Coalescence of Elastic Blisters Filled with a Viscous Fluid.

Pockets of viscous fluid coalescing beneath an elastic sheet are encountered in a wide range of natural phenomena and engineering processes, spanning across scales. As the pockets merge, a bridge is formed with a height increasing as the sheet relaxes. We study the spatiotemporal dynamics of such an elastohydrodynamic coalescence process by combining experiments, lubrication theory, and numerical simulations. The bridge height exhibits an exponential growth with time, which corresponds to a self-similar solution of the bending-driven thin-film equation. We address this unique self-similarity and the self-similar shape of the bridge, both of which are corroborated in numerical simulations and experiments.

Pressure Anisotropy in Polymer Brushes and Its Effects on Wetting.

Polymer brushes, coatings consisting of densely grafted macromolecules, experience an intrinsic lateral compressive pressure, originating from chain elasticity and excluded volume interactions. This lateral pressure complicates a proper definition of the interface and, thereby, the determination and interpretation of the interfacial tension and its relation to the wetting behavior of brushes. Here, we study the link among grafting-induced compressive lateral pressure in polymer brushes, interfacial tension, and brush wettability using coarse-grained molecular dynamics simulations. We focus on grafting densities and polymer-liquid affinities such that the polymer and liquid do not tend to mix. For these systems, a central result is that the liquid contact angle is independent of the grafting density, which implies that the grafting-induced lateral compressive pressure in the brush does not influence its wettability. Although the definition of brush interfacial tensions is complicated by the grafting-induced pressure, the difference in the interfacial tension between wet and dry brushes is perfectly well-defined. We confirm explicitly from Young's law that this difference offers an accurate description of the brush wettability. We then explore a method to isolate the grafting-induced contribution to the lateral pressure, assuming the interfacial tension is independent of grafting density. This scenario indeed allows disentanglement of interfacial and grafting effects for a broad range of parameters, except close to the mixing point. We separately discuss the latter case in light of autophobic dewetting.

A unifying Rayleigh-Plesset-type equation for bubbles in viscoelastic media.

Understanding the ultrasound pressure-driven dynamics of microbubbles confined in viscoelastic materials is relevant for multiple biomedical applications, ranging from contrast-enhanced ultrasound imaging to ultrasound-assisted drug delivery. The volumetric oscillations of spherical bubbles are analyzed using the Rayleigh-Plesset equation, which describes the conservation of mass and momentum in the surrounding medium. Several studies have considered an extension of the Rayleigh-Plesset equation for bubbles embedded into viscoelastic media, but these are restricted to a particular choice of constitutive model and/or to small deformations. Here, we derive a unifying equation applicable to bubbles in viscoelastic media with arbitrary complex moduli and that can account for large bubble deformations. To derive this equation, we borrow concepts from finite-strain theory. We validate our approach by comparing the result of our model to previously published results and extend it to show how microbubbles behave in arbitrary viscoelastic materials. In particular, we use our viscoelastic Rayleigh-Plesset model to compute the bubble dynamics in benchmarked viscoelastic liquids and solids.

Adhesive creases: bifurcation, morphology and their (apparent) self-similarity.

An elastic material that experiences strong compression parallel to its free surface can exhibit sharp surface folds. Such creases arise due to an instability where a self-contacting fold appears on the surface, often observed in growing tissues or swelling gels. Self-adhesion of the contact is known to affect the bifurcation behavior and morphology of these structures, yet a quantitative description remains elusive. From numerical simulations and an energy analysis we resolve how adhesion quantitatively affects both morphology and bifurcation behavior. It is found that a reduced energy is able to accurately describe the bifurcation, in terms of an effective scaling that collapses the data very well. The model accurately describes how adhesion hinders crease nucleation. Furthermore, we show that the free surface profiles in the presence of surface tension exhibit self-similarity, and can be collapsed onto a universal curve.

Drawing liquid bridges from a thin viscous film.

When a particle, such as dust, contacts a thin liquid film covering a surface it is trapped by the liquid. This effect is caused by the formation of a meniscus, resulting in a capillary force that makes the particle adhere to the surface. While capillary adhesion is well-characterised in static situations, the dynamic formation of the liquid bridge after the initial contact is highly intricate. Here, we experimentally study the evolution of a liquid bridge after a glass sphere is gently brought into contact with a thin viscous film. It is found that the contact creates a ripple on the thin film, which influences the growth of the meniscus. Initially, the ripple and the meniscus are coupled and exhibit similar dynamics. This initial regime is well accounted for by a scaling law derived from lubrication theory. At a later stage, the ripple is "detached" from the liquid bridge, leading to a second regime of bridge dynamics. As a result, capillary forces are time-dependent, highlighting the importance of dynamics on adhesion.

When Elasticity Affects Drop Coalescence.

The breakup and coalescence of drops are elementary topological transitions in interfacial flows. The breakup of a drop changes dramatically when polymers are added to the fluid. With the strong elongation of the polymers during the process, long threads connecting the two droplets appear prior to their eventual pinch-off. Here, we demonstrate how elasticity affects drop coalescence, the complement of the much studied drop pinch-off. We reveal the emergence of an elastic singularity, characterized by a diverging interface curvature at the point of coalescence. Intriguingly, while the polymers dictate the spatial features of coalescence, they hardly affect the temporal evolution of the bridge. These results are explained using a novel viscoelastic similarity analysis and are relevant for drops created in biofluids, coating sprays, and inkjet printing.

Pinning-Induced Folding-Unfolding Asymmetry in Adhesive Creases.

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.

Droplets Sit and Slide Anisotropically on Soft, Stretched Substrates.

Anisotropically wetting substrates enable useful control of droplet behavior across a range of applications. Usually, these involve chemically or physically patterning the substrate surface, or applying gradients in properties like temperature or electrical field. Here, we show that a flat, stretched, uniform soft substrate also exhibits asymmetric wetting, both in terms of how droplets slide and in their static shape. Droplet dynamics are strongly affected by stretch: glycerol droplets on silicone substrates with a 23% stretch slide 67% faster in the direction parallel to the applied stretch than in the perpendicular direction. Contrary to classical wetting theory, static droplets in equilibrium appear elongated, oriented parallel to the stretch direction. Both effects arise from droplet-induced deformations of the substrate near the contact line.

Wetting of Two-Component Drops: Marangoni Contraction Versus Autophobing.

The wetting properties of multicomponent liquids are crucial to numerous industrial applications. The mechanisms that determine the contact angles for such liquids remain poorly understood, with many intricacies arising due to complex physical phenomena, for example, due to the presence of surfactants. Here, we consider two-component drops that consist of mixtures of vicinal alkanediols and water. These diols behave surfactant-like in water. However, the contact angles of such mixtures on solid substrates are surprisingly large. We experimentally reveal that the contact angle is determined by two separate mechanisms of completely different nature, namely, Marangoni contraction (hydrodynamic) and autophobing (molecular). The competition between these effects can even inhibit Marangoni contraction, highlighting the importance of molecular structures in physico-chemical hydrodynamics.

Gradient-dynamics model for liquid drops on elastic substrates.

The wetting of soft elastic substrates exhibits many features that have no counterpart on rigid surfaces. Modelling the detailed elastocapillary interactions is challenging, and has so far been limited to single contact lines or single drops. Here we propose a reduced long-wave model that captures the main qualitative features of statics and dynamics of soft wetting, but which can be applied to ensembles of droplets. The model has the form of a gradient dynamics on an underlying free energy that reflects capillarity, wettability and compressional elasticity. With the model we first recover the double transition in the equilibrium contact angles that occurs when increasing substrate softness from ideally rigid towards very soft (i.e., liquid). Second, the spreading of single drops of partially and completely wetting liquids is considered showing that known dependencies of the dynamic contact angle on contact line velocity are well reproduced. Finally, we go beyond the single droplet picture and consider the coarsening for a two-drop system as well as for a large ensemble of drops. It is shown that the dominant coarsening mode changes with substrate softness in a nontrivial way.

The role of entropy in wetting of polymer brushes.

The wetting of polymer brushes exhibits a much richer phenomenology than wetting of normal solid substrates. These brushes allow for three wetting states, which are partial wetting, complete wetting and mixing. Here, we study the transitions between these wetting states for brushes in contact with polymer melts and compare them to predictions using enthalpic arguments based on brush and melt interactions. We show that the transitions are shifted compared to the enthalpic predictions and that the shifts can be positive or negative depending on the length of the melt polymer and the brush grafting density. The reason for this is that these brush and melt parameters can have a positive or negative effect on the entropic contribution to the free energy of the system. Our results highlight the relevance of entropy in predicting the exact wetting transitions, which is important for the design of brush-based coating applications.

Elastic Rayleigh-Plateau instability: dynamical selection of nonlinear states.

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.

Nanoscopic interactions of colloidal particles can suppress millimetre drop splashing.

The splashing of liquid drops onto a solid surface is important for a wide range of applications, including combustion and spray coating. As the drop hits the solid surface, the liquid is ejected into a thin horizontal sheet expanding radially over the substrate. Above a critical impact velocity, the liquid sheet is forced to separate from the solid surface by the ambient air, and breaks up into smaller droplets. Despite many applications involving complex fluids, their effects on splashing remain mostly unexplored. Here we show that the splashing of a nanoparticle dispersion can be suppressed at higher impact velocities by the interactions of the nanoparticles with the solid surface. Although the dispersion drop first shows the classical transition from deposition to splashing when increasing the impact velocity, no splashing is observed above a second higher critical impact velocity. This result goes against the commonly accepted understanding of splashing, that a higher impact velocity should lead to even more pronounced splashing. Our findings open new possibilities to deposit large amount of complex liquids at high speeds.

Self-Similar Liquid Lens Coalescence.

A basic feature of liquid drops is that they can merge upon contact to form a larger drop. In spite of its importance to various applications, drop coalescence on prewetted substrates has received little attention. Here, we experimentally and theoretically reveal the dynamics of drop coalescence on a thick layer of a low viscosity liquid. It is shown that these so-called "liquid lenses" merge by the self-similar vertical growth of a bridge connecting the two lenses. Using a slender analysis, we derive similarity solutions corresponding to the viscous and inertial limits. Excellent agreement is found with the experiments without any adjustable parameters, capturing both the spatial and temporal structures of the flow during coalescence. Finally, we consider the crossover between the two regimes and show that all data of different lens viscosities collapse on a single curve capturing the full range of the coalescence dynamics.

Desorption energy of soft particles from a fluid interface.

The efficiency of soft particles to stabilize emulsions is examined by measuring their desorption free energy, i.e., the mechanical work required to detach the particle from a fluid interface. Here, we consider rubber-like elastic as well as microgel particles, using coarse-grained molecular dynamics simulations. The energy of desorption is computed for two and three-dimensional configurations by means of the mean thermodynamic integration method. It is shown that the softness affects the particle-interface binding in two opposing directions as compared to rigid particles. On the one hand, a soft particle spreads at the interface and thereby removes a larger unfavorable liquid-liquid contact area compared to rigid particles. On the other hand, softness provides the particle with an additional degree of freedom to get reshaped instead of deforming the interface, resulting in a smaller restoring force during the detachment. It is shown that the first effect prevails so that a soft spherical particle attaches to the fluid interface more strongly than rigid spheres. Finally, we consider microgel particles both in the swollen and in the collapsed state. Surprisingly, we find that the latter has a larger binding energy. All results are rationalised using thermodynamic arguments and thereby offer detailed insights into the desorption energy of soft particles from fluid interfaces.

Inverse leidenfrost drop manipulation using menisci.

Drops deposited on an evaporating liquid bath can be maintained in an inverse Leidenfrost state by the vapor emanating from the bath, making them levitate and hover without effective friction. These perfectly non-wetting droplets create a depression in the liquid interface that sustains their weight, which generates repellent forces when they approach a meniscus rising against a wall. Here, we study this reflection in detail, and show that frictionless Leidenfrost drops are a simple and efficient tool to probe the shape of an unknown interface. We then use the menisci to control the motion of the otherwise elusive drops. We create waveguides to direct and accelerate them and use parabolic walls to reflect and focus them. This could be particularly beneficial in the scale up of droplet cryopreservation processes: capillary interactions can be used to transport, gather and collect vitrified biological samples in absence of contact and contamination.

Escape dynamics of liquid droplets confined between soft interfaces: non-inertial coalescence cascades.

We have studied the motion of liquid droplets located in the contact zone of two soft solids that are pressed together inside a liquid. The driving force of the motion is the gradient of elastic contact pressure. Upon reaching the perimeter of the contact spot, the droplets coalesce with the surrounding bulk liquid either in a continuous or discontinuous fashion. Droplets that exhibit complete coalescence move with a speed proportional to the pressure gradient along their trajectory. However, droplets that undergo partial coalescence cascades (up to 9 were observed) do not. The latter also move significantly slower. We have identified surface roughness as a potential mechanism causing the contrasting behavior.

Non-axisymmetric elastohydrodynamic solid-liquid-solid dewetting: Experiments and numerical modelling.

We have studied the dewetting dynamics of partially wetting liquid films confined between a soft elastic hemisphere and an elastomer layer by means of systematic experiments. We focused on the experimentally most relevant case of non-axisymmetric dewetting, which initiated at the locations of minimum film thickness near the perimeter of the contact area. We found the contact line speed to be highly anisotropic in this case. It is significantly faster in the azimuthal direction along the perimeter of the contact spot than in the radially inwards direction. We developed a three-dimensional, fully coupled numerical model that reproduces many features observed in the experiments.

On the shape of giant soap bubbles.

We study the effect of gravity on giant soap bubbles and show that it becomes dominant above the critical size [Formula: see text], where [Formula: see text] is the mean thickness of the soap film and [Formula: see text] is the capillary length ([Formula: see text] stands for vapor-liquid surface tension, and [Formula: see text] stands for the liquid density). We first show experimentally that large soap bubbles do not retain a spherical shape but flatten when increasing their size. A theoretical model is then developed to account for this effect, predicting the shape based on mechanical equilibrium. In stark contrast to liquid drops, we show that there is no mechanical limit of the height of giant bubble shapes. In practice, the physicochemical constraints imposed by surfactant molecules limit the access to this large asymptotic domain. However, by an exact analogy, it is shown how the giant bubble shapes can be realized by large inflatable structures.

Soft electrowetting.

Electrowetting is a commonly used tool to manipulate sessile drops on hydrophobic surfaces. By applying an external voltage over a liquid and a dielectric-coated surface, one achieves a reduction of the macroscopic contact angles for increasing voltage. The electrostatic forces all play out near the contact line, on a scale of the order of the thickness of the solid dielectric layer. Here we explore the case where the dielectric is a soft elastic layer, which deforms elastically under the effect of electrostatic and capillary forces. The wetting behaviour is quantified by measurements of the static and dynamic contact angles, complemented by confocal microscopy to reveal the elastic deformations. Even though the mechanics near the contact line is highly intricate, the macroscopic contact angles can be understood from global conservation laws in the spirit of Young-Lippmann. The key finding is that, while elasticity has no effect on the static electrowetting angle, the substrate's viscoelasticity completely dictates the spreading dynamics of electrowetting.