General methodology for evaluating the adhesion force of drops and bubbles on solid surfaces

Estimating sliding drop width via side-view features using recurrent neural networks

High speed side-view videos of sliding drops enable researchers to investigate drop dynamics and surface properties. However, understanding the physics of sliding requires knowledge of the drop width. A front-view perspective of the drop is necessary. In particular, the drop's width is a crucial parameter owing to its association with the friction force. Incorporating extra cameras or mirrors to monitor changes in the width of drops from a front-view perspective is cumbersome and limits the viewing area. This limitation impedes a comprehensive analysis of sliding drops, especially when they interact with surface defects. Our study explores the use of various regression and multivariate sequence analysis (MSA) models to estimate the drop width at a solid surface solely from side-view videos. This approach eliminates the need to incorporate additional equipment into the experimental setup. In addition, it ensures an unlimited viewing area of sliding drops. The Long Short Term Memory (LSTM) model with a 20 sliding window size has the best performance with the lowest root mean square error (RMSE) of 67 µm. Within the spectrum of drop widths in our dataset, ranging from 1.6 to 4.4 mm, this RMSE indicates that we can predict the width of sliding drops with an error of 2.4%. Furthermore, the applied LSTM model provides a drop width across the whole sliding length of 5 cm, previously unattainable.

Soft wetting: Substrate softness- and time-dependent droplet/bubble adhesion

HYPOTHESIS

The droplet/bubble adhesion characteristics depend on the length of the droplet/bubble three-phase contact line. Since the deformation caused by the liquid-gas interfacial tension on the soft substrate, referred as to the wetting ridge, retards contact line spreading and retraction, we conjecture that the droplet/bubble adhesion characteristics depend also on the substrate softness.

EXPERIMENTS

Soft substrates with various shear moduli are prepared and characterized by the spreading and receding dynamics of water droplets and underwater bubbles. Snap-in and normal adhesion forces of droplets/bubbles on such soft substrates are directly measured along with the visualized droplet/bubble shape profiles.

FINDINGS

The droplet/bubble snap-in force, which corresponds to the short-time spreading dynamics, decreases with a decrease in the substrate shear modulus because of the retarded contact line spreading. The droplet maximal adhesion force on a soft substrate can be counterintuitively either smaller or larger than its counterpart on the rigid substrate depending on different dwelling times, i.e., the droplet/bubble-substrate contact time before droplet/bubble-substrate separation. The former is attributed to the retarded contact line spreading, whereas the latter is attributed to the retarded contact line retraction. The substrate softness- and dwelling time-dependent droplet/bubble adhesion reported in this study will benefit various applications related to soft substrates.

Advances in superhydrophobic material research: from preparation to electrified railway protection

Freezing is a serious problem that affects the power, transport, and transmission industries and is a major concern for the national economy and safety. Currently, several engineering de-icing methods, such as thermal, mechanical, and chemical de-icing, have shown problems related to energy consumption, efficiency, and the environment. Superhydrophobic materials have high droplet contact and roll angles, which can reduce the droplet residence and ice adhesion on their surfaces and have unique advantages in the self-cleaning and anti-icing fields. This paper introduces the development of infiltration theory and superhydrophobic materials and their principles of anti-icing and de-icing. Herein, the preparation and coating methods of superhydrophobic materials in applications are summarised, the performance and lifetime issues of superhydrophobic materials in applications are clarified, and the research progress on superhydrophobic materials in different fields is reviewed. Prospects for the application of superhydrophobic materials in electrified railways are also presented. A feasibility study was conducted to solve some of the existing problems of electrified railways, providing a theoretical basis for the development of electrified railways.

Surface Charge Deposition by Moving Drops Reduces Contact Angles

Slide electrification-the spontaneous charge separation by sliding aqueous drops-can lead to an electrostatic potential in the order of 1 kV and change drop motion substantially. To find out how slide electrification influences the contact angles of moving drops, we analyzed the dynamic contact angles of aqueous drops sliding down tilted plates with insulated surfaces, grounded surfaces, and while grounding the drop. The observed decrease in dynamic contact angles at different salt concentrations is attributed to two effects: An electrocapillary reduction of contact angles caused by drop charging and a change in the free surface energy of the solid due to surface charging.

Bioinspired Wire-on-Pillar Magneto-Responsive Superhydrophobic Arrays

Versatile surfaces demonstrating multiple interfacial functionalities are highly demanded as a surface typically serves various duties and faces multiple challenges in real practice. However, such versatile surfaces are rarely reported mainly due to the challenges in integrating multiple structural characteristics. Here, by mimicking lotus leaves, butterfly wing, and respiratory cilia, we develop a surface termed wire-on-pillar magneto-responsive superhydrophobic arrays (WP-MRSA), which possess interfacial properties of structural superhydrophobicity, anisotropicity, stimuli responsiveness, and flexibility. By combining soft lithography and self-alignment of iron-laden aerosols under a magnetic field, iron-laden wires are planted atop prefabricated pillar arrays, resulting in well-ordered, sparse, high-aspect-ratio, flexible, and superhydrophobic wires, which largely deflect in response to a magnetic field. This unique integration of structural properties and configurations enables various functionalities, such as on-demand control of droplet impact dynamics, real-time regulation of surface lateral adhesion force, fast removal and sorting of objects, and precise manipulation of droplets for selective reactions. Those functionalities benefit various applications especially droplet-based microfluidics and active self-cleaning surfaces.

Experimental Investigation of Dropwise Condensation Shedding by Shearing Airflow in Microgravity Using Different Surface Coatings

The shedding kinematics of water droplets in a condensation environment when exposed to aerodynamic forces in microgravity was studied. Understanding the shedding of droplets from a surface is a critical part of the dropwise condensation process for improving heat transfer. Because gravity as a droplet removal technique is not available in space, the use of airflow to shed droplets is considered for condensing heat exchangers in environmental control and life support systems. Surface coatings affect drop adhesion, and here, four different surfaces (PMMA, PS, PTFE, and SHS) and various droplet sizes (80, 60, and 40 μL) were used to understand the above phenomenon. It was found that the critical velocity to shed a droplet in microgravity was up to 8% lower than that in normal gravity. Also, the effect of the droplet size was investigated for both microgravity and normal gravity; the shedding velocity was lower for microgravity, and it decreased as droplet size increased. Increasing the hydrophobicity of the coating decreased the critical velocity for shedding. Finally, the droplet was found to detach from superhydrophobic surfaces in microgravity. The detachment of droplets from the substrate will hamper the condensation process that can produce a larger fresh area; also, detachment of droplets and entrainment in airflow counter the concept of removing moisture from the air in a dehumidification process.

Retention Forces for Drops on Microstructured Superhydrophobic Surfaces

Accurate models of retention forces between drops and superhydrophobic (SH) surfaces are required to predict drop dynamics on the surface. This retention force is, in turn, useful in modeling heat transfer rates for dropwise condensation on a SH surface. Drop contact angle distribution and base area on SH surfaces are essential factors for predicting retention forces. The present work measures the contact angle distribution and base area shapes of various drop sizes over a wide range of solid fraction for inclined microstructured SH surfaces at the point of drop departure. Base area shape was found to be well approximated using two ellipses with different aspect ratios, and the contact angle distribution was found to be best fit by a sigmoid function. At an incline near the roll-off angle, drop base area for surfaces with solid fraction close to 1 and close to 0 were found to be nearly circular, whereas the base area of drops on surfaces with an intermediate solid fraction deviated from circular behavior. In this work, maximum advancing and minimum receding contact angles were found as a function of solid fraction and used to calculate retention forces. Contact angle distribution and base area shapes are then used to calculate retention forces between drops and SH surfaces. These calculations are compared with the component of measured drop weight acting parallel to the plane on a tilted surface for validation. Previous retention force studies that investigate base area shape and contact angle distribution for smooth surfaces are not applicable for microstructured SH surfaces. The work shows that using a sigmoid contact angle distribution and modified base area shape yields retention forces that are on average 50% better than previously reported methods. Retention forces for smooth and SH surfaces calculated in this study were used to suggest retention force factor values for varying solid fraction surfaces.

Spontaneous Charging of Drops on Lubricant-Infused Surfaces

When a drop of a polar liquid slides over a hydrophobic surface, it acquires a charge. As a result, the surface charges oppositely. For applications such as the generation of electric energy, lubricant-infused surfaces (LIS) may be important because they show a low friction for drops. However, slide electrification on LIS has not been studied yet. Here, slide electrification on lubricant-infused surfaces was studied by measuring the charge generated by series of water drops sliding down inclined surfaces. As LIS, we used PDMS-coated glass with micrometer-thick silicone oil films on top. For PDMS-coated glass without lubricant, the charge for the first drop is highest. Then it decreases and saturates at a steady state charge per drop. With lubricant, the drop charge starts from 0, then it increases and reaches a maximum charge per drop. Afterward, it decreases again before reaching its steady-state value. This dependency is not a unique phenomenon for lubricant-infused PDMS; it also occurs on lubricant-infused micropillar surfaces. We attribute this dependency of charge on drop numbers to a change in surface conductivity and depletion of lubricant. These findings are helpful for understanding the charge process and optimizing solid-liquid nanogenerator devices in applications.

Biphilic Surfaces with Optimum Hydrophobic Islands on a Superhydrophobic Background for Dropwise Flow Condensation

Sustaining dropwise condensation is of great importance in many applications, especially in confined spaces. In this regard, superhydrophobic surfaces enhance condensation heat transfer performance due to the discrete droplet formation and rapid removal. On the other hand, droplets tend to nucleate easier and faster on hydrophobic surfaces compared to superhydrophobic ones. To take advantage of the mixed wettability, we fabricated biphilic surfaces and integrated them to small channels to assess their effect on thermal performance in flow condensation in small channels. Hydrophobic islands in the range of 100-900 μm diameter were fabricated using a combination of wet etching, surface functionalization, and physical vapor deposition (PVD) techniques. Condensation experiments were performed in a minichannel with a length, width, and height of 37, 10, and 1 mm, respectively. Here, we report optimum island diameters for the hydrophobic islands in terms of the maximum thermal performance. We show that considering the optimum point for each steam mass flux corresponding to the best heat transfer performance, the condensation heat transfer coefficient is increased by 51, 48, 42, 40, and 36% compared to the plain reference hydrophobic surface for steam mass fluxes of 10, 20, 30, 40, and 50 kg/m² s, respectively. The optimum island diameters are obtained as 200, 300, 400, 400, and 500 μm, with the ratios of hydrophobic to superhydrophobic surface areas (A* = A_hydrophobic/A_{superhydrophobic}) of 3.2, 7.6, 14.4, 14.4, and 24.4%, for steam mass fluxes of 10, 20, 30, 40, and 50 kg/m² s, respectively. The liquid film forming on the liquid-vapor interface acts as an insulation layer and generates thermal resistance, and bridges appear on the patterned areas and deteriorate the thermal performance. Therefore, it is crucial to characterize the role of droplet mobility on biphilic surfaces to avoid the occurrence of bridging. Through visualization, we demonstrate that the optimum conditions correspond to enhanced droplet nucleation and rapid sweeping regions, where droplet pinning and bridging do not occur. The trends in condensation heat transfer with surface mixed wettability can be divided into three regions: enhanced droplet nucleation and rapid sweeping, highly pinned droplet, and bridging droplet segments. We reveal that the interfacial heat transfer augmentation in the enhanced droplet nucleation and rapid sweeping region is due to both spatial control of droplet nucleation and an increase in the sweeping period. Furthermore, by fitting the experimental data, a correlation for predicting the optimum island diameter for biphilic surfaces is proposed for condensation heat transfer in confined channels, which will be a valuable guideline for engineers and researchers working on the design and development of thermal systems.

Lateral and Normal Capillary Force Evolution of a Reciprocating Liquid Bridge

Capillary forces of a shearing liquid bridge can significantly affect the friction and adhesion of interacting surfaces, but the underlying mechanisms remain unclear. We custom built a surface force apparatus (SFA, ±2 μN) equipped with in situ optical microscopy and performed normal and lateral force measurements on a reciprocating water bridge formed between two flat plates. A modified wedge method was developed to correct the unique force measurement errors caused by the changing bridge geometry and position. The results found (1) strong linear relations among the bridge shear displacement, the cosine difference between the left and right contact angles, and the lateral adhesion force and (2) the normal adhesion force increased monotonically up to 13% as the bridge geometry approached its axisymmetric state. Quasi-static force analyses based on a newly developed decahedral model showed good agreement with the experiments and improved accuracy compared with that of cylindrical or rectangular column models previously proposed in the literature. Although limited in certain aspects, this study may (1) prove helpful to the design and analysis of liquid bridge force experiments on platforms similar to the SFA used in this study and (2) help to bridge the gap between friction and liquid bridge physics in the literature.

Wetting-regulated gas-involving (photo)electrocatalysis: biomimetics in energy conversion

(Photo)electrolysis of water or gases with water to species serving as industrial feedstocks and energy carriers, such as hydrogen, ammonia, ethylene, propanol, etc., has drawn tremendous attention. Moreover, these processes can often be driven by renewable energy under ambient conditions as a sustainable alternative to traditional high-temperature and high-pressure synthesis methods. In addition to the extensive studies on catalyst development, increasing attention has been paid to the regulation of gas transport/diffusion behaviors during gas-involving (photo)electrocatalytic reactions towards the goal of creating industrially viable catalytic systems with high reaction rates, excellent long-term stabilities and near-unity selectivities. Biomimetic surfaces and systems with special wetting capabilities and structural advantages can shed light on the future design of (photo)electrodes and address long-standing challenges. This article is dedicated to bridging the fields of wetting and catalysis by reviewing the cutting-edge design methodologies of both gas-evolving and gas-consuming (photo)electrocatalytic systems. We first introduce the fundamentals of various in-air/underwater wetting states and their corresponding bioinspired structural properties. The relationship amongst the bubble transport behavior, wettability, and porosity/tortuosity is also discussed. Next, the latest implementations of wetting-related design principles for gas-evolving reactions (i.e. the hydrogen evolution reaction and oxygen evolution reaction) and gas-consuming reactions (i.e. the oxygen reduction reaction and CO2 reduction reaction) are summarized. For photoelectrode designs, additional factors are taken into account, such as light absorption and the separation, transport and recombination of photoinduced electrons and holes. The influences of wettability and 3D structuring of (photo)electrodes on the catalytic activity, stability and selectivity are analyzed to reveal the underlying mechanisms. Finally, remaining questions and related future perspectives are outlined.

Contact angle measurements: From existing methods to an open-source tool

Contact angle measurement is an effective way to investigate solid surface properties. The introduction of low-cost digital cameras, as well as software and libraries for image analysis, has made contact angle measurement potentially accessible to every laboratory. In this review, we provide a comparison of the main methods developed to evaluate contact angle from digital images, including the so-called Young-Laplace method, the circle and polynomial fittings, as well as the mask method. All methods have been implemented and compared analyzing virtual and real drop images in an open-source software, Dropen, developed as an app in MATLAB environment. The code enables single image analysis evaluation, for the robust automatic identification of the contact points and contact angle evaluation, with the goal of minimizing user inputs, automatizing the process and facilitating measurements for all users, from less experienced to advanced wetting experts. Dropen and its code are made available at BOA, the Bicocca Open Access public repository, for use and further development.

One-Step Synthesis of a Durable and Liquid-Repellent Poly(dimethylsiloxane) Coating

Coatings with low sliding angles for liquid drops have a broad range of applications. However, it remains a challenge to have a fast, easy, and universal preparation method for coatings that are long-term stable, robust, and environmentally friendly. Here, a one-step grafting-from approach is reported for poly(dimethylsiloxane) (PDMS) brushes on surfaces through spontaneous polymerization of dichlorodimethylsilane fulfilling all these requirements. Drops of a variety of liquids slide off at tilt angles below 5°. This non-stick coating with autophobicity can reduce the waste of water and solvents in cleaning. The strong covalent attachment of the PDMS brush to the substrate makes them mechanically robust and UV-tolerant. Their resistance to high temperatures and to droplet sliding erosion, combined with the low film thickness (≈8 nm) makes them ideal candidates to solve the long-term degradation issues of coatings for heat-transfer surfaces.

Directional anchoring patterned liquid-infused superamphiphobic surfaces for high-throughput droplet manipulation

High-throughput experiments involving isolated droplets based on patterned superwettable surfaces are important for various applications related to biology, chemistry, and medicine, and they have attracted a large amount of interest. This paper provides a directional anchoring liquid-infused superamphiphobic surface (DAS), via combining concepts based on the droplet-anchoring behavior of beetle backs with patterned wettability, the directional adhesion of butterfly wings, and the slippery liquid-infused surfaces (SLISs) of pitcher plants. Regularly arranged ">"-shaped SLIS patterns were created on a superamphiphobic (SAM) background through ultrafast-laser-based technology. Improved directional anchoring abilities with a sliding angle difference of 77° were achieved; this is the largest sliding angle difference in a one-dimensional direction achieved using an artificial surface, to the best of the authors' knowledge. Thanks to the directional anchoring abilities, the DAS coupled droplet 'anchoring' and 'releasing' abilities. Furthermore, a high-throughput droplet manipulation device was designed, on which a micro-droplet array with a large number of droplets can be 'captured', 'transferred', or 'released' in a single step. With the addition of lubricant, the DAS can work continuously for even more than 30 cycles without cross-contamination between different droplets. The DAS also shows good stability under an ambient atmosphere and can maintain its functionality when manipulating corrosive droplets. The DAS and corresponding high-throughput droplet manipulation method are excellent candidates for practical applications.

Bioinspired wettable-nonwettable micropatterns for emerging applications

Superhydrophilic and superhydrophobic surfaces are prevalent in nature and have received tremendous attention due to their importance in both fundamental research and practical applications. With the high interdisciplinary research and great development of microfabrication techniques, artificial wettable-nonwettable micropatterns inspired by the water-collection behavior of desert beetles have been successfully fabricated. A combination of the two extreme states of superhydrophilicity and superhydrophobicity on the same surface precisely, wettable-nonwettable micropatterns possess unique functionalities, such as controllable superwetting, anisotropic wetting, oriented adhesion, and other properties. In this review, we briefly describe the methods for fabricating wettable-nonwettable patterns, including self-assembly, electrodeposition, inkjet printing, and photolithography. We also highlight some of the emerging applications such as water collection, controllable bioadhesion, cell arrays, microreactors, printing techniques, and biosensors combined with various detection methods. Finally, the current challenges and prospects of this renascent and rapidly developing field are proposed and discussed.

Adaptation of a Styrene-Acrylic Acid Copolymer Surface to Water

Solid surfaces, in particular polymer surfaces, are able to adapt upon contact with a liquid. Adaptation results in an increase in contact angle hysteresis and influences the mobility of sliding drops on surfaces. To study adaptation and its kinetics, we synthesized a random copolymer composed of styrene and 11-25 mol% acrylic acid (PS/PAA). We measured the dynamic advancing (θ_A) and receding (θ_R) contact angles of water drops sliding down a tilted plate coated with this polymer. We measured θ_A ≈ 87° for velocities of the contact line <20 μm/s. At higher velocities, θ_A gradually increased to ∼98°. This value is similar to θ_A of a pure polystyrene (PS) film, which we studied for comparison. We associate the gradual increase in θ_A to the adaptation process to water: The presence of water leads to swelling and/or an enrichment of acid groups at the water/polymer interface. By applying the latest adaptation theory (Butt et al. Langmuir 2018, 34, 11292), we estimated the time constant of this adaptation process to be ≪1 s. For sliding water drops, θ_R is ∼10° lower compared to the reference PS surface for all tested velocities. Thus, at the receding side of a sliding drop, the surface is already enriched by acid groups. For a water drop with a width of 5 mm, the increase in contact angle hysteresis corresponds to an increase in capillary force in the range of 45-60 μN, depending on sliding velocity.

Topography-Dependent Effective Contact Line in Droplet Depinning

The mobility of a fakir state droplet on a structured surface is fundamentally determined by the effective length of a microscopic contact line. However, it is largely unknown how the surface topography determines the effective contact line length. Based on the direct measurement of droplet adhesion force and the visualization of contact line, this work shows that effective contact line length is topography dependent as opposed to prior notion. On pored surfaces, contact line is not distorted, and the effective length approaches the droplet apparent perimeter regardless of pore dimensions. On pillared surfaces, the distortion of contact line is significantly dependent on the packing density of the pillar structures so that the effective length is as small as a pillar diameter on densely packed pillars and as large as a pillar perimeter on sparsely-packed pillars, while changing linearly between the two extremes.

Droplet Impact on Suspended Metallic Meshes: Effects of Wettability, Reynolds and Weber Numbers

Liquid penetration analysis in porous media is of great importance in a wide range of applications such as ink jet printing technology, painting and textile design. This article presents an investigation of droplet impingement onto metallic meshes, aiming to provide insights by identifying and quantifying impact characteristics that are difficult to measure experimentally. For this purpose, an enhanced Volume-Of-Fluid (VOF) numerical simulation framework is utilised, previously developed in the general context of the OpenFOAM CFD Toolbox. Droplet impacts on metallic meshes are performed both experimentally and numerically with satisfactory degree of agreement. From the experimental investigation three main outcomes are observed—deposition, partial imbibition, and penetration. The penetration into suspended meshes leads to spectacular multiple jetting below the mesh. A higher amount of liquid penetration is linked to higher impact velocity, lower viscosity and larger pore size dimension. An estimation of the liquid penetration is given in order to evaluate the impregnation properties of the meshes. From the parametric analysis it is shown that liquid viscosity affects the adhesion characteristics of the drops significantly, whereas droplet break-up after the impact is mostly controlled by surface tension. Additionally, wettability characteristics are found to play an important role in both liquid penetration and droplet break-up below the mesh.

Onset time of fog collection

Fog collection is a promising solution to the worldwide water scarcity problem and is also of vital importance to industrial processes, such as recapturing water in cooling towers and mist elimination. To date, numerous studies have investigated the fog collection rate, a parameter that denotes the average performance over a long period of time. However, the initial period (referred to as onset time) between the start of the fog-laden flow and the actual collection of the captured liquid (a delay in time caused by droplet growth to a critical weight that exceeds droplet-surface retention force) has not been systematically understood. A longer onset time may result in a more serious clogging issue that deteriorates the collection rate and, hence, understanding this phenomenon is important. Here, we study how the onset time is determined by the capture and transport of fog using individual, vertical wires with various surface wettabilities and diameters, under different wind speeds. This approach allows us to derive a scaling law that correlates the onset time with the fog capture process and droplet-surface retention force, governed by aerodynamics and interfacial phenomena, respectively. In particular, the onset time decreases with an increasing rate of fog capture or a decreasing droplet-surface retention force. This study introduces an important aspect in the evaluation of fog collection and provides insights for the optimal design of fog collectors and mist eliminators.

Adaptive Wetting-Adaptation in Wetting

Many surfaces reversibly change their structure and interfacial energy upon being in contact with a liquid. Such surfaces adapt to a specific liquid. We propose the first order kinetic model to describe dynamic contact angles of such adaptive surfaces. The model is general and does not refer to a particular adaptation process. The aim of the proposed model is to provide a quantitative description of adaptive wetting and to link changes in contact angles to microscopic adaptation processes. By introducing exponentially relaxing interfacial energies and applying Young's equation locally, we predict a change of advancing and receding contact angles depending on the velocity of the contact line. Even for perfectly homogeneous and smooth surfaces, a dynamic contact angle hysteresis is obtained. As possible adaptations, we discuss changes and reconstruction of polymer surfaces or monolayers, diffusion and swelling, adsorption of surfactants, replacement of contaminants, reorientation of liquid molecules, or formation of an electric double layer.

Self-transport of underwater bubbles on a microholed hydrophobic surface with gradient wettability

Manipulation of underwater bubbles is of great importance in both scientific research and industrial applications. In this work, the motion of underwater bubbles on a microholed polydimethylsiloxane (PDMS) surface with gradient wettability is studied using a high-speed camera. It was found that underwater bubbles self-transported directionally from the smaller area fraction (SAF) to the larger area fraction (LAF) of the surface. Besides, the bubble motion was triggered by an effective depth range from hcr,min to hcr,max. Only the depth of the bubble was within the range when the self-transport motion occurred. Otherwise the bubble would adhere onto the surface eventually. The main cause for the motion is the trapped air inside the microholes, which generates the torque Tb and the retention force Fr driving the bubble directionally. The mathematical model is established to reveal the motion mechanism, which is verified by the experimental results. The outcomes of our work shed new light on the target transportation fields such as drug delivery and submarine gas collection.

A Water Droplet Pinning and Heat Transfer Characteristics on an Inclined Hydrophobic Surface

A water droplet pinning on inclined hydrophobic surface is considered and the droplet heat transfer characteristics are examined. Solution crystallization of polycarbonate is carried out to create hydrophobic characteristics on the surface. The pinning state of the water droplet on the extreme inclined hydrophobic surface (0° ≤ δ ≤ 180°, δ being the inclination angle) is assessed. Heat transfer from inclined hydrophobic surface to droplet is simulated for various droplet volumes and inclination angles in line with the experimental conditions. The findings revealed that the hydrophobic surface give rise to large amount of air being trapped within texture, which generates Magdeburg like forces between the droplet meniscus and the textured surface while contributing to droplet pinning at extreme inclination angles. Two counter rotating cells are developed for inclination angle in the range of 0° < δ < 20° and 135° < δ < 180°; however, a single circulation cell is formed inside the droplet for inclination angle of 25° ≤ δ ≤ 135°. The Nusselt number remains high for the range of inclination angle of 45° ≤ δ ≤ 135°. Convection and conduction heat transfer enhances when a single and large circulation cell is formed inside the droplet.

Receding Contact Line Motion on Nanopatterned and Micropatterned Polymer Surfaces

Surface properties such as topography and chemistry affect the motion of the three-phase contact line (solid/liquid/air), which in turn affects the contact angle of a liquid moving on a solid surface. In this work, the motion of the receding water contact line was studied on chemically and topographically patterned surfaces obtained from the dewetting of thin polymer films. The patterned surfaces consisted of hydrophilic poly(4-vinylpyridine) (P4VP) bumps, which were either microsized and sparse or nanosized and dense, on top of a hydrophobic polystyrene (PS) background layer. These patterns are designed for atmospheric water capture, for which the easy roll off of water droplets is crucial to their efficient performance. The dynamic receding water contact angle and contact line height of the patterned surfaces were measured by vertically withdrawing the surfaces from a water bath and compared to those of a flat P4VP substrate. For both the micropatterned and nanopatterned surfaces, the height of the dynamic contact lines normalized by the capillary length was characterized by the equilibrium limit that was predicted from static states. The nanopatterned surface had a faster increase in the normalized height as the capillary number increased. The dynamic receding contact angles on all surfaces studied decreased with increasing withdrawing velocity. Surprisingly, even for these patterned surfaces with high hysteresis, the dynamic receding contact angle followed the Cox-Voinov relation at capillary numbers of between 1 × 10^-5 and 5 × 10^-5.

Bubble Movement on Inclined Hydrophobic Surfaces

The movement of a single air bubble on an inclined hydrophobic surface submerged in water, including both the upward- and downward-facing sides of the surface, was investigated. A planar Teflon sheet with an apparent contact angle of a sessile water droplet of 106° was used as a hydrophobic surface. The volume of a bubble and the inclination angle of a Teflon sheet varied in the ranges 5-40 μL and 0-45°, respectively. The effects of the bubble volume on the adhesion and dynamics of the bubble were studied experimentally on the facing-up and facing-down surfaces of the submerged hydrophobic Teflon sheet, respectively, and compared. The result shows that the sliding angle has an inverse relationship with the bubble volume for both the upward- and downward-facing surfaces. However, at the same given volume, the bubble on the downward-facing surface spreads over a larger area of the hydrophobic surface than the upward-facing surface due to the greater hydrostatic pressure acting on the bubble on the downward-facing surface. This makes the lateral adhesion force of the bubble greater and requires a larger inclination angle to result in sliding.

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

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

Energy Dissipation of Moving Drops on Superhydrophobic and Superoleophobic Surfaces

A water drop moving on a superhydrophobic surface or an oil drop moving on a superoleophobic surface dissipates energy by pinning/depinning at nano- and microprotrusions. Here, we calculate the work required to form, extend, and rupture capillary bridges between the protrusions and the drop. The energy dissipated at one protrusion W_S is derived from the observable apparent receding contact angle Θ_r^app and the density of protrusions n by W_s = γ(cos Θ_r^app + 1)/n, where γ is the surface tension of the liquid. To derive an expression for W_s that links the microscopic structure of the surface to apparent contact angles, two models are considered: A superhydrophobic array of cylindrical micropillars and a superoleophobic array of stacks of microspheres. For a radius of a protrusion R and a receding materials contact angle Θ_r, we calculate the energy dissipated per protrusion as W_s = πγR²[A - ln(R/κ)]f(Θ_r). Here, A = 0.60 for cylindrical micropillars and 2.9 for stacks of spheres. κ is the capillary length. f(Θ_r) is a function which depends on Θ_r and the specific geometry, f ranges from ≈0.25 to 0.96. Combining both equations above, we can correlate the macroscopically observed apparent receding contact angle with the microscopic structure of the surface and its material properties.

Droplet Mobility Manipulation on Porous Media Using Backpressure

Wetting phenomena on hydrophobic surfaces are strongly related to the volume and pressure of gas pockets residing at the solid-liquid interface. In this study, we explore the underlying mechanisms of droplet actuation and mobility manipulation when backpressure is applied through a porous medium under a sessile pinned droplet. Reversible transitions between the initially sticky state and the slippery states are thus incited by modulating the backpressure. The sliding angles of deionized (DI) water and ethanol in DI water droplets of various volumes are presented to quantify the effect of the backpressure on the droplet mobility. For a 50 μL water droplet, the sliding angle decreases from 45 to 0° when the backpressure increases to ca. 0.60 bar. Significantly smaller backpressure levels are required for lower surface energy liquids. We shed light on the droplet actuation and movement mechanisms by means of simulations encompassing the momentum conservation and the continuity equations along with the Cahn-Hilliard phase-field equations in a 2D computational domain. The droplet actuation mechanism entails depinning of the receding contact line and movement by means of forward wave propagation reaching the front of the droplet. Eventually, the droplet skips forward. The contact line depinning is also corroborated by analytical calculations based on the governing vertical force balance, properly modified to incorporate the effect of the backpressure.

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.

On the shedding of impaled droplets: The role of transient intervening layers

Maintaining the non-wetting property of textured hydrophobic surfaces is directly related to the preservation of an intervening fluid layer (gaseous or immiscible liquid) between the droplet and substrate; once displaced, it cannot be recovered spontaneously as the fully penetrated Wenzel wetting state is energetically favorable. Here, we identify pathways for the “lifting” of droplets from the surface texture, enabling a complete Wenzel-to-Cassie-Baxter wetting state transition. This is accomplished by the hemiwicking of a transient (limited lifetime due to evaporation) low surface tension (LST) liquid, which is capable of self-assembling as an intervening underlayer, lifting the droplet from its impaled state and facilitating a skating-like behavior. In the skating phase, a critical substrate tilting angle is identified, up to which underlayer and droplet remain coupled exhibiting a pseudo-Cassie-Baxter state. For greater titling angles, the droplet, driven by inertia, detaches itself from the liquid intervening layer and transitions to a traditional Cassie-Baxter wetting state, thereby accelerating and leaving the underlayer behind. A model is also presented that elucidates the mechanism of mobility recovery. Ultimately, this work provides a better understanding of multiphase mass transfer of immiscible LST liquid-water mixtures with respect to establishing facile methods towards retaining intervening layers.

Shedding of Water Drops from a Surface under Icing Conditions

A sessile water drop exposed to an air flow will shed if the adhesion is overcome by the external aerodynamic forces on the drop. In this study, shedding of water drops were investigated under icing conditions, on surfaces with different wettabilities, from hydrophilic to superhydrophobic. A wind tunnel was used for experiments in a temperature range between -8 and 24.5 °C. Results indicate that the temperature has a major influence on the incipient motion of drop shedding. The critical air velocity (U(c)) at which a drop first starts to shed generally increases under icing conditions, indicating an increase in the adhesion force. The contact angle hysteresis (CAH) and the drop base length (L(b)) are found to be the controlling factors for adhesion. A correlation was also developed to deduce the drag coefficient, C(D) for the drop. It was found that C(D) can decrease under icing conditions. In general, a lower C(D) and higher adhesion together lead to a higher critical air velocity. However, there are systems such as water on Teflon for which the critical air velocity remains practically unaffected by temperature because of similar adhesion and C(D) values, at all temperatures tested.

VOF simulations of the contact angle dynamics during the drop spreading: standard models and a new wetting force model

INTRODUCTION

In this study,a novel numerical implementation for the adhesion of liquid droplets impacting normally on solid dry surfaces is presented. The advantage of this new approach, compared to the majority of existing models, is that the dynamic contact angle forming during the surface wetting process is not inserted as a boundary condition, but is derived implicitly by the induced fluid flow characteristics (interface shape) and the adhesion physics of the gas-liquid-surface interface (triple line), starting only from the advancing and receding equilibrium contact angles. These angles are required in order to define the wetting properties of liquid phases when interacting with a solid surface.

METHODOLOGY

The physical model is implemented as a source term in the momentum equation of a Navier-Stokes CFD flow solver as an "adhesion-like" force which acts at the triple-phase contact line as a result of capillary interactions between the liquid drop and the solid substrate. The numerical simulations capture the liquid-air interface movement by considering the volume of fluid (VOF) method and utilizing an automatic local grid refinement technique in order to increase the accuracy of the predictions at the area of interest, and simultaneously minimize numerical diffusion of the interface.

RESULTS

The proposed model is validated against previously reported experimental data of normal impingement of water droplets on dry surfaces at room temperature. A wide range of impact velocities, i.e. Weber numbers from as low as 0.2 up to 117, both for hydrophilic (θadv=10°-70°) and hydrophobic (θadv=105°-120°) surfaces, has been examined. Predictions include in addition to droplet spreading dynamics, the estimation of the dynamic contact angle; the latter is found in reasonable agreement against available experimental measurements.

CONCLUSION

It is thus concluded that theimplementation of this model is an effective approach for overcoming the need of a pre-defined dynamic contact angle law, frequently adopted as an approximate boundary condition for such simulations. Clearly, this model is mostly influential during the spreading phase for the cases of low We number impacts (We<˜80) since for high impact velocities, inertia dominates significantly over capillary forces in the initial phase of spreading.

Hierarchically nanotextured surfaces maintaining superhydrophobicity under severely adverse conditions

Superhydrophobic surfaces are highly desirable for a broad range of technologies and products affecting everyday life. Despite significant progress in recent years in understanding the principles of hydrophobicity, mostly inspired by surface designs found in nature, many man-made surfaces employ readily processable materials, ideal to demonstrate principles, but with little chance of survivability outside a very limited range of well-controlled environments. Here we focus on the rational development of robust, hierarchically nanostructured, environmentally friendly, metal-based (aluminum) superhydrophobic surfaces, which maintain their performance under severely adverse conditions. Based on their functionality, we superpose selected hydrophobic layers (i.e. self-assembled monolayers, thin films, or nanofibrous coatings) on hierarchically textured aluminum surfaces, collectively imparting high level robustness of superhydrophobicity under adverse conditions. These surfaces simultaneously exhibit chemical stability, mechanical durability and droplet impalement resistance. They impressively maintained their superhydrophobicity after exposure to severely adverse chemical environments like strong alkaline (pH ∼ 9-10), acidic (pH ∼ 2-3), and ionic solutions (3.5 weight% of sodium chloride), and could simultaneously resist water droplet impalement up to an impact velocity of 3.2 m s(-1) as well as withstand standard mechanical durability tests.

Water drops dancing on ice: how sublimation leads to drop rebound

Drop rebound is a spectacular event that appears after impact on hydrophobic or superhydrophobic surfaces but can also be induced through the so-called Leidenfrost effect. Here we demonstrate that drop rebound can also originate from another physical phenomenon, the solid substrate sublimation. Through drop impact experiments on a superhydrophobic surface, a hot plate, and solid carbon dioxide (commonly known as dry ice), we compare drop rebound based on three different physical mechanisms, which apparently share nothing in common (superhydrophobicity, evaporation, and sublimation), but lead to the same rebound phenomenon in an extremely wide temperature range, from 300 °C down to even below -79 °C. The formation and unprecedented visualization of an air vortex ring around an impacting drop are also reported.

A robust polynomial fitting approach for contact angle measurements

Polynomial fitting to drop profile offers an alternative to well-established drop shape techniques for contact angle measurements from sessile drops without a need for liquid physical properties. Here, we evaluate the accuracy of contact angles resulting from fitting polynomials of various orders to drop profiles in a Cartesian coordinate system, over a wide range of contact angles. We develop a differentiator mask to automatically find a range of required number of pixels from a drop profile over which a stable contact angle is obtained. The polynomial order that results in the longest stable regime and returns the lowest standard error and the highest correlation coefficient is selected to determine drop contact angles. We find that, unlike previous reports, a single polynomial order cannot be used to accurately estimate a wide range of contact angles and that a larger order polynomial is needed for drops with larger contact angles. Our method returns contact angles with an accuracy of <0.4° for solid-liquid systems with θ < ~60°. This compares well with the axisymmetric drop shape analysis-profile (ADSA-P) methodology results. Above about 60°, we observe significant deviations from ADSA-P results, most likely because a polynomial cannot trace the profile of drops with close-to-vertical and vertical segments. To overcome this limitation, we implement a new polynomial fitting scheme by transforming drop profiles into polar coordinate system. This eliminates the well-known problem with high curvature drops and enables estimating contact angles in a wide range with a fourth-order polynomial. We show that this approach returns dynamic contact angles with less than 0.7° error as compared to ADSA-P, for the solid-liquid systems tested. This new approach is a powerful alternative to drop shape techniques for estimating contact angles of drops regardless of drop symmetry and without a need for liquid properties.

Dynamic measurement of the force required to move a liquid drop on a solid surface

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.

Wetting on the microscale: shape of a liquid drop on a microstructured surface at different length scales

Describing wetting of a liquid on a rough or structured surface is a challenge because of the wide range of involved length scales. Nano- and micrometer-sized textures cause pinning of the contact line, reflected in a hysteresis of the contact angle. To investigate contact angles at different length scales, we imaged water drops on arrays of 5 μm high poly(dimethylsiloxane) micropillars. The drops were imaged by laser scanning confocal microscopy (LSCM), which allowed us to quantitatively analyze the local and large-scale drop profile simultaneously. Deviations of the shape of drops from a sphere decay at two different length scales. Close to the pillars, the amplitude of deviations decays exponentially within 1-2 μm. The drop profile approached a sphere at a length scale 1 order of magnitude larger than the pillars' height. The height and position dependence of the contact angles can be understood from the interplay of pinning of the contact line, the principal curvatures set by the topography of the substrate, and the minimization of the air-water interfaces.

Drops sitting on a tilted plate: receding and advancing pinning

The wetting behavior of a liquid drop sitting on an inclined plane is investigated experimentally and theoretically. Using Surface Evolver, the numerical simulations are performed based on the liquid-induced defect model, in which only two thermodynamic parameters (solid-liquid interfacial tensions before and after wetting) are required. A drop with contact angle (CA) equal to θ is first placed on a horizontal plate, and then the plate is tilted. Two cases are studied: (i) θ is adjusted to the advancing CA (θ(a)) before tilting, and (ii) θ is adjusted to the receding CA (θ(r)) before tilting. In the first case, the uphill CA declines and the downhill CA remains unchanged upon inclination. When the tilted drop stays at rest, the pinning of the receding part of the contact line (receding pinning) and the depinning of the advancing part of the contact line (advancing depinning) are observed. The free energy analysis reveals that upon inclination, the reduction of the solid-liquid free energy dominates over the increment of the liquid-gas free energy associated with shape deformation. In the second case, the downhill CA grows and the uphill CA remains the same upon inclination. Advancing pinning and receding depinning are noted for the tilted drop at rest. The free energy analysis indicates that upon inclination, the decrease of the liquid-gas free energy compensates the increment of the solid-liquid free energy. The experimental results are in good agreement with those of simulations.