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Wetting of carbon surfaces is one of the most widespread, yet poorly understood, physical phenomena. Control over wetting properties underpins the operation of aqueous energy-storage devices and carbon-based filtration systems. Electrowetting, the variation in the contact angle with an applied potential, is the most straightforward way of introducing control over wetting. Here, we study electrowetting directly on graphitic surfaces with the use of aqueous electrolytes to show that reversible control of wetting can be achieved and quantitatively understood using models of the interfacial capacitance. We manifest that the use of highly concentrated aqueous electrolytes induces a fully symmetric and reversible wetting behavior without degradation of the substrate within the unprecedented potential window of 2.8 V. We demonstrate where the classical "Young-Lippmann" models apply, and break down, and discuss reasons for the latter, establishing relations among the applied bias, the electrolyte concentration, and the resultant contact angle. The approach is extended to electrowetting at the liquid|liquid interface, where a concentrated aqueous electrolyte drives reversibly the electrowetting response of an insulating organic phase with a significantly decreased potential threshold. In summary, this study highlights the beneficial effect of highly concentrated aqueous electrolytes on the electrowettability of carbon surfaces, being directly related to the performance of carbon-based aqueous energy-storage systems and electronic and microfluidic devices.

Everyday experience confirms the tendency of adhesive films to detach from spheroidal regions of rigid substrates -- what is a petty frustration when placing a sticky bandage onto an elbow or knee is a more serious matter in the coating and painting industries. Irrespective of their resistance to bending, a key driver of such phenomena is Gauss' \textit{Theorema Egregium}, which implies that naturally flat sheets cannot conform to doubly-curved surfaces without developing a strain whose magnitude grows sharply with the curved area. Previous attempts to characterize the onset of curvature-induced delamination, and the complex patterns it gives rise to, assumed a dewetting-like mechanism in which the propensity of two materials to form contact through interfacial energy is modified by an elastic energy penalty. We show that this approach may characterize moderately bendable adhesive sheets, but fails qualitatively to describe the curvature-induced delamination of ultrathin films, whose mechanics is governed by their propensity to buckle under minute levels of compression. Combining mechanical and geometrical considerations, we introduce a minimal model for curvature-induced delamination that accounts for two elementary buckling motifs, shallow "rucks" and localized "folds". We predict nontrivial scaling rules for the onset of curvature-induced delamination and various features of the emerging patterns, which compare well with experimental observations. Beyond gaining control on the use of ultrathin adhesives in cutting edge technologies such as stretchable electronics, our analysis is a significant step towards quantifying the multiscale morphological complexity that emerges upon imposing geometrical and mechanical constraints on highly bendable solid objects., File includes supplementary information appendix

Viscous flow in the narrow gap between a rigid plate and a confined elastic solid has been observed to “choke” at high flow rates, due to the deforming solid making contact with the plate and sealing the gap. When the viscous flow is driven by injection of a gas bubble, the advancing meniscus is susceptible to the viscous-fingering instability. By comparing fingering experiments with axisymmetric numerical simulations, we demonstrate that, depending on the width of the fingers, the fingering instability can either promote or suppress choking, i.e., cause the system to choke when an axisymmetric system would not, or vice versa.

The giant Amazonian waterlily (genus Victoria ) produces the largest floating leaves in the plant kingdom. The leaves’ notable vasculature has inspired artists, engineers, and architects for centuries. Despite the aesthetic appeal and scale of this botanical enigma, little is known about the mechanics of these extraordinary leaves. For example, how do these leaves achieve gigantic proportions? We show that the geometric form of the leaf is structurally more efficient than those of other smaller species of waterlily. In particular, the spatially varying thickness and regular branching of the primary veins ensures the structural integrity necessary for extensive coverage of the water surface, enabling optimal light capture despite a relatively low leaf biomass. Leaf gigantism in waterlilies may have been driven by selection pressures favoring a large surface area at an economical material cost, for outcompeting other plants in fast-drying ephemeral pools.

The wrinkling of thin elastic objects provides a means of generating regular patterning at small scales in applications ranging from photovoltaics to microfluidic devices. Static wrinkle patterns are known to be governed by an energetic balance between the object's bending stiffness and an effective substrate stiffness, which may originate from a true substrate stiffness or from tension and curvature along the wrinkles. Here we investigate dynamic wrinkling, induced by the impact of a solid sphere onto an ultra-thin polymer sheet floating on water. The vertical deflection of the sheet's centre induced by impact draws material radially inwards, resulting in an azimuthal compression that is relieved by the wrinkling of the entire sheet. We show that this wrinkling is truly dynamic, exhibiting features that are qualitatively different to those seen in quasi-static wrinkling experiments. Moreover, we show that the wrinkles coarsen dynamically because of the inhibiting effect of the fluid inertia. This dynamic coarsening can be understood heuristically as the result of a dynamic stiffness, which dominates the static stiffnesses reported thus far, and allows new controls of wrinkle wavelength., Comment: 8 pages, 4 figures. Please see published version for supplementary movies and SI Appendix

The flow of a viscous gravity current over a lubricating layer of fluid is modelled using lubrication theory. We study the case of an axisymmetric current with constant influx which allows for a similarity solution, which depends on three parameters: a non-dimensional influx rate ${\mathcal{Q}}$; a viscosity ratio $m$ between the lower and upper layer fluid; and a relative density difference $\unicode[STIX]{x1D700}$. The limit of equal densities $\unicode[STIX]{x1D700}=0$ is singular, as the interfacial evolution equation changes nature from parabolic to hyperbolic. Theoretical analysis of this limit reveals that a discontinuity, or shock, in the interfacial height forms above a critical viscosity ratio $m_{crit}=3/2$, i.e. for a sufficiently less viscous upper-layer fluid. The physical mechanism for shock formation is described, which is based on advective steepening of the interface between the two fluids and relies on the lack of a contribution to the pressure gradient from the interfacial slope for equal-density fluids. In the limit of small but non-zero density differences, local travelling-wave solutions are found which regularise the singular structure of a potential shock and lead to a constraint on the possible shock heights in the form of an Oleinik entropy condition. Calculation of a simplified time-dependent system reveals the appropriate boundary conditions for the late-time similarity solution, which includes a shock at the nose of the current for $m>3/2$. The numerically calculated similarity solutions compare well to experimental measurements with respect to the predictions of self-similarity, the radial extent and the self-similar top-surface shapes of the current.

Significance Harnessing flow–structure interactions has enabled the development of fluidic analogs of electronic circuit components, e.g., fluidic capacitors that store fluid much like an electrical capacitor stores charge. These soft components function in response to the flow; integrated into microfluidic devices, they remove the need for external actuation, thereby facilitating deployment outside of the laboratory. We describe a fluidic fuse that exploits the flow-induced deformation of a soft elastomer and identify the critical flow rate above which the flow is interrupted. This paves the way for the integration of passive flow limiters into microfluidic devices., After centuries of striving for structural rigidity, engineers and scientists alike are increasingly looking to harness the deformation, buckling, and failure of soft materials for functionality. In fluidic devices, soft deformable components that respond to the flow have the advantage of being passive; they do not require external actuation. Harnessing flow-induced deformation for passive functionality provides a means of developing flow analogs of electronic circuit components such as fluidic diodes and capacitors. The electronic component that has so far been overlooked in the microfluidics literature—the fuse—is a passive safety device that relies on a controlled failure mechanism (melting) to protect a circuit from overcurrent. Here, we describe how a compliant Hele-Shaw cell behaves in a manner analogous to the electrical fuse; above a critical flux, the flow-induced deformation of the cell blocks the outflow, interrupting (choking) the flow. In particular, the pressure distribution within the fluid applies a spatially variant normal force to the soft boundary, which causes nonuniform deformation. As a consequence of lateral confinement and incompressibility of the soft material, this flow-induced elastic deformation manifests as bulging near the cell outflow; bulges that come into contact with the rigid cell roof interrupt the flow. We identify two nondimensional parameters that govern the central deflection and the choking of the cell, respectively. This study therefore provides the mechanical foundations for engineering passive-flow limiters into fluidic devices.

We investigate impact of a sphere onto a floating elastic sheet and the resulting formation and evolution of wrinkles in the sheet. Following impact, we observe a radially propagating wave, beyond which the sheet remains approximately planar but is decorated by a series of radial wrinkles whose wavelength grows in time. We develop a mathematical model to describe these phenomena by exploiting the asymptotic limit in which the bending stiffness is small compared to stresses in the sheet. The results of this analysis show that, at a time $t$ after impact, the transverse wave is located at a radial distance $r\sim t^{1/2}$ from the impactor, in contrast to the classic $r\sim t^{2/3}$ scaling observed for capillary--inertia ripples produced by dropping a stone into a pond. We describe the shape of this wave, starting from the simplest case of a point impactor, but subsequently addressing a finite-radius spherical impactor, contrasting this case with the classic Wagner theory of impact. We show also that the coarsening of wrinkles in the flat portion of the sheet is controlled by the inertia of the underlying liquid: short-wavelength, small-amplitude wrinkles form at early times since they accommodate the geometrically-imposed compression without significantly displacing the underlying liquid. As time progresses, the liquid accelerates and the wrinkles grow larger and coarsen. We explain this coarsening quantitatively using numerical simulations and scaling arguments, and we compare our predictions with experimental data., 30 pages, 9 figures. Small edits toaccepted version

From human tissue to fruits, many soft materials are coated by a thin layer of a stiffer material. While the primary role of such a coating is often to protect the softer material, the thin, stiff coating also has an important effect on the mechanical behaviour of the composite material, making it appear significantly stiffer than the underlying material. We study this cloaking effect of a coating for the particular case of indentation tests, which measure the 'firmness' of the composite solid: we use a combination of theory and experiment to characterize the firmness quantitatively. We find that the indenter size plays a key role in determining the effectiveness of cloaking: small indenters feel a mixture of the material properties of the coating and of the substrate, while large indenters sense largely the unadulterated substrate.

Dynamic buckling may occur when a load is rapidly applied to, or removed from, an elastic object at rest. In contrast to its static counterpart, dynamic buckling offers a wide range of accessible patterns depending on the parameters of the system and the dynamics of the load. To study these effects, we consider experimentally the dynamics of an elastic ring in a soap film when part of the film is suddenly removed. The resulting change in tension applied to the ring creates a range of interesting patterns that cannot be easily accessed in static experiments. Depending on the aspect ratio of the ring's cross section, high-mode buckling patterns are found in the plane of the remaining soap film or out of the plane. Paradoxically, while inertia is required to observe these non-trivial modes, the selected pattern does not depend on inertia itself. The evolution of this pattern beyond the initial instability is studied experimentally and explained through theoretical arguments linking dynamics to pattern selection and mode growth. We also explore the influence of dynamic loading and show numerically that by imposing a rate of loading that competes with the growth rate of instability, the observed pattern can be selected and controlled., 6 pages, 5 figures

© 2018 Cambridge University Press. The two-dimensional dynamics of a thin film of viscous fluid spreading between a permeable horizontal plate and an overlying thin elastic sheet is explored. We use a lubrication model to describe the balance between the elastic stress, the hydrostatic pressure gradient and the viscous resistance of the flow, as fluid spreads laterally from a source and simultaneously drains through the plate. A family of asymptotic solutions are described in which the flow is dominated by either the hydrostatic pressure gradient or the elastic stress associated with the deformation of the sheet. In these solutions, although the deformation of the sheet above the porous plate arises from the fluid flow below the sheet, the fluid typically separates from the sheet a short distance upstream of the full extent of the draining zone, with the region of flow being driven purely by the hydrostatic pressure gradient. As a result, an air gap develops below the sheet up to the point where it touches back down onto the plate. With a very light or stiff elastic sheet, this touchdown point may extend far beyond the fluid draining zone, but otherwise it is similar to the extent of the draining zone.

We show how anisotropic, grooved features facilitate the trapping and directed transport of droplets on lubricated, liquid-shedding surfaces. Capillary action pins droplets to topographic surface features, enabling transport along the feature while inhibiting motion across (or detachment from) the feature. We demonstrate the robustness of this capillary-based mechanism for directed droplet transport on slippery surfaces by combining experiments on synthetic, lubricant-infused surfaces with observations on the natural trapping surface of a carnivorous pitcher plant. Controlling liquid navigation on synthetic surfaces promises to unlock significant potential in droplet-based technologies. Our observations also offer novel insight into the evolution of the Nepenthes pitcher plant, indicating that the ‘pitfall’ trapping mechanism is enhanced by the lubricant-infused, macroscopic grooves on the slippery peristome surface, which guide prey into the trap in a way that is more tightly controlled than previously considered.

The preference of thin flat sheets to bend rather than stretch, combined with results from Geometry, mean that changes in a thin sheet's Gaussian curvature are prohibitively expensive. As a result, an imposed curvature in one principal direction inhibits bending in the other: so-called curvature-induced rigidity. Here, we study the buckling behaviour of a rectangular strip of finite thickness held horizontally in a gravitational field, but with a transverse curvature imposed at one end. The finite thickness of the sheet limits the efficacy of curvature-induced rigidity in two ways: (i) finite bending stiffness acts to `uncurve' the sheet, even if this costs some stretching energy, and (ii) for sufficiently long strips, finite weight deforms the strip downwards, releasing some of its gravitational potential energy. We find the critical imposed curvature required to prevent buckling (or, equivalently, to rigidify the strip), determining the dependence on geometrical and constitutive parameters, as well as describing the buckled shape of the strip well beyond the threshold for buckling. In doing so, we quantify the intuitive understanding of curvature-induced rigidity that we gain from curving the crust of a slice of pizza to prevent it from drooping downwards as we eat., To appear in EPL. 12 pages, 8 figures + 11 pages supplementary material

We study the interaction between capillary forces and deformation in the context of a deformable capillary adhesive: a clamped, tense membrane is adhered to a rigid substrate by the surface tension of a liquid droplet. We find that the equilibrium adhesive force for this elastocapillary adhesive is significantly enhanced in comparison to the capillary adhesion between rigid plates. In particular, the equilibrium adhesion force is orders of magnitude greater when the membrane is sufficiently deformed to contact the substrate. From a dynamic perspective, however, the formation of a fluid-filled dimple slows this approach to contact and means that stable attachment is only achieved if adhesion is maintained for a minimum time. The inclusion of a variable membrane tension (as a means of modifying the deformability) gives additional control over the system, allowing new detachment strategies to be explored., Comment: 18 pages, accepted for publication in Phys. Rev. Fluids

We present the results of an experimental and theoretical investigation into the influence of proximate boundaries on the motion of an rotationally oscillating sphere in a viscous fluid. The angular oscillations of the sphere are controlled using the magnetic torque generated by a spatially uniform, oscillatory magnetic field which interacts with a small magnet embedded within the sphere. We study the motion of the sphere in the vicinity of stationary walls that are parallel and perpendicular to the rotational axis of the sphere, and near a second passive sphere that is non-magnetic and free to move. We find that rigid boundaries introduce viscous resistance to motion that acts to suppress the oscillations of the driven sphere. The amount of viscous resistance depends on the orientation of the wall with respect to the axis of rotation of the oscillating sphere. A passive sphere also introduces viscous resistance to motion, but for this case the rotational oscillations of the active sphere establish a standing wave that imparts vorticity to the fluid and induces oscillations of the passive sphere. The standing wave is analogous to the case of an oscillating plate in a viscous fluid; the amplitude of the wave decays exponentially with radial distance from the surface of the oscillating sphere. The standing wave introduces a phase lag between the motion of the active sphere and the response of the passive sphere which increases linearly with separation distance.

The results of an experimental investigation into the motion of linked spheres at low Reynolds number are presented. Small permanent magnets were embedded in the spheres and torques were generated by application of an external magnetic field. Pairs of neutrally buoyant spheres, connected by either glass rods or thin elastic struts, move in a reciprocal orbit when driven by an oscillatory field. An array of three spheres linked by elastic struts buckles in a periodic, non-reciprocal manner. The induced magneto-elastic buckling propels the elemental swimmer and we find that the geometrical asymmetry of the device, introduced by the struts of different lengths, determines the swimming direction. We propose that this novel method of creating movement remotely is suitable for miniaturization.

The localized loading of an elastic sheet floating on a liquid bath occurs at scales from a frog sitting on a lily pad to a volcano supported by the Earth’s tectonic plates. The load is supported by a combination of the stresses within the sheet (which may include applied tensions from, for example, surface tension) and the hydrostatic pressure in the liquid. At the same time, the sheet deforms, and may wrinkle, because of the load. We study this problem in terms of the (relatively weak) applied tension and the indentation depth. For small indentation depths, we find that the force–indentation curve is linear with a stiffness that we characterize in terms of the applied tension and bending stiffness of the sheet. At larger indentations, the force–indentation curve becomes nonlinear and the sheet is subject to a wrinkling instability. We study this wrinkling instability close to the buckling threshold and calculate both the number of wrinkles at onset and the indentation depth at onset, comparing our theoretical results with experiments. Finally, we contrast our results with those previously reported for very thin, highly bendable membranes., Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473 (2206), ISSN:1364-5021, ISSN:1471-2946, ISSN:0080-4630, ISSN:0950-1207

© 2015, Springer-Verlag Berlin Heidelberg.The results of an experimental investigation into a sphere performing torsional oscillations in a Stokes flow are presented. A novel experimental set-up was developed, which enabled the motion of the sphere to be remotely controlled through application of an oscillatory magnetic field. The response of the sphere to the applied field was characterised in terms of the viscous, magnetic and gravitational torques acting on the sphere. A mathematical model of the system was developed, and good agreement was found between experimental, numerical and theoretical results. The flow resulting from the motion of the sphere was measured, and the fluid velocity was found to have an inverse square dependence on radial distance from the sphere. The good agreement between measurements and the analytical solutions for both fluid velocity and angular displacement of the sphere indicates that the flow may be considered Stokesian, thus providing an excellent basis for experimental and theoretical characterisation of hydrodynamic interactions between multiple oscillating spheres at low Reynolds number.

We present the results of an experimental investigation into the effects of a sinusoidal modulation of the rotation rate on the segregation patterns formed in thin drum of granular material. The modulation transforms the base pattern formed under steady conditions by splitting or merging the initial streaks. Specifically, the relation between the frequency of modulation and the rotation rate determines the number of streaks which develop from the base state. The results are in accord with those of Fiedor and Ottino [J. Fluid. Mech. 533, 223 (2005)10.1017/S0022112005003952], and we show that their ideas apply over a wide range of parameter space. Furthermore, we provide evidence that the observed relationship is maintained for filling fractions far from 50% and generalize the result in terms of the geometry of the granular deposit.

Microscale process engineering requires precise control of bubbles and droplets. We investigate geometry-induced control and find that a centered constriction in the cross section of rectangular tubes can lead to new families of steadily propagating bubbles, which localize in the least-constricted regions of the cross section. Tuning the constriction geometry can cause a switchlike transition from centered to localized bubbles at a critical value of the flow rate: a mechanism for flow-rate-driven bubble control. The accompanying large change in bubble volume could be significant for liquid recovery applications. © 2009 American Institute of Physics.

We report the results of an experimental investigation into buckling in elastic and plastic cellular materials under dynamic compression. The buckling instabilities are in the form of a global pattern switch where the square array of circular holes is transformed into a set of orthogonal ellipses. Properties of the instabilities in the elastic and plastic cellular materials are compared and contrasted. The case of the elastic structure is considered as a delayed pitchfork bifurcation. On the other hand, the response of the plastic lattice is complex, and an irreversible global instability is only found above a critical compression rate.

It is becoming increasingly recognized that nonlinear phenomena give an opportunity to provide robust control of the properties of soft metamaterials. A class of elastic instabilities are discussed which arise when a soft cellular material is compressed. The global nature of the induced pattern switch makes it a prime candidate for controlling macroscopic photonic and auxetic properties of the material. We demonstrate the robustness of the phenomena using a range of soft materials and show how the shape of the repeat unit of the periodic pattern can be used to influence the global characteristics of the soft solid.