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Examples of fluid flows driven by undulating boundaries are found in nature across many different length scales. Even though different driving mechanisms have evolved in distinct environments, they perform essentially the same function: directional transport of liquid. Nature-inspired strategies have been adopted in engineered devices to manipulate and direct flow. Here, we demonstrate how an undulating boundary generates large-scale pumping of a thin liquid near the liquid-air interface. Two dimensional traveling waves on the undulator, a canonical strategy to transport fluid at low Reynolds numbers, surprisingly lead to flow rates that depend non-monotonically on the wave speed. Through an asymptotic analysis of the thin-film equations that account for gravity and surface tension, we predict the observed optimal speed that maximizes pumping. Our findings reveal a novel mode of pumping with less energy dissipation near a free surface compared to a rigid boundary.

Polymer networks and biological tissues are often swollen by a solvent, such that their properties emerge from a coupling between swelling and elastic stress. This poroelastic coupling becomes particularly intricate in wetting, adhesion, and creasing, for which sharp folds appear that can even lead to phase separation. Here we resolve the singular nature of poroelastic surface folds and determine the solvent distribution in the vicinity of the fold-tip. Surprisingly, two opposite scenarios emerge depending on the angle of the fold. In obtuse folds such as creases, it is found that the solvent is completely expelled near the crease-tip, according to a nontrivial spatial distribution. For wetting ridges with acute fold angles, the solvent migration is reversed as compared to creasing, and the degree of swelling is maximal at the fold-tip. We discuss how our poroelastic fold-analysis offers an explanation for phase separation, fracture and contact angle hysteresis., Comment: 5 pages, 3 figures, supplementary material attached as anciliary file

In nature, high-speed raindrops often impact and spread on particulate surfaces (e.g., soil, plant leaves with spores or pollen). We study the dynamics of droplet impact on a loosely packed monolayer of particles by combining experimental and mathematical approaches. We find that the presence of mobile particles lowers the critical impact velocity at which the droplet exhibits corona splashing, as the particle area fraction is systematically increased. We rationalize this experimental observation by considering the jamming of frictional particles at the spreading rim. Elucidating the splashing transition of the drop on a particulate bed can lead to a better understanding of soil loss and erosion from falling raindrops.

The compression of soft elastic matter and biological tissue can lead to creasing, an instability where a surface folds sharply into periodic self-contacts. Intriguingly, the unfolding of the surface upon releasing the strain is usually not perfect: small scars remain that serve as nuclei for creases during repeated compressions. Here we present creasing experiments with sticky polymer surfaces, using confocal microscopy, which resolve the contact line region where folding and unfolding occurs. It is found that surface tension induces a second fold, at the edge of the self-contact, which leads to a singular elastic stress and self-similar crease morphologies. However, these profiles exhibit an intrinsic folding-unfolding asymmetry that is caused by contact line pinning, in a way that resembles wetting of liquids on imperfect solids. Contact line pinning is therefore a key element of creasing: it inhibits complete unfolding and gives soft surfaces a folding memory., Comment: 8 pages, 6 figures

A slender thread of elastic hydrogel is susceptible to a surface instability that is reminiscent of the classical Rayleigh-Plateau instability of liquid jets. The final, highly nonlinear states that are observed in experiments arise from a competition between capillarity and large elastic deformations. Combining a slender analysis and fully three-dimensional numerical simulations, we present the phase map of all possible morphologies for an unstable neo-Hookean cylinder subjected to capillary forces. Interestingly, for softer cylinders we find the coexistence of two distinct configurations, namely, cylinders-on-a-string and beads-on-a-string. It is shown that for a given set of parameters, the final pattern is selected via a dynamical evolution. To capture this, we compute the dispersion relation and determine the characteristic wavelength of the dynamically selected profiles. The validity of the "slender" results is confirmed via simulations and these results are consistent with experiments on elastic and viscoelastic threads., Comment: 14 pages, 6 figures

Elastohydrodynamic lubrication, or simply soft lubrication, refers to the motion of deformable objects near a boundary lubricated by a fluid, and is one of the key physical mechanisms to minimise friction and wear in natural and engineered systems. Hence it is of particular interest to relate the thickness of the lubricant layer to the entrainment (sliding/rolling) velocity, the mechanical loading exerted onto the contacting elements, and properties of the elastic boundary. In this work we provide an overview of the various regimes of soft lubrication for two-dimensional cylinders in lubricated contact with compliant walls. We discuss the limits of small and large entrainment velocity, which is equivalent to large and small elastic deformations, as the cylinder moves near thick or thin elastic layers. The analysis focusses on thin elastic coatings, both compressible and incompressible, for which analytical scaling laws are not yet available in the regime of large deformations. By analysing the elastohydrodynamic boundary layers that appear at the edge of the contact, we establish the missing scaling laws - including prefactors. As such, we offer a rather complete overview of physically relevant limits of soft lubrication., Comment: 21 pages, 8 figures

The interface of a soft hydrogel is easily deformed when it is in contact with particles, droplets or cells. Here we compute the intricate shapes of hydrogel menisci due to the indentation of point particles. The analysis is based on a free energy formulation, by which we also assess the interaction laws between neighbouring particles on hydrogel interfaces, similar to the "Cheerios effect". It is shown how the meniscus formed around the particles results from a competition between surface tension, elasticity and hydrostatic pressure inside the gel. We provide a detailed overview of the various scaling laws, which are governed by a characteristic shear modulus $G^*=\sqrt{\gamma\rho g}$ that is based on surface tension $\gamma$ and gravity $\rho g$. Stiffer materials exhibit a solid-like response while softer materials are more liquid-like. The importance of $G^*$ is further illustrated by examining the Rayleigh-Taylor instability of soft hydrogels., Comment: 7 pages, 3 figures

Recent experiments have shown that liquid drops on highly deformable substrates exhibit mutual interactions. This is similar to the Cheerios effect, the capillary interaction of solid particles at a liquid interface, but now the roles of solid and liquid are reversed. Here we present a dynamical theory for this inverted Cheerios effect, taking into account elasticity, capillarity and the viscoelastic rheology of the substrate. We compute the velocity at which droplets attract, or repel, as a function of their separation. The theory is compared to a simplified model in which the viscoelastic dissipation is treated as a localized force at the contact line. It is found that the two models differ only at small separation between the droplets, and both of them accurately describe experimental observations., Comment: 11 pages, 8 figures

Lubrication flows appear in many applications in engineering, biophysics, and in nature. Separation of surfaces and minimisation of friction and wear is achieved when the lubrication fluid builds up a lift force. In this paper we analyse soft lubricated contacts by treating the solid walls as viscoelastic: soft materials are typically not purely elastic, but dissipate energy under dynamical loading conditions. We present a method for viscoelastic lubrication and focus on three canonical examples, namely Kelvin-Voigt-, Standard Linear-, and Power Law-rheology. It is shown how the solid viscoelasticity affects the lubrication process when the timescale of loading becomes comparable to the rheological timescale. We derive asymptotic relations between lift force and sliding velocity, which give scaling laws that inherit a signature of the rheology. In all cases the lift is found to decrease with respect to purely elastic systems., Comment: 14 pages, 3 figures

We consider the dynamic snapping instability of elastic beams and shells. Using the Kirchhoff rod and F\"{o}ppl-von K\'{a}rm\'{a}n plate equations, we study the stability, deformation modes, and snap-through dynamics of an elastic arch with clamped boundaries and subject to a concentrated load. For parameters typical of everyday and technological applications of snapping, we show that the stretchability of the arch plays a critical role in determining not only the post-buckling mode of deformation but also the timescale of snapping and the frequency of the arch's vibrations about its final equilibrium state. We show that the growth rate of the snap-through instability and its subsequent ringing frequency can both be interpreted physically as the result of a sound wave in the material propagating over a distance comparable to the length of the arch. Finally, we extend our analysis of the ringing frequency of indented arches to understand the `pop' heard when everted shell structures snap-through to their stable state. Remarkably, we find that not only are the scaling laws for the ringing frequencies in these two scenarios identical but also the respective prefactors are numerically close; this allows us to develop a master curve for the frequency of ringing in snapping beams and shells.