Reversal of Solvent Migration in Poroelastic Folds.

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.

Soft wetting with (a)symmetric Shuttleworth effect.

The wetting of soft polymer substrates brings in multiple complexities when compared with the wetting on rigid substrates. The contact angle of the liquid is no longer governed by Young's Law, but is affected by the substrate's bulk and surface deformations. On top of that, elastic interfaces exhibit a surface energy that depends on how much they are stretched-a feature known as the Shuttleworth effect (or as surface-elasticity). Here, we present two models through which we explore the wetting of drops in the presence of a strong Shuttleworth effect. The first model is macroscopic in character and consistently accounts for large deformations via a neo-Hookean elasticity. The second model is based on a mesoscopic description of wetting, using a reduced description of the substrate's elasticity. While the second model is more empirical in terms of the elasticity, it enables a gradient dynamics formulation for soft wetting dynamics. We provide a detailed comparison between the equilibrium states predicted by the two models, from which we deduce robust features of soft wetting in the presence of a strong Shuttleworth effect. Specifically, we show that the (a)symmetry of the Shuttleworth effect between the 'dry' and 'wet' states governs horizontal deformations in the substrate. Our results are discussed in the light of recent experiments on the wettability of stretched substrates.

The relationship between viscoelasticity and elasticity.

Soft materials that are subjected to large deformations exhibit an extremely rich phenomenology, with properties lying in between those of simple fluids and those of elastic solids. In the continuum description of these systems, one typically follows either the route of solid mechanics (Lagrangian description) or the route of fluid mechanics (Eulerian description). The purpose of this review is to highlight the relationship between the theories of viscoelasticity and of elasticity, and to leverage this connection in contemporary soft matter problems. We review the principles governing models for viscoelastic liquids, for example solutions of flexible polymers. Such materials are characterized by a relaxation time λ, over which stresses relax. We recall the kinematics and elastic response of large deformations, and show which polymer models do (and which do not) correspond to a nonlinear elastic solid in the limit λ → ∞. With this insight, we split the work done by elastic stresses into reversible and dissipative parts, and establish the general form of the conservation law for the total energy. The elastic correspondence can offer an insightful tool for a broad class of problems; as an illustration, we show how the presence or absence of an elastic limit determines the fate of an elastic thread during capillary instability.

Spreading on viscoelastic solids: are contact angles selected by Neumann's law?

The spreading of liquid drops on soft substrates is extremely slow, owing to strong viscoelastic dissipation inside the solid. A detailed understanding of the spreading dynamics has remained elusive, partly owing to the difficulty in quantifying the strong viscoelastic deformations below the contact line that determine the shape of moving wetting ridges. Here we present direct experimental visualisations of the dynamic wetting ridge using shadowgraphic imaging, complemented with measurements of the liquid contact angle. It is observed that the wetting ridge exhibits a rotation that follows exactly the dynamic liquid contact angle - as was previously hypothesized [Karpitschka et al., Nat. Commun., 2015, 6, 7891]. This experimentally proves that, despite the contact line motion, the wetting ridge is still governed by Neumann's law. Furthermore, our experiments suggest that moving contact lines lead to a variable surface tension of the substrate. We therefore set up a new theory that incorporates the influence of surface strain, for the first time including the so-called Shuttleworth effect into the dynamical theory for soft wetting. It includes a detailed analysis of the boundary conditions at the contact line, complemented by a dissipation analysis, which shows, again, the validity of Neumann's balance.

Turning Drops into Bubbles: Cavitation by Vapor Diffusion through Elastic Networks.

Some members of the vegetal kingdom can achieve surprisingly fast movements making use of a clever combination of evaporation, elasticity, and cavitation. In this process, enthalpic energy is transformed into elastic energy and suddenly released in a cavitation event which produces kinetic energy. Here, we study this unusual energy transformation by a model system: A droplet in an elastic medium shrinks slowly by diffusion and eventually transforms into a bubble by a rapid cavitation event. The experiments reveal the cavity dynamics over the extremely disparate timescales of the process, spanning 9 orders of magnitude. We model the initial shrinkage as a classical diffusive process, while the sudden bubble growth and oscillations are described using an inertial-(visco)elastic model, in excellent agreement with the experiments. Such a model system could serve as a new paradigm for motile synthetic materials.

Liquid Helix: How Capillary Jets Adhere to Vertical Cylinders.

From everyday experience, we all know that a solid edge can deflect a liquid flowing over it significantly, up to the point where the liquid completely sticks to the solid. Although important in pouring, printing, and extrusion processes, there is no predictive model of this so-called "teapot effect." By grazing vertical cylinders with inclined capillary liquid jets, here we use the teapot effect to attach the jet to the solid and form a new structure: the liquid helix. Using mass and momentum conservation along the liquid stream, we first quantitatively predict the shape of the helix and then provide a parameter-free inertial-capillary adhesion model for the jet deflection and critical velocity for helix formation.

Dynamic Solid Surface Tension Causes Droplet Pinning and Depinning.

The contact line of a liquid drop on a solid exerts a nanometrically sharp surface traction. This provides an unprecedented tool to study highly localized and dynamic surface deformations of soft polymer networks. One of the outstanding problems in this context is the stick-slip instability, observed above a critical velocity, during which the contact line periodically depins from its own wetting ridge. Time-resolved measurements of the solid deformation are challenging, and the mechanism of dynamical depinning has remained elusive. Here we present direct visualisations of the dynamic wetting ridge formed by water spreading on a PDMS gel. Unexpectedly, it is found that the opening angle of the wetting ridge increases with speed, which cannot be attributed to bulk rheology, but points to a dynamical increase of the solid's surface tensions. From this we derive the criterion for depinning that is confirmed experimentally. Our findings reveal a deep connection between stick-slip processes and newly identified dynamical surface effects.

Drop spreading and gelation of thermoresponsive polymers.

Spreading and solidification of liquid droplets are elementary processes of relevance for additive manufacturing. Here we investigate the effect of heat transfer on spreading of a thermoresponsive solution (Pluronic F127) that undergoes a sol-gel transition above a critical temperature Tm. By controlling the concentration of Pluronic F127 we systematically vary Tm, while also imposing a broad range of temperatures of the solid and the liquid. We subsequently monitor the spreading dynamics over several orders of magnitude in time and determine when solidification stops the spreading. It is found that the main parameter is the difference between the substrate temperature and Tm, pointing to a local mechanism for arrest near the contact line. Unexpectedly, the spreading is also found to stop below the gelation temperature, which we attribute to a local enhancement in polymer concentration due to evaporation near the contact line.

Cusp-Shaped Elastic Creases and Furrows.

The surfaces of growing biological tissues, swelling gels, and compressed rubbers do not remain smooth, but frequently exhibit highly localized inward folds. We reveal the morphology of this surface folding in a novel experimental setup, which permits us to deform the surface of a soft gel in a controlled fashion. The interface first forms a sharp furrow, whose tip size decreases rapidly with deformation. Above a critical deformation, the furrow bifurcates to an inward folded crease of vanishing tip size. We show experimentally and numerically that both creases and furrows exhibit a universal cusp shape, whose width scales like y^{3/2} at a distance y from the tip. We provide a similarity theory that captures the singular profiles before and after the self-folding bifurcation, and derive the length of the fold from finite deformation elasticity.

Pattern Formation by Staphylococcus epidermidis via Droplet Evaporation on Micropillars Arrays at a Surface.

We evaluate the effect of epoxy surface structuring on the evaporation of water droplets containing Staphylococcus epidermidis (S. epidermidis). During evaporation, droplets with S. epidermidis cells yield to complex wetting patterns such as the zipping-wetting1-3 and the coffee-stain effects. Depending on the height of the microstructure, the wetting fronts propagate circularly or in a stepwise manner, leading to the formation of octagonal or square-shaped deposition patterns.4,5 We observed that the shape of the dried droplets has considerable influence on the local spatial distribution of S. epidermidis deposited between micropillars. These changes are attributed to an unexplored interplay between the zipping-wetting1 and the coffee-stain6 effects in polygonally shaped droplets containing S. epidermidis. Induced capillary flows during evaporation of S. epidermidis are modeled with polystyrene particles. Bacterial viability measurements for S. epidermidis show high viability of planktonic cells, but low biomass deposition on the microstructured surfaces. Our findings provide insights into design criteria for the development of microstructured surfaces on which bacterial propagation could be controlled, limiting the use of biocides.

Droplets move over viscoelastic substrates by surfing a ridge.

Liquid drops on soft solids generate strong deformations below the contact line, resulting from a balance of capillary and elastic forces. The movement of these drops may cause strong, potentially singular dissipation in the soft solid. Here we show that a drop on a soft substrate moves by surfing a ridge: the initially flat solid surface is deformed into a sharp ridge whose orientation angle depends on the contact line velocity. We measure this angle for water on a silicone gel and develop a theory based on the substrate rheology. We quantitatively recover the dynamic contact angle and provide a mechanism for stick-slip motion when a drop is forced strongly: the contact line depins and slides down the wetting ridge, forming a new one after a transient. We anticipate that our theory will have implications in problems such as self-organization of cell tissues or the design of capillarity-based microrheometers.

Universality of tip singularity formation in freezing water drops.

A drop of water deposited on a cold plate freezes into an ice drop with a pointy tip. While this phenomenon clearly finds its origin in the expansion of water upon freezing, a quantitative description of the tip singularity has remained elusive. Here we demonstrate how the geometry of the freezing front, determined by heat transfer considerations, is crucial for the tip formation. We perform systematic measurements of the angles of the conical tip, and reveal the dynamics of the solidification front in a Hele-Shaw geometry. It is found that the cone angle is independent of substrate temperature and wetting angle, suggesting a universal, self-similar mechanism that does not depend on the rate of solidification. We propose a model for the freezing front and derive resulting tip angles analytically, in good agreement with the experiments.

Universal spreading of water drops on complex surfaces.

A drop of water spreads very rapidly just after it is gently deposited on a solid surface. Here we experimentally investigate how these early stages of spreading are influenced by different types of surface complexity. In particular, we consider micro-textured substrates, chemically striped substrates and soft substrates. For all these complex substrates, it is found that there always exists an inertial regime where the radius r of the wetted area grows as r ∼ t(1/2). For perfectly wetting substrates, this regime extends over several decades in time, whereas we observe a deviation from a pure power-law for partially wetting substrates. Our experiments reveal that even the cross-over from the 1/2 power law to the final equilibrium radius displays a universal dynamics. This cross-over is governed only by the final contact angle, regardless of the details of the substrate.

Influence of droplet geometry on the coalescence of low viscosity drops.

The coalescence of water drops on a substrate is studied experimentally. We focus on the rapid growth of the bridge connecting the two drops, which very quickly after contact ensues from a balance of surface tension and liquid inertia. For drops with contact angles below 90°, we find that the bridge grows with a self-similar dynamics that is characterized by a height h~t(2/3). By contrast, the geometry of coalescence changes dramatically for contact angles at 90°, for which we observe h~t(1/2), just as for freely suspended spherical drops in the inertial regime. We present a geometric model that quantitatively captures the transition from 2/3 to 1/2 exponent, and unifies the inertial coalescence of sessile drops and freely suspended drops.

Symmetric and asymmetric coalescence of drops on a substrate.

The coalescence of viscous drops on a substrate is studied experimentally and theoretically. We consider cases where the drops can have different contact angles, leading to a very asymmetric coalescence process. Side view experiments reveal that the "bridge" connecting the drops evolves with self-similar dynamics, providing a new perspective on the coalescence of sessile drops. We show that the universal shape of the bridge is accurately described by similarity solutions of the one-dimensional lubrication equation. Our theory predicts that, once the drops are connected on a microscopic scale, the bridge grows linearly in time with a strong dependence on the contact angles. Without any adjustable parameters, we find quantitative agreement with all experiments.

Thick films of viscous fluid coating a plate withdrawn from a liquid reservoir.

We consider the deposition of a film of viscous liquid on a flat plate being withdrawn from a bath, experimentally and theoretically. For any plate speed U, there is a range of "thick" film solutions whose thickness scales like U{1/2} for small U. These solutions are realized for a partially wetting liquid, while for a perfectly wetting liquid the classical Landau-Levich-Derjaguin film is observed, whose thickness scales like U{2/3}. The thick film is distinguished from the Landau-Levich-Derjaguin film by a dip in its spatial profile at the transition to the bath. We calculate the phase diagram for the existence of stationary film solutions as well as the film profiles and find excellent agreement with experiment.

Theory of the collapsing axisymmetric cavity.

We investigate the collapse of an axisymmetric cavity or bubble inside a fluid of small viscosity, like water. Any effects of the gas inside the cavity as well as of the fluid viscosity are neglected. Using a slender-body description, we compute the local scaling exponent alpha=dlnh_{0}/dlnt' of the minimum radius h_{0} of the cavity, where t' is the time from collapse. The exponent alpha very slowly approaches a universal value according to alpha=1/2+1/[4 square root [-ln(t')]]. Thus, as observed in a number of recent experiments, the scaling can easily be interpreted as evidence of a single nontrivial scaling exponent. Our predictions are confirmed by numerical simulations.