Role of statistical properties of randomly rough surfaces in controlling superhydrophobicity

Exploring the dynamics of viscoelastic adhesion in rough line contacts

Modeling the adhesion of viscoelastic rough surfaces is a recent challenge in contact mechanics. Existing models have primarily focused on simple systems with smooth topography or single roughness scale due to the co-action of roughness and viscoelasticity leading to elastic instabilities and rate-dependent behavior, resulting in complex adhesion dynamics. In this study, we propose a numerical model based on a finite element methodology to investigate the adhesion between a randomly rough profile and a viscoelastic half-plane. Approach-retraction simulations are performed under controlled displacement conditions of the rough indenter. The results demonstrate that viscous effects dampen the roughness-induced instabilities in both the approach and retraction phases. Interestingly, even when viscous effects are negligible, the pull-off stress, i.e., the maximum tensile stress required to detach the surfaces, is found to depend on the stiffness modulus and maximum load reached during the approach. Furthermore, when unloading is performed from a relaxed state of the viscoelastic half-plane, both adhesion hysteresis and pull-off stress are monotonic increasing functions of the speed. Conversely, when retraction begins from an unrelaxed state of the material, the maximum pull-off stress and hysteretic loss are obtained at intermediate velocities.

Effect of Structural Features on the Superhydrophobicity of SiO2-Based Coatings

A detailed correlation between topographical features and wettability of chemically modified coatings based on silica nanoparticles (SiO₂) was performed. In this study, hierarchical structures were prepared by the layer-by-layer (LbL) technique using two different approaches: random roughened surfaces were obtained by exploring stacking defects spontaneously arisen after 15, 30, and 45 assembly cycles of 22 nm SiO₂, and a particular structure, commonly known as raspberry-like, was obtained by depositing 22 nm SiO₂ over the first deposited 400 nm SiO₂. As an intrinsic attribute of the assembly process, the average slope of random roughened surfaces seems to be constant and virtually independent of the number of deposited layers. Additionally, the local slopes are always lower than a critical value (Φ_crit) required to stabilize the solid-liquid-air interface; thus, a fully wetted Wenzel state is invariably observed with water contact angles (WCAs) ∼130°. On the other hand, since the local slopes of the raspberry-like structure follow a nearly spherical curvature, small SiO₂ can stabilize the solid-liquid-air interface by increasing the local contact angle and avoid the deep penetration of water into the surface asperities, resulting in a WCA ∼167°. The results also suggest that nanoroughness might also play an important role in the pinning effect of the solid-liquid-air contact line, favoring the maintenance of superhydrophobicity of raspberry-like surfaces.

Statistical Heuristic Wettability Analysis of Randomly Textured Surfaces

The liquid repellency enabled by air bubbles trapped within surface roughness features has drawn the attention of many researchers over the past century. The effects of surface roughness on superhydrophobicity have been extensively studied, mainly using regularly textured, idealized geometries. In comparison, fewer works have investigated the wettability of randomly textured surfaces, although they are much more similar to scalable and bioinspired surfaces. In this work, we investigated whether prior theories developed for understanding the wettability of regularly structured surfaces may be extended to randomly rough surfaces. Sandpapers of varying grit size, when hydrophobized, served as model randomly rough surfaces. Two analyses were conducted. In the first, termed the nonstatistical approach, direct imaging of the surfaces was used to extract an effective texture size and spacing, based on particle analysis and Delaunay triangulation. In the second, termed the statistical approach, two metrology parameters, sample autocorrelation length and mean periodicity, served as the effective texture size and spacing. Overall, the statistical method predicted water contact angles better than the nonstatistical approach, especially for surfaces in the fully wetted Wenzel state or fully nonwetted Cassie state. For surfaces exhibiting a mixed Cassie state of wetting, neither approach was able to predict the apparent contact angles precisely, likely due to the propagation of wetting in three dimensions, as two-dimensional analysis was used to derive the theories of wetting investigated. Estimates on the pressure stability of the nonwetted states were underpredicted when using the statistical parameters. In summation, when randomly rough surfaces exhibit a distribution of texture sizes and spacings, current theories of wettability cannot be directly implemented by a simple mapping using statistical metrology parameters.

The Influence of Microscale Surface Roughness on Water-Droplet Contact Electrification

When water comes in contact with a hydrophobic fluoropolymer, a triboelectric charge tends to form on the surface. Here, it is investigated how the triboelectric charge formed upon contact with water drops depends on the microscale surface statistics of the polymer. In particular, it is found that the transition to a superhydrophobic fakir state results in a considerable reduction in triboelectric contact charge, due to a reduced liquid?solid contact area. Thus, when processing charge-sensitive electronic systems one may want to utilize such surfaces promoting reduced tribocharging. This also has implications for energy harvesting purposes, where one may collect electrical energy by letting water droplets move on the polymer with an interdigitated current-collecting electrode on its back side. In such a situation, it is observed that the surfaces promoting the superhydrophobic fakir state give rise to larger water droplet velocities and smaller collected charge, which explains the need for careful assessment of surface treatment before applying microstructured polymers for water droplet energy harvesting.

Bi-Gaussian Stratified Wetting Model on Rough Surfaces

Wetting mechanisms on rough surfaces were understood from either a monolayer or a multiscale perspective. However, it has recently been shown that the bi-Gaussian stratified nature of real surfaces should be accounted for when modeling mechanisms of lubrication, sealing, contact, friction, acoustic emission, and manufacture. In this work, a model combining Wenzel and Cassie theories was put forward to predict the static contact angle of a droplet on a bi-Gaussian stratified surface. The model was initially applied to numerically simulated surfaces and subsequently demonstrated on hydrophilic steel and hydrophobic self-assembled monolayer specimens with preset bi-Gaussian stratified topographies. In the Wenzel state, both the upper and the lower surface components are fully wetted. In the Cassie state, the upper component is still completely wetted, while the lower component serves as gas traps and reservoirs. By this model, wetting evolution was assessed, and the existence of different wetting states and potential state transitions was predicted.

Effect of drop volume and surface statistics on the superhydrophobicity of randomly rough substrates

In this paper, a simple theoretical approach is developed with the aim of evaluating shape, interfacial pressure, apparent contact angle and contact area of liquid drops gently deposed on randomly rough surfaces. This method can be useful to characterize the superhydrophobic properties of rough substrates, and to investigate the contact behavior of impacting drops. We assume that (i) the size of the apparent liquid-solid contact area is much larger than the micromorphology of the substrate, and (ii) a composite interface is always formed at the microscale. Results show apparent contact angle and liquid-solid area fraction are slightly influenced by the drop volume only at relatively high values of the root mean square roughness h _rms, whereas the effect of volume is practically negligible at small h _rms. The main statistical quantity affecting the superhydrophobic properties is found to be the Wenzel roughness parameter r _W, which depends on the average slope of the surface heights. Moreover, transition from the Cassie-Baxter state to the Wenzel one is observed when r _W reduces below a certain critical value, and theoretical predictions are found to be in good agreement with experimental data. Finally, the present method can be conveniently exploited to evaluate the occurrence of pinning phenomena in the case of impacting drops, as the Wenzel critical pressure for liquid penetration gives an estimation of the maximum impact pressure tolerated by the surface without pinning occurring.

Designing Self-Healing Superhydrophobic Surfaces with Exceptional Mechanical Durability

The past decade saw a drastic increase in the understanding and applications of superhydrophobic surfaces (SHSs). Water beads up and effortlessly rolls off a SHS due to its combination of low surface energy and texture. Whether being used for drag reduction, stain repellency, self-cleaning, fog harvesting, or heat transfer applications (to name a few), the durability of a SHS is critically important. Although a handful of purportedly durable SHSs have been reported, there are still no criteria available for systematically designing a durable SHS. In the first part of this work, we discuss two new design parameters that can be used to develop mechanically durable SHSs via the spray coating of different binders and fillers. These parameters aid in the rational selection of material components and allow one to predict the capillary resistance to wetting of any SHS from a simple topographical analysis. We show that not all combinations of sprayable components generate SHSs, and mechanically durable components do not necessarily generate mechanically durable SHSs. Moreover, even the most durable SHSs can eventually become damaged. In the second part, utilizing our new parameters, we design and fabricate physically and chemically self-healing SHSs. The most promising surface is fabricated from a fluorinated polyurethane elastomer (FPU) and the extremely hydrophobic small molecule 1H,1H,2H,2H-heptadecafluorodecyl polyhedral oligomeric silsesquioxane (F-POSS). A sprayed FPU/F-POSS surface can recover its superhydrophobicity even after being abraded, scratched, burned, plasma-cleaned, flattened, sonicated, and chemically attacked.

Lattice Boltzmann Simulation of Droplets Impacting on Superhydrophobic Surfaces with Randomly Distributed Rough Structures

Superhydrophobic surfaces have attracted much attention in environmental control because of their excellent water-repellent properties. A successful design of superhydrophobic surfaces requires a correct understanding of the influences of surface roughness on water-repellent behaviors. Here, a new approach, a mesoscale lattice Boltzmann simulation approach, is proposed and used to model the dynamic behavior of droplets impacting on surfaces with randomly distributed rough microstructures. The fast Fourier transformation method is used to generate non-Gaussian randomly distributed rough surfaces, with the skewness and kurtosis obtained from real surfaces. Then, droplets impacting on the rough surfaces are modeled. It is found that the shape of droplet spreading is obviously affected by the distributions of surface asperity. Decreasing the skewness and keeping the kurtosis around 3 is an effective method to enhance the ability of droplet rebound. The new approach gives more detailed insights into the design of superhydrophobic surfaces.

Oil-Infused Superhydrophobic Silicone Material for Low Ice Adhesion with Long-Term Infusion Stability

A new approach for anti-icing materials was created to combat the effects of ice accretion and adhesion. The concept combines the strengths of individual characteristics for low ice adhesion based on elasticity, superhydrophobicity, and slippery liquid infused porous surfaces (SLIPS) for an optimal combination of high water repellency and ice-phobicity. This was achieved by replicating microtextures from a laser-irradiated aluminum substrate to an oil-infused polydimethylsiloxane (PDMS) elastomer, the result of which is a flexible, superhydrophobic, and lubricated material. This design provides multiple strategies of icing protection through high water repellency to retard ice accretion and with elasticity and oil infusion for low ice adhesion in a single material. Studies showed that an infusion of silicone oils with viscosity at 100 cSt and below 8 wt % in PDMS solution is sufficient to reduce the ice shear strength to an average of 38 kPa while maintaining contact angles and roll-off angles of above 150° and below 10°, respectively. This ice-adhesion value is a ∼95% reduction from a bare aluminum surface and ∼30% reduction from a microtextured, superhydrophobic PDMS material without oil infusion. In addition, three-month aging studies showed that the wetting and ice-adhesion performance of this material did not significantly degrade.

Superhydrophobic hierarchical arrays fabricated by a scalable colloidal lithography approach

Here we report an unconventional colloidal lithography approach for fabricating a variety of periodic polymer nanostructures with tunable geometries and hydrophobic properties. Wafer-sized, double-layer, non-close-packed silica colloidal crystal embedded in a polymer matrix is first assembled by a scalable spin-coating technology. The unusual non-close-packed crystal structure combined with a thin polymer film separating the top and the bottom colloidal layers render great versatility in templating periodic nanostructures, including arrays of nanovoids, nanorings, and hierarchical nanovoids. These different geometries result in varied fractions of entrapped air in between the templated nanostructures, which in turn lead to different apparent water contact angles. Superhydrophobic surfaces with >150° water contact angles and <5° contact angle hysteresis are achieved on fluorosilane-modified polymer hierarchical nanovoid arrays with large fractions of entrapped air. The experimental contact angle measurements are complemented with theoretical predictions using the Cassie's model to gain insights into the fundamental microstructure-dewetting property relationships. The experimental and theoretical contact angles follow the same trends as determined by the unique hierarchical structures of the templated periodic arrays.

Characterization for Cassie-Wenzel wetting transition based on the force response in the process of squeezing liquid drops by two parallel superhydrophobic surfaces

Application of superhydrophobic surfaces is partly limited by the escaping of the entrapped air beneath the liquid sitting on the superhydrophobic surfaces, i.e., the so-called Cassie-Wenzel wetting transition. Here, to characterize this wetting transition, a linear force response relation with certain abnormal systematic deflection showing the wetting transition information is constructed for the process of squeezing the test liquid drop by two parallel structured (superhydrophobic) surfaces. The linear force response relation is validated by replotting the experimental data from the former work. And then the wetting transition information is investigated on a numerically generated force response curve with certain errors by taking into account the liquid pressure variation during the wetting transition. Results show that the wetting transition can cause an obvious bulge on the linear force response curve. We believe that this method has a potential application in characterizing the robustness of superhydrophobic surfaces.

The nature of inherent bactericidal activity: insights from the nanotopology of three species of dragonfly

While insect wings are widely recognised as multi-functional, recent work showed that this extends to extensive bactericidal activity brought about by cell deformation and lysis on the wing nanotopology. We now quantitatively show that subtle changes to this topography result in substantial changes in bactericidal activity that are able to span an order of magnitude. Notably, the chemical composition of the lipid nanopillars was seen by XPS and synchrotron FTIR microspectroscopy to be similar across these activity differences. Modelling the interaction between bacterial cells and the wing surface lipids of 3 species of dragonflies, that inhabit similar environments, but with distinctly different behavioural repertoires, provided the relationship between surface structure and antibacterial functionality. In doing so, these principal behavioural patterns correlated with the demands for antimicrobial efficiency dictated by differences in their foraging strategies. This work now reveals a new feature in the design elegance of natural multi-functional surfaces as well providing insights into the bactericidal mechanism underlying inherently antimicrobial materials, while suggesting that nanotopology is related to the evolutionary development of a species through the demands of its behavioural repertoire. The underlying relationship between the processes of wetting, adhesion and capillarity of the lipid nanopillars and bactericidal efficiency suggests new prospects for purely mechano-responsive antibacterial surfaces.

Fluid contact angle on solid surfaces: Role of multiscale surface roughness

We present a simple analytical model and an exact numerical study which explain the role of roughness on different length scales for the fluid contact angle on rough solid surfaces. We show that there is no simple relation between the distribution of surface slopes and the fluid contact angle. In particular, surfaces with the same distribution of slopes may exhibit very different contact angles depending on the range of length-scales over which the surfaces have roughness.

Development of a superhydrophobic polybenzoxazine surface with self-cleaning and reversible water adhesion properties

A superhydrophobic polybenzoxazine surface with self-cleaning properties is obtained, and is resistant to solvents and corrosive liquids.

Atmospheric Ice Adhesion on Water-Repellent Coatings: Wetting and Surface Topology Effects

Recent studies have shown the potential of water-repellent surfaces such as superhydrophobic surfaces in delaying ice accretion and reducing ice adhesion. However, conflicting trends in superhydrophobic ice adhesion strength were reported by previous studies. Hence, this investigation was performed to study the ice adhesion strength of hydrophobic and superhydrophobic coatings under realistic atmospheric icing conditions, i.e., supercooled spray of 20 μm mean volume diameter (MVD) droplets in a freezing (-20 °C), thermally homogeneous environment. The ice was released in a tensile direction by underside air pressure in a Mode-1 ice fracture condition. Results showed a strong effect of water repellency (increased contact and receding angles) on ice adhesion strength for hydrophobic surfaces. However, the extreme water repellency of nanocomposite superhydrophobic surfaces did not provide further adhesion strength reductions. Rather, ice adhesion strength for superhydrophobic surfaces depended primarily on the surface topology spatial parameter of autocorrelation length (Sal), whereby surface features in close proximities associated with a higher capillary pressure were better able to resist droplet penetration. Effects from other surface height parameters (e.g., arithmetic mean roughness, kurtosis, and skewness) were secondary.

Statistical theory of wetting of liquid drops on superhydrophobic randomly rough surfaces

It is well known that hydrophobic surfaces may become superhydrophobic when their surface is properly roughened. However, the role of roughness is not yet very clear, notwithstanding several theoretical and experimental investigations. In the present paper, we propose a relatively simple theory aiming at calculating the apparent contact angle (ACA) and the contact area occurring in the case of drops gently deposited on two-dimensional randomly rough surfaces. Our theory applies both to isotropic and anisotropic rough surfaces, although in the latter case the predicted ACA has to be interpreted as the average contact angle at the triple line. We assume large separation of scales, i.e., that the spectral content of the surface lies in a range of wavelengths much smaller than the size of the apparent liquid-solid contact area. Results show that anisotropy negligibly affects the ACA, and a very reasonable agreement is obtained between theoretical ACA values and experimental data.

An effective medium approach to predict the apparent contact angle of drops on super-hydrophobic randomly rough surfaces

The apparent contact angle of large 2D drops with randomly rough self-affine profiles is numerically investigated. The numerical approach is based upon the assumption of large separation of length scales, i.e. it is assumed that the roughness length scales are much smaller than the drop size, thus making it possible to treat the problem through a mean-field like approach relying on the large-separation of scales. The apparent contact angle at equilibrium is calculated in all wetting regimes from full wetting (Wenzel state) to partial wetting (Cassie state). It was found that for very large values of the roughness Wenzel parameter (r(W) > -1/ cos θ(Y), where θ(Y) is the Young's contact angle), the interface approaches the perfect non-wetting condition and the apparent contact angle is almost equal to 180°. The results are compared with the case of roughness on one single scale (sinusoidal surface) and it is found that, given the same value of the Wenzel roughness parameter rW, the apparent contact angle is much larger for the case of a randomly rough surface, proving that the multi-scale character of randomly rough surfaces is a key factor to enhance superhydrophobicity. Moreover, it is shown that for millimetre-sized drops, the actual drop pressure at static equilibrium weakly affects the wetting regime, which instead seems to be dominated by the roughness parameter. For this reason a methodology to estimate the apparent contact angle is proposed, which relies only upon the micro-scale properties of the rough surface.

Sustainable drag reduction in turbulent Taylor-Couette flows by depositing sprayable superhydrophobic surfaces

We demonstrate a reduction in the measured inner wall shear stress in moderately turbulent Taylor-Couette flows by depositing sprayable superhydrophobic microstructures on the inner rotor surface. The magnitude of reduction becomes progressively larger as the Reynolds number increases up to a value of 22% at Re=8.0×10(4). We show that the mean skin friction coefficient C(f) in the presence of the superhydrophobic coating can be fitted to a modified Prandtl-von Kármán-type relationship of the form (C(f)/2)(-1/2)=Mln (Re(C(f)/2)(1/2))+N+(b/Δr)Re(C(f)/2)(1/2) from which we extract an effective slip length of b≈19  μm. The dimensionless effective slip length b(+)=b/δ(ν), where δ(ν) is the viscous length scale, is the key parameter that governs the drag reduction and is shown to scale as b(+)∼Re(1/2) in the limit of high Re.

The effect of drop volume and micropillar shape on the apparent contact angle of ordered microstructured surfaces

In the present paper, we propose a new theoretical approach to evaluate the shape and apparent contact angle (ACA) of a drop gently deposited on microstructured superhydrophobic surfaces. We exploit the very large separation of scales between the drop size and the features of the micromorphology of the interface to propose a numerical methodology to calculate the apparent contact area and apparent contact angle. In agreement with very recent experiments, calculations show that, in the case of surfaces made of conical micropillars, the ACA may take values very close to 180° not depending on the size of the liquid drop. At large drop volumes, the shape of the drop deviates from the spherical one as a result of the gravity effects, but it is noteworthy that the apparent contact angle does not change at all. Our calculations shows that this holds true also for different pillar shapes, showing that, for any given Young contact angle of the solid constituting the pillars, the ACA is an intrinsic property of the surface microgeometry.