Contact angle hysteresis on superhydrophobic stripes

Soft wetting: an analytical model for pillar topography- and softness-dependent droplet depinning force

The extent to which a droplet pins on a textured substrate is determined by the dynamics of the contact line and the liquid-vapor interface. However, the synergistic contribution of contact line sliding and interface distortion to the droplet depinning force remains unknown. More strikingly, current models fail to predict the depinning force per unit length of droplets on soft pillar arrays. Therefore, we fabricate soft pillar arrays with varying geometrical dimensions and mechanical properties and measure the depinning forces per unit length by allowing droplets to evaporate on such substrates. We then analyze the decrease in excess Gibbs free energy of the apparent droplet caused by the detachment of the droplet boundary from the previously pinned pillars. In contrast to prior notions, based on the measured decreases in excess Gibbs free energy, we find that the coefficient, that governs the ratio of interface distortion's contribution to the depinning force to that of the sliding contact line, increases with a decrease in pillar packing density. By considering the combined contribution from contact line sliding, liquid-vapor interface distortion, and pillar deflection, we introduce an analytical model to predict the droplet depinning force per unit length and corroborate the model using experimental data reported in this and prior studies.

Application of the Lattice-Boltzmann method to wetting on anisotropic textured surfaces: Characterization of the liquid-solid interface

HYPOTHESIS

To understand the relationship between topography and wetting, it is not enough to study the contact angle. Indeed, the liquid-solid interface plays an important role in wetting. However, data such as the total triple line length, the wetting area and the anchoring depth are inaccessible or difficult to obtain experimentally. This work proposes to overcome the experimental limitations by using a numerical approach to characterize the wetting behavior on textured surfaces.

METHODS

The wetting behavior of an anisotropic textured surface was compared for both experimental and numerical approaches. The experimental wetting is characterized by sessile drop experiments. The simulations were performed by applying the pseudo-potential Lattice-Boltzmann method. The numerical approach was then used to predict the wetting behavior of different materials.

FINDINGS

The simulations capture both the wetting state and the contact angle, in accordance with the experimental observation. Without making any assumptions about the interfacial shape and anchoring, the simulation allows to characterize the liquid-solid interface by quantifying the total length of the triple line and the wetting area. Simultaneously, the simulations enable the characterization of impregnation within textures for complex mixed regimes.

Development of a Coating-Less Aluminum Superhydrophobic Gradient for Spontaneous Water Droplet Motion Using One-Step Laser-Ablation

Nature shows various approaches to create superhydrophobicity, such as the lotus leaf, where the superhydrophobic (SHPB) surface arising from its hierarchical surface consists of random microscale bumps with superimposed nanoscale hairs. Some natural systems, such as the hydrophilic silk of some spider's webs, even allow the passive transport of water droplets from one part of a surface to another by creating gradients in surface tension and Laplace pressure. We look to combine both ideas and replicate the superb water repellence of the lotus leaf and the surface tension gradient-driven motion of the spider silk to form an all-metal, coating-less surface that promotes spontaneous droplet motion. We present the design, fabrication, and investigation of such superhydrophobic gradient surfaces on aluminum, which are aimed at spontaneous water droplet movement for improved surface water management. One surface demonstrates a droplet travel distance of almost 2 mm for a 11 μL droplet volume. We also present surfaces that map the theoretical ranges of the surface tension gradient surfaces tested here.

Study of Micro- and Nanopatterned Aluminum Surfaces Using Different Microfabrication Processes for Water Management

Superhydrophobic surfaces demonstrate extreme water-repellence, promoting drop-wise over film-wise condensation, increasing liquid mobility, and reducing thermal resistance for heat-exchanger applications. Introducing topographic structures can lead to modified surface free energy, as inspired by natural systems like the lotus leaf, potentially allowing coating-free ice- and frost-free surfaces under certain conditions. This work presents a study of coating-free aluminum micro/nanopatterns fabricated using micromilling or laser-etching techniques and the resultant wetting properties. Our review and experiments clarify the roles of line-edge-roughness and microstructural geometry from each microfabrication technique, which manifests in technique-specific nano- to midmicro-scale roughness, producing a hierarchical structure in both cases. For micromilling, line-edge-roughness consists of jagged burrs of 1-8 μm thickness with 10-25 μm periodicity along the microlines with constantly changing height on the order of 1-20 μm. These effects simultaneously raise the water contact angle from 52° (unprocessed aluminum) up to 136° but with strong edge pinning effects. On the other hand, laser-etched surfaces exhibit line-edge-roughness with a microstructure of 3-20 μm width and 5-10 μm in height superimposed with evenly spread spikes of 50-250 nm. This results in a high contact angle (>150°) coupled with a low contact angle hysteresis (<15°), promoting superhydrophobicity on a coating-free aluminum surface. It is also shown that for certain cases, line-edge-roughness is more important for the resultant wetting properties than the structure geometry.

Fabrication Optimization of Ultra-Scalable Nanostructured Aluminum-Alloy Surfaces

Aluminum and its alloys are widely used in various industries. Aluminum plays an important role in heat transfer applications, where enhancing the overall system performance through surface nanostructuring is achieved. Combining optimized nanostructures with a conformal hydrophobic coating leads to superhydrophobicity, which enables coalescence induced droplet jumping, enhanced condensation heat transfer, and delayed frosting. Hence, the development of a rapid, energy-efficient, and highly scalable fabrication method for rendering aluminum superhydrophobic is crucial. Here, we employ a simple, ultrascalable fabrication method to create boehmite nanostructures on aluminum. We systematically explore the influence of fabrication conditions such as water immersion time and immersion temperature, on the created nanostructure morphology and resultant nanostructure length scale. We achieved optimized structures and fabrication procedures for best droplet jumping performance as measured by total manufacturing energy utilization, fabrication time, and total cost. The wettability of the nanostructures was studied using the modified Cassie-Baxter model. To better differentiate performance of the fabricated superhydrophobic surfaces, we quantify the role of the nanostructure morphology to corresponding condensation and antifrosting performance through study of droplet jumping behavior and frost propagation dynamics. The effect of aluminum substrate composition (alloy) on wettability, condensation and antifrosting performance was investigated, providing important directions for proper substrate selection. Our findings indicate that the presence of trace alloying elements play a previously unobserved and important role on wettability, condensation, and frosting behavior via the inclusion of defect sites on the surface that are difficult to remove and act as pinning locations to increase liquid-solid adhesion. Our work provides optimization strategies for the fabrication of ultrascalable aluminum and aluminum alloy superhydrophobic surfaces for a variety of applications.

Biomimetic Approach for the Elaboration of Highly Hydrophobic Surfaces: Study of the Links between Morphology and Wettability

This investigation of morphology-wetting links was performed using a biomimetic approach. Three natural leaves' surfaces were studied: two bamboo varieties and Ginkgo Biloba. Multiscale surface topographies were analyzed by SEM observations, FFT, and Gaussian filtering. A PDMS replicating protocol of natural surfaces was proposed in order to study the purely morphological contribution to wetting. High static contact angles, close to 135∘, were measured on PDMS replicated surfaces. Compared to flat PDMS, the increase in static contact angle due to purely morphological contribution was around 20∘. Such an increase in contact angle was obtained despite loss of the nanometric scale during the replication process. Moreover, a significant decrease of the hysteresis contact angle was measured on PDMS replicas. The value of the contact angle hysteresis moved from 40∘ for flat PDMS to less than 10∘ for textured replicated surfaces. The wetting behavior of multiscale textured surfaces was then studied in the frame of the Wenzel and Cassie-Baxter models. Whereas the classical laws made it possible to describe the wetting behavior of the ginkgo biloba replications, a hierarchical model was developed to depict the wetting behavior of both bamboo species.

Study of wetting of the animal retinas by Water and organic liquids and its Implications for ophthalmology

Interfacial properties of the animal retinas are reported. Wetting of the retina-retinal pigment epithelium-choroid-sclera tissues of cow, sheep, and pig eyes by water, silicone and castor oil was explored experimentally. Both water and silicone oils demonstrated complete wetting of the retina, regardless of the viscosity of the silicone oil, whereas the castor oil demonstrated a partial wetting regime. Similar wetting regimes were observed for sheep, cow and pig retinas. The intact surface of animal retina was found to be both hydrophilic and oleophilic. Wetting experiments with double sandwich oil/water layers were performed. Water demonstrated stronger affinity to the retina than silicone and castor oils, and eventually replaced the oils at the liquid/retina interface. We conclude that aqueous solutions continuously secreted in the living eye may displace silicone oil from the retinal surface and contribute to retinal re-detachment. Study of dynamics of wetting of the animal retina by water and organic oils is reported. The exponent describing the dynamics of spreading of the castor oil is lower than that predicted by the Tanner law. Castor oil may provide more effective tamponade than silicone oil.

Toward an Understanding of Magnetic Displacement of Floating Diamagnetic Bodies, I: Experimental Findings

Diamagnetic objects (polymer and metallic plates and spheres, ceramic beads, and liquid marbles), floating on water, and a variety of organic liquids may be driven by a steady magnetic field of 0.1 T, registered at the water-vapor surface. Diamagnetic bodies are attracted to the magnet, when the apparent contact angle at the solid/liquid interface is obtuse and repelled from the magnet, when the angle is acute. Cold plasma-treated polyolefin rafts and spheres, demonstrating underwater floating, are repelled by a permanent magnet. Addition of a surfactant to the water, as well as cold plasma treatment of the polyolefin bodies, can turn the attraction into the repulsion. We conjecture that the observed effects are caused by the interplay of two main phenomena. The first is the gravity, which induces sliding of the particle on the deformed liquid/vapor interface (the Moses effect). The second cause is the hysteresis of the contact angle at the bodies' boundaries.

Fog Collection on Polyethylene Terephthalate (PET) Fibers: Influence of Cross Section and Surface Structure

Fog-collecting meshes show a great potential in ensuring the availability of a supply of sustainable freshwater in certain arid regions. In most cases, the meshes are made of hydrophilic smooth fibers. Based on the study of plant surfaces, we analyzed the fog collection using various polyethylene terephthalate (PET) fibers with different cross sections and surface structures with the aim of developing optimized biomimetic fog collectors. Water droplet movement and the onset of dripping from fiber samples were compared. Fibers with round, oval, and rectangular cross sections with round edges showed higher fog-collection performance than those with other cross sections. However, other parameters, for example, width, surface structure, wettability, and so forth, also influenced the performance. The directional delivery of the collected fog droplets by wavy/v-shaped microgrooves on the surface of the fibers enhances the formation of a water film and their fog collection. A numerical simulation of the water droplet spreading behavior strongly supports these findings. Therefore, our study suggests the use of fibers with a round cross section, a microgrooved surface, and an optimized width for an efficient fog collection.

Stability of Cassie-Baxter wetting states on microstructured surfaces

A stable Cassie-Baxter (CB) wetting state is indispensable for the superhydrophobicity of solid surfaces. In this paper, we analyze the equilibrium and stability of CB wetting states. Using an energy approach, the stability criteria of CB wetting states are established for solid surfaces with either two- or three-dimensional symmetric microstructures. A generic method is presented to calculate the critical pressure at which the CB state on a microstructured solid surface collapses. The method holds for microstructures with arbitrary generatrix, and explicit solutions are derived for a few representative microstructures with a straight or circular generatrix. In addition, some possible strategies are proposed to design surface structures with stable CB wetting states from the viewpoints of geometry and chemistry.

Probing effective slippage on superhydrophobic stripes by atomic force microscopy

While the effective slippage of water past superhydrophobic surfaces has been studied over a decade, theoretical predictions have never been properly confirmed by experiments. Here we measure a drag force on a sphere approaching a plane decorated by superhydrophobic grooves and compare the results with the predictions of semi-analytical theory developed here, which employs the gas cushion model to calculate the local slip length at the gas sectors. We demonstrate that at intermediate and large (compared to a texture period) separations the half-sum of longitudinal and transverse effective slip lengths can be deduced from the force-distance curve by using the known analytical theory of hydrodynamic interaction of a sphere with a homogeneous slipping plane. This half-sum is shown to depend on the fraction of gas sectors and its value is in excellent agreement with theoretical predictions. At small distances the half-sum of effective longitudinal and transverse slip lengths becomes separation-dependent, and is in quantitative agreement with the predictions of our semi-analytical theory.

Stability and break-up of thin liquid films on patterned and structured surfaces

Solid surfaces with chemical patterning or topographical structure have attracted attention due to many potential applications such as manufacture of flexible electronics, microfluidic devices, microscale cooling systems, as well as development of self-cleaning, antifogging, and antimicrobial surfaces. In many configurations involving patterned or structured surfaces, liquid films are in contact with such solid surfaces and the issue of film stability becomes important. Studies of stability in this context have been largely focused on specific applications and often not connected to each other. The purpose of the present review is to provide a unified view of the topic of stability and rupture of liquid films on patterned and structured surfaces, with particular focus on common mathematical methods, such as lubrication approximation for the liquid flow, bifurcation analysis, and Floquet theory, which can be used for a wide variety of problems. The physical mechanisms of the instability discussed include disjoining pressure, thermocapillarity, and classical hydrodynamic instability of gravity-driven flows. Motion of a contact line formed after the film rupture is also discussed, with emphasis on how the receding contact angle is expected to depend on the small-scale properties of the substrate.

Wetting hysteresis induced by nanodefects

Wetting of actual surfaces involves diverse hysteretic phenomena stemming from ever-present imperfections. Here, we clarify the origin of wetting hysteresis for a liquid front advancing or receding across an isolated defect of nanometric size. Various kinds of chemical and topographical nanodefects, which represent salient features of actual heterogeneous surfaces, are investigated. The most probable wetting path across surface heterogeneities is identified by combining, within an innovative approach, microscopic classical density functional theory and the string method devised for the study of rare events. The computed rugged free-energy landscape demonstrates that hysteresis emerges as a consequence of metastable pinning of the liquid front at the defects; the barriers for thermally activated defect crossing, the pinning force, and hysteresis are quantified and related to the geometry and chemistry of the defects allowing for the occurrence of nanoscopic effects. The main result of our calculations is that even weak nanoscale defects, which are difficult to characterize in generic microfluidic experiments, can be the source of a plethora of hysteretical phenomena, including the pinning of nanobubbles.

Electrospun Fibrous Membranes with Super-large-strain Electric Superhydrophobicity

Large-strain elastic superhydrophobicity is highly desirable for its enhanced use performance and functional reliability in mechanically dynamic environments, but remains challenging to develop. Here we have, for the first time, proven that an elastic fibrous membrane after surface hydrophobization can maintain superhydrophobicity during one-directional (uniaxial) stretching to a strain as high as 1500% and two-direction (biaxial) stretching to a strain up to 700%. The fibrous membrane can withstand at least 1,000 cycles of repeated stretching without losing the superhydrophobicity. Stretching slightly increases the membrane air permeability and reduces water breakthrough pressure. It is highly stable in acid and base environments. Such a permeable, highly-elastic superhydrophobic membrane may open up novel applications in membrane separation, healthcare, functional textile and energy fields.

Principles of transverse flow fractionation of microparticles in superhydrophobic channels

We propose a concept of fractionation of micron-sized particles in a microfluidic device with a bottom wall decorated by superhydrophobic stripes. The stripes are oriented at an angle α to the direction of a driving force, G, which generally includes an applied pressure gradient and gravity. Separation relies on the initial sedimentation of particles under gravity in the main forward flow, and their subsequent lateral deflection near a superhydrophobic wall due to generation of a secondary flow transverse to G. We provide some theoretical arguments allowing us to quantify the transverse displacement of particles in the microfluidic channel, and confirm the validity of theoretical predictions in test experiments with monodisperse fractions of microparticles. Our results can guide the design of superhydrophobic microfluidic devices for efficient sorting of microparticles with a relatively small difference in size and density.

Surface Fraction Dependence of Contact Angles Induced by Kinks in the Triple Line

On periodic superhydrophobic surfaces the receding contact angle often scales with the surface fraction, as expected from a simple rule of mixture, the Cassie relation. However, it has been argued that energy averaging breaks down owing to line pinning, and that line fraction scaling should apply instead. From experiments and simulations we show that proper inclusion of triple line defects introduce surface fraction scaling in the line depinning threshold. In contrast to the Cassie relation and in agreement with the data, this dependence is strongly nonlinear due to triple line elasticity.