We investigate the transition between the Cassie-Baxter and Wenzel states of a slowly evaporating, micron-scale drop on a superhydrophobic surface. In two dimensions analytical results show that there are two collapse mechanisms. For long posts the drop collapses when it is able to overcome the free energy barrier presented by the hydrophobic posts. For short posts, as the drop loses volume, its curvature increases allowing it to touch the surface below the posts. We emphasise the importance of the contact line retreating across the surface as the drop becomes smaller: this often preempts the collapse. In a quasi-three dimensional simulation we find similar behaviour, with the additional feature that the drop can de-pin from all but the peripheral posts, so that its base resembles an inverted bowl.
The mechanism of the collapse of the superhydrophobic state is elucidated for submerged nanoscale textures forming a three-dimensional interconnected vapor domain. This key issue for the design of nanotextures poses significant simulation challenges as it is characterized by diverse time and length scales. State-of-the-art atomistic rare events simulations are applied for overcoming the long time scales connected with the large free energy barriers. In such interconnected surface cavities wetting starts with the formation of a liquid finger between two pillars. This break of symmetry induces a…
We use a free energy lattice Boltzmann approach to investigate numerically the dynamics of drops moving across superhydrophobic surfaces. The surfaces comprise a regular array of posts small compared to the drop size. For drops suspended on the posts the velocity increases as the number of posts decreases. We show that this is because the velocity is primarily determined by the contact angle which, in turn, depends on the area covered by posts. Collapsed drops, which fill the interstices between the posts, behave in a very different way. The posts now impede the drop behaviour and the velocity…
We investigate contact angle hysteresis on chemically patterned and superhydrophobic surfaces, as the drop volume is quasi-statically increased and decreased. We consider both two, and three, dimensions using analytical and numerical approaches to minimise the free energy of the drop. In two dimensions we find, in agreement with other authors, a slip, jump, stick motion of the contact line. In three dimensions this behaviour persists, but the position and magnitude of the contact line jumps are sensitive to the details of the surface patterning. In two dimensions we identify analytically the a…
Copper oxide nanostructures with spherical (0D), needle (1D) and hierarchical cauliflower (3D) morphologies are used to demonstrate superhydrophobic, superoleophobic and slippery behavior. These nanostructures are synthesized on galvanized steel substrates using a simple chemical bath deposition method by tuning precursor concentration. Subsequent coating of low surface energy polymer, polydimethylsiloxane, results in superhydrophobicity with water contact angle ~160(2)° and critical sliding angle ~2°. When functionalized with low-surface energy perfluoroalkyl silane, these surfaces display hi…
Rough or textured hydrophobic surfaces are dubbed superhydrophobic due to their numerous desirable properties, such as water repellency and interfacial slip. Superhydrophobicity stems from an aversion for water to wet the surface texture, so that a water droplet in the superhydrophobic "Cassie state", contacts only the tips of the rough hydrophobic surface. However, superhydrophobicity is remarkably fragile, and can break down due to the wetting of the surface texture to yield the "Wenzel state" under various conditions, such as elevated pressures or droplet impact. Moreover, due to large ener…
We investigate the dynamics of micron-scale drops pushed across a hydrophobic or superhydrophobic surface. The velocity profile across the drop varies from quadratic to linear with increasing height, indicating a crossover from a sliding to a rolling motion. We identify a mesoscopic slip capillary number which depends only on the motion of the contact line and the shape of the drop, and show that the angular velocity of the rolling increases with increasing viscosity. For drops on superhydrophobic surfaces we argue that a tank treading advance from post to post replaces the diffusive relaxatio…
Liquid droplets impacting a superhydrophobic surface decorated with micro-scale posts often bounce off the surface. However, by decreasing the impact velocity droplets may land on the surface in a fakir state, and by increasing it posts may impale droplets that are then stuck on the surface. We use a two-phase lattice-Boltzmann model to simulate droplet impact on superhydrophobic surfaces, and show that it may result in a fakir state also for reasonable high impact velocities. This happens more easily if the surface is made more hydrophobic or the post height is increased, thereby making the i…
We consider the equilibrium behaviour and dynamics of liquid drops on a superhydrophobic surface patterned with sawtooth ridges or posts. Due to the anisotropic geometry of the surface patterning, the contact line can preferentially depin from one side of the ratchets, leading to a novel, partially suspended, superhydrophobic state. In both this configuration, and the collapsed state, the drops show strong directional contact angle hysteresis as they are pushed across the surface. The easy direction is, however, different for the two states. This observation allows us to interpret recent exper…
We present a lattice Boltzmann solution of the equations of motion describing the spreading of droplets on topologically patterned substrates. We apply it to model superhydrophobic behaviour on surfaces covered by an array of micron-scale posts. We find that the patterning results in a substantial increase in contact angle, from $110^o$ to $156^o$. The dynamics of the transition from drops suspended on top of the posts to drops collapsed in the grooves is described.
Wetting of sessile bubbles on solid and liquid surfaces has been studied. A model is presented for the contact angle of a sessile bubble based on a modified Young equation - the experimental results agree with the model. A hydrophilic surface results in a bubble contact angle of 90 deg whereas on a superhydrophobic surface one observes 134 deg. For hydrophilic surfaces, the bubble angle diminishes with bubble radius - whereas on a superhydrophobic surface, the bubble angle increases. The size of the Plateau borders governs the bubble contact angle - depending on the wetting of the surface.
When a liquid drops impinges a hydrophobic rough surface it can either bounce off the surface (fakir droplets) or be impaled and strongly stuck on it (Wenzel droplets). The analysis of drop impact and quasi static ''loading'' experiments on model microfabricated surfaces allows to clearly identify the forces hindering the impalement transitions. A simple semi-quantitative model is proposed to account for the observed relation between the surface topography and the robustness of fakir non-wetting states. Motivated by potential applications in microfluidics and in the fabrication of self cleanin…
We present in this letter an experimental characterization of liquid flow slippage over superhydrophobic surfaces made of carbon nanotube forests, incorporated in microchannels. We make use of a micro-PIV (Particule Image Velocimetry) technique to achieve the submicrometric resolution on the flow profile necessary for accurate measurement of the surface hydrodynamic properties. We demonstrate boundary slippage on the Cassie superhydrophobic state, associated with slip lengths of a few microns, while a vanishing slip length is found in the Wenzel state, when the liquid impregnates the surface. …
The leaves of many plants are superhydrophobic, a property that may have evolved to clean the leaves by encouraging water droplets to bead up and roll off. Superhydrophobic surfaces can also exhibit reduced friction and liquids flowing over such surfaces have been found to slip in apparent violations of the classical no-slip boundary condition. Here we introduce slip into a model for rolling droplets on superhydrophobic surfaces and investigate under what conditions slip might be important for the steady state motion. In particular, we examine three limiting cases where dissipation in the roll…
In a recent Letter (Phys. Rev. Lett. vol 96, 066001 (2006), ref [1]), Choi and Kim reported slip lengths of a few tens of microns for water on nanoengineered superhydrophobic surfaces, on the basis of rheometry (cone-and-plate) measurements. We show that the experimental uncertainty in the experiment of Ref. [1], expressed in term of slip lengths, lies in the range 20 - 100 micrometers, which is precisely the order of magnitude of the reported slip lengths. Moreover we point out a systematic bias expected on the superhydrophobic surfaces. We thus infer that it is not possible to draw out any c…
Friction between contacting solid surfaces is a dominant force on the micro-scale and a major consideration in the design of MEMS. Non-contact fluid bearings have been investigated as a way to mitigate this issue. Here we discuss a new design for surface tension-supported thrust bearings utilizing patterned superhydrophobic surfaces to achieve improved drag reduction. We examine sources of instability in the design, and demonstrate that it can be simply modeled and has superior stiffness as compared to other designs.
In this paper we apply topology optimization to micro-structured superhydrophobic surfaces for the first time. It has been experimentally observed that a droplet suspended on a brush of micrometric posts shows a high static contact angle and low roll-off angle. To keep the fluid from penetrating the space between the posts, we search for an optimal post cross section, that minimizes the vertical displacement of the liquid-air interface at the base of the drop when a pressure difference is applied. Topology optimisation proves effective in this framework, showing that posts with a branching cro…
We use mesoscale simulations to study the depinning of a receding contact line on a superhydrophobic surface patterned by a regular array of posts. In order that the simulations are feasible, we introduce a novel geometry where a column of liquid dewets a capillary bounded by a superhydrophobic plane which faces a smooth hydrophilic wall of variable contact angle. We present results for the dependence of the depinning angle on the shape and spacing of the posts, and discuss the form of the meniscus at depinning. We find, in agreement with [17], that the local post concentration is a primary fa…
Engineering surfaces that promote rapid drop detachment is of importance to a wide range of applications including anti-icing, dropwise condensation6, and self-cleaning. Here we show how superhydrophobic surfaces patterned with lattices of submillimetre-scale posts decorated with nano-textures can generate a counter-intuitive bouncing regime: drops spread on impact and then leave the surface in a flattened, pancake shape without retracting. This allows for a four-fold reduction in contact time compared to conventional complete rebound. We demonstrate that the pancake bouncing results from the …
We study experimentally the enhancement of splashing due to solidification. Investigating the impact of water drops on dry smooth surfaces, we show that the transition velocity to splash can be drastically reduced by cooling the surface below the liquid melting temperature. We find that at very low temperatures (below $-60 ^\circ \rm C$), the splashing behaviour becomes independent of surface undercooling and presents the same characteristics as on ambient temperature superhydrophobic surfaces. This resemblance arises from an increase of the dynamic advancing contact angle of the lamella with …
A full characterization of the water flow past a silicon superhydrophobic surface with longitudinal micro-grooves enclosed in a microfluidic device is presented. Fluorescence microscopy images of the flow seeded with fluorescent passive tracers were digitally processed to measure both the velocity field and the position and shape of the liquid-air interfaces at the superhydrophobic surface. The simultaneous access to the meniscus and velocity profiles allows us to put under a strict test the no-shear boundary condition at the liquid-air interface. Surprisingly, our measurements show that air p…
We study the slippage on hierarchical fractal superhydrophobic surfaces, and find an unexpected rich behavior for hydrodynamic friction on these surfaces. We develop a scaling law approach for the effective slip length, which is validated by numerical resolution of the hydrodynamic equations. Our results demonstrate that slippage does strongly depend on the fractal dimension, and is found to be always smaller on fractal surfaces as compared to surfaces with regular patterns. This shows that in contrast to naive expectations, the value of effective contact angle is not sufficient to infer the a…
In this paper the effect of pressure on the contact angle of a water drop on superhydrophobic Carbon Nanotube (CNT) forests is studied. Superhydrophobic CNT forests are obtained from a new and simple functionalization strategy, based on the gold-thiol affinity. Using a specifically devised experimental setup, we then show that these surfaces are able to withstand high excess pressures (larger than 10 kPa) without transiting toward a roughness-invaded state, therefore preserving their low adhesion properties. Together with the relatively low technical cost of the process, this robustness versus…
Macro-textured superhydrophobic surfaces can reduce droplet-substrate contact times of impacting water droplets, however, surface designs with similar performance for significantly more viscous liquids are missing, despite their importance in nature and technology such as for chemical shielding, food staining repellency, and supercooled (viscous) water droplet removal in anti-icing applications. Here, we introduce a deterministic, controllable and up-scalable method to fabricate superhydrophobic surfaces with a 3D-printed architecture, combining arrays of alternating surface protrusions and in…
We investigate the wetting properties of surfaces patterned with fine elastic hairs, with an emphasis on identifying superhydrophobic states on hydrophilic hairs. We formulate a two dimensional model of a large drop in contact with a row of equispaced elastic hairs and, by minimising the free energy of the model, identify the stable and metastable states. In particular we concentrate on "partially suspended" states, where the hairs bend to support the drop -- singlet states where all hairs bend in the same direction, and doublet states where neighbouring hairs bend in opposite directions -- an…
Gaseous layers (plastrons) trapped on the surfaces of immersed hydrophobic surfaces are critical for their function. Fibrillar morphologies offer a natural pathway, yet they are limited to a narrow range of liquid-surface systems and are vulnerable to pressure fluctuations that irreversibly destroy the plastron. Inspired by the convexly grooved surfaces of water fern (Salvinia) leaves that support their fibrous outgrowths, we study the plastron formation on 3D-printed dual-scale surfaces with elliptical interconnected microgrooves. The groove curvature stabilizes a seed gas layer (SGL) that fa…
There is a huge interest in developing super-repellent surfaces for anti-fouling and heat transfer applications. To characterize the wetting properties of such surfaces, the most common approach is to place a millimetric-sized droplet and measure its contact angles. The adhesion and friction forces can then be indirectly inferred from the Furmidge's relation. While easy to implement, contact angle measurements are semi-quantitative and cannot resolve wetting variations on a surface. Here, we attach a micrometric-sized droplet to an Atomic Force Microscope cantilever to directly measure adhesio…
Liquid drops on textured surfaces show different dynamical behaviors depending on their wetting states. They are extremely mobile when they are supported by composite solid-liquid-air interfaces (Cassie-Baxter state) and immobile when they fully wet the textured surfaces (Wenzel state). By reversibly switching between these two states, it will be possible to achieve large control over the fluid dynamics. Unfortunately, these wetting transitions are usually prevented by surface energy barriers. We demonstrate here a new and simple design paradigm, consisting of parallel grooves of appropriate a…
Rough surfaces submerged in a liquid can remain almost dry if the liquid does not fully wet the roughness and gases are sustained in roughness grooves. Such partially dry surfaces can help reduce drag or enhance boiling. Gases sustained in roughness grooves would be composed of air and the vapor phase of the liquid itself. The thermodynamics of sustaining vapor was considered in a prior work [Patankar, Soft Matter, 2010, 6:1613]. Here, the thermodynamics of sustaining gases (e.g. air) is considered. Governing equations are presented along with a solution methodology to determine a critical con…
Although realizing wetting transitions of droplets spontaneously on solid rough surfaces is quite challenging, it is becoming a key research topic in many practical applications which require highly efficient removal of liquid. We report wetting transitions of condensed droplets occurring spontaneously on pillared surfaces with two-tier roughness owing to excellent superhydrophobicity. The phenomenon results from further decreased Laplace pressure on the top side of the individual droplet when its size becomes comparable to the scale of the micropillars, which leads to a surprising robust spon…
Droplet deposition after impact on superhydrophobic surfaces has been an important area of study in recent years due to its potential application in reduction of pesticides usage. Minute amounts of long chain polymers added to water has been known to arrest the droplet rebound effect on superhydrophobic surfaces. Previous studies have attributed different reasons like extensional viscosity, dominance of elastic stresses or slowing down of contact line in retraction phase due to stretching of polymer chains. The present study attempts to unravel the existence of critical criteria of polymer con…
Recent experiments with droplets impacting a macro-textured superhydrophobic surfaces revealed new regimes of bouncing with a remarkable reduction of the contact time. We present here a comprehensive numerical study that reveals the physics behind these new bouncing regimes and quantify the role played by various external and internal forces that effect the dynamics of a drop impacting a complex surface. For the first time, three-dimensional simulations involving macro-textured surfaces are performed. Aside from demonstrating that simulations reproduce experiments in a quantitative manner, the…
The design of a robust superhydrophobic surface is a widely pursued topic.While many investigations are limited to applications with high impact velocities (for raindrops of the order of a few m/s), the essence of robustness is yet to be analyzed for applications involving quasi-static liquid transfer.To achieve robustness with high impact velocities, the surface parameters (geometrical details, chemistry) have to be selected from a narrow range of permissible values, which often entail additional manufacturing costs.From the dual perspectives of thermodynamics and mechanics, we analyze the si…
We study here the microscopic deformations of elastic lamellae constituting a superhydrophobic substrate under different wetting conditions of a sessile droplet using electrowetting. The deformation profiles of the lamellae are experimentally evaluated using confocal microscopy. These experimental results are then explained using a variational principle formalism within the framework of linear elasticity. We show that the local deformation profile of a lamella is mainly controlled by the net horizontal component of the capillary forces acting on its top due to the pinned droplet contact line. …
The free-energy barrier of filling a spherical cavity having an inner wall of various wettabiities is studied. The morphology and free energy of a lens-shaped droplet are determined from the minimum of the free energy. The effect of line tension on the free energy is also studied. Then, the equilibrium contact angle of the droplet is determined from the generalized Young's equation. By increasing the droplet volume within the spherical cavity, the droplet morphology changes from spherical with an equilibrium contact angle of $180^{\circ}$ to a lens with a convex meniscus, where the morphologic…
In this paper we have derived Young's, Wenzel's and Cassie-Baxter's equations using conceptual model rather than showing rigorous derivation to help the new-comers in this field. We then pointed out that if the substrate is initially hydorphilic then one can modify the surface morphology and make the substrate to become hydrophobic or superhydrophobic. But, if the substrate is initially hydrophobic then one can only make it superhydrophobic but not hydrophilic by modifying the surface morphology using the formalisms mentioned in this paper
Self-cleaning surfaces often make use of superhydrophobic coatings that repel water. Here, we report a hydrophobic Si nanospring surface, that effectively suppresses wetting by repelling water droplets. We investigated the dynamic response of Si nanospring arrays fabricated by glancing angle deposition. The vertical standing nanospring arrays were approximately 250 nm tall and 60 nm apart, which allowed the droplets to rebound within a few milliseconds after contact. Amazingly, the morphology of the nanostructures influences the impact dynamics. The rebound time and coefficient of restitution …
Water drop impacting a superhydrophobic surface (SHS) rebounds completely with remarkable elasticity. For such an impact, the balance between the inertial and capillary forces ascertain the contact time. This is found to be fairly constant for any macroscopically flat SHS and for a given drop volume. Recently, various studies have shown that breaking the radial symmetry during the drop impact can significantly reduce the contact time below that of a flat SHS. One such study has been performed on a cylindrical SHS with a curvature comparable to the drop. The reduction in contact time has been a…
Thousands of plant and animal species have been observed to have superhydrophobic surfaces that lead to various novel behaviors [1-5]. These observations have inspired attempts to create artificial superhydrophobic surfaces, given such surfaces have multitudinous applications [6-13]. Superhydrophobicity is an enhanced effect of surface roughness and there are known relationships that correlate surface roughness and superhydrophobicity, based on the underlying physics. However, while these recognize the level of roughness they tell us little about the independent effect of its scale. Thus, they…
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…
This fluid dynamics video shows the different interaction mechanisms of coalescence-induced droplet jumping during condensation on a nanostructured superhydrophobic surface. High speed imaging was used to show jumping behavior on superhydrophobic copper oxide and carbon nanotube surfaces. Videos demonstrating multi-jumping droplets, jumping droplet return to the surface, and droplet-droplet electrostatic repulsions were analyzed. Experiments using external electric fields in conjunction with high speed imaging in a custom built experimental chamber were used to show that all coalescence-induce…
Superhydrophobcity is a well-known wetting phenomenon found in numerous plants and insects. It is achieved by the combination of the surfaces chemical properties and its surface roughness. Inspired by nature, numerous synthetic superhydrophobic surfaces have been developed for various applications. Designated surface coating is one of the fabrication routes to achieve the superhydrophobicity. Yet, many of these coatings, such as fluorine-based formulations, may pose severe health and environmental risks, limiting the applicability. Herein, we present a new family of superhydrophobic coatings c…
When a drop of water is placed on a rough surface, there are two possible extreme regimes of wetting: the one called Cassie-Baxter (CB) with air pockets trapped underneath the droplet and the one characterized by the homogeneous wetting of the surface, called the Wenzel (W) state. A way to investigate the transition between these two states is by means of evaporation experiments, in which the droplet starts in a CB state and, as its volume decreases, penetrates the surface's grooves, reaching a W state. Here we present a theoretical model based on the global interfacial energies for CB and W s…
A falling liquid drop, after impact on a rigid substrate, deforms and spreads, owing to the normal reaction force. Subsequently, if the substrate is non-wetting, the drop retracts and then jumps off. As we show here, not only is the impact itself associated with a distinct peak in the temporal evolution of the normal force, but also the jump-off, which was hitherto unknown. We characterize both peaks and elucidate how they relate to the different stages of the drop impact process. The time at which the second peak appears coincides with the formation of a Worthington jet, emerging through flow…
Water condensation was studied on silanized (superhydrophobic) and fluorinated (superoleophobic) micro-rough aluminum surfaces of the same topography. Condensation on superhydrophobic surfaces occurred via film-wise mechanism, whereas on superoleophobic surfaces it was drop-wise. The difference in the pathways of condensation was attributed to the various energy barriers separating the Cassie and Wenzel wetting states on the investigated surfaces. The higher barriers inherent for superoleophobic surfaces promoted the drop-wise condensation. Triple-stage kinetics of growth of droplets condensed…
Superhydrophobic surfaces (SHSs) have the potential to achieve large drag reduction for internal and external flow applications. However, experiments have shown inconsistent results, with many studies reporting significantly reduced performance. Recently, it has been proposed that surfactants, ubiquitous in flow applications, could be responsible, by creating adverse Marangoni stresses. Yet, testing this hypothesis is challenging. Careful experiments with purified water show large interfacial stresses and, paradoxically, adding surfactants yields barely measurable drag increases. This suggests…
Superrepellency is a favorable non-wetting situation featured by a dramatically reduced solid/liquid contact region with extremely low adhesion. However, drop impact often brings out a notable extension of the contact region associated with rather enhanced water affinity, such renders irreversible breakdowns of superhydrophobicity. Here, we report an alternative outcome, a repeated Cassie-Wenzel-Cassie (CWC) wetting state transition in the microscale occurs when a drop impacts a two-tier superhydrophobic surface, which exhibits a striking contrast to the conventional perspective. Influences of…
Superhydrophobicity is connected to the presence of gas pockets within surface asperities. Upon increasing the pressure this "suspended" state may collapse, causing the complete wetting of the rough surface. In order to quantitatively characterize this process on nanostructured surfaces, we perform rare-event atomistic simulations at different pressures and for several texture geometries. Such approach allows us to identify for each pressure the stable and metastable states and the free energy barriers separating them. Results show that, by starting from the superhydrophobic state and increasi…
The spreading dynamics of Newtonian liquids have been extensively studied in hydrophilic and hydrophobic surfaces and its behavior has been extensively explored over the last years. However, drop impact of Non-Newtonian liquids still needs further study. Luu and Forterre (J. Fluid Mech., 632, 2009) successfully found scaling laws for yield-stress fluids on hydrophilic surfaces. They also uncovered interesting and yet unexplained regimes when the impact was performed on a superhydrophobic surface. In this work, we perform drop impact experiments on micro-patterned surfaces with two types of non…
