Superhydrophobic Textures for Microfluidics

Engineering superhydrophobicity: a survey of coating techniques for silicone-based oil-water separation membranes

Oil spills in the ocean and the release of contaminated wastewater from industries cause significant harm to the ecosystem and water sources. To tackle this environmental problem, oil-water mixture separation has been the subject of extensive research over the past few decades. Improving oil absorbents is crucial in removing organic contaminants from wastewater produced by industrial activities. To this end, there is an increasing need for materials that can efficiently and flexibly recover oils from contaminated ocean waters, industrial wastewater, and other sources. Silicones are often used for this purpose because of their exceptional mechanical and thermal durability, as well as their low toxicity. The materials produced from silicones, such as foam, sponge, or substrate, exhibit excellent oil-absorbing properties (maximum oil absorption range, 23.2-77 g/g) and outstanding compression cycles. This article review highlights the advancements in the manufacturing of silicone-based products that have been extensively researched for oil-water separation. Understanding the interdependencies that determine the structure, performance, and manufacturing strategy is essential to producing selective oil absorbents with more commercial potential in the future. Recycling of silicones has also become increasingly important as a goal for the circular economy.

Preparation of Oriented Superhydrophobic Surface to Reduce Agglomeration in Preparing Melt Marbles

Numerous innovative granulation techniques utilizing the concept of liquid marbles have been proposed before. However, these processes frequently encounter issues such as collisions, aggregation, and fragmentation of liquid/melt marble during the granulation process. In this study, the oriented superhydrophobic surface (OSS) was successfully prepared by utilizing copper wire to solve the above problem, facilitating efficient batch production and guided transportation of uniform marbles. The parameters and mechanisms of this process were thoroughly studied. The optimized structure is that the copper wire spacing (d) and height (h) are set as 1.0 and 0.1 mm, respectively. This resulted in a surface contact angle (CA) of 156° and anisotropic sliding (ΔSA) of 16.3 ± 1.34°. Using the prepared substrate, high-quality urea products were successfully obtained through the controlled transport of urea melt marbles. The mechanism of guided and directional drag reduction, based on the solid/solid contact on the surface, is proposed. These findings in this study have significant implications for improving granulation processes.

A review on slip boundary conditions at the nanoscale: recent development and applications

The slip boundary condition for nanoflows is a key component of nanohydrodynamics theory, and can play a significant role in the design and fabrication of nanofluidic devices. In this review, focused on the slip boundary conditions for nanoconfined liquid flows, we firstly summarize some basic concepts about slip length including its definition and categories. Then, the effects of different interfacial properties on slip length are analyzed. On strong hydrophilic surfaces, a negative slip length exists and varies with the external driving force. In addition, depending on whether there is a true slip length, the amplitude of surface roughness has different influences on the effective slip length. The composition of surface textures, including isotropic and anisotropic textures, can also affect the effective slip length. Finally, potential applications of nanofluidics with a tunable slip length are discussed and future directions related to slip boundary conditions for nanoscale flow systems are addressed.

Fabricating low-cost, robust superhydrophobic coatings with re-entrant topology for self-cleaning, corrosion inhibition, and oil-water separation

HYPOTHESIS

The superhydrophobic surfaces with re-entrant microstructures are known to provide robust superhydrophobicity by enhancing the energy barrier for Cassie-Baxter to Wenzel transition. However, the fabrication of such structured surfaces often involves sophisticated techniques and expensive ingredients.

EXPERIMENTS

Herein, a multifunctional, low-cost, and fluorine-free superhydrophobic coating with re-entrant surface topology was fabricated using fly ash (FA) and room-temperature-vulcanizing silicone. A systematic study was performed to evaluate the coating properties and durability. The robustness was evaluated as a function of particle size and inter-particle spacing. The performance in self-cleaning, corrosion inhibition and oil-water separation has been presented.

FINDINGS

The synthesized coatings are substrate-versatile and demonstrate superhydrophobic behavior. The close-packed coating of re-entrant FA particles attained via vibration compaction was seen to provide high robustness. The coatings retain their superhydrophobicity after multiple cycles of tape-peeling and exposure to environmental factors including temperature, pH, and UV radiation. These coatings exhibit excellent corrosion inhibition (corrosion efficiency > 99.999%), outperforming the majority of the previously reported superhydrophobic coatings. It also displays excellent self-cleaning property and high separation efficiencies in oil-water separation (>99%). We envision that such FA-based superhydrophobic coatings can solve the issues of synthesizing cheaper, sustainable, and robust superhydrophobic surfaces while simultaneously opening new avenues for FA utilization.

High-Resolution Laser-Induced Graphene from Photoresist

The fabrication of patterned graphene electronics at high resolution is an important challenge for many applications in microelectronics. Here, we demonstrate the conversion of positive photoresist (PR), commonly employed in the commercial manufacture of consumer electronics, into laser-induced graphene (LIG). Sequential lasing converts the PR photopolymer first into amorphous carbon, then to photoresist-derived LIG (PR-LIG). The resulting material possesses good conductivity and is easily doped with metal or other additives for additional functionality. Furthermore, photolithographic exposure of PR prior to lasing enables the generation of PR-LIG patterns small enough to be invisible to the naked eye. By exploiting PR as a photopatternable LIG precursor, PR-LIG can be synthesized with a spatial resolution of ∼10 μm, up to 15 times smaller than conventional LIG patterning methods. The patterning of these small PR-LIG features could offer a powerful and broadly accessible strategy for the fabrication of microscale LIG-derived nanocomposites for on-chip devices.

Potential of Superhydrophobic Surface for Blood-Contacting Medical Devices

Medical devices are indispensable in the healthcare setting, ranging from diagnostic tools to therapeutic instruments, and even supporting equipment. However, these medical devices may be associated with life-threatening complications when exposed to blood. To date, medical device-related infections have been a major drawback causing high mortality. Device-induced hemolysis, albeit often neglected, results in negative impacts, including thrombotic events. Various strategies have been approached to overcome these issues, but the outcomes are yet to be considered as successful. Recently, superhydrophobic materials or coatings have been brought to attention in various fields. Superhydrophobic surfaces are proposed to be ideal blood-compatible biomaterials attributed to their beneficial characteristics. Reports have substantiated the blood repellence of a superhydrophobic surface, which helps to prevent damage on blood cells upon cell-surface interaction, thereby alleviating subsequent complications. The anti-biofouling effect of superhydrophobic surfaces is also desired in medical devices as it resists the adhesion of organic substances, such as blood cells and microorganisms. In this review, we will focus on the discussion about the potential contribution of superhydrophobic surfaces on enhancing the hemocompatibility of blood-contacting medical devices.

Preparation of superhydrophobic nylon-56/cotton-interwoven fabric with dopamine-assisted use of thiol-ene click chemistry

With the help of dopamine, we constructed a hydroxyl-rich secondary reaction platform on a surface formed by interwoven nylon 56 and cotton fibres. Octadecyl mercaptan and vinyl trimethoxysilane (VTMS) are used for the click coupling preparation of superhydrophobic reagents, which are grafted onto polydopamine aggregates and successfully used to prepare superhydrophobic nylon 56/cotton-interwoven fabric. The static contact angle was 161° and the sliding angle was 8°. Note that the prepared superhydrophobic fabric can withstand corrosive liquids, water washing, ultraviolet radiation and mechanical abrasion, it has excellent superhydrophobic stability, and self-cleaning and oil–water-separation functionalities. This simple, fast and environmentally friendly method can be applied to other substrates and shows tremendous potential for expanding the field of superhydrophobic applications.

Preparation process of superhydrophobic textiles.

Towards controlled bubble nucleation in microreactors for enhanced mass transport

The exact location of bubbles with respect to the catalytic layer impacts the microreactor performance. In this work, we propose to control bubble nucleation using micropits to maximize the microreactor efficiency.

Heat-Free Biomimetic Metal Molding on Soft Substrates

Fabrication of bio-templated metallic structures is limited by differences in properties, processing conditions, packing, and material state(s). Herein, by using undercooled metal particles, differences in modulus and processing temperatures can be overcome. Adoption of autonomous processes such as self-filtration, capillary pressure, and evaporative concentration leads to enhanced packing, stabilization (jamming) and point sintering with phase change to create solid metal replicas of complex bio-based features. Differentiation of subtle differences between cultivars of the rose flower with reproduction over large areas shows that this biomimetic metal patterning (BIOMAP) is a versatile method to replicate biological features either as positive or negative reliefs irrespective of the substrate. Using rose petal patterns, we illustrate the versatility of bio-templated mapping with undercooled metal particles at ambient conditions, and with unprecedented efficiency for metal structures.

Directional Droplet Transport Mediated by Circular Groove Arrays. Part I: Experimental Findings

Directional transport of liquid droplets is crucial for various applications including water harvesting, anti-icing, and condensation heat transfer. Here, bouncing of water droplets with patterned superhydrophobic surfaces composed of circular equidistant grooves was studied. The directional transport of droplets toward the pole of the grooves was observed. The impact of the Weber number, initial polar distance r, and geometrical parameters of the surface on the directional droplet bouncing was experimentally explored. The nature of bouncing was switched when the Weber numbers exceeded We ≅ 20-25. The rebouncing height was slightly dependent on the initial polar coordinate of the impact point for a fixed We, whereas it grew for We > 20. The weak dependence of the droplet spreading time on the Weber number was close to the dependence predicted by the Hertz bouncing, thus evidencing the negligible influence of viscosity in the process. Change in the scaling exponent describing the dependence of the normalized spreading time on the Weber number was registered for We ≅ 25. The universal dependence of the offset distance ΔL of the droplets on the Weber number ΔL/D₀ ∼ We^1.5 was established. The normalized offset distance decreased with the normalized initial polar distance as ΔL/D₀ ∼ (r/S)^-1, where D₀ and S are the droplet diameter and groove width, respectively. This research may yield more insights into droplet bouncing on patterned surfaces and offer more options in directed droplet transportation.

The Development of Electroconvection at the Surface of a Heterogeneous Cation-Exchange Membrane Modified with Perfluorosulfonic Acid Polymer Film Containing Titanium Oxide

One way to enhance mass transfer and reduce fouling in wastewater electrodialysis is stimulation of electroconvective mixing of the solution adjoining membranes by modifying their surfaces. Several samples were prepared by casting the perfluorosulfonic acid (PFSA) polymer film doped with TiO₂ nanoparticles onto the surface of the heterogeneous cation-exchange membrane MK-40. It is found that changes in surface characteristics conditioned by such modification lead to an increase in the limiting current density due to the stimulation of electroconvection, which develops according to the mechanism of electroosmosis of the first kind. The greatest increase in the current compared to the pristine membrane can be obtained by modification with the film being 20 μm thick and containing 3 wt% of TiO₂. The sample containing 6 wt% of TiO₂ provides higher mass transfer in overlimiting current modes due to the development of nonequilibrium electroconvection. A 1.5-fold increase in the thickness of the modifying film reduces the positive effect of introducing TiO₂ nanoparticles due to (1) partial shielding of the nanoparticles on the surface of the modified membrane; (2) a decrease in the tangential component of the electric force, which affects the development of electroconvection.

Slippery Liquid Infused Porous TiO2/SnO2 Nanocomposite Thin Films via Aerosol Assisted Chemical Vapor Deposition with Anti-Icing and Fog Retardant Properties

Exceptional anti-icing and antifogging devices have been synthesized through combination of micro- and/or nanoscale hierarchical thin films followed by a modification with a surface lubricant. Aerosol assisted chemical vapor deposition (AACVD) of single source titanium and tin precursors generated titanium dioxide (TiO₂)/tin dioxide (SnO₂) composite thin films. Variation in solvent type and/or combination notably impacted on the resulting intricate surface morphologies, which, upon Krytox lubricant modification, generated slippery liquid infused porous surfaces (SLIPS). The surface topography had a profound effect on the degree of surface ice and fog accumulation. The highest functioning films comprised of hybrid spherical/flowery surface structures generated using a mixed ethyl acetate/dichloromethane solvent system. These films retarded ice formation for >30 min at -10 °C and maintained a high level of sample transparency upon suspension above a heated water bath.

Surface topographies of biomimetic superamphiphobic materials: design criteria, fabrication and performance

Superamphiphobicity is a wetting phenomenon that not only water but also oils or organic solvents with low surface tension exhibit large contact angles above 150° along with low contact angle hysteresis on solid surface. It is well known that both chemical constituent and surface roughness have impacts on the wettability of solid surface. Herein, several fundamental wetting states and design criteria for re-entrant structures are introduced first. Then, various chemical modification materials endowing solid substrates low surface energy are summarized subsequently. Furthermore, roughening processes conferring hierarchical or re-entrant topographic structures on surfaces are classified based on different types of topographies abstracted from the natural oil-repellent creatures (mushroom-like structures) as well as bio-inspired superamphiphobic surfaces (i.e., randomly distributed nanostructures, regularly patterned microstructures and other complex hierarchical structures). Significantly, the impalement pressure and formulated rules of various re-entrant profiles are recommended in detail. At the same time, fabrication, outstanding performances such as mechanical durability, chemical stability are also mentioned according to different types of morphologies. Beyond that, current fabrication obstacles and future prospects are proposed simultaneously in the end.

Sliding friction and contact angle hysteresis of droplets on microhole-structured surfaces

Microstructured surfaces with continuous solid topography have many potential applications in biology and industry. To understand the liquid transport property of microstructured surfaces with continuous solid topography, we studied the sliding behavior of a droplet on microhole-structured surfaces. We found that the sliding friction of the droplet increased with increasing solid area fraction due to enlarged apparent contact area and enhanced contact angle hysteresis. By introducing a correction factor to the modified Cassie-Baxter relation, we proposed an improved theoretical model to better predict the apparent receding contact angle. Our experimental data also revealed that the geometric topology of surface microstructures could affect the sliding friction with microhole-decorated surfaces, exhibiting a larger resistance than that for micropillar-decorated surfaces. Assisted by optical microscopy, we attributed this topology effect to the continuity and the true total length of the three-phase contact line at the receding edge during the sliding. Our study provides new insights into the liquid sliding behavior on microstructured surfaces with different topologies, which may help better design functional surfaces with special liquid transport properties.

Advective superdiffusion in superhydrophobic microchannels

We consider pressure-driven flows in wide microchannels, and discuss how a transverse shear, generated by misaligned superhydrophobic walls, impacts cross-sectional spreading of Brownian particles. We show that such a transverse shear can induce an advective superdiffusion, which strongly enhances dispersion of particles compared to a normal diffusion, and that maximal cross-sectional spreading corresponds to a crossover between its subballistic and superballistic regimes. This allows us to argue that an advective superdiffusion can be used for boosting dispersion of particles at smaller Péclet numbers compared to known concepts of passive microfluidic mixing. This implies that our superdiffusion scenario allows one efficient mixing of much smaller particles or using much thinner microchannels than methods, which are currently being exploited.

Inexpensive and non-toxic water repellent coatings comprising SiO2 nanoparticles and long chain fatty acids

Special wettability durable coatings, with average water contact angles exceeding 140°, have been fabricated utilising functionalised hydrophobic-SiO₂ (H-SiO₂) particles embedded in fatty acids. The inexpensive and non-toxic H-SiO₂ particles imparted delicate lotus leaf inspired hierarchical surface nano-morphologies while the fatty acid modification afforded a suitable drop in surface energy. Comparison studies were carried out to explore the effects of fatty acid chain length and pipette as opposed to spray coating deposition methods on the coatings hydrophobicity. It was determined that the longest chain length fatty acid coatings showed enhanced hydrophobic properties due to their extended hydrophobic alkyl chain. A pipette deposited suspension containing H-SiO₂ nanoparticles and octadecanoic acid generated a coating with the most favourable average water contact and tilting angles of 142 ± 6° and 16 ± 2° respectively.

Special wettability durable coatings, with water contact angles exceeding 140°, have been fabricated using inexpensive and non-toxic functionalised hydrophobic-silica nanoparticles embedded in fatty acids.

Continuous electroosmotic sorting of particles in grooved microchannels

We propose a novel microfluidic fractionation concept suitable for neutrally buoyant micron-sized particles. This approach takes advantage of the ability of grooved channel walls oriented at an angle to the direction of an external electric field to generate a transverse electroosmotic flow. Using computer simulations, we first demonstrate that the velocity of this secondary transverse flow depends on the distance from the wall, so neutrally buoyant particles, depending on their size and initial location, will experience different lateral displacements. We then optimize the geometry and orientation of the surface texture of the channel walls to maximize the efficiency of particle fractionation. Our method is illustrated in a full scale computer experiment where we mimic the typical microchannel with a bottom grooved wall and a source of polydisperse particles that are carried along the channel by the forward electroosmotic flow. Our simulations show that the particle dispersion can be efficiently separated by size even in a channel that is only a few texture periods long. These results can guide the design of novel microfluidic devices for efficient sorting of microparticles.

Ultimate Stable Underwater Superhydrophobic State

Underwater metastability hinders the durable application of superhydrophobic surfaces. In this work, through thermodynamic analysis, we theoretically demonstrate the existence of an ultimate stable state on underwater superhydrophobic surfaces. Such a state is achieved by the synergy of mechanical balance and chemical diffusion equilibrium across the entrapped liquid-air interfaces. By using confocal microscopy, we in situ examine the ultimate stable states on structured hydrophobic surfaces patterned with cylindrical micropores in different pressure and flow conditions. The equilibrium morphology of the meniscus is tuned by the dissolved gas saturation degree within a critical range at a given liquid pressure. Moreover, with fresh lotus leaves, we prove that the ultimate stable state can also be realized on randomly rough superhydrophobic surfaces. The finding here paves the way for applying superhydrophobic surfaces in environments with different liquid pressure and flow conditions.

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.

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.

Superoleophobic Surfaces Obtained via Hierarchical Metallic Meshes

Hierarchical metallic surfaces demonstrating pronounced water and oil repellence are reported. The surfaces were manufactured with stainless-steel microporous meshes, which were etched with perfluorononanoic acid. As a result, a hierarchical relief was created, characterized by roughness at micro- and sub-microscales. Pronounced superoleophobicity was registered with regard to canola, castor, sesame, flax, crude (petroleum), and engine oils. Relatively high sliding angles were recorded for 5 μL turpentine, olive, and silicone oil droplets. The stability of the Cassie-like air trapping wetting state, established with water/ethanol solutions, is reported. The omniphobicity of the surfaces is due to the interplay of their hierarchical relief and surface fluorination.

Scaling Hydrodynamic Boundary Conditions of Microstructured Surfaces in the Thin Channel Limit

Despite its importance in many applications and processes, a complete and unified view on how nano- and microscale asperities influence hydrodynamic interactions has yet to be reached. In particular, the effects of surface structure can be expected to become more dominant when the length scale of the asperities or textures becomes comparable to that of the fluid flow. Here we analyze the hydrodynamic drainage of a viscous silicone oil squeezed between a smooth plane and a surface decorated with hexagonal arrays of lyophilic microsized cylindrical posts. For all micropost arrays studied, the periodicity of the structures was much larger than the separation range of our measurements. In this thin channel geometry, we find the hydrodynamic drainage and separation forces for the micropost arrays cannot be fully described by existing boundary condition models for interfacial slip or a no-slip shifted plane. Instead, our results show that the influence of the microposts on the hydrodynamic drag exhibits three distinct regimes as a function of separation. For large separations, a no slip boundary condition (Reynolds theory) is observed for all surfaces until a critical (intermediate) separation, below which the position of the no-slip plane scales with surface separation until reaching a maximum, just before contact. Below this separation, a sharp decrease in the no-slip plane position then suggests that a boundary condition of a smooth surface is recovered at contact.

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.

Flexible conformable hydrophobized surfaces for turbulent flow drag reduction

In recent years extensive work has been focused onto using superhydrophobic surfaces for drag reduction applications. Superhydrophobic surfaces retain a gas layer, called a plastron, when submerged underwater in the Cassie-Baxter state with water in contact with the tops of surface roughness features. In this state the plastron allows slip to occur across the surface which results in a drag reduction. In this work we report flexible and relatively large area superhydrophobic surfaces produced using two different methods: Large roughness features were created by electrodeposition on copper meshes; Small roughness features were created by embedding carbon nanoparticles (soot) into Polydimethylsiloxane (PDMS). Both samples were made into cylinders with a diameter under 12 mm. To characterize the samples, scanning electron microscope (SEM) images and confocal microscope images were taken. The confocal microscope images were taken with each sample submerged in water to show the extent of the plastron. The hydrophobized electrodeposited copper mesh cylinders showed drag reductions of up to 32% when comparing the superhydrophobic state with a wetted out state. The soot covered cylinders achieved a 30% drag reduction when comparing the superhydrophobic state to a plain cylinder. These results were obtained for turbulent flows with Reynolds numbers 10,000 to 32,500.

Surface adhesive forces: a metric describing the drag-reducing effects of superhydrophobic coatings

Nanomaterials with superhydrophobic properties are promising as drag-reducing coatings. However, debates regarding whether superhydrophobic surfaces are favorable for drag reduction require further clarification. A quantified water adhesive force measurement is proposed as a metric and its effectiveness demonstrated using three typical superhydrophobic coatings on model ships with in situ sailing tests.

Flows and mixing in channels with misaligned superhydrophobic walls

Aligned superhydrophobic surfaces with the same texture orientation reduce drag in the channel and generate secondary flows transverse to the direction of the applied pressure gradient. Here we show that a transverse shear can be easily generated by using superhydrophobic channels with misaligned textured surfaces. We propose a general theoretical approach to quantify this transverse flow by introducing the concept of an effective shear tensor. To illustrate its use, we present approximate theoretical solutions and Dissipative Particle Dynamics simulations for striped superhydrophobic channels. Our results demonstrate that the transverse shear leads to complex flow patterns, which provide a new mechanism of a passive vertical mixing at the scale of a texture period. Depending on the value of Reynolds number two different scenarios occur. At relatively low Reynolds number the flow represents a transverse shear superimposed with two corotating vortices. For larger Reynolds number these vortices become isolated, by suppressing fluid transport in the transverse direction.

Improving the durability of a drag-reducing nanocoating by enhancing its mechanical stability

The durability of superhydrophobic surface is a major problem to restrict industrial application of superhydrophobic materials from laboratory research, which can be attributed to a more general issue of mechanical stability for superhydrophobic coatings. Therefore, in order to handle this issue, we have fabricated a mechanically stable drag-reducing coating composed of elastic polydimethylsiloxane (PDMS) and hydrophobic copper particles on model ships, which can resist mechanical abrasion and has displayed a durable drag-reducing effect. In comparison with normal Au superhydrophobic coatings, the as-prepared PDMS/copper coatings showed durable drag reduction performance with a similar drag-reducing rate before (26%) and after (24%) mechanical abrasion. The mechanism for the enhanced mechanical stability and maintained drag reduction of the superhydrophobic surfaces was investigated through characterizations of surface morphology, surface wettability, and water adhesive force evaluation before and after abrasion. This is the first demonstration to realize the application of durable drag reduction by improving the mechanical stability of superhydrophobic coatings. We do believe that superhydrophobic surfaces with good resistance to mechanical abrasion or scratching may draw wide attention and gain significant applications with durable drag-reducing properties.

Gas cushion model and hydrodynamic boundary conditions for superhydrophobic textures

Superhydrophobic Cassie textures with trapped gas bubbles reduce drag, by generating large effective slip, which is important for a variety of applications that involve a manipulation of liquids at the small scale. Here we discuss how the dissipation in the gas phase of textures modifies their friction properties. We propose an operator method, which allows us to map the flow in the gas subphase to a local slip boundary condition at the liquid-gas interface. The determined uniquely local slip length depends on the viscosity contrast and underlying topography, and can be immediately used to evaluate an effective slip of the texture. Besides superlubricating Cassie surfaces, our approach is valid for rough surfaces impregnated by a low-viscosity "lubricant," and even for Wenzel textures, where a liquid follows the surface relief. These results provide a framework for the rational design of textured surfaces for numerous applications.

Interfacial slip on rough, patterned and soft surfaces: a review of experiments and simulations

Advancements in the fabrication of microfluidic and nanofluidic devices and the study of liquids in confined geometries rely on understanding the boundary conditions for the flow of liquids at solid surfaces. Over the past ten years, a large number of research groups have turned to investigating flow boundary conditions, and the occurrence of interfacial slip has become increasingly well-accepted and understood. While the dependence of slip on surface wettability is fairly well understood, the effect of other surface modifications that affect surface roughness, structure and compliance, on interfacial slip is still under intense investigation. In this paper we review investigations published in the past ten years on boundary conditions for flow on complex surfaces, by which we mean rough and structured surfaces, surfaces decorated with chemical patterns, grafted with polymer layers, with adsorbed nanobubbles, and superhydrophobic surfaces. The review is divided in two interconnected parts, the first dedicated to physical experiments and the second to computational experiments on interfacial slip of simple (Newtonian) liquids on these complex surfaces. Our work is intended as an entry-level review for researchers moving into the field of interfacial slip, and as an indication of outstanding problems that need to be addressed for the field to reach full maturity.

Electrokinetic instability near charge-selective hydrophobic surfaces

The influence of the texture of a hydrophobic surface on the electro-osmotic slip of the second kind and the electrokinetic instability near charge selective surfaces (permselective membranes, electrodes, or systems of microchannels and nanochannels) is investigated theoretically using a simple model based on the Rubinstein-Zaltzman approach. A simple formula is derived to evaluate the decrease in the instability threshold due to hydrophobicity. The study is complemented by numerical investigations both of linear and nonlinear instabilities near a hydrophobic membrane surface. Theory predicts a significant enhancement of the ion flux to the surface and shows a good qualitative agreement with the available experimental data.

Effective slip-length tensor for a flow over weakly slipping stripes

We discuss the flow past a flat heterogeneous solid surface decorated by slipping stripes. The spatially varying slip length, b(y), is assumed to be small compared to the scale of the heterogeneities, L, but finite. For such weakly slipping surfaces, earlier analyses have predicted that the effective slip length is simply given by the surface-averaged slip length, which implies that the effective slip-length tensor becomes isotropic. Here we show that a different scenario is expected if the local slip length has steplike jumps at the edges of slipping heterogeneities. In this case, the next-to-leading term in an expansion of the effective slip-length tensor in powers of max[b(y)/L] becomes comparable to the leading-order term, but anisotropic, even at very small b(y)/L. This leads to an anisotropy of the effective slip and to its significant reduction compared to the surface-averaged value. The asymptotic formulas are tested by numerical solutions and are in agreement with results of dissipative particle dynamics simulations.