How liquid-liquid phase separation induces active spreading.

The interplay between phase separation and wetting of multicomponent mixtures is ubiquitous in nature and technology and recently gained significant attention across scientific disciplines, due to the discovery of biomolecular condensates. It is well understood that sessile droplets, undergoing phase separation in a static wetting configuration, exhibit microdroplet nucleation at their contact lines, forming an oil ring during later stages. However, very little is known about the dynamic counterpart, when phase separation occurs in a nonequilibrium wetting configuration, i.e., spreading droplets. Here we show that liquid-liquid phase separation strongly couples to the spreading motion of three-phase contact lines. Thus, the classical Cox-Voinov law is not applicable anymore, because phase separation adds an active spreading force beyond the capillary driving. Intriguingly, we observe that spreading starts well before any visible nucleation of microdroplets in the main droplet. Using high-speed ellipsometry, we further demonstrate that the evaporation-induced enrichment, together with surface forces, causes an even earlier nucleation in the wetting precursor film around the droplet, initiating the observed wetting transition. We expect our findings to improve the fundamental understanding of phase separation processes that involve dynamical contact lines and/or surface forces, with implications in a wide range of applications, from oil recovery or inkjet printing to material synthesis and biomolecular condensates.

Marangoni spreading and contracting three-component droplets on completely wetting surfaces.

SignificanceThe shape and dynamics of small sessile droplets are dictated by capillary forces. For liquid mixtures, evaporation adds spatio-temporal modulation to these forces that can either enhance or inhibit droplet spreading, depending on the direction of the resulting Marangoni flow. This work experimentally and numerically demonstrates the coexistence of two antagonistic Marangoni flows in a ternary mixture. Played against each other, they can choreograph a boomerang-like wetting motion: Droplets initially rapidly spread, then contract into a compact cap shape. While such a behavior has been impossible in wetting scenarios of simple liquids, it enables spread-retract-remove surface processing with the addition of a single small liquid volume, demonstrated here in a surface-cleaning experiment.

Droplet tilings for rapid exploration of spatially constrained many-body systems.

Geometry in materials is a key concept which can determine material behavior in ordering, frustration, and fragmentation. More specifically, the behavior of interacting degrees of freedom subject to arbitrary geometric constraints has the potential to be used for engineering materials with exotic phase behavior. While advances in lithography have allowed for an experimental exploration of geometry on ordering that has no precedent in nature, many of these methods are low throughput or the underlying dynamics remain difficult to observe directly. Here, we introduce an experimental system that enables the study of interacting many-body dynamics by exploiting the physics of multidroplet evaporation subject to two-dimensional spatial constraints. We find that a high-energy initial state of this system settles into frustrated, metastable states with relaxation on two timescales. We understand this process using a minimal dynamical model that simulates the overdamped dynamics of motile droplets by identifying the force exerted on a given droplet as being proportional to the two-dimensional vapor gradients established by its neighbors. Finally, we demonstrate the flexibility of this platform by presenting experimental realizations of droplet-lattice systems representing different spin degrees of freedom and lattice geometries. Our platform enables a rapid and low-cost means to directly visualize dynamics associated with complex many-body systems interacting via long-range interactions. More generally, this platform opens up the rich design space between geometry and interactions for rapid exploration with minimal resources.

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.

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.

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.

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.

Living System Adapts Harmonics of Peristaltic Wave for Cost-Efficient Optimization of Pumping Performance.

Wavelike patterns driving transport are ubiquitous in life. Peristaltic pumps are a paradigm of efficient mass transport by contraction driven flows-often limited by energetic constraints. We show that a cost-efficient increase in pumping performance can be achieved by modulating the phase difference between harmonics to increase occlusion. In experiments we find a phase difference shift in the living peristalsis model P. polycephalum as dynamic response to forced mass transport. Our findings provide a novel metric for wavelike patterns and demonstrate the crucial role of nonlinearities in life.

Peeling an elastic film from a soft viscoelastic adhesive: experiments and scaling laws.

The functionality of adhesives relies on their response under the application of a load. Yet, it has remained a challenge to quantitatively relate the macroscopic dynamics of peeling to the dissipative processes inside the adhesive layer. Here we investigate the peeling of a reversible adhesive made of a polymer gel, measuring the relationship between the peeling force, the peeling velocity, and the geometry of the interface at small-scale. Experiments are compared to a theory based on the linear viscoelastic response of the adhesive, augmented with an elastocapillary regularization approach. This theory, fully quantitative in the limit of small surface deformations, demonstrates the emergence of a "wetting" angle at the contact line and exhibits scaling laws for peeling which are in good agreement with the experimental results. Our findings provide a new strategy for design of reversible adhesives, by quantitatively combining wetting, geometry and dissipation.

Liquid drops attract or repel by the inverted Cheerios effect.

Solid particles floating at a liquid interface exhibit a long-ranged attraction mediated by surface tension. In the absence of bulk elasticity, this is the dominant lateral interaction of mechanical origin. Here, we show that an analogous long-range interaction occurs between adjacent droplets on solid substrates, which crucially relies on a combination of capillarity and bulk elasticity. We experimentally observe the interaction between droplets on soft gels and provide a theoretical framework that quantitatively predicts the interaction force between the droplets. Remarkably, we find that, although on thick substrates the interaction is purely attractive and leads to drop-drop coalescence, for relatively thin substrates a short-range repulsion occurs, which prevents the two drops from coming into direct contact. This versatile interaction is the liquid-on-solid analog of the "Cheerios effect." The effect will strongly influence the condensation and coarsening of drops on soft polymer films, and has potential implications for colloidal assembly and mechanobiology.

Marangoni Contraction of Evaporating Sessile Droplets of Binary Mixtures.

The Marangoni contraction of sessile drops of a binary mixture of a volatile and a nonvolatile liquid has been investigated experimentally and theoretically. The origin of the contraction is the locally inhomogeneous evaporation rate of sessile drops. This leads to surface tension gradients and thus to a Marangoni flow. Simulations show that the interplay of Marangoni flow, capillary flow, diffusive transport, and evaporative losses can establish a quasistationary drop profile with an apparent nonzero contact angle even if both liquid components individually wet the substrate completely. Experiments with different solvents, initial mass fractions, and gaseous environments reveal a previously unknown universal power-law relation between the apparent contact angle and the relative undersaturation of the ambient atmosphere: θapp ∼ (RHeq - RH)1/3. This experimentally observed power law is in quantitative agreement with simulation results. The exponent can also be inferred from a scaling analysis of the hydrodynamic-evaporative evolution equations of a binary mixture of liquids with different volatilities.

Shape of a sessile drop on a flat surface covered with a liquid film.

Motivated by the development of lubricant-infused slippery surfaces, we study a sessile drop of a nonvolatile (ionic) liquid which is embedded in a slowly evaporating lubricant film (n-decane) on a horizontal, planar solid substrate. Using laser scanning confocal microscopy we imaged the evolution of the shape of the liquid/liquid and liquid/air interfaces, including the angles between them. Results are compared to solutions of the generalized Laplace equations describing the drop profile and the annular wetting ridge. For all film thicknesses, experimental results agree quantitatively with the calculated drop and film shapes. With the verified theory we can predict height and volume of the wetting ridge. Two regimes can be distinguished: for macroscopically thick films (excess lubrication) the meniscus size is insensitive to changes in film thickness. Once the film is thin enough that surface forces between the lubricant/air and solid/lubricant interfaces become significant the meniscus changes significantly with varying film thickness (starved lubrication). The size of the meniscus is particularly relevant because it affects sliding angles of drops on lubricant-infused surfaces.

Dynamical theory of the inverted cheerios effect.

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.

Surface tension regularizes the crack singularity of adhesion.

The elastic and adhesive properties of a solid surface can be quantified by indenting it with a rigid sphere. Indentation tests are classically described by the JKR-law when the solid is very stiff, while recent work highlights the importance of surface tension for exceedingly soft materials. Here we show that surface tension plays a crucial role even in stiff solids: Young's wetting angle emerges as a boundary condition and this regularizes the crack-like singularity at the edge of adhesive contacts. We find that the edge region exhibits a universal, self-similar structure that emerges from the balance of surface tension and elasticity. The similarity theory is solved analytically and provides a complete description of adhesive contacts, by which we reconcile global adhesion laws and local contact mechanics.

Periodic Precipitation Patterns during Coalescence of Reacting Sessile Droplets.

The coalescence behavior of two sessile drops that contain different chemical reactants (cerium nitrate and oxalic acid) and its impact on the formation of the solid precipitate (cerium oxalate) are investigated. With different liquids, the surface tension difference in the moment of drop-drop contact can induce a Marangoni flow. This flow can strongly influence the drop-drop coalescence behavior and thus, with reacting liquids, also the reaction and its products (through the liquid mixing). In our study we find three distinctly different coalescence behaviors ("barrier", "intermediate", "noncoalescence"), in contrast to only two behaviors that were observed in the case of nonreacting liquids. The amount of liquid mixing and thus the precipitation rate are very different for the three cases. The "intermediate" case, which exhibits the strongest mixing, has been studied in more detail. For high oxalic acid concentrations, mainly needle-like aggregates, and for low concentrations, mainly flower-like precipitate morphologies are obtained. In a transition range of the oxalic acid concentration, both morphologies can be produced. With the applied coalescence conditions, the different aggregate particles are arranged and fixed in a precipitate raft in a regular, periodic line pattern. This confirms the drop-drop coalescence configuration as a convection-reaction-diffusion system, which can have stationary as well as oscillatory behavior depending on the system parameters.

The evaporation behavior of sessile droplets from aqueous saline solutions.

Quantitative experiments on the evaporation from sessile droplets of aqueous saline (NaCl) solutions show a strong dependence on salt concentration and droplet shape. The experiments were performed with seven decades of initial NaCl concentrations, with various droplet sizes and with different contact angles. The evaporation rate is significantly lower for high salt concentrations and small contact angles than what is expected from the well-accepted diffusion-controlled evaporation scenario for sessile droplets, even if the change of the vapor pressure due to the salt is taken into account. Particle tracking velocimetry reveals that this modification of the evaporation behavior is caused by marangoni flows that are induced by surface tension gradients originating from the local evaporative peripheral salt enrichment. In addition it is found that already very low salt concentrations lead to a pinning of the three phase contact line. Whereas droplets with concentration ≥10(-6) M NaCl are pinned as soon as evaporation starts, droplets with lower salt concentration do evaporate in a constant contact angle mode. Aside from new, fundamental insights the findings are also relevant for a better understanding of the widespread phenomenon of corrosion initiated by sessile droplets.

Coalescence and noncoalescence of sessile drops: impact of surface forces.

Due to capillarity, sessile droplets of identical liquids will instantaneously fuse when they come in contact at their three-phase lines. However, with drops of different, completely miscible liquids, instantaneous coalescence can be suppressed. Instead, the drops remain in a state of noncoalescence for some time, with the two drop bodies connected only by a thin neck. The reason for this noncoalescence is the surface tension difference, Δγ, between the liquids. If Δγ is sufficiently large, then it induces a sufficiently strong Marangoni flow, which keeps the main drop bodies temporarily separated. Studies with spreading drops have revealed that the boundary between instantaneous coalescence and noncoalescence is sharp (Karpitschka, S.; Riegler, H. J. Fluid. Mech. 2014, 743, R1). The boundary is a function of two parameters only: Δγ and Θ(a), the arithmetic mean of the contact angles in the moment of drop-drop contact. It appears plausible that surface forces (the disjoining pressure) could also influence the coalescence behavior. However, in experiments with spreading drops, surface forces always promote coalescence and their influence might be obscured. Therefore, we present here coalescence experiments with partially wetting liquids and compare the results to the spreading case. We adjust different equilibrium contact angles (i.e., different surface forces) with different substrate surface coatings. As for spreading drops, we observe a sharp boundary between regimes of coalescence and noncoalescence. The boundary follows the same power law relation for both partially and completely wetting cases. Therefore, we conclude that surface forces have no significant, explicit influence on the coalescence behavior of sessile drops from different miscible liquids.

Travelling fronts of the CO oxidation on Pd(111) with coverage-dependent diffusion.

In this work, we study a surface reaction on Pd(111) crystals under ultra-high-vacuum conditions that can be modeled by two coupled reaction-diffusion equations. In the bistable regime, the reaction exhibits travelling fronts that can be observed experimentally using photo electron emission microscopy. The spatial profile of the fronts reveals a coverage-dependent diffusivity for one of the species. We propose a method to solve the nonlinear eigenvalue problem and compute the direction and the speed of the fronts based on a geometrical construction in phase-space. This method successfully captures the dependence of the speed on control parameters and diffusivities.

Quantifying gliding forces of filamentous cyanobacteria by self-buckling.

Filamentous cyanobacteria are one of the oldest and today still most abundant lifeforms on earth, with manifold implications in ecology and economics. Their flexible filaments, often several hundred cells long, exhibit gliding motility in contact with solid surfaces. The underlying force generating mechanism is not yet understood. Here, we demonstrate that propulsion forces and friction coefficients are strongly coupled in the gliding motility of filamentous cyanobacteria. We directly measure their bending moduli using micropipette force sensors, and quantify propulsion and friction forces by analyzing their self-buckling behavior, complemented with analytical theory and simulations. The results indicate that slime extrusion unlikely generates the gliding forces, but support adhesion-based hypotheses, similar to the better-studied single-celled myxobacteria. The critical self-buckling lengths align well with the peaks of natural length distributions, indicating the importance of self-buckling for the organization of their collective in natural and artificial settings.