Abstract: The parameters critical in determining the behaviour of a fibrous medium wetted with a single liquid drop are identified as fibre flexibility, fibre geometry and drop volume. In a study of the behaviour of liquid droplets on flexible fibres, Camille Duprat and colleagues identify six parameters that control how a droplet wets the fibres, including droplet size and mechanical properties of the fibres. Depending on the parameters, the droplet can remain tightly spherical, bridging the fibres; partially wet the fibres; or fully wet them, causing the fibres to cling together. The authors demonstrate using a natural system — a goose feather — that by adjusting drop volume it is possible to control the matting of fibre arrays. From a technological perspective, careful control of these parameters offers the prospect of adjusting the adsorption of droplets for functional microstructured materials. Furthermore, drop volume can be used to control wetting in sprays such as hairsprays, and in the de-oiling of birds contaminated by oil spillage. Fibrous media are functional and versatile materials, as demonstrated by their ubiquity both in natural systems such as feathers1,2,3,4 and adhesive pads5 and in engineered systems from nanotextured surfaces6 to textile products7, where they offer benefits in filtration, insulation, wetting and colouring. The elasticity and high aspect ratios of the fibres allow deformation under capillary forces, which cause mechanical damage8, matting5,9 self-assembly10,11 or colour changes12, with many industrial and ecological consequences. Attempts to understand these systems have mostly focused on the wetting of rigid fibres13,14,15,16,17 or on elastocapillary effects in planar geometries18 and on a fibre brush withdrawn from an infinite bath19. Here we consider the frequently encountered case of a liquid drop deposited on a flexible fibre array and show that flexibility, fibre geometry and drop volume are the crucial parameters that are necessary to understand the various observations referred to above. We identify the conditions required for a drop to remain compact with minimal spreading or to cause a pair of elastic fibres to coalesce. We find that there is a critical volume of liquid, and, hence, a critical drop size, above which this coalescence does not occur. We also identify a drop size that maximizes liquid capture. For both wetting and deformation of the substrates, we present rules that are deduced from the geometric and material properties of the fibres and the volume of the drop. These ideas are applicable to a wide range of fibrous materials, as we illustrate with examples for feathers, beetle tarsi, sprays and microfabricated systems.

Abstract: The commonly accepted description of drops impacting on a surface typically ignores the essential role of the air that is trapped between the impacting drop and the surface. Here we describe a new imaging modality that is sensitive to the behavior right at the surface. We show that a very thin film of air, only a few tens of nanometers thick, remains trapped between the falling drop and the surface as the drop spreads. The thin film of air serves to lubricate the drop enabling the fluid to skate on the air film laterally outward at surprisingly high velocities, consistent with theoretical predictions. Eventually this thin film of air breaks down as the fluid wets the surface via a spinodal-like mechanism. Our results show that the dynamics of impacting drops are much more complex than previously thought, with a rich array of unexpected phenomena that require rethinking classic paradigms.

Abstract: [1] Coalescence of cloud droplets is essential for the production of small raindrops at a given vertical distance above the cloud base (Dp). The rate of droplet coalescence is determined mainly by droplet size, spectrum width and concentrations. The droplet condensational growth is determined by the number of activated CCN (Na) and height above cloud base. Here we show that when the droplet mean volume radius, rv, exceeds ∼13 μm, or when droplet effective radius (re) exceeds ∼14 μm, considerable precipitation mass (>0.03 g kg−1) is likely to be present in growing convective clouds. This is because the rate of droplet coalescence is proportional to ∼rv5 which practically implies the existence of a threshold rv above which efficient warm rain formation can occur, and also because the vertical profile of rv, even in diluted clouds, nearly follows the theoretical adiabatic condensational growth curve. The small observed deviations are mainly caused by deviations from purely inhomogeneous mixing which cause partial droplet evaporation. Consequently, Dp must theoretically change nearly linearly with Na. This is confirmed here observationally, where increasing Na by 100 per milligram (≈cm3 at cloud base) of air, resulted in an increase of ∼280 m in Dpfor both Israeli and Indian deep convective clouds. This means that in highly polluted clouds or where strong cloud-base updrafts occur, clouds have to grow well above the freezing level, even in tropical atmosphere, before precipitation forms either by warm or by mixed-phase processes.

Abstract: In 2004, Kim and Chan carried out torsional oscillator measurements of solid helium confined in porous Vycor glass and found an abrupt drop in the resonant period below 200 mK. The period drop was interpreted as probable experimental evidence of nonclassical rotational inertia. This experiment sparked considerable activities in the studies of superfluidity in solid helium. More recent ultrasound and torsional oscillator studies, however, found evidence that shear modulus stiffening is responsible for at least a fraction of the period drop found in bulk solid helium samples. The experimental configuration of Kim and Chan makes it unavoidable to have a small amount of bulk solid inside the torsion cell containing the Vycor disk. We report here the results of a new helium in Vycor experiment with a design that is completely free from any bulk solid shear modulus stiffening effect. We found no measurable period drop that can be attributed to nonclassical rotational inertia.

Abstract: Nanostructured surfaces which manifest superhydrophobic properties during water condensation have a potential to dramatically enhance energy efficiency in power generation and desalination systems. Although various such surfaces have been reported, their development has been fortuitous, not driven by an understanding of the underlying physical processes. In this work, we perform a comprehensive study of microscale water condensation dynamics on nanostructured superhydrophobic surfaces made using a variety of synthetic methods. We demonstrate that the growth mechanism of individual water microdroplets on these surfaces is universal and independent of the surface architecture. The key role of the nanoscale topography is confinement of the base area of forming droplets, which allows droplets to grow only through contact angle increase. The nearly spherical droplets formed in this fashion become highly mobile after coalescence. By comparing experimentally observed drop growth with interface free energy calculations, we show that the minimum observed confined microdroplet base diameter depends directly on the nanoscale surface roughness and degree of interfacial wetting. Specifically, we show that the microscale condensation mechanism depends on the height of a liquid film with volume equal to the fill volume between the nanostructures. This introduced roughness length scale is a universal metric that allows for facile comparison of arbitrarily complex surface architectures. We use this new fundamental insight to develop quantitative design guidelines for superhydrophobic surfaces intended for condensation applications.

Abstract: The contact angle that a liquid drop makes on a soft substrate does not obey the classical Young’s relation, since the solid is deformed elastically by the action of the capillary forces. The finite elasticity of the solid also renders the contact angles differently from those predicted by Neumann’s law, which applies when the drop is floating on another liquid. Here, we derive an elastocapillary model for contact angles on a soft solid by coupling a mean-field model for the molecular interactions to elasticity. We demonstrate that the limit of a vanishing elastic modulus yields Neumann’s law or a variation thereof, depending on the force transmission in the solid surface layer. The change in contact angle from the rigid limit to the soft limit appears when the length scale defined by the ratio of surface tension to elastic modulus γ/E reaches the range of molecular interactio

Abstract: Whether a thin filament of liquid separates into two or more droplets or eventually condenses lengthwise to form a single larger drop depends on the liquid's density, viscosity, and surface tension and on the initial dimensions of the filament. Surface tension drives two competing processes, pinching-off and shortening, and the relative time scales of these, controlled by the balance between capillary and viscous forces, determine the final outcome. Here we provide experimental evidence for the conditions under which a liquid filament will break up into drops, in terms of a wide range of two dimensionless quantities: the aspect ratio of the filament and the Ohnesorge number. Filaments which do not break up into multiple droplets demand a high liquid viscosity or a small aspect ratio.

Abstract: Liquid drops hitting solid surfaces deform substantially under the influence of the ambient air that needs to be squeezed out before the liquid actually touches the solid. Nanometer- and microsecond-resolved dual wavelength interferometry reveals a complex evolution of the interface between the drop and the gas layer underneath. For intermediate impact speeds (We∼1…10) the layer thickness can develop one or two local minima—reproduced in numerical calculations—that eventually lead to the nucleation of solid-liquid contact at a We-dependent radial position, from a film thickness >200 nm. Solid-liquid contact spreads at a speed involving capillarity, liquid viscosity and inertia.

Abstract: The splashing of a drop impacting onto a liquid pool produces a range of different sized microdroplets. At high impact velocities, the most significant source of these droplets is a thin liquid jet emerging at the start of the impact from the neck that connects the drop to the pool. We use ultrahigh-speed video imaging in combination with high-resolution numerical simulations to show how this ejecta gives way to irregular splashing. At higher Reynolds numbers, its base becomes unstable, shedding vortex rings into the liquid from the free surface in an axisymmetric von Karman vortex street, thus breaking the ejecta sheet as it forms.

Abstract: We present an experimental study of drop impact on a solid surface in the spreading regime with no splashing. Using the space–time-resolved Fourier transform profilometry technique, we can follow the evolution of the drop shape during the impact. We show that a self-similar dynamical regime drives the drop spreading until the growth of a viscous boundary layer from the substrate selects a residual minimal film thickness. Finally, we discuss the interplay between capillary and viscous effects in the spreading dynamics, which suggests a pertinent impact parameter.

Abstract: The coalescence-induced condensate drop motion on some superhydrophobic surfaces (SHSs) has attracted increasing attention because of its potential applications in sustained dropwise condensation, water collection, anti-icing, and anticorrosion. However, an investigation of the mechanism of such self-propelled motion including the factors for designing such SHSs is still limited. In this article, we fabricated a series of superhydrophobic copper surfaces with nanoribbon structures using wet chemical oxidation followed by fluorization treatment. We then systematically studied the influence of surface roughness and the chemical properties of as-prepared surfaces on the spontaneous motion of condensate drops. We quantified the "frequency" of the condensate drop motion based on microscopic sequential images and showed that the trend of this frequency varied with the nanoribbon structure and extent of fluorination. More obvious spontaneous condensate drop motion was observed on surfaces with a higher extent of fluorization and nanostructures possessing sufficiently narrow spacing and higher perpendicularity. We attribute this enhanced drop mobility to the stable Cassie state of condensate drops in the dynamic dropwise condensation process that is determined by the nanoscale morphology and local surface energy.

Abstract: The structural and interfacial properties of nanoscopic liquid drops are assessed by means of mechanical, thermodynamical, and statistical mechanical approaches that are discussed in detail, including original developments at both the macroscopic level and the microscopic level of density functional theory (DFT). With a novel analysis we show that a purely macroscopic (static) mechanical treatment can lead to a qualitatively reasonable description of the surface tension and the Tolman length of a liquid drop; the latter parameter, which characterizes the curvature dependence of the tension, is found to be negative and has a magnitude of about a half of the molecular dimension. A mechanical slant cannot, however, be considered satisfactory for small finite-size systems where fluctuation effects are significant. From the opposite perspective, a curvature expansion of the macroscopic thermodynamic properties (density and chemical potential) is then used to demonstrate that a purely thermodynamic approach of this type cannot in itself correctly account for the curvature correction of the surface tension of liquid drops. We emphasize that any approach, e.g., classical nucleation theory, which is based on a purely macroscopic viewpoint, does not lead to a reliable representation when the radius of the drop becomes microscopic. The description of the enhanced inhomogeneity exhibited by small drops (particularly in the dense interior) necessitates a treatment at the molecular level to account for finite-size and surface effects correctly. The so-called mechanical route, which corresponds to a molecular-level extension of the macroscopic theory of elasticity and is particularly popular in molecular dynamics simulation, also appears to be unreliable due to the inherent ambiguity in the definition of the microscopic pressure tensor, an observation which has been known for decades but is frequently ignored. The union of the theory of capillarity (developed in the nineteenth century by Gibbs and then promoted by Tolman) with a microscopic DFT treatment allows for a direct and unambiguous description of the interfacial properties of drops of arbitrary size; DFT provides all of the bulk and surface characteristics of the system that are required to uniquely define its thermodynamic properties. In this vein, we propose a non-local mean-field DFT for Lennard-Jones (LJ) fluids to examine drops of varying size. A comparison of the predictions of our DFT with recent simulation data based on a second-order fluctuation analysis (Sampayo et al 2010 J. Chem. Phys. 132 141101) reveals the consistency of the two treatments. This observation highlights the significance of fluctuation effects in small drops, which give rise to additional entropic (thermal non-mechanical) contributions, in contrast to what one observes in the case of planar interfaces which are governed by the laws of mechanical equilibrium. A small negative Tolman length (which is found to be about a tenth of the molecular diameter) and a non-monotonic behaviour of the surface tension with the drop radius are predicted for the LJ fluid. Finally, the limits of the validity of the Tolman approach, the effect of the range of the intermolecular potential, and the behaviour of bubbles are briefly discussed.

Abstract: We measured the forces required to slide sessile drops over surfaces. The forces were measured by means of a vertical deflectable capillary stuck in the drop. The drop adhesion force instrument (DAFI) allowed the investigation of the dynamic lateral adhesion force of water drops of 0.1 to 2 μL volume at defined velocities. On flat PDMS surfaces, the dynamic lateral adhesion force increases linearly with the diameter of the contact area of the solid–liquid interface and linearly with the sliding velocity. The movement of the drop relative to the surfaces enabled us to resolve the pinning of the three-phase contact line to individual defects. We further investigated a 3D superhydrophobic pillar array. The depinning of the receding part of the rim of the drop occurred almost simultaneously from four to five pillars, giving rise to peaks in the lateral adhesion force.

Abstract: The coalesce-induced condensate drop motion on some superhydrophobic surfaces (SHSs) has attracted increasing attention because of its wide potential applications. However, microscopic mechanism of spontaneous motion has not been discussed thoroughly. In this study, we fabricated two types of superhydrophobic copper surfaces with sisal-like nanoribbon structures and defoliation-like nanosheet structures by different wet chemical oxidation process and followed by same fluorization treatment. With lotus leaf and butterfly wing as control samples, the spontaneous motion phenomenon of condensate drops on these four kinds of SHSs was investigated by using optical microscope under ambient conditions. The results showed that among all four types of SHSs, only superhydrophobic copper surfaces with sisal-like nanoribbon structures showed obvious spontaneous motion of condensate drops, especially when the relative humidity was higher. The microscopic mechanism of spontaneous motion was discussed in relation to the states of condensate drops on different nanostructures. It shows that the instantaneous Cassie state of condensed droplets prior to coalescence plays a key role in determining whether the coalesced drop departs, whereas only SHS possessing nanostructures with small enough Wenzel roughness parameter r (at least <2.1) and nanogaps forming high enough Laplace pressure favors the formation of the instantaneous Cassie state by completing the Wenzel-Cassie transition.

Abstract: Using stereolithography, 20 different structural variations comprised of millimeter diameter holes surrounded by trenches, plateaus, or micro-ring structures were prepared and tested for their ability to stably hold arrays of microliter sized droplets within the structures over an extended period of time. The micro-ring structures were the most effective in stabilizing droplets against mechanical and chemical perturbations. After confirming the importance of micro-ring structures using rapid prototyping, we developed an injection molding tool for mass production of polystyrene 3D cell culture plates with an array of 384 such micro-ring surrounded through-hole structures. These newly designed and injection molded polystyrene 384 hanging drop array plates with micro-rings were stable and robust against mechanical perturbations as well as surface fouling-facilitated droplet spreading making them capable of long term cell spheroid culture of up to 22 days within the droplet array. This is a significant improvement over previously reported 384 hanging drop array plates which are susceptible to small mechanical shocks and could not reliably maintain hanging drops for longer than a few days. With enhanced droplet stability, the hanging drop array plates with micro-ring structures provide better platforms and open up new opportunities for high-throughput preparation of microscale 3D cell constructs for drug screening and cell analysis.

Abstract: Stable drop jettability is mandatory for a successful, technical scale inkjet printing, and accordingly, this aspect has attracted much attention in fundamental and applied research. Previous studies were mainly focused on Newtonian fluids or polymer solutions. Here, we have investigated the drop jetting for zinc oxide (ZnO) particulate suspensions. Generally, the inverse Ohnesorge number Z = Oh–1, which relates viscous forces to inertia and surface tension, is sufficient to predict the jettability of single phase fluids. For the inkjet printer setup used here, jetting was possible for Newtonian fluids with 2.5 < Z < 26, but in the identical Z-range, nonjetting and nozzle clogging occurred for certain suspensions. A so-called ring-slit device, which allows for simultaneous formation and detection of aggregates in strongly converging flow fields, and single particle detecting techniques, which allow for an accurate determination of the number and size of micrometer-sized aggregates in suspensions of nanopa...

Abstract: When a drop impacts at low velocity onto a pool surface, a hemispheric air layer cushions and can delay direct contact. Herein we use ultra-high-speed video to study the rupture of this layer, to explain the resulting variety of observed distribution of bubbles. The size and distribution of micro-bubbles is determined by the number and location of the primary punctures. Isolated holes lead to the formation of bubble necklaces when the edges of two growing holes meet, whereas bubble nets are produced by regular shedding of micro-bubbles from a sawtooth edge instability. For the most viscous liquids the air film contracts more rapidly than the capillary–viscous velocity through repeated spontaneous ruptures of the edge. From the speed of hole opening and the total volume of micro-bubbles we conclude that the air sheet ruptures when its thickness approaches .

Abstract: While nanoparticle adsorption to fluid interfaces has been studied from a fundamental standpoint and exploited in application, the reverse process, that is, desorption and disassembly, remains relatively unexplored. Here we demonstrate the forced desorption of gold nanoparticles capped with amphiphilic ligands from an oil–water interface. A monolayer of nanoparticles is allowed to spontaneously form by adsorption from an aqueous suspension onto a drop of oil and is subsequently compressed by decreasing the drop volume. The surface pressure is monitored by pendant drop tensiometry throughout the process. Upon compression, the nanoparticles are mechanically forced out of the interface into the aqueous phase. An optical method is developed to measure the nanoparticle area density in situ. We show that desorption occurs at a coverage that corresponds to close packing of the ligand-capped particles, suggesting that ligand-induced repulsion plays a crucial role in this process.

Abstract: We report the drop impact characteristics on four hydrophobic surfaces with different well-scale structures (smooth, nano, micro, and hierarchical micro/nano) and the effects of those structures on the behavior of water drops during impact. The specimens were fabricated using silicon wet etching, black silicon formation, or the combination of these methods. On the surfaces, the microstructures form obstacles to drop spreading and retracting, the nanostructures give extreme water-repellency, and the hierarchical micro/nanostructures facilitate drop fragmentation. The maximum spreading factor (D*max) differed among the structures. On the basis of published models of D*max, we interpret the results of our experiment and suggest reasonable explanations for these differences. Especially, the micro/nanostructures caused instability of the interface between liquid and air at Weber number We > ∼80 and impacting drops fragmented at We > ∼150.

Abstract: This investigation is focused on the behavior of nanofluid single drops in the liquid–liquid extraction process. The chemical system of toluene–acetic acid–water was used, and the drops were organic nanofluids containing magnetite or alumina nanoparticles. Synthesized nanoparticles were modified with fatty acids for hydrophobicity and ease of dispersion in the organic phase and were then characterized using different methods. Maximum enhancements in the rate of mass transfer of 157% and 121% were achieved using about 0.002 wt % magnetite and alumina nanoparticles, respectively; however, a decreasing variation was observed at higher concentrations. The microconvection and particle aggregation due to the interpenetration layers can provide this kind of variation. For the aim of modeling, the determined enhancement factors were correlated with an empirical expression that can be used, together with the Newman equation, for the prediction of the overall mass-transfer coefficient.

Abstract: Compound drops arise from the contact of three immiscible fluids and can assume various geometric forms based on the interfacial chemistry of the phases involved. Here we present a study of a new class of compound drops that is sessile on a solid surface. The possible geometries are demonstrated experimentally with appropriate fluid combinations and accounted for with a quantitative theoretical description. Although such systems are broadly controlled by relative interfacial energies, subtleties such as the van der Waals force and effects of micro-gravity, despite drop sizes being well below the capillary length, come into play in determining the equilibrium state that is achieved. The drying of a compound sessile drop was measured experimentally, and the process revealed a novel transition between different characteristic configurations of compound sessile drops. Such drops may prove to be useful as the first step towards development of functional surfaces in applications such as soft optics, photonics and surface encapsulation.

Abstract: We fully characterize the natural evaporation of human drops of blood from substrates and substrate-dependent behavior. The heat flux adsorbed by the drops for evaporation is measured by means of a heat flux meter. A side-view measurement enables access to the drop contact angle, wetting diameter, and initial height. A top-view camera allows for the monitoring of the drying regime (deposition, gelation, and fracturation). This directly measured heat flux is related to the evaporative mass flux obtained from the mass of the drop, and the two show good agreement. Both types of measurements indicate that regardless of the substrate type, there is first a linearly decreasing regime of evaporation when the drop is mostly liquid and a second regime characterized by a sharp decrease. We show that the evaporation dynamics are influenced by the substrate’s wettability but not by the substrate’s thermal diffusivity. The different regimes of evaporation exhibited by glass and metallic substrates are explained in terms of evaporation fluxes at the drop surface. In the case of wetting drops (below 40 deg), the evaporation flux is very impor- tant along the drop periphery and decreases across the interface, whereas in the case of nonwetting drops (about 90 deg), the evaporation flux is almost uniform across the droplet’s surface. We show that these different evaporation fluxes strongly influence the drying behavior. In the case of metallic substrates, this enables the formation of a uni- form "glassy skin" around the droplet surface and, in the case of glass substrates, the for- mation a skin along the drop periphery with an inward gelation front. This behavior is analyzed in terms of the competition between the drying time and the gel formation time. Unstable drop surfaces were observed at high initial contact angles and are very similar to those of polymer drops

Abstract: Water drops dispersed in chloroform and stabilized with phospholipids become adhesive if a bad solvent for lipids, such as silicone oil, is added to the continuous phase. In this way, two sticking drops are separated by a bilayer of phospholipids. By using microfluidic technologies, we probe the stability and properties of such membranes likewise encountered in foams or vesicles. We first establish the stability diagram of adhering drop pairs as a function of the continuous phase composition. We found two regimes of destabilization of the bilayer. The first one concerns a competition between the dynamics of adhesion and the transport of surfactants toward the interfaces that leads to a dilute surfactant coverage. The second one corresponds to a dense surface coverage where the lifetime distribution of the bilayer exponentially decreases as a signature of a nucleation process. In the stable regime, we observe the propagation of adhesion among a concentrated collection of drops. This is another remarkable i...

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