Suzie Protière

Dynamical phenomena: Walking and orbiting droplets

Small drops can bounce indefinitely on a bath of the same liquid if the container is oscillated vertically at a sufficiently high acceleration. Here we show that bouncing droplets can be made to ‘walk’ at constant horizontal velocity on the liquid surface by increasing this acceleration. This transition yields a new type of localized state with particle–wave duality: surface capillary waves emanate from a bouncing drop, which self-propels by interaction with its own wave and becomes a walker. When two walkers come close, they interact through their waves and this ‘collision’ may cause the two walkers to orbit around each other.

Wetting of flexible fibre arrays

Fibrous media are functional and versatile materials, as demonstrated by their ubiquity both in natural systems such as feathers and adhesive pads and in engineered systems from nanotextured surfaces to textile products, where they offer benefits in filtration, insulation, wetting and colouring. The elasticity and high aspect ratios of the fibres allow deformation under capillary forces, which cause mechanical damage, matting self-assembly or colour changes, with many industrial and ecological consequences. Attempts to understand these systems have mostly focused on the wetting of rigid fibres or on elastocapillary effects in planar geometries and on a fibre brush withdrawn from an infinite bath. Here we consider the frequently encountered case of a liquid drop deposited on a flexible fibre array and show that flexibility, fibre geometry and drop volume are the crucial parameters that are necessary to understand the various observations referred to above. We identify the conditions required for a drop to remain compact with minimal spreading or to cause a pair of elastic fibres to coalesce. We find that there is a critical volume of liquid, and, hence, a critical drop size, above which this coalescence does not occur. We also identify a drop size that maximizes liquid capture. For both wetting and deformation of the substrates, we present rules that are deduced from the geometric and material properties of the fibres and the volume of the drop. These ideas are applicable to a wide range of fibrous materials, as we illustrate with examples for feathers, beetle tarsi, sprays and microfabricated systems.

Particle–wave association on a fluid interface

A small liquid drop can be kept bouncing on the surface of a bath of the same fluid for an unlimited time when this substrate oscillates vertically. With fluids of low viscosity the repeated collisions generate a surface wave at the bouncing frequency. The various dynamical regimes of the association of the drop with its wave are investigated first. The drop, usually a simple ‘bouncer’, undergoes a drift bifurcation when the forcing amplitude is increased. It thus becomes a ‘walker’ propagating at a constant velocity on the interface. This transition occurs just below the Faraday instability threshold, when the drop becomes a local emitter of a parametrically forced wave. A model of the particle–wave interaction accounts for this drift bifurcation. The self-organization of several identical bouncers is also investigated. At low forcing, bouncers form bound states or crystal-like aggregates. At larger forcing, the collisions between walkers reveal that their interaction can be either repulsive or attractive, depending on their distance apart. The attraction leads to the spontaneous formation of orbiting pairs, the possible orbit diameters forming a discrete set. A theoretical model of the non-local interaction resulting from the interference of the waves is given. The nature of the interaction is thus clarified and the various types of self-organization recovered.

Gravity-induced encapsulation of liquids by destabilization of granular rafts

Droplets and bubbles coated by a protective armour of particles find numerous applications in encapsulation, stabilization of emulsions and foams, and flotation techniques. Here we study the role of a body force, such as in flotation, as a means of continuous encapsulation by particles. We use dense particles, which self-assemble into rafts, at oil-water interfaces. We show that these rafts can be spontaneously or controllably destabilized into armoured oil-in-water droplets, which highlights a possible role for common granular materials in environmental remediation. We further present a method for continuous production and discuss the generalization of our approach towards colloidal scales.

Wetting on two parallel fibers: drop to column transitions

While the shape and stability of drops on single cylindrical fibers have received vast attention, there are few studies that consider a drop sitting between two fibers, which is a first step toward understanding the wetting of larger fibrous networks. In this paper, we investigate experimentally the behavior of a finite volume of liquid on two parallel rigid fibers. The liquid wetting the fibers can adopt two distinct equilibrium shapes: a compact approximately hemispherical drop shape or a long liquid column of constant cross-section. These two morphologies depend on the inter-fiber distance, the liquid volume, the fiber radius and the liquid–fiber contact angle. We study the transitions between a drop shape and a column by incrementally varying the inter-fiber distance and find that the transition depends on the global geometry of the system as well as on the volume of liquid. For totally wetting drops, we identify the regions where the drops or columns prevail, and find that there is a region where both morphologies are stable, and the transitions from one state to the other are hysteretic. These switches in morphologies may be used to manipulate or transport liquid at small scales.

Orbital motion of bouncing drops

Usually a drop placed at the surface of the same liquid coalesces within a few tenths of seconds. Here we present an experiment in which this coalescence process is inhibited by vibrating the liquid on which the drop is placed. The drop can then bounce on the surface of the liquid for an unlimited amount of time. In a recent article, the acceleration threshold for which drops of various sizes keep bouncing on the surface was determined. The crucial role of the intermediate air film to prevent the coalescence process was thus demonstrated. For liquids of low viscosity, just below the Faraday instability threshold, the bouncing drop undergoes a drift bifurcation and starts moving in the horizontal plane. Figure 1 shows a drop “walking” across the surface of the liquid at constant velocity. The liquid used is silicon oil of viscosity 20 10−3 Pa s, the forcing frequency is f0 =80 Hz, and the forcing acceleration is m /g 3.9. The picture shows that the drop falls on the slope of the wave it formed at its previous bounce, thus giving the drop its horizontal motion. Also, the formed wave is Doppler shifted: the wavelength is shorter ahead of the walker and longer behind it. The formed wave is periodically altered by the drop’s next bounce. When two walkers are placed at the surface of the liquid, the two drops will interact via their waves. Figures 2 and 3 show the result of an attractive collision of two identical walkers via their waves. The two drops are then orbiting FIG. 1.

Capillary stretching of fibers

We study the interaction of a finite volume of liquid with two parallel thin flexible fibers. A tension along the fibers is imposed and may be varied. We report two morphologies, i.e. two types of wet adhesion: a weak capillary adhesion, where a liquid drop bridges the fibers, and a strong elastocapillary adhesion where the liquid is spread between two collapsed fibers. We show that geometry, capillarity and stretching are the key parameters at play. We describe the collapse and detachment of the fibers as a function of two nondimensional parameters, arising from the geometry of the system and a balance between capillary and stretching energies. In addition, we show that the morphology, thus the capillary adhesion, can be controlled by changing the tension within the fibers.

Wrinkles, folds, and plasticity in granular rafts

We investigate the mechanical response of a compressed monolayer of large and dense particles at a liquid-fluid interface: a granular raft. Upon compression, rafts first wrinkle; then, as the confinement increases, the deformation localizes in a unique fold. This characteristic buckling pattern is usually associated to floating elastic sheets and as a result, particle laden interfaces are often modeled as such. Here, we push this analogy to its limits by comparing the first quantitative measurements of the raft morphology to a theoretical continuous elastic model of the interface. We show that although powerful to describe the wrinkle wavelength, the wrinkle-to-fold transition and the fold shape, this elastic description does not capture the finer details of the experiment. We describe an unpredicted secondary wavelength, a compression discrepancy with the model and a hysteretic behavior during compression cycles, all of which are a signature of the intrinsic discrete and frictional nature of granular rafts. It suggests also that these composite materials exhibit both plastic transition and jamming dynamics.

Sinking a Granular Raft

We report experiments that yield new insights on the behavior of granular rafts at an oil-water interface. We show that these particle aggregates can float or sink depending on dimensionless parameters taking into account the particle densities and size and the densities of the two fluids. We characterize the raft shape and stability and propose a model to predict its shape and maximum length to remain afloat. Finally we find that wrinkles and folds appear along the raft due to compression by its own weight, which can trigger destabilization. These features are characteristics of an elastic instability, which we discuss, including the limitations of our model.

The compression of a heavy floating elastic film

We study the effect of film density on the uniaxial compression of thin elastic films at a liquid-fluid interface. Using a combination of experiments and theory, we show that dense films first wrinkle and then fold as the compression is increased, similarly to what has been reported when the film density is neglected. However, we highlight the changes in the shape of the fold induced by the films own weight and extend the model of Diamant and Witten [Phys. Rev. Lett., 2011, 107, 164302] to understand these changes. In particular, we suggest that it is the weight of the film that breaks the up-down symmetry apparent from previous models, but elusive experimentally. We then compress the film beyond the point of self-contact and observe a new behaviour dependent on the film density: the single fold that forms after wrinkling transitions into a closed loop after self-contact, encapsulating a cylindrical droplet of the upper fluid. The encapsulated drop either causes the loop to bend upward or to sink deeper as the compression is increased, depending on the relative buoyancy of the drop-film combination. We propose a model to qualitatively explain this behaviour. Finally, we discuss the relevance of the different buckling modes predicted in previous theoretical studies and highlight the important role of surface tension in the shape of the fold that is observed from the side-an aspect that is usually neglected in theoretical analyses.