Assessing the accuracy of contact angle measurements for sessile drops on liquid-repellent surfaces

Transition of Liquid Drops on Microstructured Hygrophobic Surfaces from the Impaled Wenzel State to the "Fakir" Cassie-Baxter State

Low adhesion of liquids on solid surfaces can be achieved with protrusions that minimize the contact area between the liquid and the solid. The wetting state where an air cushion forms under the drop is known as the Cassie-Baxter state. Surfaces where liquids form macroscopic contact angles above 150° are called superhydrophobic and superhygrophobic, if we refer to water or any liquid, respectively. The Cassie state is desirable for applications, but it is usually unstable compared to the Wenzel state, where the drop is in direct contact with the rough surface. The Cassie-to-Wenzel transition can be triggered by an increase in pressure and vibrations, but the inverse Wenzel-to-Cassie is much more difficult to observe. Here, we examine under what conditions the Wenzel-to-Cassie transition is triggered when the microscopic contact angle changes abruptly. For this, we applied a lubricant of low surface tension around drops that were in the Wenzel state on microstructured surfaces. The increase of the microscopic contact angle lifted the drop from the rough surface, when the pillar height and spacing are large and small, respectively. Numerical calculations for the drop-lubricant interface showed that the surface geometry requirements for the Wenzel-to-Cassie transition are stricter than the ones for the stability of the Cassie state. A surface geometry where the Cassie state is more stable than the Wenzel for a given Laplace pressure of the drop may not always allow the Wenzel-to-Cassie transition to take place. Therefore, the stability of the Cassie state is a necessary but insufficient condition for the inverse transition.

Fundamentals and Applications of Surface Wetting

In an era defined by an insatiable thirst for sustainable energy solutions, responsible water management, and cutting-edge lab-on-a-chip diagnostics, surface wettability plays a pivotal role in these fields. The seamless integration of fundamental research and the following demonstration of applications on these groundbreaking technologies hinges on manipulating fluid through surface wettability, significantly optimizing performance, enhancing efficiency, and advancing overall sustainability. This Review explores the behavior of liquids when they engage with engineered surfaces, delving into the far-reaching implications of these interactions in various applications. Specifically, we explore surface wetting, dissecting it into three distinctive facets. First, we delve into the fundamental principles that underpin surface wetting. Next, we navigate the intricate liquid-surface interactions, unraveling the complex interplay of various fluid dynamics, as well as heat- and mass-transport mechanisms. Finally, we report on the practical realm, where we scrutinize the myriad applications of these principles in everyday processes and real-world scenarios.

Effect of Camera Parallax Angle on the Accuracy of Static Contact Angle Measurements

Measuring the contact angle at the solid/liquid/vapor triple point in sessile drop experiments is one of the most popular and simple ways to quantify the wettability of surfaces and determine the surface free energy. Despite decades of technical advancements in contact angle measurements, which allowed for improving the precision of sessile drop measurements below ±1°, an often overlooked source of experimental error in these measurements originates from the camera's parallax angle (PA) - the angle between the camera optical axis and the sample stage surface. Here, we quantified the systematic errors in the measurement of contact angles due to the acquisition of drop images at finite PA values by simulating sessile drop experiments in which synthetic drops were created using the Young-Laplace equation. The absolute contact angle error induced by imaging drops at nonzero PAs was found to increase as the true contact angle (TCA) deviates from 90° and resulted in an overestimation (underestimation) of the contact angle for drops having TCAs lower (higher) than 90°. The computed absolute contact angle error reaches values as high as -20° (+12.2°) for drops having a TCA of 175° (5°) when imaged with a PA of 10°, thus indicating the importance of considering the PA when accurately quantifying contact angles in sessile drop experiments. The shape and, by extension, volume of the sessile drop was also found to affect the magnitude of the absolute contact angle error as sessile drops with higher apex curvatures exhibited lower absolute error than those with lower curvatures at any given PA. The outcomes of this work provide guidelines for minimizing systematic errors in sessile drop measurements due to the collection of drop images at nonzero PAs.

Bézier Curve Method to Compute Various Meniscus Shapes

This paper is an extension of our earlier paper in which it was shown that the meniscus shape in a cylindrical capillary could be computed by solving the Young-Laplace equation via optimization of a Bézier curve. This work extends the previous work by demonstrating that the method is applicable to predict the meniscus shape not only in a cylindrical capillary but also in other cases, such as at a tilted plate, between two plates, and for a sessile drop. Numerous works have attempted previously to solve the Young-Laplace equation, and their results all agree with this paper's validating its method. All the preceding approaches, however, used special techniques to solve the differential equation, while the Bézier curve method proposed in this work is more simple, which allows it to maintain greater computational simplicity. Moreover, the Bézier curve method can be applied to solve many other different differential equations in the same way as shown in this work. The effect of the Bézier curve degree on the precision of prediction was also thoroughly investigated. It was found that the 4th degree Bézier curve was required to predict the meniscus shape precisely in a cylindrical capillary, against a tilted plate, and between two plates, while the 5th degree was required for the shape of the sessile drop.

Machine learning enabled orthogonal camera goniometry for accurate and robust contact angle measurements

Characterization of surface wettability plays an integral role in physical, chemical, and biological processes. However, the conventional fitting algorithms are not suitable for accurate estimation of wetting properties, especially on hydrophilic surfaces, due to optical distortions triggered by changes in the focal length of the moving drops. Therefore, here we present an original setup coupled with Convolutional Neural Networks (CNN) for estimation of Contact Angle (CA). The developed algorithm is trained on 3375 ground truth images (at different front-lit illuminations), less sensitive to the edges of the drops, and retains its stability for images that are synthetically blurred with higher Gaussian Blurring (GB) values (GB: 0-22) if compared to existing goniometers (GB: 0-12). Besides, the proposed technique can precisely analyze drops of various colors and chemistries on different surfaces. Finally, our automated orthogonal camera goniometer has a significantly lower average standard deviation (6.7° vs. 14.6°) and coefficient of variation (14.9 vs. 29.2%) than the existing techniques and enables wettability assessment of non-spherical drops on heterogeneous surfaces.

Atmospheric Pressure Plasma Polymerisation of D-Limonene and Its Antimicrobial Activity

Antibacterial coating is necessary to prevent biofilm-forming bacteria from colonising medical tools causing infection and sepsis in patients. The recent coating strategies such as immobilisation of antimicrobial materials and low-pressure plasma polymerisation may require multiple processing steps involving a high-vacuum system and time-consuming process. Some of those have limited efficacy and durability. Here, we report a rapid and one-step atmospheric pressure plasma polymerisation (APPP) of D-limonene to produce nano-thin films with hydrophobic-like properties for antibacterial applications. The influence of plasma polymerisation time on the thickness, surface characteristic, and chemical composition of the plasma-polymerised films was systematically investigated. Results showed that the nano-thin films deposited at 1 min on glass substrate are optically transparent and homogenous, with a thickness of 44.3 ± 4.8 nm, a smooth surface with an average roughness of 0.23 ± 0.02 nm. For its antimicrobial activity, the biofilm assay evaluation revealed a significant 94% decrease in the number of Escherichia coli (E. coli) compared to the control sample. More importantly, the resultant nano-thin films exhibited a potent bactericidal effect that can distort and rupture the membrane of the treated bacteria. These findings provide important insights into the development of bacteria-resistant and biocompatible coatings on the arbitrary substrate in a straightforward and cost-effective route at atmospheric pressure.

Scanning Drop Friction Force Microscopy

Wetting imperfections are omnipresent on surfaces. They cause contact angle hysteresis and determine the wetting dynamics. Still, existing techniques (e.g., contact angle goniometry) are not sufficient to localize inhomogeneities and image wetting variations. We overcome these limitations through scanning drop friction force microscopy (sDoFFI). In sDoFFI, a 15 μL drop of Milli-Q water is raster-scanned over a surface. The friction force (lateral adhesion force) acting on the moving contact line is plotted against the drop position. Using sDoFFI, we obtained 2D wetting maps of the samples having sizes in the order of several square centimeters. We mapped areas with distinct wetting properties such as those present on a natural surface (e.g., a rose petal), a technically relevant superhydrophobic surface (e.g., Glaco paint), and an in-house prepared model of inhomogeneous surfaces featuring defined areas with low and high contact angle hysteresis. sDoFFI detects features that are smaller than 0.5 mm in size. Furthermore, we quantified the sliding behavior of drops across the boundary separating areas with different contact angles on the model sample. The sliding of a drop across this transition line follows a characteristic stick-slip motion. We use the variation in force signals, advancing and receding contact line velocities, and advancing and receding contact angles to identify zones of stick and slip. When scanning the drop from low to high contact angle hysteresis, the drop undergoes a stick-slip-stick-slip motion at the interline. Sliding from high to low contact angle hysteresis is characterized by the slip-stick-slip motion. The sDoFFI is a new tool for 2D characterization of wetting properties, which is applicable to laboratory-based samples but also characterizes biological and commercial surfaces.

A Scalable Haze-Free Antireflective Hierarchical Surface with Self-Cleaning Capability

The lotus effect indicates that a superhydrophobic, self-cleaning surface can be obtained by roughening the topography of a hydrophobic surface. However, attaining high transmittance and clarity through a roughened surface remains challenging because of its strong scattering characteristics. Here, a haze-free, antireflective superhydrophobic surface that consists of hierarchically designed nanoparticles is demonstrated. Close-packed, deep-subwavelength-scale colloidal silica nanoparticles and their upper, chain-like fumed silica nanoparticles individually fulfill haze-free broadband antireflection and self-cleaning functions. These double-layered hierarchical surfaces are obtained via a scalable spraying process that permits precise control over the coating morphology to attain the desired optical and wetting properties. They provide a "specular" visible transmittance of >97% when double-side coated and a record-high self-cleaning capability with a near-zero sliding angle. Self-cleaning experiments on photovoltaic devices verify that the developed surfaces can significantly enhance power conversion efficiencies and aid in retaining pristine device performance in a dusty environment.

A Modified Contact Angle Measurement Process to Suppress Oil Drop Spreading and Improve Precision

Static contact angle measurement is a widely applied method for wettability assessment. Despite its convenience, it suffers from errors induced by contact angle hysteresis, material heterogeneity, and other factors. This paper discusses the oil drop spreading phenomenon that was frequently observed during contact angle measurements. Experimental tests showed that this phenomenon is closely related to surfactants in the surrounding phase, the remaining oil on the rock surface, and oil inside the surrounding phase. A modified contact angle measurement process was proposed. In the modified method, deionized water was used as the surrounding phase, and a rock surface cleaning step was added. Subsequent measurements showed a very low chance of oil drop spreading and improved precision. A further comparison study showed that, when the surrounding phase was deionized water, the measured contact angle values tended to be closer to intermediate-wet conditions compared to the values measured in clean surfactant solutions. This difference became more significant when the surface was strongly water-wet or strongly oil-wet. As a result, the developed process has two prerequisites: that the in-situ contact angle values inside surfactant solutions are not required, and that the wettability alteration induced by the surfactant solution is irreversible.

Live imaging of micro and macro wettability variations of carbonate oil reservoirs for enhanced oil recovery and CO2 trapping/storage

Carbonate hydrocarbon reservoirs are considered as potential candidates for chemically enhanced oil recovery and for CO₂ geological storage. However, investigation of one main controlling parameter-wettability-is usually performed by conventional integral methods at the core-scale. Moreover, literature reports show that wettability distribution may vary at the micro-scale due to the chemical heterogeneity of the reservoir and residing fluids. These differences may profoundly affect the derivation of other reservoir parameters such as relative permeability and capillary pressure, thus rendering subsequent simulations inaccurate. Here we developed an innovative approach by comparing the wettability distribution on carbonates at micro and macro-scale by combining live-imaging of controlled condensation experiments and X-ray mapping with sessile drop technique. The wettability was quantified by measuring the differences in contact angles before and after aging in palmitic, stearic and naphthenic acids. Furthermore, the influence of organic acids on wettability was examined at micro-scale, which revealed wetting heterogeneity of the surface (i.e., mixed wettability), while corresponding macro-scale measurements indicated hydrophobic wetting properties. The thickness of the adsorbed acid layer was determined, and it was correlated with the wetting properties. These findings bring into question the applicability of macro-scale data in reservoir modeling for enhanced oil recovery and geological storage of greenhouse gases.

Robust and durable liquid-repellent surfaces

This review provides a comprehensive summary of characterization, design, fabrication, and application of robust and durable liquid-repellent surfaces.

Force-Based Wetting Characterization of Stochastic Superhydrophobic Coatings at Nanonewton Sensitivity

Superhydrophobic coatings have extraordinary properties like self-cleaning and staying dry, and have recently appeared on industrial and consumer markets. The stochastic nature of the coating components and coating processes (e.g., spraying, painting) affects the uniformity of the water repellency across the coated substrate. The wetting properties of those coatings are typically quantified on macroscale using contact angle goniometry (CAG). Here, highly sensitive force-based methods, scanning droplet adhesion microscopy (SDAM), and micropipette force sensor (MFS), are used, to quantify the microscale heterogeneity in the wetting properties of stochastic superhydrophobic coatings with irregular surface topography that cannot be investigated by CAG. By mapping the wetting adhesion forces with SDAM and friction forces with MFS, it is demonstrated that even the best coatings on the market are prone to heterogeneities that induce stick-slip motion of droplets. Thus, owing to their high spatial and force resolution, the advantages of these techniques over CAG are demonstrated.

Visualizing and Quantifying Wettability Alteration by Silica Nanofluids

An aqueous suspension of silica nanoparticles or nanofluid can alter the wettability of surfaces, specifically by making them hydrophilic and oil-repellent under water. Wettability alteration by nanofluids has important technological applications, including for enhanced oil recovery and heat transfer processes. A common way to characterize the wettability alteration is by measuring the contact angles of an oil droplet with and without nanoparticles. While easy to perform, contact angle measurements do not fully capture the wettability changes to the surface. Here, we employed several complementary techniques, such as cryo-scanning electron microscopy, confocal fluorescence and reflection interference contrast microscopy, and droplet probe atomic force microscopy (AFM), to visualize and quantify the wettability alterations by fumed silica nanoparticles. We found that nanoparticles adsorbed onto glass surfaces to form a porous layer with hierarchical micro- and nanostructures. The porous layer can trap a thin water film, which reduces contact between the oil droplet and the solid substrate. As a result, even a small addition of nanoparticles (0.1 wt %) lowers the adhesion force for a 20 μm sized oil droplet by more than 400 times from 210 ± 10 to 0.5 ± 0.3 nN as measured by using droplet probe AFM. Finally, we show that silica nanofluids can improve oil recovery rates by 8% in a micromodel with glass channels that resemble a physical rock network.

A Critical Review of Membrane Wettability in Membrane Distillation from the Perspective of Interfacial Interactions

Hydrophobic membranes used in membrane distillation (MD) systems are often subject to wetting during long-term operation. Thus, it is of great importance to fully understand factors that influence the wettability of hydrophobic membranes and their impact on the overall separation efficiency that can be achieved in MD systems. This Critical Review summarizes both fundamental and applied aspects of membrane wetting with particular emphasis on interfacial interaction between the membrane and solutes in the feed solution. First, the theoretical background of surface wetting, including the relationship between wettability and interfacial interaction, definition and measurement of contact angle, surface tension, surface free energy, adhesion force, and liquid entry pressure, is described. Second, the nature of wettability, membrane wetting mechanisms, influence of membrane properties, feed characteristics and operating conditions on membrane wetting, and evolution of membrane wetting are reviewed in the context of an MD process. Third, specific membrane features that increase resistance to wetting (e.g., superhydrophobic, omniphobic, and Janus membranes) are discussed briefly followed by the comparison of various cleaning approaches to restore membrane hydrophobicity. Finally, challenges with the prevention of membrane wetting are summarized, and future work is proposed to improve the use of MD technology in a variety of applications.

Friction and Adhesion of Microparticle Suspensions on Repellent Surfaces

With the recent advancements in the development and application of repellent surfaces, both in air and under liquid medium, accurate characterization of repellence behavior is critical in understanding the mechanism behind many observed phenomena and to exploit them for novel applications. Conventionally, the repellence behavior of a surface is characterized by the optical measurement of the dynamic contact angle of the target (to be repelled) liquid on the test surface. However, as already established in the literature, optical measurements are prone to appreciable error, especially for repellent surfaces with high contact angles. Here, we present an alternative, more accurate force-based characterization method of both friction and adhesion forces of microparticle-laden aqueous droplets over various repellent surfaces, where the force signature is captured by probing the surface with a droplet of the test liquid mounted at the tip of a flexible cantilever and then tracking the deflection of the tip of the cantilever as the probe droplet interacts with the surface. A systematic investigation of the response of repellent surfaces toward droplets with different microparticle concentrations reveals the dependency and sensitivity of measured adhesion and friction signature toward particle concentration. A comparison with the theoretical estimate from optical goniometry highlights the deviation of the theoretical data from experimentally measured values and further substantiates the need for such a force-based approach for accurate characterization of repellence behavior.

The Shape of Heavy Droplets on Superhydrophobic Surfaces

An analytical model is developed to describe the shape of heavy droplets on solid surfaces with arbitrary wetting properties (corresponding to the contact angles ranging from 0 to 180°). This model, based on a surface of revolution by rotating two elliptic arcs, reduces to the ellipsoid model for a hydrophilic case. Experimental measurements are also conducted to verify the model. It shows that the mean curvature distribution of the developed model agrees well with that of real droplets on hydrophobic surfaces, even on superhydrophobic surfaces. For water droplets with a volume up to 1000 μL on superhydrophobic surfaces having a 162° contact angle, the errors of the predicted heights, maximum radius, and wetting radius using this model are less than 1.7%, which suggests the capability of this model in studying the wettability of heavy droplets. This model provides an accurate theoretical basis for designing and controlling the spread, transport, condensation, and evaporation of heavy droplets on superhydrophobic surfaces.

A tri-component knee plug for the 3rd generation of autologous chondrocyte implantation

Here, we report a newly designed knee plug to be used in the 3rd generation of Autologous Chondrocyte Implantation (ACI) in order to heal the damaged knee cartilage. It is composed of three components: The first component (Bone Portion) is a 3D printed hard scaffold with large pores (~ 850 µm), made by hydroxyapatite and β-tricalcium phosphate to accommodate the bony parts underneath the knee cartilage. It is a cylinder with a diameter of 20 mm and height of 7.5 mm, with a slight dome shape on top. The plug also comprises a Cartilage Portion (component 2) which is a 3D printed gelatin/elastin/sodium-hyaluronate soft thick porous membrane with large pores to accommodate chondrocytes. Cartilage Portion is secured on top of the Bone Portion using mechanical interlocking by designing specific knobs in the 3D printed construct of the Cartilage Portion. The third component of the plug (Film) is a stitchable permeable membrane consisting of polycaprolactone (PCL) on top of the Cartilage Portion to facilitate sliding of the knee joint and to hold the entire plug in place while allowing nutrients delivery to the Cartilage Portion. The PCL Film is prepared using a combination of film casting and sacrificial material leaching with a pore size of 10 µm. It is surface modified to have specific affinity with the Cartilage Portion. The detailed design criteria and production process of this plug is presented in this report. Full in vitro analyses have been performed, which indicate the compatibility of the different components of the plug relative to their expected functions.

Quantifying Surface Wetting Properties Using Droplet Probe Atomic Force Microscopy

The functional properties of a surface, such as its anti-fogging or anti-fouling performance, are influenced by its wettability. To quantify surface wettability, the most common approach is to measure the contact angles of a liquid droplet on the surface. While well established and relatively easy to perform, contact angle measurements were developed to describe macroscopic wetting properties and are difficult to perform for submillimetric droplets. Moreover, they cannot spatially resolve surface heterogeneities that can contribute to surface fouling. To address these shortcomings, we report on using an atomic force microscopy technique to quantitatively measure the interaction forces between a microdroplet and a surface with piconewton force resolution. We show how our technique can be used to spatially map topographical and chemical heterogeneities with micron resolution.

Adaptive Wetting of Polydimethylsiloxane

To better understand the wetting of cross-linked polydimethylsiloxane (PDMS), we measured advancing and receding contact angles of sessile water drops on cross-linked PDMS as a function of contact line velocity (up to 100 μm/s). Three types of samples were investigated: pristine PDMS, PDMS where oligomers were removed by toluene treatment, and PDMS with an enriched concentration of oligomers. Depending on the velocity of advancing contact lines and the contact time with water, different modes of wetting were observed: one with a relatively low contact angle hysteresis (Δθ ≈ 10°) and one with a larger hysteresis. We attribute the low hysteresis state, called the lubricated state, to the enrichment of free oligomers at the water-PDMS interface. The enrichment of oligomers is induced by drop contact. The kinetics of the transition to the lubricated state can be described by adaptation theory. PDMS adapts to the presence of water by an enrichment of free oligomers at the interface and a correlated reduction in interfacial tension.

Lotus Effect and Friction: Does Nonsticky Mean Slippery?

Lotus-effect-based superhydrophobicity is one of the most celebrated applications of biomimetics in materials science. Due to a combination of controlled surface roughness (surface patterns) and low-surface energy coatings, superhydrophobic surfaces repel water and, to some extent, other liquids. However, many applications require surfaces which are water-repellent but provide high friction. An example would be highway or runway pavements, which should support high wheel–pavement traction. Despite a common perception that making a surface non-wet also makes it slippery, the correlation between non-wetting and low friction is not always direct. This is because friction and wetting involve many mechanisms and because adhesion cannot be characterized by a single factor. We review relevant adhesion mechanisms and parameters (the interfacial energy, contact angle, contact angle hysteresis, and specific fracture energy) and discuss the complex interrelation between friction and wetting, which is crucial for the design of biomimetic functional surfaces.

Mapping micrometer-scale wetting properties of superhydrophobic surfaces

There is a huge interest in developing superrepellent surfaces for antifouling and heat-transfer applications. To characterize the wetting properties of such surfaces, the most common approach is to place a millimetric-sized droplet and measure its contact angles. The adhesion and friction forces can then be inferred indirectly using Furmidge's relation. While easy to implement, contact angle measurements are semiquantitative and cannot resolve wetting variations on a surface. Here, we attach a micrometric-sized droplet to an atomic force microscope cantilever to directly measure adhesion and friction forces with nanonewton force resolutions. We spatially map the micrometer-scale wetting properties of superhydrophobic surfaces and observe the time-resolved pinning-depinning dynamics as the droplet detaches from or moves across the surface.

Wetting Transition on Liquid-Repellent Surfaces Probed by Surface Force Measurements and Confocal Imaging

Superhydrophobic surfaces in the Cassie-Baxter wetting state retain an air layer at the surface which prevents liquid water from reaching into the porous surface structure. In this work we explore how addition of ethanol, which reduces the surface tension, influences the wetting properties of superhydrophobic and smooth hydrophobic surfaces. Wetting properties are measured by dynamic contact angles, and the air layer at the superhydrophobic surface is visualized by laser scanning confocal microscopy. Colloidal probe atomic force microscopy measurements between a hydrophobic microsphere and the macroscopic surfaces showed that the presence of ethanol strongly affects the interaction forces. When the macroscopic surface is superhydrophobic, attractive forces extending up to a few micrometers are observed on retraction in water and in 20 vol % ethanol, signifying the presence of a large and growing gas capillary. Submicrometer attractive forces are observed between the probe particle and a smooth hydrophobic surface, and in this case a smaller gas capillary is formed. Addition of ethanol results in markedly different effects between superhydrophobic and hydrophobic surfaces. In particular, we show that the receding contact angle on the superhydrophobic surface is of paramount importance for describing the interaction forces.

Uncertainties in contact angle goniometry

The most widely used method to quantify the wetting properties of surfaces is by measuring contact angles. Even though contact angle goniometry is a powerful technique for characterizing wetting properties, it is not accurate for very hydrophobic surfaces. As the technique relies on image processing, it has inherent errors due to optical limitations, especially near the three-phase contact line. This leads to uncertainties in the positioning of the baseline, which can cause large errors in the measured contact angles. In this paper, we systematically evaluate these errors both theoretically and experimentally, focusing on the importance of image resolution. For ∼9 microliter droplet, displacement of the baseline by a single pixel leads to errors of approximately ±0.5° to ±1° for contact angles up to 150°, and errors increase rapidly in the superhydrophobic regime, up to ±8°. The error in the contact angle can be slightly reduced by increasing the image resolution, but cannot be eliminated entirely.

Experimental and Theoretical Investigation of Droplet Evaporation on Heated Hydrophilic and Hydrophobic Surfaces

The evaporation characteristics of sessile droplets on heated hydrophobic and hydrophilic surfaces are investigated. Results are reported for the evaporation of water droplet volumes covering a range of shapes dominated by surface tension or gravity and over a range of temperatures between 40 and 60 °C. The weight evolution and total time of evaporation is measured using a novel self-contained heating stage on a high resolution analytical balance, which has advantages over visualization measurement techniques as it allows free choice of the initial droplet size and surface and the ability to record the droplet evaporation right through to the final stages of droplet life. Evaporation is modeled through a combination of a constant contact area and a constant contact angle model with the switch from the former to the latter occurring when the contact angle falls below its predetermined receding value. Theoretical results compare well with the experimental results for the hydrophobic substrate. However, a significant deviation is observed for the hydrophilic substrate due to the combined effects of the droplet surface cooling due to evaporation and buoyancy effects that are not included in the model. The proposed method of using the stick-slip model offers a convenient means of modeling droplet evaporation by mimicking the drying modes based on initial measurements of the static and receding contact angles.

Oscillating Magnetic Drop: How to Grade Water-Repellent Surfaces

Evaluation of superhydrophobic (SH) surfaces based on contact angle measurements is challenging due to the high mobility of drops and the resolution limits of optical goniometry. For this reason, some alternatives to drop-shape methods have been proposed such as the damped-oscillatory motion of ferrofluid sessile drops produced by an external magnetic field. This approach provides information on surface friction (lateral/shear adhesion) from the kinetic energy dissipation of the drop. In this work, we used this method to compare the low adhesion of four commercial SH coatings (Neverwet, WX2100, Ultraever dry, Hydrobead) formed on glass substrates. As ferrofluid, we used a maghemite aqueous suspension (2% v/v) synthesized ad hoc. The rolling magnetic drop is used as a probe to explore shear solid–liquid adhesion. Additionally, drop energy dissipates due to velocity-dependent viscous stresses developed close to the solid–liquid interface. By fitting the damped harmonic oscillations, we estimated the decay time on each coating. The SH coatings were statistically different by using the mean damping time. The differences found between SH coatings could be ascribed to surface–drop adhesion (contact angle hysteresis and apparent contact area). By using this methodology, we were able to grade meaningfully the liquid-repelling properties of superhydrophobic surfaces.

Capillary bridge technique to study superhydrophobic surfaces

We present here the use of the capillary bridge technique to study the wetting properties (advancing and receding contact angles) of transparent, textured and superhydrophobic surfaces over large wetted area. Apparent contact angles on such surfaces are classically measured using a goniometer in combination with video camera side visualization and a drop shape analysis. Recent experiments of Schellenberger et al. [F. Schellenberger, N. Encinas, D. Vollmer and H. J. Butt, Phys. Rev. Lett., 2016, 116(9), 096101] show that this method can significantly underestimate the apparent advancing contact angle. We use for the first time the capillary bridge setup for such textured surfaces, leading to a large (up to several cm2) wetted area, instead of having a reduced contact zone as in the drop case (mm2 or less). (1) We show here how to use the method and its characteristics to explore the wetting properties of superhydrophobic surfaces. We have developed a new analysis method in order to obtain the value of the contact angle for any position of the substrate. (2) We compare with the classical drop side view method, showing that advancing contact angles are systematically higher. (3) We compare to a few existing models, concluding a good agreement for receding values but not for advancing angles, for which models must be refined.

The meniscus on the outside of a circular cylinder: From microscopic to macroscopic scales

We systematically study the meniscus on the outside of a small circular cylinder vertically immersed in a liquid bath in a cylindrical container that is coaxial with the cylinder. The cylinder has a radius R much smaller than the capillary length, κ^-1, and the container radius, L, is varied from a small value comparable to R to ∞. In the limit of L≪κ^-1, we analytically solve the general Young-Laplace equation governing the meniscus profile and show that the meniscus height, Δh, scales approximately with Rln(L/R). In the opposite limit where L≫κ^-1,Δh becomes independent of L and scales with Rln(κ^-1/R). We implement a numerical scheme to solve the general Young-Laplace equation for an arbitrary L and demonstrate the crossover of the meniscus profile between these two limits. The crossover region has been determined to be roughly 0.4κ^-1≲L≲4κ^-1. An approximate analytical expression has been found for Δh, enabling its accurate prediction at any values of L that ranges from microscopic to macroscopic scales.

Effect of Moving Contact Line's Curvature on Dynamic Wetting of non-Newtonian Fluids

The curvature of the contact line is always changing with the dynamic wetting condition. Using a modified Wilhelmy plate method and the sessile drop method, this study experimentally investigated the dynamic wetting process of several kinds of Newtonian and non-Newtonian fluids. The results show that the curvature of the moving contact line strongly affects the relationship θ_D = f( U) for non-Newtonian fluids but has no effect on Newtonian fluids. The effect is more obvious with the stronger non-Newtonian fluids. The theoretical relationship derived from the Navier-Stokes equations established for spontaneous spreading indicates that the moving contact line curvature affects the relationship θ_D = f( U) for shear-thinning fluids and shear-thickening fluids in a different way, which agrees with the forced wetting experimental results for shear-thinning fluids in both this work and the previous one on the fluid showing shear-thickening rheology. A force balance relation of the braking force and driving force for the moving contact line is used to explain the internal mechanism about how the curvature of the contact line affects θ_D during wetting process.

Superoleophobic Slippery Lubricant-Infused Surfaces: Combining Two Extremes in the Same Surface

The ability to create superoleophobic surfaces repellent toward low-surface-tension liquids is important for various applications, and has been recently demonstrated using re-entrant or doubly re-entrant microtopography. Liquid droplets on such surfaces feature composite liquid-solid-air interfaces, whereas composite liquid-lubricant-air interfaces would have potential for additional repellency. Here, the development of a novel slippery superoleophobic surface with low adhesion is demonstrated via combining doubly re-entrant microtopography with slippery lubricant-infused porous surfaces. This is realized by using 3D direct laser writing to fabricate doubly re-entrant micropillars with dedicated nanostructures on top of each pillar. The top nanostructures stabilize the impregnated slippery lubricant, while the re-entrant geometry of the micropillars prevents lubricant from spreading. The slippery layer reduces the adhesion of liquid to the pillars, as proved using scanning droplet adhesion microscopy (SDAM), while the doubly re-entrant micropillars make the surface superoleophobic. This novel interface combining two extremes, superoleophobicity and slippery lubricant-infused surface, is of importance for designing superoleophobic and superhydrophobic surfaces with advanced liquid repellent, anti-icing, or anti-fouling properties.

Origins of Extreme Liquid Repellency on Structured, Flat, and Lubricated Hydrophobic Surfaces

There are currently three main classes of liquid-repellent surfaces: micro- or nanostructured superhydrophobic surfaces, flat surfaces grafted with "liquidlike" polymer brushes, and lubricated surfaces. Despite recent progress, the mechanistic explanation for the differences in droplet behavior on such surfaces is still under debate. Here, we measure the dissipative force acting on a droplet moving on representatives of these surfaces at different velocities U=0.01-1  mm/s using a cantilever force sensor with submicronewton accuracy and correlate it to the contact line dynamics observed using optical interferometry at high spatial (micron) and temporal (<0.1  s) resolutions. We find that the dissipative force-due to very different physical mechanisms at the contact line-is independent of velocity on superhydrophobic surfaces but depends nonlinearly on velocity for flat and lubricated surfaces. The techniques and insights presented here will inform future work on liquid-repellent surfaces and enable their rational design.

Cassie-Levitated Droplets for Distortion-Free Low-Energy Solid-Liquid Interactions

Despite the rapid advent of superomniphobic materials, there is a lack of methodologies to accurately investigate the ultralow-energy interactions taking place on these interfaces. For instance, universally employed models such as the pendant droplet often fail to provide representative information on the wetting properties of superomniphobic surfaces. The delicate balance between the forces acting at the droplet-surface and droplet-needle interfaces can easily result in heavily distorted droplet profiles. Here, we introduce a Cassie-levitating droplet model which overcomes the limitations of the pendant droplet model, allowing a distortion-free assessment of the interactions between super(amphi)omniphobic materials and low surface tension liquids. Comparative analysis in wetting of low surface tension fluids such as hexadecane (∼27.47 mN/m) on superamphiphobic surfaces via the Cassie-levitating and pendant droplet models reveals up to 70° (800%) deviations in the estimated contact angle hysteresis. A theoretical framework is developed to assess experimentally observed profile distortions against ideal gravity-induced sagging of droplet shapes during dynamic droplet expansion and contraction cycles. Notably, pendant droplets resulted in up to 50% distortion while the Cassie-levitating ones achieved less than just 10%. We believe that the Cassie-levitating droplet model bears ample potential for the characterization of the rapidly emerging family of superomniphobic materials, setting the basis for their future engineering in numerous emerging applications.

Mapping microscale wetting variations on biological and synthetic water-repellent surfaces

Droplets slip and bounce on superhydrophobic surfaces, enabling remarkable functions in biology and technology. These surfaces often contain microscopic irregularities in surface texture and chemical composition, which may affect or even govern macroscopic wetting phenomena. However, effective ways to quantify and map microscopic variations of wettability are still missing, because existing contact angle and force-based methods lack sensitivity and spatial resolution. Here, we introduce wetting maps that visualize local variations in wetting through droplet adhesion forces, which correlate with wettability. We develop scanning droplet adhesion microscopy, a technique to obtain wetting maps with spatial resolution down to 10 µm and three orders of magnitude better force sensitivity than current tensiometers. The microscope allows characterization of challenging non-flat surfaces, like the butterfly wing, previously difficult to characterize by contact angle method due to obscured view. Furthermore, the technique reveals wetting heterogeneity of micropillared model surfaces previously assumed to be uniform.

Friction and Wetting Transitions of Magnetic Droplets on Micropillared Superhydrophobic Surfaces

Reliable characterization of wetting properties is essential for the development and optimization of superhydrophobic surfaces. Here, the dynamics of superhydrophobicity is studied including droplet friction and wetting transitions by using droplet oscillations on micropillared surfaces. Analyzing droplet oscillations by high-speed camera makes it possible to obtain energy dissipation parameters such as contact angle hysteresis force and viscous damping coefficients, which indicate pinning and viscous losses, respectively. It is shown that the dissipative forces increase with increasing solid fraction and magnetic force. For 10 µm diameter pillars, the solid fraction range within which droplet oscillations are possible is between 0.97% and 2.18%. Beyond the upper limit, the oscillations become heavily damped due to high friction force. Below the lower limit, the droplet is no longer supported by the pillar tops and undergoes a Cassie-Wenzel transition. This transition is found to occur at lower pressure for a moving droplet than for a static droplet. The findings can help to optimize micropillared surfaces for low-friction droplet transport.

Retention of Antibacterial Activity in Geranium Plasma Polymer Thin Films

Bacterial colonisation of biomedical devices demands novel antibacterial coatings. Plasma-enabled treatment is an established technique for selective modification of physicochemical characteristics of the surface and deposition of polymer thin films. We investigated the retention of inherent antibacterial activity in geranium based plasma polymer thin films. Attachment and biofilm formation by Staphylococcus aureus, Pseudomonas aeruginosa, and Escherichia coli was significantly reduced on the surfaces of samples fabricated at 10 W radio frequency (RF) power, compared to that of control or films fabricated at higher input power. This was attributed to lower contact angle and retention of original chemical functionality in the polymer films fabricated under low input power conditions. The topography of all surfaces was uniform and smooth, with surface roughness of 0.18 and 0.69 nm for films fabricated at 10 W and 100 W, respectively. Hardness and elastic modules of films increased with input power. Independent of input power, films were optically transparent within the visible wavelength range, with the main absorption at ~290 nm and optical band gap of ~3.6 eV. These results suggest that geranium extract-derived polymers may potentially be used as antibacterial coatings for contact lenses.

Contact Angle Measurement of Small Capillary Length Liquid in Super-repelled State

The difficulty of measuring very large contact angles (>150 degrees) has become more relevant with the increased popularity of super-repellent surfaces. Measurement is more difficult for dynamic contact angles, for which theoretical profiles do not fit well, and small capillary length liquids, whose sessile droplets sag by gravity. Here, we expand the issue to the limit by investigating dynamic contact angles of liquids with an extremely small capillary length (<1.0 mm), empowered by the superomniphobic surface that can super-repel even fluorinated solvents, which highly wet all materials. Numerically simulating and experimentally testing 13 different liquids on the superomniphobic surface, we discover their dynamic contact angles can be measured with a consistent accuracy despite their vastly different capillary lengths if one keeps the lens magnification inversely proportional to the capillary length. Verifying the droplet equator height is a key parameter, we propose a new Bond number defined by the equator height and optical resolution to represent the measurement accuracy of large contact angles. Despite negligible improvement for most liquids today, the proposed approach teaches how to measure very large contact angles with consistent accuracy when any of the liquids in consideration has a capillary length below 1.0 mm.

Omnidirectional Self-Assembly of Transparent Superoleophobic Nanotextures

Engineering surface textures that are highly transparent and repel water, oil, and other low surface energy fluids can transform our interaction with wet environments. Despite extensive progress, current top-down methods are based on directional line-of-sight fabrication mechanisms that are limited by scale and cannot be applied to highly uneven, curved, and enclosed surfaces, while bottom-up techniques often suffer from poor optical transparency. Here, we present an approach that enables the rapid, omnidirectional synthesis of flexible and up to 99.97% transparent superhydrophobic and -oleophobic textures on many variable surface types. These features are obtained by the spontaneous formation of a multi re-entrant morphology during the controlled self-assembly of nanoparticle aerosols. We also develop a mathematical model to explain and control the self-assembly dynamics, providing important insights for the rational engineering of functional materials. We envision that our findings represent a significant advance in imparting superoleophobicity and superamphiphobicity to a so-far inapplicable family of materials and geometries for multifunctional applications.

Interfacial Particle Dynamics: One and Two Step Yielding in Colloidal Glass

The yielding behavior of silica nanoparticles partitioned at an air-aqueous interface is reported. Linear viscoelasticity of the particle-laden interface can be retrieved via a time-dependent and electrolyte-dependent superposition, and the applicability of the "soft glassy rheology" (SGR) model is confirmed. With increasing electrolyte concentration (φ^elect) in the aqueous subphase, a nonergodic state is achieved with particle dynamics arrested first from attraction induced bonding bridges and then from the cage effect of particle jamming, manifesting in a two-step yielding process under large amplitude oscillation strain (LAOS). The Lissajous curves disclose a shear-induced in-cage particle redisplacement within oscillation cycles between the two yielding steps, exhibiting a "strain softening" transitioning to "strain stiffening" as the interparticle attraction increases. By varying φ^elect and the particle spreading concentration, φ^SiO₂, a variety of phase transitions from fluid- to gel- and glass-like can be unified to construct a state diagram mapping the yielding behaviors from one-step to two-step before finally exhibiting one-step yielding at high φ^elect and φ^SiO₂.

Remodeling of Super-hydrophobic Surfaces

An experimental study on the underlying mechanisms of structured super-hydrophobic surfaces was recently published [ Butt, H.-J.; et al. How Water Advances on Superhydrophobic Surfaces. Phys. Rev. Lett. 2016, 116, 096101 . DOI: 10.1103/PhysRevLett.116.096101 ]. After depositing small drops of water, Butt's group inclined their surfaces to initiate movement. They examined the contact between the water and structured surfaces with confocal microscopy. They observed that drops were suspended atop the protruding features and movement of water was different at the advancing and receding edges. At the advancing edge, the water interface descended downward and draped itself across the features. At the receding edge, water jumped from one feature to the next. As Butt and co-workers did not test their data against any existing model, that is done in this paper. Here, a previously proposed model that employs linear averaging at the contact line was adapted to their surfaces in an attempt to estimate their contact and sliding angles. Predictions from the model generally agreed with their experimental measurements.

Effect of Gravity on the Configuration of Droplets on Two-Dimensional Physically Patterned Surfaces

Wetting of solid surfaces is important for many potential applications, including the design of low-drag and antifouling/self-cleaning surfaces, and it is usually quantified by the contact angle and by contact angle hysteresis. Both the chemistry and the physical patterning of the surface are known to affect the contact angle. In studying the wetting of such surfaces, most models focus on the small Bond number (Bo) limit in which the effect of gravity is negligible, which simplifies free energy calculations. In this work, we employ a thermodynamic model for surfaces patterned with two-dimensional asperities, which remains applicable for nonzero Bo. We employ two versions of the model: one in which we require the liquid-vapor interface to remain a circular cap, and another in which we allow the liquid-vapor interface to deform. We find that the effects of gravity are twofold. First, drops with larger Bo tend to flatten and spread across the surface relative to the same size drops with Bo = 0. Second, gravity makes it more favorable for drops to penetrate surface asperities compared to the case of Bo = 0, which also tends to lower the contact angles. The main effect of droplet deformation is to produce larger contact angles for the same wetting configuration. Finally, we compare our model predictions with relevant experimental observations. We find very close agreement with the experiments, thereby validating our theoretical model.

How Water Advances on Superhydrophobic Surfaces

Superliquid repellency can be achieved by nano- and microstructuring surfaces in such a way that protrusions entrap air underneath the liquid. It is still not known how the three-phase contact line advances on such structured surfaces. In contrast to a smooth surface, where the contact line can advance continuously, on a superliquid-repellent surface, the contact line has to overcome an air gap between protrusions. Here, we apply laser scanning confocal microscopy to get the first microscopic videos of water drops advancing on a superhydrophobic array of micropillars. In contrast to common belief, the liquid surface gradually bends down until it touches the top face of the next micropillars. The apparent advancing contact angle is 180°. On the receding side, pinning to the top faces of the micropillars determines the apparent receding contact angle. Based on these observations, we propose that the apparent receding contact angle should be used for characterizing superliquid-repellent surfaces rather than the apparent advancing contact angle and hysteresis.