Beyond Wenzel and Cassie-Baxter: second-order effects on the wetting of rough surfaces

Influence of chemistry and topography on the wettability of copper

To understand the complex interplay of topography and surface chemistry in wetting, fundamental studies investigating both parameters are needed. Due to the sensitivity of wetting to miniscule changes in one of the parameters it is imperative to precisely control the experimental approach. A profound understanding of their influence on wetting facilitates a tailored design of surfaces with unique functionality. We present a multi-step study: The influence of surface chemistry is analyzed by determining the adsorption of volatile carbonous species (A) and by sputter deposition of metallic copper and copper oxides on flat copper substrates (B). A precise surface topography is created by laser processing. Isotropic topography is created by ps laser processing (C), and hierarchical anisotropic line patterns are produced by direct laser interference patterning (DLIP) with different pulse durations (D). Our results reveal that the long-term wetting response of polished copper surfaces stabilizes with time despite ongoing accumulation of hydrocarbons and is dominated by this adsorption layer over the oxide state of the substrate (Cu, CuO, Cu2O). The surfaces' wetting response can be precisely tuned by tailoring the topography via laser processing. The sub-pattern morphology of primary line-like patterns showed great impact on the static contact angle, wetting anisotropy, and water adhesion. An increased roughness inside the pattern valleys combined with a minor roughness on pattern peaks favors air-inclusions, isotropic hydrophobicity, and low water adhesion. Increasing depth of the primary topography can also induce air-inclusions despite increasing peak roughness while time dependent wetting transitions were observed.

Controlled Wrinkle Patterning on Thin Films to Improve Hydrophobicity

Controlling surface morphology is one of the main strategies used to tune surface hydrophobic and icephobic properties. Taking advantage of coating growth by initiated chemical vapor deposition, random and ordered wrinkles were induced on a thin film of polyperfluorodecyl acrylate (pPFDA) deposited on polydimethylsiloxane (PDMS) to simultaneously modify surface chemistry and morphology. A range of wrinkles of different wavelengths were studied, and how the wrinkle characteristics change with varying coating thickness. Ordered wrinkles enhanced hydrophobicity more when compared to random wrinkles, with a noticeable effect for coating thickness on the order of hundreds of nanometers. An insight into the mechanism of surface wrinkling and its effect on freezing delay is also provided, and promising results were found on ordered wrinkles, where a freezing delay was observed.

Two-Photon Polymerization of Butterfly Wing Scale Inspired Surfaces with Anisotropic Wettability

Wings of Morph aega butterflies are natural surfaces that exhibit anisotropic liquid wettability. The direction-dependent arrangement of the wing scales creates orientation-turnable microstructures with two distinct contact modes for liquid droplets. Enabled by recent developments in additive manufacturing, such natural surface designs coupled with hydrophobicity play a crucial role in applications such as self-cleaning, anti-icing, and fluidic manipulation. However, the interplay among resolution, architecture, and performance of bioinspired structures is barely achieved. Herein, inspired by the wing scales of the Morpho aega butterfly, full-scale synthetic surfaces with anisotropic wettability fabricated by two-photon polymerization are reported. The quality of the artificial butterfly scale is improved by optimizing the laser scanning strategy and the objective lens movement path. The corresponding contact angles of water on the fabricated architecture with various design parameters are measured, and the anisotropic fluidic wettability is investigated. Results demonstrate that tuning the geometrical parameters and spatial arrangement of the artificial wing scales enables anisotropic behaviors of the droplet's motion. The measured results also indicate a reverse phenomenon of the fabricated surfaces in contrast to their natural counterparts, possibly attributed to the significant difference in equilibrium wettability between the fabricated microstructures and the natural Morpho aega surface. These findings are utilized to design next-generation fluid-controllable interfaces for manipulating liquid mobility on synthetic surfaces.

Contact angle of ethanol, water, and their mixtures on stainless steel surfaces in dense carbon dioxide

HYPOTHESIS

Contact angle can be a key parameter in chemical engineering. However, the development and the optimization of numerous processes using supercritical CO2, considered as environmentally friendly, require new measurements under dense CO2 atmosphere. Besides, the influence of the roughness or the wetting regime on the contact angle is known at ambient conditions but remains to be discussed for systems under high pressure.

EXPERIMENTAL

Contact angle measurements of ethanol, water, and their mixtures, with ethanol mass fractions ranging from 0.25 to 0.75, on two stainless steels in saturated CO2 at pressures ranging from 0.1 MPa to 15.1 MPa, and at313 K and 333 K were carried out in a set-up improving mass transfer between the studied liquid and the continuous fluid phase. Stainless steel surfaces have been characterized by atomic force and scanning electron microscopies allowing the application of the Wenzel equation.

FINDINGS

Ethanol wetted totally both stainless steels while contact angles of all other liquids were increased by the rise of pressure, with contact angles up to 128° for water at 15.1 MPa. Trapped bubbles were observed at the solid/liquid interface and the bubble formation is discussed. Furthermore, the potential influence of bubble presence on the wetting regime is prospected through the question: could the pressure rise modify the wetting regime?

Multiphase displacement manipulated by micro/nanoparticle suspensions in porous media via microfluidic experiments: From interface science to multiphase flow patterns

Multiphase displacement in porous media can be adjusted by micro/nanoparticle suspensions, which is widespread in many scientific and industrial contexts. Direct visualization of suspension flow dynamics and corresponding multiphase patterns is crucial to understanding displacement mechanisms and eventually optimizing these processes in geological, biological, chemical, and other engineering systems. However, suspension flow inside the opaque realistic porous media makes direct observation challenging. The advances in microfluidic experiments have provided us with alternative methods to observe suspension influence on the interface and multiphase flow behaviors at high temporal and spatial resolutions. Macroscale processes are controlled by microscale interfacial behaviors, which are affected by multiple physical factors, such as particle adsorption, capillarity, and hydrodynamics. These properties exerted on the suspension flow in porous media may lead to interesting interfacial phenomena and new displacement consequences. As an underpinning science, understanding and controlling the suspension transport process from interface to flow patterns in porous media is critical for a lower operating cost to improve resource production while reducing harmful emissions and other environmental impacts. This review summarizes the basic properties of different micro/nanoparticle suspensions and the state-of-the-art microfluidic techniques for displacement research activities in porous media. Various suspension transport behaviors and displacement mechanisms explored by microfluidic experiments are comprehensively reviewed. This review is expected to boost both experimental and theoretical understanding of suspension transport and interfacial interaction processes in porous media. It also brings forward the challenges and opportunities for future research in controlling complex fluid flow in porous media for diverse applications.

Fabrication of high performance TFN membrane incorporated with graphene oxide via support-free interfacial polymerization

A high-performance thin film nanocomposite (TFN) membrane containing graphene oxide (GO) nanosheets was constructed using a support-free interfacial polymerization (SFIP) technique. In this study, an ultrathin composited polyamide (PA) nanofilm was synthesized at the free piperazine (PIP)-GO suspension/trimesoyl chloride (TMC) interface, followed by transfer onto a polysulfone (PSf) UF substrate. The impact of GO loading (0, 0.1, 0.5, or 1 mg/mL) on the physiochemical properties, surface morphology, and hydrophilicity of the composited PA layer and membrane separation performance was investigated. It was found that the GO-modified TFN membranes showed ultra-high hydrophilicity due to the increase in the number of carboxyl and hydroxyl groups in the PA layer. We propose that GO nanosheets play a key role in improving membrane permeability because a strong hydration layer is formed between the water molecules and GO (embedded in the PA layer), acting as a protective film and minimizing the chance of foulants contacting the membrane surface. Compared with TFC, TFN-GO-0.5 simultaneously exhibited a higher water permeability of up to 12.8 L·m^-2·h^-1·bar^-1 (58.1% higher than the TFC membrane) and a higher Na₂SO₄ rejection of approximately 98.4%. Moreover, the introduction of GO nanosheets into TFN membrane resulted in an improved antifouling performance. This facile SFIP method reveals the potential of GO nanosheets for the development of high performance TFN membranes.

Functionalization of hydrophobic nonwoven cotton fabric for oil and water repellency

Highly hydrophobic surfaces exhibit a remarkable feature in the repellency of oil and water. However, the relatively complex preparation process, high costs, and harmful compounds have largely limited their applications. This research aim is to fabricate hydrophobic nonwoven fabrics with low-cost and nontoxic materials. Despite various wettable materials, nonwoven cotton fabric material bearing hydrophobic surfaces has been received significant attention. This is mainly owing to its easy handling, high flexibility, environment friendly, low cost, biodegradability, high efficiency, and easily scalable fabrication. In this study, a simple chemical modification method using hexadecyltrimethoxysilane (HDTMS) with ethanol which is a better method in comparison with other methods since it is an inexpensive, simple method, and offers an easy adjustment of chemical composition required for a surface to show hydrophobic behaviors. The wetting behavior of cotton samples was investigated by water contact angle measurement. The best result comes from 2 ml HDTMS with 40 ml ethanol at 60 °C. The result shows that the treated cotton fabrics exhibited excellent chemical stability and outstanding non-wettability with the WCA of 126 ± 2°. It also shows that standard oil and water repellency, which offers an opportunity to accelerate the large-scale production of hydrophobic textile materials for new industrial applications.

Graphic abstract

Predictive Analysis of Wettability of Al-Si Based Multiphase Alloys and Aluminum Matrix Composites by Machine Learning and Physical Modeling

Wetting of multiphase alloys and their composites depends on multiple parameters, and these relationships are difficult to predict from first principles only. We study correlations between the composition, surface finish, and microstructure of Al-Si alloys (Si content 7-50%) and Al metal matrix composites (MMCs) with graphite (Gr), NiAl₃, and SiC and the water contact angle (CA) experimentally, theoretically, and with machine learning (ML) techniques. Their surface properties were modified by mechanical abrasion, etching, and addition of alloying elements. An ML approach was developed to investigate correlations between the predictor variables (properties of the materials) and the CA. Theoretical models of wetting of rough surfaces (Wenzel, Cassie-Baxter, and their modifications) do not fully capture the CA, while ML models follow the experimental values. A full factorial design is utilized with combinations of all levels of the predictor factors (grit size, silicon percentage, droplet size, elapsed time, etching, reinforcing particles). To map the predictor variables to the response variables, 409 experimental data points were applied to train and test various supervised ML models, namely, regression, artificial neural network (ANN), chi-square automatic interaction detection (CHAID), extreme gradient boosting (XGBoost), and random forest. The correlations between the most significant factors and CA are explored through visualization techniques. The most accurately trained model shows a strong positive linear correlation (r > 0.9) between predicted and observed CA values in the test set, indicating the robustness of the model. The experimental measurements and artificial intelligence results demonstrate that CA increases following mechanically abrading the surface, etching, and adding Gr to the surface. The ML methods are promising to predict wetting properties and to provide a deeper understanding of the physical phenomena associated with the wettability of metallic alloys and their metal matrix composites.

Numerical Calculation of Apparent Contact Angles on the Hierarchical Surface with Array Microstructures by Wire Electrical Discharge Machining

It is necessary to theoretically research wettability in superhydrophobic surface fabrication. Here, a numerical calculation approach is proposed for determining the contact angle of the water droplets on array micropillars by wire electrical discharge machining (WEDM). A hierarchical model is employed for these array microstructures, including mechanical analysis for a water droplet placed on a smooth array and wettability evaluation on the morphology of the WEDM surface. On pillars, equations are listed to solve the apparent contact angle according to force balance of gravity, tension, and pressure. As for the WEDM morphology, temperature simulation and measurement are carried out, and then the effect of roughness on surface wettability is studied. Constructed formulas predict the contact angle, and then the effect of geometric dimensions is obtained. In order to verify the assumption, array micropillars with different cross-profiles are prepared using high-speed WEDM on the Al alloy surface. Through the results of contact angle determination, the numerical calculation is carried out. This theoretical prediction is beneficial for improving the fabrication of the superhydrophobic surface by WEDM.

Corrosion resistance of a superhydrophobic dodecyltrimethoxysilane coating on magnesium alloy AZ31 fabricated by one-step electrodeposition

A superhydrophobic and corrosion-resistant coating with a hierarchical macro/nanostructure was constructed by one-step electrodeposition of dodecyltrimethoxysilane (e-DTMS) on Mg alloy AZ31.

New insights into unusual droplets: from mediating the wettability to manipulating the locomotion modes

The ability to manipulate droplets can be utilized to develop various smart sensors or actuators, endowing them with fascinating applications for drug delivery, detection of target analytes, environmental monitoring, intelligent control, and so on. However, the stimuli-responsive superhydrophobic/superhydrophilic materials for normal water droplets cannot satisfy the requirements from some certain circumstances, i.e., liquid lenses and biosensors (detection of various additives in water/blood droplets). Stimuli-responsive wetting/dewetting behaviors of exceptional droplets are open issues and are attracting much attention from across the world. In this perspective article, the unconventional droplets are divided into three categories: ionic or surfactant additives in water droplets, oil droplets, and bubble droplets. We first introduce several classical wettability models of droplets and some methods to achieve wettability transition. The unusual droplet motion is also introduced in detail. There are four main types of locomotion modes, which are vertical rebound motion, lateral motion, self-propulsion motion, and anisotropic wettability controlled sliding behavior. The driving mechanism for the droplet motion is briefly introduced as well. Some approaches to achieve this manipulation goal, such as light irradiation, electronic, magnetic, acid-base, thermal, and mechanical ways will be taken into consideration. Finally, the current researches on unconventional droplets extending to polymer droplets and liquid metal droplets on the surface of special wettability materials are summarized and the prospect of unconventional droplet research directions in the field of on-demand transport application will be proposed.

A Volume-Corrected Wenzel Model

The Wenzel model, commonly used for predicting the equilibrium contact angle (CA) of drops which penetrate the asperities of a rough surface, does not account for the liquid volume stored in the asperities. Interestingly, many previous experimental and molecular dynamics studies have noted discrepancies between observed CAs and those predicted by the Wenzel model because of this neglected liquid volume. Here, we apply a thermodynamic model to wetting of periodically patterned surfaces to derive a volume-corrected Wenzel equation in the limit of small pattern wavelength (compared to drop size). We show that the corrected equilibrium CA is smaller than that predicted by the Wenzel equation and that the reduction in CA can be significant when the liquid volume within the asperities becomes non-negligible compared to the total droplet volume. In such cases, the corrected CAs agree reasonably well with experimental observations and results of molecular dynamics simulations reported in previous studies.

Symmetry-breaking morphological transitions at chemically nanopatterned walls

We study the structure and morphological changes of fluids that are in contact with solid composites formed by alternating and microscopically wide stripes of two different materials. One type of the stripes interacts with the fluid via long-ranged Lennard-Jones-like potential and tends to be completely wet, while the other type is purely repulsive and thus tends to be completely dry. We consider closed systems with a fixed number of particles that allows for stabilization of fluid configurations breaking the lateral symmetry of the wall potential. These include liquid morphologies corresponding to a sessile drop that is formed by a sequence of bridging transitions that connect neighboring wet regions adsorbed at the attractive stripes. We study the character of the transitions depending on the wall composition, stripes width, and system size. Using a (classical) nonlocal density functional theory (DFT), we show that the transitions between different liquid morphologies are typically weakly first-order but become rounded if the wavelength of the system is lower than a certain critical value L_{c}. We also argue that in the thermodynamic limit, i.e., for macroscopically large systems, the wall becomes wet via an infinite sequence of first-order bridging transitions that are, however, getting rapidly weaker and weaker and eventually become indistinguishable from a continuous process as the size of the bridging drop increases. Finally, we construct the global phase diagram and study the density dependence of the contact angle of the bridging drops using DFT density profiles and a simple macroscopic theory.

Dynamics of droplet impingement on bioinspired surface: insights into spreading, anomalous stickiness and break-up

Inspired by the self-cleaning ability of lotus leaves and stickiness (towards water) of rose petals, we investigate the droplet impact dynamics on such bioinspired substrates. Impact studies are carried out with water droplets for a range of impact velocities on glass, PDMS and soft lithographically fabricated replicas of the lotus leaf and rose petals, which exhibit near identical wetting properties as that of the original biological entities. In this work, we investigate the spreading, dewetting and droplet break-up mechanisms subsequent to impact. Surprisingly, the rose petal and lotus leaf replicas manifest similar impact dynamics. The observation is extremely intriguing and counterintuitive, as rose petal and its replicas are sticky in contrast to lotus leaves. However, these observations are based on experiments performed with sessile water droplets. By contrast, in the current study, we find that rose petal replicas exhibit non-sticky behaviour at the short time scale ∼ ( O ( 10 - 3 ) )  s similar to that exhibited by lotus leaf replicas. Air entrapment in the micrometre features of bioinspired surfaces prevent frictional dissipation of droplet kinetic energy, leading to contact edge recession. We have also unveiled interesting universal physics that govern the spreading, recession of the contact edge and subsequent break-up modes (ligament or bulb-ligament) of the droplet.

Reply to Comment on "Solid-Liquid Work of Adhesion"

Extrand's interpretation in his "Comment on "Solid-Liquid Work of Adhesion" by Tadmor and Coworkers" may lead to an important discussion and physical understanding of the problem. Below, we compare the two approaches and elucidate the differences to put them in the right perspective.

Why re-entrant surface topography is needed for robust oleophobicity

Surface patterns affect wetting properties of solid materials allowing manipulation of the phase state of an adjacent fluid. The best known example of this effect is the superhydrophobic composite (Cassie-Baxter) interface with vapour/air pockets between the solid and liquid. Mathematically, the effect of surface micropatterns can be studied by an averaging technique similarly to the method of separation of motions in dynamics. However, averaged parameters are insufficient for robust superhydrophobic and superoleophobic surfaces because additional topography features are important: hierarchical organization and re-entrant roughness. The latter is crucial for the oleophobicity because it enhances the stability of a composite interface. The re-entrant topography can be achieved by various methods. Understanding the role of re-entrant surface topography gives us new insights on the multitude of wetting scenarios beyond the standard Wenzel and Cassie-Baxter models.This article is part of the themed issue 'Bioinspired hierarchically structured surfaces for green science'.

The Influence of Structure Heights and Opening Angles of Micro- and Nanocones on the Macroscopic Surface Wetting Properties

We discuss the influence of surface structure, namely the height and opening angles of nano- and microcones on the surface wettability. We show experimental evidence that the opening angle of the cones is the critical parameter on sample superhydrophobicity, namely static contact angles and roll-off angles. The textured surfaces are fabricated on silicon wafers by using a simple one-step method of reactive ion etching at different processing time and gas flow rates. By using hydrophobic coating or hydrophilic surface treatment, we are able to switch the surface wettability from superhydrophilic to superhydrophobic without altering surface structures. In addition, we show examples of polymer replicas (polypropylene and poly(methyl methacrylate) with different wettability, fabricated by injection moulding using templates of the silicon cone-structures.