretical considerations and show the validity of these estimates by using an experimental buckling assay to deduce the Young's modulus.Introduction. -Particle covered liquid interfaces are increasingly being exploited in a wide variety of technological and medical applications [1]. Coating a liquid drop with a hydrophobic powder renders the drop non-wetting with the resulting liquid marbles free to roll on rigid surfaces or even float on water [2], a feature that has also proven useful as an adaptation to life on small scales [3]. In a similar vein, it is hoped that by encapsulating the active ingredients of drugs within a monolayer of colloidal particles (thereby forming a colloidosome [4]) more medicines will soon be administered by inhalation, so improving their efficacy. In the latter case, the particle coated interface exists only in the preliminary stages of manufacture, but in neither case have previous investigations been concerned with understanding the properties of particle monolayers at liquid interfaces. In this article, we show that in fact such particle monolayers behave collectively like 2-dimensional elastic solids and further, we characterize the properties of this two-dimensional solid.A variety of solid-like behaviours are observed for monolayers of hydrophobic particles sprinkled densely onto an air-water interface for a wide range (2.5 µm -6 mm) of particle sizes. For example, such a monolayer buckles under sufficient static compressive loading (see figs. 1 (a) and (b)) demonstrating that it can support an anisotropic stress. This stress state can only be supported by a material with a non-zero shear modulus, which is the signature of a solid. Once the compressive stress is removed, the monolayer returns rapidly (∼ O(0.1)s) to the undeformed state, ironing out the wrinkles formed by the buckling. This elasticity is also reminiscent of a solid and is in stark contrast to what is commonly observed in both dry

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.pattern formation | thin-film buckling T hin films are among the ubiquitous examples of flexible structures that buckle under compressive loads. More interestingly, these buckling instabilities usually develop into wrinkled patterns that provide a dramatic display of the applied stress field (1, 2). Wrinkles align perpendicularly to the compression direction, depicting the principal lines of stress and providing a geometric tool for mechanical characterization. Traditional buckling theory is regularly used to understand these patterns in the near-threshold (NT) regime, in which the deformations are small perturbations of the initial flat state. However, it has been known since Wagner (3, 4) that, when the exerted loads are well in excess of those necessary to initiate buckling, the asymptotic state of the plate is very different from the one observed under NT conditions. In this far-from-threshold (FFT) regime, the stress nearly vanishes in the compression direction and wrinkles mark the region where the compressive stress has collapsed.Two complementary approaches have provided some insight into wrinkled sheets under FFT loading conditions. In a 1961 paper (5), Stein and Hedgepeth computed the asymptotic stress field in infinitely thin sheets under compression by assuming a vanishing component of the stress tensor along the compression direction. They further showed how such an asymptotic stress field yields the extent of wrinkles in several basic examples. A s...