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The rupture of soap films is traditionally described by a law accounting for a balance between momentum and surface tension forces, derived independently by Taylor and Culick in the 1960s. This law is highly relevant to the dynamics of thin liquid films of jets when viscous effects are negligible. However, the minute amounts of surfactant molecules present in soap films play a major role in interfacial rheology, and may result in complex behaviour. Petit et al. (J. Fluid Mech., vol. 774, 2015, R3) challenge standard thin film dynamics via intriguing experiments conducted with highly elastic surfactants. Unexpected structures reminiscent of faults are observed. [ABSTRACT FROM PUBLISHER]

When microdroplets with quasi‐spherical contact angles coalesce together on a low‐adhesion substrate, the capillary‐inertial expansion of the liquid bridge induces a dramatic out‐of‐plane jumping event due to symmetry breaking. From the onset of merging, droplet jumping initiates after a capillary‐inertial time scale of tci∼1–100 ${t}_{\text{ci}}\sim 1\mbox{--}\,100$ μs with characteristic jumping speeds of order vj∼0.1 ${v}_{{\rm{j}}}\sim 0.1$ m/s. This coalescence‐induced jumping‐droplet effect is most commonly observed among a population of growing dew droplets on a superhydrophobic condenser, but can also occur by colliding deposited droplets together or during droplet sliding on fog harvesters. In this review, we cover the historical development of capillary‐inertial jumping droplets, summarize the decade‐long effort to rationalize the ultra‐low energy conversion efficiency and critical droplet size of the phenomenon, and then present 15 variations on a theme of jumping. Capillary‐inertial jumping droplets are not only a visceral illustration of the surprising power of surface tension at the microscale but they also have the potential to enhance phase‐change heat transfer, enable self‐cleaning surfaces, combat frost formation, harvest energy, and govern the rate of disease spread for wheat crops. [ABSTRACT FROM AUTHOR]

This paper presents the derivation of the homogenized equations that describe the macroscopic mechanical response of elastomers filled with liquid inclusions in the setting of small quasistatic deformations. The derivation is carried out for materials with periodic microstructure by means of a two-scale asymptotic analysis. The focus is on the non-dissipative case when the elastomer is an elastic solid, the liquid making up the inclusions is an elastic fluid, the interfaces separating the solid elastomer from the liquid inclusions are elastic interfaces featuring an initial surface tension, and the inclusions are initially n -spherical (n = 2 , 3 ) in shape. Remarkably, in spite of the presence of local residual stresses within the inclusions due to an initial surface tension at the interfaces, the macroscopic response of such filled elastomers turns out to be that of a linear elastic solid that is free of residual stresses and hence one that is simply characterized by an effective modulus of elasticity L ‾ . What is more, in spite of the fact that the local moduli of elasticity in the bulk and the interfaces do not possess minor symmetries (due to the presence of residual stresses and the initial surface tension at the interfaces), the resulting effective modulus of elasticity L ‾ does possess the standard minor symmetries of a conventional linear elastic solid, that is, L ‾ i j k l = L ‾ j i k l = L ‾ i j l k . As an illustrative application, numerical results are worked out and analyzed for the effective modulus of elasticity of isotropic suspensions of incompressible liquid 2-spherical inclusions of monodisperse size embedded in an isotropic incompressible elastomer. [ABSTRACT FROM AUTHOR]

Although liquid-repellent surfaces are in demand in many applications, their use is limited by the Cassie state's sustainability to environmental factors, such as the repellency of liquids with a surface tension lower than that of water. This phenomenon remains not fully understood, despite a well-developed theory. In the current work, wetting of femtosecond laser-textured aluminum surfaces for probe liquids with a surface tension of 72.8–21.2 mN/m was considered. The resulting patterns were an array of pillars at the micro level and fractal-like structures at the nano level. These structured surfaces were treated with alkoxysilanes and oleic acid. All textured samples exhibited a Cassie state with water, and contact angles greater than 150° were achieved with silane-treated surfaces. A decrease in the surface tension of the probe liquid led to а transition to the Wetzel state at 44–46 mN/m for alkoxysilanes and at 52 mN/m for oleic acid. A typical shape of the textured surface wetting curve is proposed. It was shown that the determined values of the surface tension of the Cassie-Wenzel transition were 10–15 mN/m lower than those predicted by the Cassie equations. [ABSTRACT FROM AUTHOR]

Herein, we present the imbibition-induced, spontaneous, and selective wetting characteristics of gallium-based liquid metal alloys on a metallized surface with micro-scale topographical features. Gallium-based liquid metal alloys are fascinating materials that have enormous surface tension; therefore, they are difficult to pattern into films. The complete wetting of eutectic alloy of gallium and indium is realized on microstructured copper surfaces in the presence of HCl vapor, which removes the native oxide from the liquid metal alloy. This wetting is numerically explained based on the Wenzel's model and imbibition process, revealing that the dimensions of the microstructures are critical for effective imbibition-driven wetting of the liquid metal. Further, we demonstrate that the spontaneous wetting of the liquid metal can be directed selectively along the microstructured region on the metallic surface to create patterns. This simple process enables the uniform coating and patterning of the liquid metal over large areas without an external force or complex processing. We demonstrate that the liquid metal-patterned substrates maintain electrical connection even in a stretched state and after repetitive stretching cycles. Liquid metals that have enormous surface tension are difficult to pattern into films. Here, authors report the spontaneous and selective wetting of a gallium-based liquid metal, which is induced by imbibition on a micro-structured metallized substrate. [ABSTRACT FROM AUTHOR]

When a droplet is placed on a soft surface, surface tension deforms the substrate, creating a capillary ridge. We study how the motion of the ridge dissipates energy in microscopic droplets. Using a micropipette based method, we are able to simultaneously image and measure forces on a microscopic droplet moving at a constant speed along a soft film supported on a rigid substrate. Changing the thickness of the thin film tunes the effective stiffness of the substrate. Thus we can control the ridge size without altering the surface chemistry. We find that the dissipation depends strongly on the film thickness, decreasing monotonically as effective stiffness increases. This monotonic trend is beyond the realm of small deformation theory, but can be explained with a simple scaling analysis. Elastic deformation of soft substrates occurs upon wetting, yet it is challenging to follow its dynamics at a microscale. Khattak et al. show that the force required to pull a droplet along a soft surface decreases monotonically as the film thickness decreases and explain the phenomenon using a scaling analysis. [ABSTRACT FROM AUTHOR]

Marangoni effect plays an important role in many industrial applications where a surface tension gradient induces fluid flow, e.g., the cleaning process of silicon wafers and the welding process of melted metal. Surface tension gradient can also be caused by a spatially varying temperature field which, in the absence of gravity, is solely responsible for driving a large scale convective flow. NASA STDC-1 (Surface Tension Driven Convection) experiments performed on USML-1 Spacelab missions in 1992 were designed to study thermocapillary flows in microgravity. Since then these experiments have become a benchmark in thermocapillary studies in the absence of gravity. However, interpretation of results of the original STDC-1 experiments remains challenging due to the low resolution of the available data. Analysis of the velocity field in those experiments was limited to a single tracking method without systematic and comparative studies. In the present study, we utilize multiple state-of-the-art Particle Image Velocimetry and Particle Tracking Velocimetry tools to extract the flow field from NASA STDCE-1 videos and compare the experimental data to the numerical results from COMSOL Multiphysics® v5.6. Finally, we discuss how our findings of temperature-driven Marangoni flow in the microgravity setting can improve future experiments and analysis. [ABSTRACT FROM AUTHOR]

The force on a solid rod partially immersed in a liquid is commonly used to determine the liquid-vapor surface tension by equating the measured force required to remove the rod from the liquid to the vertical component of the liquid-vapor surface tension. Here, we study how this process is affected when the rod is compliant. For equilibrium, we enforce force and configurational energy balance, including contributions from elastic energy. We show that, in general, the contact angle does not equal that given by Young's equation. If surface stresses are tensile, the strain in the immersed part of the rod is found to be compressive and to depend only on the solid-liquid surface stress. The strain in the dry part of the rod can be either tensile or compressive, depending on a combination of parameters that we identify. We also provide results for compliant plates partially immersed in a liquid under plane strain and plane stress. Our results can be used to extract solid surface stresses from such experiments. [ABSTRACT FROM AUTHOR]

Previous linear bifurcation analyses have evidenced that an axially stretched soft cylindrical tube may develop an infinite-wavelength (localized) instability when one or both of its lateral surfaces are under sufficient surface tension. Phase transition interpretations have also highlighted that the tube admits a final evolved 'two-phase' state. How the localized instability initiates and evolves into the final 'two-phase' state is still a matter of contention, and this is the focus of the current study. Through a weakly nonlinear analysis conducted for a general material model, the initial sub-critical bifurcation solution is found to be localized bulging or necking depending on whether the axial stretch is greater or less than a certain threshold value. At this threshold value, an exceptionally super-critical kink-wave solution arises in place of localization. A thorough interpretation of the anticipated post-bifurcation behaviour based on our theoretical results is also given, and this is supported by finite-element method simulations. [ABSTRACT FROM AUTHOR]

Interfacial stability is important for many processes involving heat and mass transfer across two immiscible phases. For the evaporation of a binary solution with one component more volatile than the other, gradients in surface tension can arise. These gradients can ultimately destabilize the liquid–gas interface. We study the evaporation of an ethanol–water solution, for which ethanol is more volatile. The solution is contained in a horizontal Hele-Shaw cell which is open from one end to allow for evaporation into air. A Marangoni instability is then triggered at the liquid–air interface. We study the temporal evolution of the instability through its effects on the bulk of the liquid. More specifically, the growth of convective cells is measured with confocal microscopy and the velocity field with microparticle image velocimetry. The results of numerical simulations based on quasi-two-dimensional equations satisfactorily compare with the experimental observations, even without consideration of evaporative cooling, although this cooling can play an extra role in experiments. Furthermore, a linear stability analysis applied to a simplified version of the quasi-two-dimensional equations showed reasonably good agreement with the results from simulations at early times, when the instability has just been triggered and before coarsening. In particular, we find a critical Marangoni number below which a regime of stability is predicted. [ABSTRACT FROM AUTHOR]

Surface waves are excited at the boundary of a mechanically vibrated cylindrical container and are referred to as edge waves. Resonant waves are considered, which are formed by a travelling wave formed at the edge and constructively interfering with its centre reflection. These waves exhibit an axisymmetric spatial structure defined by the mode number $n$. Viscoelastic effects are investigated using two materials with tunable properties; (i) glycerol/water mixtures (viscosity) and (ii) agarose gels (elasticity). Long-exposure white-light imaging is used to quantify the magnitude of the wave slope from which frequency-response diagrams are obtained via frequency sweeps. Resonance peaks and bandwidths are identified. These results show that for a given $n$ , the resonance frequency decreases with viscosity and increases with elasticity. The amplitude of the resonance peaks are much lower for gels and decrease further with mode number, indicating that much larger driving amplitudes are needed to overcome the elasticity and excite edge waves. The natural frequencies for a viscoelastic fluid in a cylindrical container with a pinned contact-line are computed from a theoretical model that depends upon the dimensionless Ohnesorge number ${Oh}$ , elastocapillary number ${Ec}$ and Bond number ${Bo}$. All show good agreement with experimental observations. The eigenvalue problem is equivalent to the classic damped-driven oscillator model on linear operators with viscosity appearing as a damping force and elasticity and surface tension as restorative forces, consistent with our physical interpretation of these viscoelastic effects. [ABSTRACT FROM AUTHOR]

Our understanding of animal locomotion in air and water has progressed considerably, based on studies of their wakes. Wake vortices are the hallmarks of momentum transfer and enable an inverse inference of the forces applied by animals. Such approach has recently been extended to locomotion at the air-water interface, focusing on the familiar water striders and their dual hallmarks, surface capillary waves and bulk water vortices, produced by their paddling legs. However, the principal mechanisms of propulsion used in this type of locomotion remain a matter of debate. We confirm that the main force driving propulsion is the capillary force resulting from surface tension, and that interface relaxation makes a major contribution to the increase in vorticity of the water bulk. There is therefore no one-to-one mapping between forces and hallmarks in the fluid. Locomotion at the air-water interface for animals with virtual oars much larger than the size of their legs thus requires specific treatment outside the existing framework based on immersed propulsive appendices. [ABSTRACT FROM AUTHOR]

Thin membranes that may be exposed to water droplet deposition have been used in various industrial and research fields. Deflection of these membranes by water droplets may greatly affect their characteristics. Therefore, it is important to predict deflection of these thin membranes by water droplets. Here, the contact angle effect of a sessile drop was analyzed by a combination of deformation and surface energy; the deflection of elastomer thin membranes was investigated by experiment and simulation. Circular thin membranes were fabricated comprising various materials (i.e., expanded polytetrafluoroethylene, polytetrafluoroethylene, and polyethylene). Modal characteristics for thin membranes mounted on a ring fixture were measured when all edge points were clamped. Based on the measured fundamental frequency, initial tension was determined in accordance with circular thin membrane vibration theory. A numerical model was derived to describe the water droplet profile and membrane deflection by thermodynamics and mechanical energy. Contact angles and profiles were measured for three types of thin membrane and for various water droplet sizes, using a high-speed camera. Deflections were measured using a laser sensor with water droplets of various sizes and various contact angles, along with various ethanol concentrations on the thin membrane. Experimental results were consistent with simulation results. The degree of nonlinearity could be ignored for thin membranes with water droplet volume of ≤ 200 μ L . Maximum deflection of various thin membranes and various contact angles could be predicted using compensation factors. Maximum deflection of the thin membrane could be sufficiently predicted when considering the contact angle effect. [ABSTRACT FROM AUTHOR]

Liquid marble, an emerging platform for digital microfluidics, has shown its potential in biomedical applications, cosmetics, and chemical industries. Recently, the manipulation and fundamental aspects of liquid marbles have been reported and attracted attention from the microfluidics community. Insights into their physical and chemical properties allow liquid marbles to be utilised in practical applications. This review summarises and revisits the effect of capillarity on the formation of liquid marbles and how it affects the effective surface tension as well as their robustness. The paper also systematically discusses the applied aspect of capillarity of the carrier liquid for transporting floating liquid marbles. [ABSTRACT FROM AUTHOR]

Capillarity is the familiar manifestation of the cohesion of liquids. Since Laplace (Traité de mécanique céleste, vol. IV, supplément au livre X: Sur l'action capillaire, 1805, pp. 1–65), we know that intense attractive forces between the molecules bridge the small with the large as they shape liquid/vapour interfaces at the macroscopic scale through the concept of surface tension (menisci, drops, bubbles, puddles, liquid rise in tubes, etc. ...). We concentrate on situations where liquids 'disgregate', following the neologism of Clausius (Phil. Mag., vol. 24 (159), 1862, pp. 81–97), meaning that they fragment by the action of deformation stresses whose intensity competes with that of cohesion forces. Various examples, including explosions, blow-ups, hard and soft impacts and shears applied to liquid jets, sheets and drops are reviewed. They concern applications ranging from liquid propulsion, agricultural spraying, to the formation of ocean spray, raindrops and human exhalations by violent respiratory events. In spite of their diversity, the various modes of fragment production share an ultimate common phenomenology – the ligament dynamics – suggesting that the final stable droplet size distribution can be interpreted from elementary principles. [ABSTRACT FROM AUTHOR]

This paper presents the topology optimization of hierarchical microtextures for wetting behavior in the Cassie-Baxter mode, considering a structural unit of the hierarchical microtexture composed of base and secondary structures. The geometrical configuration of the considered structural unit can be described as a fiber bundle composed of an external surface of the base structure and the pattern of the secondary structures. Thus, two design variables are defined, one for the external surface of the base structure, and the other for the pattern of the secondary structures. The Young-Laplace equation, including a term depending on the mean curvature of the external surface, is used to describe the liquid/vapor interface imposed with a surface tension in the Cassie-Baxter mode. To overcome the difficulty of numerically computing the second-order derivative of the external surface, two partial differential equation filters are sequentially applied to the design variable of the base structure to ensure the numerical accuracy and feasibility of using an efficient linear-element-based finite element method to solve the Young-Laplace equation. To improve the performance of the hierarchical microtextures, the volume of the liquid bulges suspended at the liquid/vapor interface in the Cassie-Baxter mode, before the transition into the Wenzel mode, is minimized to optimize the match between the external surface of the base structure and the pattern of the secondary structures. In the topology optimization process, penalization of the material density of the surface tension is achieved by an artificial Marangoni phenomenon. In numerical examples, solid surfaces are tiled into textures with axial symmetry, radial symmetry, chirality, and quasiperiodicity; and structural units are derived consisting of base structures with peak shapes and dense secondary structures surrounding the crests of the peaks. The optimized performance of the derived structural units has been confirmed by comparisons. [ABSTRACT FROM AUTHOR]

We study here experimentally, numerically and using a lubrication approach, the shape, velocity and lubrication film thickness distribution of a droplet rising in a vertical Hele-Shaw cell. The droplet is surrounded by a stationary immiscible fluid and moves purely due to buoyancy. A low density difference between the two media helps to operate in a regime with capillary number $Ca$ lying between $0.03$ and $0.35$ , where $Ca=\unicode[STIX]{x1D707}_{o}U_{d}/\unicode[STIX]{x1D6FE}$ is built with the surrounding oil viscosity $\unicode[STIX]{x1D707}_{o}$ , the droplet velocity $U_{d}$ and surface tension $\unicode[STIX]{x1D6FE}$. The experimental data show that in this regime the droplet velocity is not influenced by the thickness of the thin lubricating film and the dynamic meniscus. For iso-viscous cases, experimental and three-dimensional numerical results of the film thickness distribution agree well with each other. The mean film thickness is well captured by the Aussillous & Quéré (Phys. Fluids, vol. 12 (10), 2000, pp. 2367–2371) model with fitting parameters. The droplet also exhibits the 'catamaran' shape that has been identified experimentally for a pressure-driven counterpart (Huerre et al., Phys. Rev. Lett., vol. 115 (6), 2015, 064501). This pattern has been rationalized using a two-dimensional lubrication equation. In particular, we show that this peculiar film thickness distribution is intrinsically related to the anisotropy of the fluxes induced by the droplet's motion. [ABSTRACT FROM AUTHOR]

Surface energy outside the contact zone, which is not accounted for in the classical Johnson–Kendall–Roberts (JKR) model, can play an essential role in adhesion mechanics of soft particles. An open problem in the adhesion mechanics of soft elastic particles is how to achieve an explicit expression for the surface energy outside the contact zone in terms of the two JKR-type variables (a, δ), where a is the radius of the contact zone and δ is the relative approach of two bodies. The present work aims to develop an ellipsoidal cap model for the surface energy outside the contact zone of a soft elastic particle on a rigid substrate in terms of the two JKR-type variables (a, δ). An explicit expression for the surface energy outside the contact zone is derived, and simple asymptotic equations are obtained to determine the two unknowns (a, δ). The validity and accuracy of the derived expression and asymptotic equations are verified by good agreement with the Young–Dupre equation in the absence of an external applied force, and are also justified by good agreement of the predicted pull-off force with known results available in recent literature. [ABSTRACT FROM AUTHOR]

We present a computational method that can be applied to capture surface stress and surface tension-driven effects in both stiff, crystalline nanostructures, like size-dependent mechanical properties, and soft solids, like elastocapillary effects. We show that the method is equivalent to the classical Young-Laplace model. The method is based on converting surface tension and surface elasticity on a zero-thickness surface to an initial stress and corresponding elastic properties on a finite thickness shell, where the consideration of geometric nonlinearity enables capturing the out-of-plane component of the surface tension that results for curved surfaces through evaluation of the surface stress in the deformed configuration. In doing so, we are able to use commercially available finite element technology, and thus do not require consideration and implementation of the classical Young-Laplace equation. Several examples are presented to demonstrate the capability of the methodology for modeling surface stress in both soft solids and crystalline nanostructures. [ABSTRACT FROM AUTHOR]

A new physical method, the sessile drop accelerometry (SDACC) for the study and measurement of the interfacial energies of solid-liquid-gas systems, is tested and discussed in this study. The laboratory instrument and technique—a combination of a drop shape analyzer with high-speed camera and a laboratory drop tower- and the evaluation algorithms, were designed to calculate the interfacial energies as a function of the geometrical changes of a sessile droplet shape due to the effect of “switching off” gravity during the experiment. The method bases on Thermodynamics of Interfaces and differs from the conventional approach of the two hundred-years-old Young’s equation in that it assumes a thermodynamic equilibrium between interfaces, rather than a balance of tensions on a point of the solid-liquid-gas contour line. A comparison of the mathematical model that supports the method with the widely accepted Young‘s equation is discussed in detail in this study. The method opens new possibilities to develop surface characterization procedures by submitting the solid-liquid-system to artificial generated and uniform force fields. [ABSTRACT FROM AUTHOR]

We present a novel method of actuating a microliter droplet held within a Hele-Shaw cell by means of the surface tension gradient orMarangoni effect. A food color droplet is first injected within the gap formed by the parallel plates to produce a cylindrical droplet, followed by a lateral injection of a lower surface tension droplet. Our results show the actuation of the food color droplet, for various droplet volumes and viscosities. Analytical studies on the effect of contact angle on distance traveled are presented. Numerical values of the Marangoni force showgood agreementwith analytical values. Mathematical analysis shows the surface tension difference required for actuation, and how the surface tension changes as a function of angular position on the droplet. [ABSTRACT FROM AUTHOR]

Theories of wetting have a long history and they are intensively used in interpreting experimental data. Nevertheless, many basic aspects, such as the pinning of a contact line and contact angle hysteresis, are still poorly understood. The development of a rigorous consensus theory has suffered from concepts that are based on faulty intuitions. These include the force interpretation of Young's equation, the use of the principle of minimizing the global free energy, and the concepts of the work of adhesion and the mechanical surface tension on a solid. In this paper, the appropriate treatment of the basic ingredients of surface thermodynamics is discussed and the route towards the physically justified theoretical approach on wetting is outlined. [ABSTRACT FROM AUTHOR]

The Kirchhoff-Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a soap film, with the filament being modeled as a Kirchhoff rod and the action of the spanning surface being solely due to surface tension. Adopting a variational approach, we define an energy associated with shape deformations of the system and then derive general equilibrium and (linear) stability conditions by considering the first and second variations of the energy functional. We analyze in detail the transition to instability of flat circular configurations, which are ground states for the system in the absence of surface tension, when the latter is progressively increased. Such a theoretical study is particularly useful here, since the many different perturbations that can lead to instability make it challenging to perform an exhaustive experimental investigation. We generalize previous results, since we allow the filament to possess a curved intrinsic shape and also to display anisotropic flexural properties (as happens when the cross section of the filament is noncircular). This is accomplished by using a rod energy which is familiar from the modeling of DNA filaments. We find that the presence of intrinsic curvature is necessary to obtain a first buckling mode which is not purely tangent to the spanning surface. We also elucidate the role of twisting buckling modes, which become relevant in the presence of flexural anisotropy. [ABSTRACT FROM AUTHOR]

When a fluid-immersed array of supported plates or pillars is dried, evaporation leads to the formation of menisci on the tips of the plates or pillars that bring them together to form complex patterns. Building on prior experimental observations, we use a combination of theory and computation to understand the nature of this instability and its evolution in both the two- and three-dimensional setting of the problem. For the case of plates, we explicitly derive the interaction torques based on the relevant physical parameters associated with pillar deformation, contact-line pinning/depinning and fluid volume changes. A Bloch-wave analysis for our periodic mechanical system captures the window of volumeswhere the two-plate eigenvalue characterizes the onset of the coalescence instability. We then study the evolution of these binary clusters and their eventual elastic arrest using numerical simulations that account for evaporative dynamics coupled to capillary coalescence. This explains both the formation of hierarchical clusters and the sensitive dependence of the final structures on initial perturbations, as seen in our experiments. We then generalize our analysis to treat the problem of pillar collapse in three dimensions, where the fluid domain is completely connected and the interface is a minimal surface with the uniform mean curvature. Our theory and simulations capture the salient features of experimental observations in a range of different situations and may thus be useful in controlling the ensuing patterns. [ABSTRACT FROM AUTHOR]

Small objects that are more dense than water may still float at the air-water interface because of surface tension. Whether this is possible depends not only on the density and size of the object, but also on its shape and surface properties, whether other objects are nearby, and how gently the object is placed at the interface. This review surveys recent work to quantify when objects can float and when they must sink. Much interest in this area has been driven by studies of the adaptations of water-walking insects to life at interfaces. I therefore discuss these results in the context of this and other applications. [ABSTRACT FROM AUTHOR]

The capillary force of a liquid drop has a great impact on the mechanical behaviors of a polymer microtube. To further explore this capillary effect, we examine the buckling condition and finite deformation of a hollow microfiber surrounded by a droplet. The Eulerian rod model and thin-walled shell model are both adopted to predict the critical value of the capillary force acting on the microfiber. According to the Mooney-Rivlin model, we calculate the true axial stress of the microtube under the combined action of surface tension and Laplace pressure. The numerical results show that the value of the true axial stress is closely related to the Young's contact angle, droplet volume and characteristic sizes of the microtube. Our findings address that proper control over surface wettability may improve the performance optimization of micro-devices, and these analyses may produce ideas in the areas of nanofabrication, electrospinning and tissue engineering. [ABSTRACT FROM AUTHOR]

Surface wetting is an important phenomenon in many industrial processes including micro- and nanofluidics. The wetting characteristics depend on the surface tension forces at the three-phase contact line and can be altered by introducing patterned groove structures. This study investigates the effect of the grooves on the transition in the wetting behavior between the Cassie to Wenzel regimes. The experiments demonstrate that the wettability on a patterned surface depends on the spacing factor ( S = channel depth/channel width). The spacing factor influences the contact angle, contact angle hysteresis, and the transition characteristics between the Cassie and Wenzel states. It was noted that under certain conditions ( S > 1) the droplet behaved as a Cassie droplet, while exhibiting Wenzel wetting the rest of the time on the silicon microchannels tested. This criterion was used to design the groove structures on the sidewall of the proton exchange membrane fuel cell gas channel to remove the water effectively. The water coming from the land region into the gas channel is pulled by the grooves to the top wall where the airflow aided in its removal. Also, the contact angles measured on the surfaces were compared with the classical models that use wetted area, and the contact line model that uses the three-phase contact line length. It was found in our experiments that the contact line model predicts the contact angle on the patterned groove surfaces more accurately than the classical models. [ABSTRACT FROM AUTHOR]

Ten splash-form tektites from the Australasian strewn field, with masses ranging from 21.20 to 175.00 g and exhibiting a variety of shapes (teardrop, ellipsoid, dumbbell, disk), have been imaged using a high-resolution laser digitizer. Despite challenges due to the samples' rounded shapes and pitted surfaces, the images were combined to create 3-D tektite models, which captured surface features with a high fidelity (≈30 voxel mm−2) and from which volume could be measured noninvasively. The laser-derived density for the tektites averaged 2.41 ± 0.11 g cm−3. Corresponding densities obtained via the Archimedean bead method averaged 2.36 ± 0.05 g cm−3. In addition to their curational value, the 3-D models can be used to calculate the tektites' moments of inertia and rotation periods while in flight, as a probe of their formation environment. Typical tektite rotation periods are estimated to be on the order of 1 s. Numerical simulations of air flow around the models at Reynolds numbers ranging from 1 to 106 suggest that the relative velocity of the tektites with respect to the air must have been <10 m s−1 during viscous deformation. This low relative velocity is consistent with tektite material being carried along by expanding gases in the early time following the impact. [ABSTRACT FROM AUTHOR]

The interactions between water droplets and elastic films were examined by acquiring droplet and PDMS film images using a high-speed visualization technique. The contact angle with a water droplet and the deflection of a PDMS thin polymer film were measured from the images and compared with the values calculated from modified cantilever theory. The contact angle and deflection of the PDMS thin plate increased with increasing droplet volume. The static behavior of the elasto-capillarity effect was confirmed by theory and experiment. The dynamic behavior of an elastic film was also examined using the AC electro-wetting condition. The elastic polymer with a droplet was vibrating at double the frequency of the excited AC frequency. The amplitude of vibration increased with increasing AC voltage. These results can be used to design practical microactuators. Graphical Abstract: [Figure not available: see fulltext.]. [ABSTRACT FROM AUTHOR]

We present a fluid-mechanical model of the coalescence of a number of elastic objects due to surface tension. We consider an array of spring–block elements separated by thin liquid films, whose dynamics are modelled using lubrication theory. With this simplified model of elastocapillary coalescence, we present the results of numerical simulations for a large number of elements, $N=O(10^4)$. A linear stability analysis shows that pairwise coalescence is always the most unstable mode of deformation. However, the numerical simulations show that the cluster sizes actually produced by coalescence from a small white-noise perturbation have a distribution that depends on the relative strength of surface tension and elasticity, as measured by an elastocapillary number $K$. Both the maximum cluster size and the mean cluster size scale like $K^{-1/2}$ for small $K$. An analytical solution for the response of the system to a localized perturbation shows that such perturbations generate propagating disturbance fronts, which leave behind ‘frozen-in’ clusters of a predictable size that also depends on $K$. A good quantitative comparison between the cluster-size statistics from noisy perturbations and this ‘frozen-in’ cluster size suggests that propagating fronts may play a crucial role in the dynamics of coalescence. [ABSTRACT FROM PUBLISHER]

Porous carbon materials with high specific surface areas and superhydrophobicity have attracted much research interest due to their potential application in the areas of water filtration, water/oil separation, and oil-spill cleanup. Most reported superhydrophobic porous carbon materials are fabricated by complex processes involving the use of catalysts and high temperatures but with low throughput. Here, we present a facile single-step method for fabricating porous carbon nanoparticle (CNP) networks with selective absorbability for water and oils via the glow discharge of hydrocarbon plasma without a catalyst at room temperature. Porous CNP networks were grown by the continuous deposition of CNPs at a relatively high deposition pressure. By varying the fluorine content, the porous CNP networks exhibited tunable repellence against liquids with various degrees of surface tension. These porous CNP networks could be applied for the separation of not only water/oil mixtures but also mixtures of liquids with different surface tension levels. [ABSTRACT FROM AUTHOR]

We present a theoretical study of the abnormal deformation of micro-beams induced by a droplet placed on their top/bottom surfaces. The bending moments and deflections of the micro-beams are derived in consideration of the surface tension and Laplacian pressure difference of the droplet. The deflection curves show that the cantilever inevitably tilts upwards with a droplet on its top surface, and most parts of the simply supported beam and clamped–clamped beam will bend upwards when a droplet is adhered to their bottom surfaces. These anomalous deformation behaviors have been verified by our finite element simulations. We also demonstrate what extent of the boundary conditions will affect the deflection curves of the micro-beams during the variation of the droplet’s parameters. Understanding this abnormal bending mechanism of the beams can be beneficial to some industry applications, such as the micro-electro-mechanical systems (MEMS) and the micro/nano-measurement, which can provide the inspiration of engineering more precision micro-sensors. [ABSTRACT FROM PUBLISHER]

Capillary origami uses surface tension to fold and shape solid films and membranes into three-dimensional structures. It uses the fact that solid surfaces, no matter how hydrophobic, will tend to adhere to and wrap around the surface of a liquid. In this work, we report that a superhydrophobic coating can be created, which can completely suppress wrapping as a contacting water droplet evaporates. We also show that using a wetting azeotropic solution of allyl alcohol, which penetrates the surface features, can enhance liquid adhesion and create more powerful Capillary Origami. These findings create the possibility of selectively shaping membrane substrates. [ABSTRACT FROM AUTHOR]

Capillary forces present during the manufacturing and operation of microelectromechanical structures have been shown to cause collapse of these structures. Once collapsed these structures may permanently adhere together. In this paper we study the adhesion of a microstructure represented by a double cantilever beam (DCB); such adhesion is driven by both the capillary forces from a liquid droplet located between the DCB and the adhesion forces between the solids. The DCB is modeled using both a beam theory that accounts for geometrical nonlinearity and the linearized beam theory. This model rigorously couples DCB deformation, capillary forces, meniscus movement and adhesion, and reveals four dimensionless parameters that govern the adhesion problem. How changes in these parameters influence the capillary forces, the length of the contact zone, and the contact force is discussed in detail. [ABSTRACT FROM PUBLISHER]

The wetting of solid surfaces is treated. The Young and receding contact angles are experimentally unattainable values for the majority of solid surfaces. Actually, we always observe the apparent contact angle. This makes the characterization of wetting of real surfaces problematic. It is proposed in this paper to characterize wetting of real surfaces with the advancing contact angle and the minimum work of adhesion calculated according to the Dupre equation. The advancing contact angle, which depends slightly on the experimental technique used for its measurement, corresponds to the maximal solid/liquid surface tension and correspondingly to the minimal work of adhesion, calculated according to the Dupre equation. [ABSTRACT FROM AUTHOR]

Liquid bridges with moving contact lines are relevant in a variety of natural and industrial settings, ranging from printing processes to the feeding of birds. While it is often assumed that the liquid bridge is two-dimensional in nature, there are many applications where either the stretching motion or the presence of a feature on a bounding surface lead to three-dimensional effects. To investigate this we solve Stokes equations using the finite-element method for the stretching of a three-dimensional liquid bridge between two flat surfaces, one stationary and one moving. We first consider an initially cylindrical liquid bridge that is stretched using either a combination of extension and shear or extension and rotation, while keeping the contact lines pinned in place. We find that whereas a shearing motion does not alter the distribution of liquid between the two plates, rotation leads to an increase in the amount of liquid resting on the stationary plate as breakup is approached. This suggests that a relative rotation of one surface can be used to improve liquid transfer to the other surface. We then consider the extension of non-cylindrical bridges with moving contact lines. We find that dynamic wetting, characterized through a contact line friction parameter, plays a key role in preventing the contact line from deviating significantly from its original shape as breakup is approached. By adjusting the friction on both plates it is possible to drastically improve the amount of liquid transferred to one surface while maintaining the fidelity of the liquid pattern. [ABSTRACT FROM PUBLISHER]

Elastocapillary phenomena involving elastic deformation of solid structures coupled with capillary effects of liquid droplets/films can be observed in a diversity of fields, e.g., biology and microelectromechanical systems (MEMS). Understanding the physical mechanisms underlying these phenomena is of great interest for the design of new materials and devices by utilizing the effects of surface tension at micro and nano scales. In this paper, some recent developments in the investigations on elastocapillary phenomena are briefly reviewed. Especially, we consider the deformation, adhesion, self-assembly, buckling and wrinkling of materials and devices induced by surface tensions or capillary forces. The main attention is paid to the experimental results of these phenomena and the theoretical analysis methods based on continuum mechanics. Additionally, the applications of these studies in the fields of MEMS, micro/nanometrology, and biomimetic design of advanced materials and devices are discussed. [ABSTRACT FROM AUTHOR]

Smooth wrinkles and sharply crumpled regions are familiar motifs in biological or synthetic sheets, such as rapidly growing plant leaves and crushed foils. Previous studies have addressed both morphological types, but the generic route whereby a featureless sheet develops a complex shape remains elusive. Here we show that this route proceeds through an unusual sequence of distinct symmetry-breaking instabilities. The object of our study is an ultrathin circular sheet stretched over a liquid drop. As the curvature is gradually increased, the surface tension stretching the sheet over the drop causes compression along circles of latitude. The compression is relieved first by a transition into a wrinkle pattern, and then into a crumpled state via a continuous transition. Our data provide conclusive evidence that wrinkle patterns in highly bendable sheets are not described by classical buckling methods, but rather by a theory which assumes that wrinkles completely relax the compressive stress. With this understanding we recognize the observed sequence of transitions as distinct symmetry breakings of the shape and the stress field. The axial symmetry of the shape is broken upon wrinkling but the underlying stress field preserves this symmetry. Thus, the wrinkle-to-crumple transition marks symmetrybreaking of the stress in highly bendable sheets. By contrast, other instabilities of sheets, such as blistering and cracking, break the homogeneity of shape and stress simultaneously. The onset of crumpling occurs when the wrinkle pattern grows to half the sheet's radius, suggesting a geometric, material-independent origin for this transition. [ABSTRACT FROM AUTHOR]

We present the results of a combined experimental and theoretical investigation of the surface-tension-driven coalescence of flexible structures. Specifically, we consider the dynamics of the rise of a wetting liquid between flexible sheets that are clamped at their upper ends. As the elasticity of the sheets is progressively increased, we observe a systematic deviation from the classical diffusive-like behaviour: the time to reach equilibrium increases dramatically and the departure from classical rise occurs sooner, trends that we elucidate via scaling analyses. Three distinct temporal regimes are identified and subsequently explored by developing a theoretical model based on lubrication theory and the linear theory of plates. The resulting free-boundary problem is solved numerically and good agreement is obtained with experiments. [ABSTRACT FROM PUBLISHER]

A drop impacting a target cutout in a thin polymer film is wrapped by the film in a dynamic sequence involving both capillary forces and inertia. Different 3D structures can be produced from a given target by slightly varying the impact parameters. A simplified mod- el for a nonlinear dynamic Elastica coupled with a drop successfully explains this shape selection and yields detailed quantitative agreement with experiments. This first venture into the largely unexplored dynamics of elastocapillary assemblies opens up the perspective of mass production of 3D packages with individual shape selection. [ABSTRACT FROM AUTHOR]

Hummingbird tongues pick up a liquid, calorie-dense food that cannot be grasped, a physical challenge that has long inspired the study of nectar-transport mechanics. Existing biophysical models predict optimal hummingbird foraging on the basis of equations that assume that fluid rises through the tongue in the same way as through capillary tubes. We demonstrate that the hummingbird tongue does not function like a pair of tiny, static tubes drawing up floral nectar via capillary action. Instead, we show that the tongue tip is a dynamic liquid-trapping device that changes configuration and shape dramatically as it moves in and out of fluids. We also show that the tongue-fluid interactions are identical in both living and dead birds, demonstrating that this mechanism is a function of the tongue structure itself, and therefore highly efficient because no energy expenditure by the bird is required to drive the opening and closing of the trap. Our results rule out previous conclusions from capillarity-based models of nectar feeding and highlight the necessity of developing a new biophysical model for nectar intake in hummingbirds. Our findings have ramifications for the study of feeding mechanics in other nectarivorous birds, and for the understanding of the evolution of nectarivory in general. We propose a conceptual mechanical explanation for this unique fluid-trapping capacity, with far-reaching practical applications (e.g., biomimetics). [ABSTRACT FROM AUTHOR]

In this article, the authors comment on the extreme non-wettability of superhydrophobic materials. The authors believe that there are unexplored implications of superhydrophobicity in terms of transport phenomena. Moreover, it discusses the challenges faced in the material design of superhydrophobic surfaces in wetting.

Splash-form tektites are glassy rocks ranging in size from roughly 1 to 100 mm that are believed to have formed from the splash of silicate liquid after a large terrestrial impact from which they are strewn over thousands of kilometres. They are found in an array of shapes including spheres, oblate ellipsoids, dumbbells, rods and possibly fragments of tori. It has recently become appreciated that surface tension and centrifugal forces associated with the rotation of fluid droplets are the main factors determining the shapes of these tektites. In this contribution, we compare the shape distribution of 1163 measured splash-form tektites with the results of the time evolution of a 3D numerical model of a rotating fluid drop with surface tension. We demonstrate that many aspects of the measured shape distribution can be explained by the results of the dynamical model. [ABSTRACT FROM AUTHOR]

We study the capillary rise of wetting liquids in the corners of different geometries and show that the meniscus rises without limit following the universal law: h(t)/a ≈ (γt/ηa)1/3, where γ and η stand for the surface tension and viscosity of the liquid while $a\,{=}\,\sqrt{\gamma/\rho g}$ is the capillary length, based on the liquid density ρ and gravity g. This law is universal in the sense that it does not depend on the geometry of the corner. [ABSTRACT FROM AUTHOR]

Abstract  Extensional rheometry has only recently been developed into a commercially available tool with the introduction of the capillary breakup extensional rheometer (CaBER). CaBER is currently being used to measure the transient extensional viscosity evolution of mid to low-viscosity viscoelastic fluids. The elegance of capillary breakup extensional experiments lies in the simplicity of the procedure. An initial step-stretch is applied to generate a fluid filament. What follows is a self-driven uniaxial extensional flow in which surface tension is balanced by the extensional stresses resulting from the capillary thinning of the liquid bridge. In this paper, we describe the results from a series of experiments in which the step-stretch parameters of final length, and the extension rate of the stretch were varied and their effects on the measured extensional viscosity and extensional relaxation time were recorded. To focus on the parameter effects, well-characterized surfactant wormlike micelle solutions, polymer solutions, and immiscible polymer blends were used to include a range of characteristic relaxation times and morphologies. Our experimental results demonstrate a strong dependence of extensional rheology on step-stretch conditions for both wormlike micelle solutions and immiscible polymer blends. Both the extensional viscosity and extensional relaxation time of the wormlike micelle solutions were found to decrease with increasing extension rate and strain of the step-stretch. For the case of the immiscible polymer blends, fast step-stretches were found to result in droplet deformation and an overshoot in the extensional viscosity which increased with increasing strain rates. Conversely, the polymer solutions tested were found to be insensitive to step-stretch parameters. In addition, numerical simulations were performed using the appropriate constitutive models to assist in both the interpretation of the CaBER results and the optimization of the experimental protocol. From our results, it is clear that any rheological results obtained using the CaBER technique must be properly considered in the context of the stretch parameters and the effects that preconditioning has on viscoelastic fluids. [ABSTRACT FROM AUTHOR]

We experimentally investigate the interfacial instability that emerges when a water droplet is deposited on a bath of glycerol-water solution. Despite the absence of surface tension to stabilize short-wavelength undulations, we observe finite-size fingers that grow and pinch off from the drop. We show that the fingering patterns formed in the experiments resultes from a balance between the outward buoyancy effect and inward Marangoni flow. This induced Marangoni flow inhibits small perturbations and acts as an effective surface tension on the miscible interface of the spreading drop. To characterize the final size and shape of the drop, we perform systematic experiments by varying the drop volume and the glycerol-water volume fraction. In addition, we have developed scaling arguments for the drop's final radius using key physical forces, and show that the final wavelength is inversely proportional to the Bond number. [ABSTRACT FROM AUTHOR]

We focus on the dynamical aspects of wetting phenomena on the nanoscale for which bulk hydrodynamic equations become invalid. At the nanoscale, phenomena that are irrelevant on the micrometer scale and larger, or that can be summarily incorporated in terms of boundary conditions, become important. Among these features are long-ranged molecular interactions such as dispersion forces, thermal fluctuations, hydrodynaniic slip, segregation of mixtures and solutions at walls, and electrical double layers. [ABSTRACT FROM AUTHOR]

We discuss in this review how the roughness of a solid impacts its wettability. We see in particular that both the apparent contact angle and the contact angle hysteresis can be dramatically affected by the presence of roughness. Owing to the development of refined methods for setting very well-controlled micro- or nanotextures on a solid, these effects are being exploited to induce novel wetting properties, such as spontaneous filmification, superhydrophobicity, superoleophobicity, and interfacial slip, that could not be achieved without roughness. [ABSTRACT FROM AUTHOR]

The relationships among contact angles, surface tensions, and surface roughness are reviewed. The various numerical formulae related to contact angles were used to predict the surface tension and wetting behavior of polymer surfaces. The apparent contact angle of a droplet deposited on a textured surface is presented, and the characteristics required for a superhydrophobic surface are described. This study also presents the effect of the sliding angles of liquid droplets on smooth and rough surfaces. The contact angle hysteresis was found to be very important in understanding the drop motion on a surface. Contact angle hystereses increased on a Wenzel-type surface, while a Cassie-Baxter type surface reduced the hystereses for the same surface roughness and surface tensions. [ABSTRACT FROM AUTHOR]

We consider the hydrodynamics of creatures capable of sustaining themselves on the water surface by means other than flotation. Particular attention is given to classifying water walkers according to their principal means of weight support and lateral propulsion. The various propulsion mechanisms are rationalized through consideration of energetics, hydrodynamic forces applied, or momentum transferred by the driving stroke. We review previous research in this area and suggest directions for future work. Special attention is given to introductory discussions of problems not previously treated in the fluid mechanics literature, with hopes of attracting physicists, applied mathematicians, and engineers to this relatively unexplored area of fluid mechanics. [ABSTRACT FROM AUTHOR]