Electric-field-enhanced condensation on superhydrophobic nanostructured surfaces

Damping the jump of coalescing droplets through substrate compliance

Sessile droplets coalescing on superhydrophobic surfaces result in spontaneous droplet jumping. Here, through coalescence experiments and fluid-structure interaction simulations for microliter droplets, we demonstrate that such droplet jumping can be damped if the underlying substrate is designed to be compliant. We show that a compliant superhydrophobic substrate with synergistic combinations of low stiffness and inertia deforms rapidly during the coalescence process to minimize the substrate reaction, thus diminishing the jumping velocity. A spring-mass system model for coalescing water droplets is proposed that successfully captures droplet motion and substrate deformation for a wide range of compliant superhydrophobic substrates. These insights can be leveraged to improve the process efficiency in multiple applications, such as designing compliant superhydrophobic substrates for minimizing the scattering of small, nanoliter-sized droplets during atmospheric water harvesting. Lastly, experiments on an exemplar butterfly wing show that droplet jumping velocity reduction can also manifest on natural superhydrophobic substrates due to their inherent compliance.

Enhancement and Predictable Guidance of Coalescence-Induced Droplet Jumping on V-Shaped Superhydrophobic Surfaces with a Ridge

Coalescence-induced droplet jumping has attracted significant attention in recent years. However, achieving a high jumping velocity while predictably regulating the jumping direction of the merged droplets by simple superhydrophobic structures remains a challenge. In this work, a novel V-shaped superhydrophobic surface with a ridge is conceived for enhanced and predictably guided coalescence-induced droplet jumping. By conducting experiments and lattice Boltzmann simulations, it is found that the presence of a ridge in the V-shaped superhydrophobic surface can modify the fluid dynamics during the droplet coalescence process, resulting in a much higher droplet jumping velocity than that achieved by the V-shaped superhydrophobic surface without a ridge. The enhancement of the droplet jumping velocity is mainly attributed to the combined effect of the earlier and more sufficient impingement between the liquid bridge and the ridge, as well as the accelerated droplet contraction by redirecting the internal liquid flow toward the jumping direction. A high normalized jumping velocity of V j * ≈ 0.71 is achieved by the newly designed surface, with a 930% increase in the energy conversion efficiency in comparison with that on a flat surface. Moreover, adjusting the opening direction of the V-groove at different groove angles is found to be an effective method to regulate the droplet jumping direction and expand the range of the jumping angle. Particularly, the droplet jumping angle can be well predicted based on the rotational angle (ω) and the groove angle (α), i.e., θj,p ≈ 90° - 0.5α - ω.

Enhanced and controlled droplet ejection on magnetic responsive polydimethylsiloxane microarrays

Efficient removal of droplets from solid surfaces is significant in various fields, including fog collection and condensation heat transfer. However, droplets removal on common surfaces with static structures often occurs passively, which limits the possibility of increasing removal efficiency and lacks intelligent controllability. In this paper, an active strategy based on extrusion ejection is proposed and demonstrated on the magnetic responsive polydimethylsiloxane (PDMS) superhydrophobic microplates (MPSM). The MPSM can reversibly transit between the upright and tilted state as the external magnetic field is alternately applied and removed. Under the magnetic field, the direction and trajectories of droplets departure can be intelligently controlled, demonstrating excellent controllability. More importantly, compared with the static structure where the droplet must reach a certain size before departure, droplets can be ejected at smaller sizes as the MPSM is tilted. These advantages are of great significance in many fields, such as a highly efficient fog harvesting system. This strategy of extrusion ejection based on dynamic surface structure control reported in this work may provide fresh ideas for efficient droplet manipulation.

Deep Learning Enabled Comprehensive Evaluation of Jumping-Droplet Condensation and Frosting

Superhydrophobicity-enabled jumping-droplet condensation and frosting have great potential in various engineering applications, ranging from heat transfer processes to antifog/frost techniques. However, monitoring such droplets is challenging due to the high frequency of droplet behaviors, cross-scale distribution of droplet sizes, and diversity of surface morphologies. Leveraging deep learning, we develop a semisupervised framework that monitors the optical observable process of condensation and frosting. This system is adept at identifying transient droplet distributions and dynamic activities, such as droplet coalescence, jumping, and frosting, on a variety of superhydrophobic surfaces. Utilizing this transient and dynamic information, various physical properties, such as heat flux, jumping characteristics, and frosting rate, can be further quantified, conveying the heat transfer and antifrost performances of each surface perceptually and comprehensively. Furthermore, this framework relies on only a small amount of annotated data and can efficiently adapt to new condensation conditions with varying surface morphologies and illumination techniques. This adaptability is beneficial for optimizing surface designs to enhance condensation heat transfer and antifrosting performance.

Bioinspired Superhydrophobic Fibrous Materials

Natural fibers with robust water repellency play an important role in adapting organisms to various environments, which has inspired the development of artificial superhydrophobic fibrous materials with applications in self-cleaning, antifogging, water harvesting, heat exchanging, catalytic reactions, and microrobots. However, these highly textured surfaces (micro/nanotextured) suffer from frequent liquid penetration in high humidity and abrasion-induced destruction of the local environment. Herein, bioinspired superhydrophobic fibrous materials are reviewed from the perspective of the dimension scale of fibers. First, the fibrous dimension characteristics of several representative natural superhydrophobic fibrous systems are summarized, along with the mechanisms involved. Then, artificial superhydrophobic fibers are summarized, along with their various applications. Nanometer-scale fibers enable superhydrophobicity by minimizing the liquid-solid contact area. Micrometer-scale fibers are advantageous for enhancing the mechanical stability of superhydrophobicity. Micrometer-scale conical fibrous structures endow a Laplace force with a particular magnitude for self-removing condensed tiny dewdrops in highly humid air and stably trapping large air pockets underwater. Furthermore, several representative surface modification strategies for constructing superhydrophobic fibers are presented. In addition, several conventional applications of superhydrophobic systems are presented. It is anticipated that the review will inspire the design and fabrication of superhydrophobic fibrous systems.

Coalescence-Induced Jumping of Nanodroplets in a Perpendicular Electric Field: A Molecular Dynamics Study

Coalescence-induced jumping has promised a substantial reduction in the droplet detachment size and consequently shows great potential for heat-transfer enhancement in dropwise condensation. In this work, using molecular dynamics simulations, the evolution dynamics of the liquid bridge and the jumping velocity during coalescence-induced nanodroplet jumping under a perpendicular electric field are studied for the first time to further promote jumping. It is found that using a constant electric field, the jumping performance at the small intensity is weakened owing to the continuously decreased interfacial tension. There is a critical intensity above which the electric field can considerably enhance the stretching effect with a stronger liquid-bridge impact and, hence, improve the jumping performance. For canceling the inhibition effect of the interfacial tension under the condition of the weak electric field, a square-pulsed electric field with a paused electrical effect at the expansion stage of the liquid bridge is proposed and presents an efficient nanodroplet jumping even using the weak electric field.

Uniform and Persistent Jumping Detachment of Condensed Nanodroplets

Realizing jumping detachment of condensed droplets from solid surfaces at the smallest sizes possible is vital for applications such as antifogging/frosting and heat transfer. For instance, if droplets uniformly jump at sizes smaller than visible light wavelengths of 400-720 nm, antifogging issues could be resolved. In comparison, the smallest droplets experimentally observed so far to jump uniformly were around 16 μm in radius. Here, we show molecular dynamics (MD) simulations of persistent droplet jumping with a uniform radius down to only 3.6 nm on superhydrophobic thin-walled lattice (TWL) nanostructures integrated with superhydrophilic nanospots. The size cutoff is attributed to the preferential cross-lattice coalescence of island droplets. As an application, the MD results exhibit a 10× boost in the heat transfer coefficient (HTC), showing a -1 scaling law with the maximum droplet radius. We provide phase diagrams for jumping and wetting behaviors to guide the design of lattice structures with advanced antidew performance.

Coalescence-Induced Droplet Jumping for Electro-Thermal Sensing

Jumping droplet condensation, whereby microdroplets (ca. 1-100 μm) coalescing on suitably designed superhydrophobic surfaces jump away from the surface, has recently been shown to have a 10× heat transfer enhancement compared to filmwise condensing surfaces. However, accurate measurements of the condensation heat flux remain a challenge due to the need for low supersaturations (<1.1) to avoid flooding. The low corresponding heat fluxes (<5 W/cm2) can result in temperature noise that exceeds the resolution of the measurement devices. Furthermore, difficulties in electro-thermal measurements such as droplet and surface electrostatic charge arise in applications where direct access to the condensing surface, such as in isolated chambers and small integrated devices, is not possible. Here, we present an optical technique that can determine the experimental electro-thermal parameters of the jumping droplet condensation process with high fidelity through the analysis of jumping droplet trajectories. To measure the heat flux, we observed the experimental trajectories of condensate droplets on superhydrophobic nanostructures and simultaneously matched them in space and time with simulated trajectories using the droplet dynamic equations of motion. Two independent approaches yielded mean heat fluxes of approximately 0.13 W/cm2 with standard deviations ranging from 0.047 to 0.095 W/cm2, a 79% reduction in error when compared with classical energy balance-based heat flux measurements. In addition, we analyzed the trajectories of electrostatically interacting droplets during flight and fitted the simulated and experimental results to achieve spatial and temporal agreement. The effect of image charges on a jumping droplet as it approaches the surface was analyzed, and the observed acceleration has been numerically quantified. Our work presents a sensing methodology of electro-thermal parameters governing jumping droplet condensation.

Electric Field-Induced Water Condensation Visualized by Vapor-Phase Transmission Electron Microscopy

Understanding the nanoscale water condensation dynamics in strong electric fields is important for improving the atmospheric modeling of cloud dynamics and emerging technologies utilizing electric fields for direct air moisture capture. Here, we use vapor-phase transmission electron microscopy (VPTEM) to directly image nanoscale condensation dynamics of sessile water droplets in electric fields. VPTEM imaging of saturated water vapor stimulated condensation of sessile water nanodroplets that grew to a size of ∼500 nm before evaporating over a time scale of a minute. Simulations showed that electron beam charging of the silicon nitride microfluidic channel windows generated electric fields of ∼10⁸ V/m, which depressed the water vapor pressure and effected rapid nucleation of nanosized liquid water droplets. A mass balance model showed that droplet growth was consistent with electric field-induced condensation, while droplet evaporation was consistent with radiolysis-induced evaporation via conversion of water to hydrogen gas. The model quantified several electron beam-sample interactions and vapor transport properties, showed that electron beam heating was insignificant, and demonstrated that literature values significantly underestimated radiolytic hydrogen production and overestimated water vapor diffusivity. This work demonstrates a method for investigating water condensation in strong electric fields and under supersaturated conditions, which is relevant to vapor-liquid equilibrium in the troposphere. While this work identifies several electron beam-sample interactions that impact condensation dynamics, quantification of these phenomena here is expected to enable delineating these artifacts from the physics of interest and accounting for them when imaging more complex vapor-liquid equilibrium phenomena with VPTEM.

Advances in micro and nanoengineered surfaces for enhancing boiling and condensation heat transfer: a review

Liquid-vapor phase change phenomena such as boiling and condensation are processes widely implemented in industrial systems such as power plants, refrigeration and air conditioning systems, desalination plants, water processing installations and thermal management devices due to their enhanced heat transfer capability when compared to single-phase processes. The last decade has seen significant advances in the development and application of micro and nanostructured surfaces to enhance phase change heat transfer. Phase change heat transfer enhancement mechanisms on micro and nanostructures are significantly different from those on conventional surfaces. In this review, we provide a comprehensive summary of the effects of micro and nanostructure morphology and surface chemistry on phase change phenomena. Our review elucidates how various rational designs of micro and nanostructures can be utilized to increase heat flux and heat transfer coefficient in the case of both boiling and condensation at different environmental conditions by manipulating surface wetting and nucleation rate. We also discuss phase change heat transfer performance of liquids having higher surface tension such as water and lower surface tension liquids such as dielectric fluids, hydrocarbons and refrigerants. We discuss the effects of micro/nanostructures on boiling and condensation in both external quiescent and internal flow conditions. The review also outlines limitations of micro/nanostructures and discusses the rational development of structures to mitigate these limitations. We end the review by summarizing recent machine learning approaches for predicting heat transfer performance of micro and nanostructured surfaces in boiling and condensation applications.

Contact line dynamics of a water drop spreading over a textured surface in the electrowetting-on-dielectric configuration

Modeling the electrowetting process of a liquid droplet placed on a hydrophobic surface in an ambient environment has several challenges over and above those of basic spreading [F. Mugele, Soft Matter 5, 3377 (2009)10.1039/b904493k]. At an external voltage below the value that causes contact angle saturation, transient spreading is augmented by contact angle reduction defined by the Young-Lippmann equation. In addition, the macroscopic equilibrium contact angle and, therefore, the spreading rate could be altered by the surface hysteresis. Beyond the saturation point, spreading reveals additional features of higher complexity [Q. Vo and T. Tran, J. Fluid Mech. 925, A19 (2021)10.1017/jfm.2021.677]. These details have been examined from experiments as well as numerical simulation in the present work. Below the saturation point, the contact angle model of Dwivedi et al. [Phys. Rev. Fluids 7, 034002 (2022)10.1103/PhysRevFluids.7.034002] with the correction related to the electric field is seen to be applicable. Beyond saturation, the experimentally determined instantaneous contact angle distribution shows two distinct functionalities with respect to the contact line velocity. The first prevails from the onset of spreading until the spreading factor attains a peak value. The second trend is initiated with the retraction of the contact line. Except for differences in parametric values, the form of the contact angle model remains unchanged. Simulations in the postsaturation regime are shown to match experimental data in terms of the transient spreading factor, drop shapes, and the instantaneous contact angle. The role of the ground wire is found to be important and the three-phase contact line formed on it has been included in simulations. Spreading dynamics of the droplet have also been studied when the ground wire is kept at a distance of 40 μm from the apex of the drop. Simulations as well as experiments, show the propagation of a capillary wave between the ground wire and the three-phase contact line. For spreading over an uncoated polydimethylsiloxane (PDMS) surface, the contact line is trapped at local pinning sites, leading to additional distortions in the instantaneous shapes acquired by the interface.

Condensation droplet sieve

Large droplets emerging during dropwise condensation impair surface properties such as anti-fogging/frosting ability and heat transfer efficiency. How to spontaneously detach massive randomly distributed droplets with controlled sizes has remained a challenge. Herein, we present a solution called condensation droplet sieve, through fabricating microscale thin-walled lattice structures coated with a superhydrophobic layer. Growing droplets were observed to jump off this surface once becoming slightly larger than the lattices. The maximum radius and residual volume of droplets were strictly confined to 16 μm and 3.2 nl/mm² respectively. We reveal that this droplet radius cut off is attributed to the large tolerance of coalescence mismatch for jumping and effective isolation of droplets between neighboring lattices. Our work brings forth a strategy for the design and fabrication of high-performance anti-dew materials.

Spontaneous droplet jumping and control of dropwise condensation are relevant for water-harvesting, heat transfer and anti-frosting applications. The authors design a superhydrophobic surface with microscale thin-walled lattice structure to achieve effective jumping of droplets with specified radius range.

Review of droplet dynamics and dropwise condensation enhancement: Theory, experiments and applications

Droplet dynamics and condensation phenomena are widespread in nature and industrial applications, and the fundamentals of various technological applications. Currently, with the rapid development of interfacial materials, microfluidics, micro/nano fabrication technology, as well as the intersection of fluid mechanics, interfacial mechanics, heat and mass transfer, thermodynamics and reaction kinetics and other disciplines, the preparation and design of various novel functional surfaces have contributed to the local modulation of droplets (including nucleation, jumping and directional migration) and the improvement of condensation heat transfer, further deepening the understanding of relevant mechanisms. The wetting and dynamic characteristics of droplets involve complex solid-liquid interfacial interactions, so that the local modulation of microdroplets and the extension of enhanced condensation heat transfer by means of complex micro/nano structures and hydrophilic/hydrophobic properties is one of the current hot topics in heat and mass transfer research. This work presents a detailed review of several scientific issues related to the droplet dynamics and dropwise condensation heat transfer under the influence of multiple factors (including fluid property, surface structure, wettability, temperature external field, etc.). Firstly, the basic theory of droplet wetting on the solid wall is introduced, and the mechanism of solid-liquid interfacial interaction involving droplet jumping and directional migration on the functional surfaces under the various influencing factors is discussed. Optimizing the surface structure for the local modulation of droplets is of guidance for condensation heat transfer. Secondly, we summarize the existing theoretical models of dropwise condensation applicable to various functional surfaces and briefly outline the current numerical models for simulating dropwise condensation at different scales, as well as the fabricating techniques of coatings and functional surfaces for enhancing heat transfer. Finally, the relevant problems and challenges are summarized and future research is discussed.

Quasi-Liquid Surfaces for Sustainable High-Performance Steam Condensation

Sustainable high-performance steam condensation is critical to reducing the size, weight, and cost of water and energy systems. It is well-known that dropwise condensation can provide a significantly higher heat-transfer coefficient than filmwise condensation. Tremendous efforts have been spent to promote dropwise condensation by achieving a nonwetting state on superhydrophobic surfaces and a slippery state on liquid-infused surfaces, but these surfaces suffer from severe durability challenges. Here, we report sustainable high-performance dropwise condensation of steam on newly developed durable quasi-liquid surfaces, which are easily made by chemically bonding quasi-liquid polymer molecules on solid substrates. As a result, the solid/water interface is changed to a quasi-liquid/water interface with minimal adhesion and extraordinary durability. The quasi-liquid surface with ultralow contact angle hysteresis down to 1° showed a heat-transfer coefficient up to 70 and 380% higher than those on conventional hydrophobic and hydrophilic surfaces, respectively. Furthermore, we demonstrated that the quasi-liquid coating exhibited a sustainable heat-transfer coefficient of 71 kW/(m² K) at a heat flux of 420 kW/m² under a prolonged period of 39 h in continuous steam condensation. Such a quasi-liquid surface has the potential to sustain high-performance dropwise condensation of steam and address the long-standing durability challenge in the field.

Depinning of Multiphase Fluid Using Light and Photo-Responsive Surfactants

The development of noninvasive and robust strategies for manipulation of droplets and bubbles is crucial in applications such as boiling and condensation, electrocatalysis, and microfluidics. In this work, we realize the swift departure of droplets and bubbles from solid substrates by introducing photoresponsive surfactants and applying asymmetric illumination, thereby inducing a "photo-Marangoni" lift force. Experiments show that a pinned toluene droplet can depart the substrate in only 0.38 s upon illumination, and the volume of an air bubble at departure is reduced by 20%, indicating significantly faster departure. These benefits can be achieved with moderate light intensities and dilute surfactant concentrations, without specially fabricated substrates, which greatly facilitates practical applications. Simulations suggest that the net departure force includes contributions from viscous stresses directly caused by the Marangoni flow, as well as from pressure buildup due to flow stagnation at the contact line. The manipulation scheme proposed here shows potential for applications requiring droplet and bubble removal from working surfaces.

Enhanced Moisture Condensation on Hierarchical Structured Superhydrophobic-Hydrophilic Patterned Surfaces

Patterned surfaces combining hydrophobic and hydrophilic properties show great promise in moisture condensation; however, a comprehensive understanding of the multiscale interfacial behavior and the further controlling method is still lacking. In this paper, we studied the moisture condensation on a hybrid superhydrophobic-hydrophilic surface with hierarchical structures from micro- to nanoscale. For the first time, we demonstrated the effects of wettability difference and microstructure size on the final condensation efficiency. By optimizing the wettability difference, sub-millimeter pattern width, and microstructure size, maximum 90% enhancement of the condensation rate was achieved as compared with the superhydrophobic surface at a subcooling of 13 K. We also demonstrated the enhanced condensation mechanism by a detailed analysis of the condensation process. Our work proposed effective and systematical methods for controlling and optimizing moisture condensation on the patterned surfaces and shed light on application integration of such promising functional surfaces.

Robust and durable liquid-repellent surfaces

This review provides a comprehensive summary of characterization, design, fabrication, and application of robust and durable liquid-repellent surfaces.

Critical conditions for whether two impacting nanodroplets can coalesce or not: a molecular simulation study

Molecular dynamics simulations are carried out to study impact-induced coalescence behaviors for the first time. When the droplets possess different impact velocities, the big difference between them could induce unconventional coalescence behaviors that exhibit non-synchronous spreading and retraction processes, and thus produce non-coalescence behaviors. At the same impact velocity, the distance of two impacting droplets plays a vital role in their coalescing dynamics. We here present the lower and upper critical values of distance in a map to determine whether two droplets after impacting can coalesce or not, which are highly dependent on the impact velocity. Moreover, simulation studies show that the upper critical value is 2(R_max - R), while the lower critical distance increases with the increase of impact velocity. This work not only helps advance our understanding of the effect of impact dynamics on the coalescence behaviors, but also shows the critical conditions for coalescence and non-coalescence behaviors, which could be considered as a new strategy to control the coalescence by tuning the impact parameters, and are expected to be used for some potential applications.

Improving heat and mass transfer rates through continuous drop-wise condensation

Drop-wise condensation (DWC) has been the focus of scientific research in vapor condensation technologies since the 20th century. Improvement of condensation rate in DWC is limited by the maximum droplet a condensation surface could sustain and the frequency of droplet shedding. Furthermore, The presence of non-condensable gases (NCG) reduces the condensation rate significantly. Here, we present continuous drop-wise condensation to overcome the need of hydrophobic surfaces while yet maintaining micron-sized droplets. By shifting focus from surface treatment to the force required to sweep off a droplet, we were able to utilize stagnation pressure of jet impingement to tune the shed droplet size. The results show that droplet size being shed can be tuned effectively by tuning the jet parameters. our experimental observations showed that the effect of NCG is greatly alleviated by utilizing this technique. An improvement by multiple folds in mass transfer compactness factor compared to state-of-the-art dehumidification technology was possible.

Dropwise condensation: From fundamentals of wetting, nucleation, and droplet mobility to performance improvement by advanced functional surfaces

As a ubiquitous vapor-liquid phase-change process, dropwise condensation has attracted tremendous research attention owing to its remarkable efficiency of energy transfer and transformative industrial potential. In recent years, advanced functional surfaces, profiting from great progress in modifying micro/nanoscale features and surface chemistry on surfaces, have led to exciting advances in both heat transfer enhancement and fundamental understanding of dropwise condensation. In this review, we discuss the development of some key components for achieving performance improvement of dropwise condensation, including surface wettability, nucleation, droplet mobility, and growth, and discuss how they can be elaborately controlled as desired using surface design. We also present an overview of dropwise condensation heat transfer enhancement on advanced functional surfaces along with the underlying mechanisms, such as jumping condensation on nanostructured superhydrophobic surfaces, and new condensation characteristics (e.g., Laplace pressure-driven droplet motion, hierarchical condensation, and sucking flow condensation) on hierarchically structured surfaces. Finally, the durability, cost, and scalability of specific functional surfaces are focused on for future industrial applications. The existing challenges, alternative strategies, as well as future perspectives, are essential in the fundamental and applied aspects for the practical implementation of dropwise condensation.

Droplet Dynamics and Freezing Delay on Nanoporous Microstructured Surfaces at Condensing Environment

Superhydrophobic surfaces have aroused great interest for being promising candidates in applications such as self-cleaning, anti-icing, and corrosion resistance. However, most of the superhydrophobic surfaces lose their anti-wettability in low surface temperature and high humidity. The loss of superhydrophobicity by condensed liquid is a very common practical incident, yet to be understood properly. Here we report the wettability of the superhydrophobic nanoporous surfaces in condensation and freezing environments. Various structured surfaces fabricated with carbon nanotubes (CNT) and coated by an ultrathin, conformal, and low surface energy layer of poly (1H,1H,2H,2H-perfluorodecylacrylate) (pPFDA) are exploited in humid conditions. Droplet impact dynamics, condensate characteristics, and freezing time delays are investigated on the CNT micropillars with various geometries along with the CNT forest and two commercially available anti-wetting coatings, NeverWet and WX2100. Nanoporous microstructured CNT pillars with the favorable topological configuration demonstrated complete droplet bouncing, significant freezing delays, and considerable durability during several icing/de-icing cycles. This study provides an understanding on the preferable geometry of the highly porous CNT micropillars for retaining hydrophobicity and preventing ice formation, which is of practical importance for the rational development of anti-wetting surfaces and their applications in low temperatures and humid conditions.

Nanostructured jumping-droplet thermal rectifier

Analogous to an electrical rectifier, a thermal rectifier (TR) can ensure that heat flows in a preferential direction. In this paper, thermal transport nonlinearity is achieved through the development of a phase-change based TR comprising an enclosed vapor chamber having separated nanostructured copper oxide superhydrophobic and superhydrophilic functional surfaces. In the forward direction, heat transfer is facilitated through evaporation on the superhydrophilic surface and self-propelled jumping-droplet condensation on the superhydrophobic surface. In the reverse direction, heat transfer is minimized due to condensate film formation within the superhydrophilic condenser and inability to return the condensed liquid to the superhydrophobic evaporator. We examine the coupled effects of gap size, coolant mass, heat transfer rate, and applied electric field on the thermal performance of the TR. A maximum thermal diodicity, defined as the ratio of forward to reverse heat transfer, of 39 is achieved.

Analytical model for drag reduction on liquid-infused structured non-wetting surfaces

Liquid-infused structured non-wetting surfaces provide alternating no-slip and partial slip boundary conditions to the fluid flow, resulting in reduced friction at the interface. In this paper, an analytical model is developed for the evaluation of effective slip and, in turn, friction factor and drag reduction on liquid-infused structured non-wetting surfaces. By considering the entire range of anisotropy and heterogeneity of the surface structures as well as the full range of partial slip offered by the infusion liquid, the present model eliminates empirical fitting or correlations that are inherent in previous studies. Based on the effective slip length, drag reduction and skin friction coefficient values for Newtonian flow between two infinite parallel plates and flow in round tubes are presented. Extension of Moody charts for non-wetting surfaces and design maps of surface meso/micro/nano texturing for achieving desired drag reduction are presented for a broad range of engineering applications. The article further presents independent validation of the model across experimental and computational data from the literature and brings together several previous studies in a unified manner.

Effect of a Superhydrophobic Surface Structure on Droplet Jumping Velocity

The coalescence-induced droplet jumping on superhydrophobic surfaces is fundamentally significant from an academic or practical viewpoint. However, approaches to enhance droplet jumping velocity are very limited. In this work, the effect of structural parameters of the triangular prism on droplet jumping is studied systematically. The results indicate that droplet jumping velocity can be greatly increased by exploiting structure effects, which is a promising reinforcement method. When the height and apex angle of the triangular prism are fixed, the droplet jumping velocity increases with the length of the triangular prism until a plateau is reached. The ratio of translational kinetic energy to released surface energy during droplet jumping is determined by the apex angle and the height of the triangular prism, which is more effective with a smaller apex angle and a larger height. The results are supposed to provide guidelines for optimization of superhydrophobic surfaces.

Coalescence-Induced Droplet Jumping

When two or more droplets coalesce on a superhydrophobic surface, the merged droplet can jump spontaneously from the surface without requiring any external energy. This phenomenon is defined as coalescence-induced droplet jumping and has received significant attention due to its potential applications in a variety of self-cleaning, anti-icing, antifrosting, and condensation heat-transfer enhancement uses. This article reviews the research and applications of coalescence-induced droplet jumping behavior in recent years, including the influence of droplet parameters on coalescence-induced droplet jumping, such as the droplet size, number, and initial velocity, to name a few. The main structure types and influence mechanism of the superhydrophobic substrates for coalescence-induced droplet jumping are described, and the potential application areas of coalescence-induced droplet jumping are summarized and forecasted.

Fractal Model for Drag Reduction on Multiscale Nonwetting Rough Surfaces

Rough surfaces in contact with a flow of fluid exhibit alternating no-slip and free shear boundary conditions at the solid-liquid and air-liquid interfaces, respectively, thereby potentially offering drag reduction benefits. The balance between the dynamic pressure in the flow and the restoring capillary pressure in the interasperity spaces determines the stability of the Cassie state of wettability and is a function of the relative extent of no-slip and free shear regions per unit surface area. In the present study, using a fractal representation of rough surface topography, an analytical model is developed to quantify the stability of the Cassie state of wettability as well as drag reduction and the friction factor for laminar flow in a rectangular channel between nonwetting multiscale rough surfaces. A systematic study is conducted to quantify the effects of fractal parameters of the surfaces and the flow Reynolds number on drag reduction and the friction factor. The studies are used to develop friction factor curves extending the classical Moody diagram to hydrophobic and superhydrophobic surfaces. On the basis of the studies, regime maps are derived for estimating the extent of drag reduction offered by hydrophobic and superhydrophobic surfaces, revealing that superhydrophobic surfaces do not always offer the best drag reduction performance. The application of the fractal model to practical topographies of nonwetting surfaces of copper, aluminum, and zinc oxide fabricated via electrodeposition and etching is also discussed.

Controlling the Jumping Angle of Coalescing Droplets Using Surface Structures

The jumping direction is an essential characteristic of jumping droplets, but it is poorly understood and uncontrollable at present. In this work, we present a method to control the jumping direction by surface structures, where the jumping direction is controlled by changing the inclination angle of the structure. The underlying mechanism is analyzed experimentally, with numerical simulations, and using a theoretical model developed to relate the jumping direction and the inclination angle for a few cases with a specific distribution. Because random droplet distributions are more common on actual condensation surfaces, a more comprehensive prediction model was developed based on a convolution neural network (CNN) to predict the jumping direction for more general cases. The input to the CNN is an image of droplets with various distribution features, which are detected by the neural network and used to predict the jumping angle. SHapley Additive exPlanations methods were then used to analyze the feature importance and to give human-understandable insights from the prediction model. This work offers avenues for improving cooling rates, anti-icing/freezing characteristics, and self-cleaning attributes and contributes to a better understanding of the jumping direction.

Enhanced Condensation on Liquid-Infused Nanoporous Surfaces by Vibration-Assisted Droplet Sweeping

Condensation is a universal phenomenon that occurs in nature and industry. Previous studies have used superhydrophobicity and liquid infusion to enable superior liquid repellency due to reduced contact angle hysteresis. However, small condensate droplets remain immobile on condensing surfaces until they grow to the departing size at which the body force can overcome the contact line pinning force. Hence, condensation heat transfer is limited by these remaining droplets that act as thermal barriers. To break these limitations, we introduce vibrational actuation to a slippery liquid-infused nanoporous surface (SLIPS) and show enhanced droplet mobility, controllable condensate repellency, and more efficient heat transfer compared to static SLIPSs. We demonstrate 39% smaller departing droplet size and 8× faster droplet departing speeds on the dynamic vibrating SLIPS compared to the nonactuated SLIPS. To understand the implications of these behaviors on heat transfer, we investigate the condensate area coverage and droplet distribution to verify enhanced dewetting on dynamic vibrating SLIPSs. Using well-validated heat transfer models, we demonstrate enhanced condensation heat transfer on dynamic SLIPSs due to the higher population of smaller condensate droplets (<100 μm). In addition to condensation heat transfer, we also show that vibrating SLIPSs can enhance droplet collection. This work utilizes the synergistic combination of surface chemistry and mechanical actuation to realize enhanced droplet mobility and heat transfer in an electrically controllable and switchable manner.

Dependencies of Surface Condensation on the Wettability and Nanostructure Size Differences

When changing surface wettability and nanostructure size, condensation behavior displays distinct features. In this work, we investigated evaporation on a flat hydrophilic surface and condensation on both hydrophilic and hydrophobic nanostructured surfaces at the nanoscale using molecular dynamics simulations. The simulation results on hydrophilic surfaces indicated that larger groove widths and heights produced more liquid argon atoms, a quicker temperature response, and slower potential energy decline. These three characteristics closely relate to condensation areas or rates, which are determined by groove width and height. For condensation heat transfer, when the groove width was small, the change of groove height had little effect, while change of groove height caused a significant variation in the heat flux with a large groove width. When the cold wall was hydrophobic, the groove height became a significant impact factor, which caused no vapor atoms to condense in the groove with a larger height. The potential energy decreased with the increase of the groove height, which demonstrates a completely opposing trend when compared with hydrophilic surfaces.

Directional liquid dynamics of interfaces with superwettability

Natural creatures use their surface structures to control directional liquid dynamics for survival. Learning from nature, artificial superwetting materials have triggered technological revolutions in many disciplines. To improve controllability, researchers have attempted to use external fields, such as thermal, light, magnetic, and electric fields, to assist or achieve controllable liquid dynamics. Emerging directional liquid transport applications have prosperously advanced in recent years but still present some challenges. This review discusses and summarizes the field of directional liquid dynamics on natural creatures and artificial surfaces with superwettabilities and ventures to propose several potential strategies to construct directional liquid transport systems for fog collection, 3D printing, energy devices, separation, soft machine, and sensor devices, which are useful for driving liquid transport or motility.

High-Throughput Stamping of Hybrid Functional Surfaces

Hydrophobic-hydrophilic hybrid surfaces, sometimes termed biphilic surfaces, have shown potential to enhance condensation and boiling heat transfer, anti-icing, and fog harvesting performance. However, state of art techniques to develop these surfaces have limited substrate selection, poor scalability, and lengthy and costly fabrication methods. Here, we develop a simple, scalable, and rapid stamping technique for hybrid surfaces with spatially controlled wettability. To enable stamping, rationally designed and prefabricated polydimethylsiloxane (PDMS) stamps, which are reusable and independent of the substrate and functional coating, were used. To demonstrate the stamping technique, we used silicon wafer, copper, and aluminum substrates functionalized with a variety of hydrophobic chemistries including heptadecafluorodecyltrimethoxy-silane, octafluorocyclobutane, and slippery omniphobic covalently attached liquids. Condensation experiments and microgoniometric characterization demonstrated that the stamped surfaces have global hydrophobicity or superhydrophobicity with localized hydrophilicity (spots) enabled by local removal of the functional coating during stamping. Stamped surfaces with superhydrophobic backgrounds and hydrophilic spots demonstrated stable coalescence induced droplet jumping. Compared to conventional techniques, our stamping method has comparable prototyping cost with reduced manufacturing time scale and cost. Our work not only presents design guidelines for the development of scalable hybrid surfaces for the study of phase change phenomena, it develops a scalable and rapid stamping protocol for the cost-effective manufacture of next-generation hybrid wettability surfaces.

Passive Anti-Flooding Superhydrophobic Surfaces

Superhydrophobic (SHPo) surfaces can provide high condensation heat transfer due to facilitated droplet removal. However, such high performance has been limited to low supersaturation conditions due to surface flooding. Here, we quantify flooding resistance defined as the rate of increase in the fraction of water-filled cavities with respect to the supersaturation level. Based on the quantitative understanding of surface flooding, we suggest effective anti-flooding strategies through tailoring the nanoscale coating heterogeneity and structure length scale. Experimental verification is conducted using CuO nanostructures having different length scales combined with hydrophobic coatings with different nanoscale heterogeneities. The proposed anti-flooding SHPo can provide a ∼130% enhanced average heat transfer coefficient with ∼14% larger supersaturation range for droplet jumping compared to a previous CuO SHPo. The proposed anti-flooding parameter and the scalable SHPo will help develop high-performance condensers for real-world applications operating in a wide range of supersaturation levels.

Dependences of Formation and Transition of the Surface Condensation Mode on Wettability and Temperature Difference

In this work, we use molecular dynamics (MD) simulations to investigate the dependences of formation and transition of surface condensation mode on wettability (β) and vapor-to-surface temperature difference (ΔT). We build a map of different surface condensation modes against β and ΔT based on plenty of MD simulation results and reveal five formation mechanisms and two transition mechanisms. At low β and ΔT, the high free energy barrier (ΔG*) prevents any surface clusters from surviving, therefore no-condensation (NC) is observed. The formation of dropwise condensation (DWC) could evolve from either nucleation or film rupture. Similarly, the formation of filmwise condensation (FWC) could evolve from either nucleation or the adsorption-induced film. The transition between NC and DWC is determined by ΔG* according to classical nucleation theory. The transition between DWC and FWC depends on the stability of condensate film; there emerges the competition between the trend that the uneven condensate film contracts and ruptures to droplets favored by lower β and the trend that the uneven condensate film continues growing promoted by higher ΔT. We finally present a schematic overview of all of the mechanisms revealed for a better understanding of the physical phenomenon of the surface condensation mode.

Dropwise condensation on solid hydrophilic surfaces

Droplet nucleation and condensation are ubiquitous phenomena in nature and industry. Over the past century, research has shown dropwise condensation heat transfer on nonwetting surfaces to be an order of magnitude higher than filmwise condensation heat transfer on wetting substrates. However, the necessity for nonwetting to achieve dropwise condensation is unclear. This article reports stable dropwise condensation on a smooth, solid, hydrophilic surface (θ_a = 38°) having low contact angle hysteresis (<3°). We show that the distribution of nano- to micro- to macroscale droplet sizes (about 100 nm to 1 mm) for coalescing droplets agrees well with the classical distribution on hydrophobic surfaces and elucidate that the wettability-governed dropwise-to-filmwise transition is mediated by the departing droplet Bond number. Our findings demonstrate that achieving stable dropwise condensation is not governed by surface intrinsic wettability, as assumed for the past eight decades, but rather, it is dictated by contact angle hysteresis.

Efficient water scavenging by cooling superhydrophobic surfaces to obtain jumping water droplets from air

Dew collection is significant in harvesting water and relieving water shortages in arid regions. However, current methods for collecting dew or steam are mainly focusing on the millimeter-sized droplets condensed on the superhydrophobic surfaces. Here, we present a concept for harvesting micro droplets that can spontaneously bounce on the cooling superhydrophobic aluminum surface with randomly micro-nano composite structures, which were fabricated by using a two-step surface structural process. Moreover, an integrated device has been developed, which consists of a triboelectric nanogenerator and the superhydrophobic aluminum sheet. We experimentally explained that the triboelectric nanogenerator, which provides an external electric field by converting wind energy to electric energy with DC voltage pulse peaks of about 60 V, can be utilized to enhance the collection capacity of the jumping water droplets.

Hierarchical Condensation

With the recent advances in surface fabrication technologies, condensation heat transfer has seen a renaissance. Hydrophobic and superhydrophobic surfaces have all been employed as a means to enhance condensate shedding, enabling micrometric droplet departure length scales. One of the main bottlenecks for achieving higher condensation efficiencies is the difficulty of shedding sub-10 μm droplets due to the increasing role played by surface adhesion and viscous limitations at nanometric length scales. To enable ultraefficient droplet shedding, we demonstrate hierarchical condensation on rationally designed copper oxide microhill structures covered with nanoscale features that enable large (∼100 μm) condensate droplets on top of the microstructures to coexist with smaller (<1 μm) droplets beneath. We use high-speed optical microscopy and focal plane shift imaging to show that hierarchical condensation is capable of efficiently removing sub-10-μm condensate droplets via both coalescence and divergent-track-assisted droplet self-transport toward the large suspended Cassie-Baxter (CB) state droplets, which eventually shed via classical gravitational shedding and thereby avoid vapor side limitations encountered with droplet jumping. Interestingly, experimental growth rate analysis showed that the presence of large CB droplets accelerates individual underlying droplet growth by ∼21% when compared to identically sized droplets not residing beneath CB droplets. Furthermore, the steady droplet shedding mechanism shifted the droplet size distribution toward smaller sizes, with ∼70% of observable underlying droplets having radii of ≤5 μm compared to ∼30% for droplets growing without shading. To elucidate the overall heat transfer performance, an analytical model was developed to show hierarchical condensation has the potential to break the limits of minimum droplet departure size governed by finite surface adhesion and viscous effects through the tailoring of structure length scale, coalescence, and self-transport. More importantly, abrasive wear tests showed that hierarchical condensation has good durability against mechanical damage to the surface. Our study not only demonstrates the potential of hierarchical condensation as a means to break the limitations of droplet jumping, it develops rational design guidelines for micro/nanostructured surfaces to enable excellent heat transfer performance as well as extended durability.

Nanograssed Zigzag Structures To Promote Coalescence-Induced Droplet Jumping

To increase the efficiency of jumping-droplet condensation, this study proposes a hierarchical superhydrophobic surface that promotes coalescence-induced jumping. Inspired by the phenomenon in which a growing droplet moves spontaneously within a superhydrophobic V structure, we fabricated nanograssed zigzag structures on the surface to induce the spontaneous motion of condensed droplets. The direction of the motion was parallel to the surface, so the condensed droplets easily coalesced on it. Compared with a conventional nanograssed superhydrophobic surface, the proposed surface increased the frequency of coalescence-induced jumping by ≥17 times and increased the cumulative volume of jumping droplets by ∼1.8 times. The proposed surface has great potential to increase the efficiency of applications such as water- and energy-harvesting and cooling systems that exploit jumping-droplet condensation.

Atmosphere-Mediated Superhydrophobicity of Rationally Designed Micro/Nanostructured Surfaces

Superhydrophobicity has received significant attention over the past three decades owing to its significant potential in self-cleaning, anti-icing and drag reduction surfaces, energy-harvesting devices, antibacterial coatings, and enhanced heat transfer applications. Superhydrophobicity can be obtained via the roughening of an intrinsically hydrophobic surface, the creation of a re-entrant geometry, or by the roughening of a hydrophilic surface followed by a conformal coating of a hydrophobic material. Intrinsically hydrophobic surfaces have poor thermophysical properties, such as thermal conductivity, and thus are not suitable for heat transfer applications. Re-entrant geometries, although versatile in applications where droplets are deposited, break down during spatially random nucleation and flood the surface. Chemical functionalization of rough metallic substrates, although promising, is not utilized because of the poor durability of conformal hydrophobic coatings. Here we develop a radically different approach to achieve stable superhydrophobicity. By utilizing laser processing and thermal oxidation of copper (Cu) to create a high surface energy hierarchical copper oxide (CuO), followed by repeatable and passive atmospheric adsorption of hydrophobic volatile organic compounds (VOCs), we show that stable superhydrophobicity with apparent advancing contact angles ≈160° and contact angle hysteresis as low as ≈20° can be achieved. We exploit the structure length scale and structure geometry-dependent VOC adsorption dynamics to rationally design CuO nanowires with enhanced superhydrophobicity. To gain an understanding of the VOC adsorption physics, we utilized X-ray photoelectron and ion mass spectroscopy to identify the chemical species deposited on our surfaces in two distinct locations: Urbana, IL, United States and Beijing, China. To test the stability of the atmosphere-mediated superhydrophobic surfaces during heterogeneous nucleation, we used high-speed optical microscopy to demonstrate the occurrence of dropwise condensation and stable coalescence-induced droplet jumping. Our work not only provides rational design guidelines for developing passively durable superhydrophobic surfaces with excellent flooding-resistance and self-healing capability but also sheds light on the key role played by the atmosphere in governing wetting.

Influence of Surface Wettability on Discharges from Water Drops in Electric Fields

It is known that electrified droplets deform and may become unstable when the electric field they are exposed to reaches a certain critical value. These instabilities are accompanied by electric discharges due to the local enhancement of the electric field caused by the deformed droplets. Here we report and highlight an interesting aspect of the behavior of unstable water droplets and discharge generation: by implementing wettability engineering, we can manipulate these discharges. We demonstrate that wettability strongly influences the shape of a droplet that is exposed to an electric field. The difference in shape is directly related to differences in the critical value of the applied electric field at which inception of discharge occurs. Using theoretical models, we can predict and sufficiently support our observations. Thus, by tailoring the wettability of the surface, we can control droplet's behavior from expediting the discharge inception to completely restricting it.

Droplet Jumping: Effects of Droplet Size, Surface Structure, Pinning, and Liquid Properties

Coalescence-induced droplet jumping has the potential to enhance the efficiency of a plethora of applications. Although binary droplet jumping is quantitatively understood from energy and hydrodynamic perspectives, multiple aspects that affect jumping behavior, including droplet size mismatch, droplet-surface interaction, and condensate thermophysical properties, remain poorly understood. Here, we develop a visualization technique utilizing microdroplet dispensing to study droplet jumping dynamics on nanostructured superhydrophobic, hierarchical superhydrophobic, and hierarchical biphilic surfaces. We show that on the nanostructured superhydrophobic surface the jumping velocity follows inertial-capillary scaling with a dimensionless velocity of 0.26 and a jumping direction perpendicular to the substrate. A droplet mismatch phase diagram was developed showing that jumping is possible for droplet size mismatch up to 70%. On the hierarchical superhydrophobic surface, jumping behavior was dependent on the ratio between the droplet radius R_i and surface structure length scale L. For small droplets ( R_i ≤ 5 L), the jumping velocity was highly scattered, with a deviation of the jumping direction from the substrate normal as high as 80°. Surface structure length scale effects were shown to vanish for large droplets ( R_i > 5 L). On the hierarchical biphilic surface, similar but more significant scattering of the jumping velocity and direction was observed. Droplet-size-dependent surface adhesion and pinning-mediated droplet rotation were responsible for the reduced jumping velocity and scattered jumping direction. Furthermore, droplet jumping studies of liquids with surface tensions as low as 38 mN/m were performed, further confirming the validity of inertial-capillary scaling for varying condensate fluids. Our work not only demonstrates a powerful platform to study droplet-droplet and droplet-surface interactions but provides insights into the role of fluid-substrate coupling as well as condensate properties during droplet jumping.

Droplet-Based Microfluidic Thermal Management Methods for High Performance Electronic Devices

Advanced thermal management methods have been the key issues for the rapid development of the electronic industry following Moore’s law. Droplet-based microfluidic cooling technologies are considered as promising solutions to conquer the major challenges of high heat flux removal and nonuniform temperature distribution in confined spaces for high performance electronic devices. In this paper, we review the state-of-the-art droplet-based microfluidic cooling methods in the literature, including the basic theory of electrocapillarity, cooling applications of continuous electrowetting (CEW), electrowetting (EW) and electrowetting-on-dielectric (EWOD), and jumping droplet microfluidic liquid handling methods. The droplet-based microfluidic cooling methods have shown an attractive capability of microscale liquid manipulation and a relatively high heat flux removal for hot spots. Recommendations are made for further research to develop advanced liquid coolant materials and the optimization of system operation parameters.

Coalescence-induced jumping of droplets on superomniphobic surfaces with macrotexture

When two liquid droplets coalesce on a superrepellent surface, the excess surface energy is partly converted to upward kinetic energy, and the coalesced droplet jumps away from the surface. However, the efficiency of this energy conversion is very low. In this work, we used a simple and passive technique consisting of superomniphobic surfaces with a macrotexture (comparable to the droplet size) to experimentally demonstrate coalescence-induced jumping with an energy conversion efficiency of 18.8% (i.e., about 570% increase compared to superomniphobic surfaces without a macrotexture). The higher energy conversion efficiency arises primarily from the effective redirection of in-plane velocity vectors to out-of-plane velocity vectors by the macrotexture. Using this higher energy conversion efficiency, we demonstrated coalescence-induced jumping of droplets with low surface tension (26.6 mN m-1) and very high viscosity (220 mPa·s). These results constitute the first-ever demonstration of coalescence-induced jumping of droplets at Ohnesorge number >1.

Condensation Heat-Transfer Performance of Thermally Stable Superhydrophobic Cerium-Oxide Surfaces

We introduce a thin (<200 nm) superhydrophobic cerium-oxide surface formed by a one-step wet chemical process to enhance the condensation heat-transfer performance with improved thermal stability compared to silane-treated surfaces. The developed cerium-oxide surface showed a superhydrophobic characteristic with a low (<5°) contact angle hysteresis because of the unique surface morphology and hydrophobicity of cerium oxide. The surface was successfully incorporated to popular engineering materials including copper, aluminum, and steel. Thermal stability of the surfaces was investigated by exposing them to hot (∼100 °C) steam conditions for 12 h. The introduced ceria surfaces could maintain active dropwise condensation after the thermal stability test, whereas silane-treated surfaces completely lost their hydrophobicity. The heat-transfer coefficient was calculated using the thermal network model incorporating the droplet size distribution and morphology obtained from the microscopic measurement. The analysis shows that the suggested cerium-oxide surfaces can provide approximately 2 times and 5 times higher heat-transfer coefficient before and after the thermal stability test, respectively, mainly because of the decrease in the thermal conduction resistance across droplets. The results indicate that the introduced nanostructured cerium-oxide surface is a promising condenser coating to enhance the droplet mobility and the resulting condensation heat-transfer performance for various thermal and environmental applications, especially those being exposed to hot steam conditions.

A review on wetting and water condensation - Perspectives for CO2 condensation

Liquefaction of vapor is a necessary, but energy intensive step in several important process industries. This review identifies possible materials and surface structures for promoting dropwise condensation, known to increase efficiency of condensation heat transfer. Research on superhydrophobic and superomniphobic surfaces promoting dropwise condensation constitutes the basis of the review. In extension of this, knowledge is extrapolated to condensation of CO₂. Global emissions of CO₂ need to be minimized in order to reduce global warming, and liquefaction of CO₂ is a necessary step in some carbon capture, transport and storage (CCS) technologies. The review is divided into three main parts: 1) An overview of recent research on superhydrophobicity and promotion of dropwise condensation of water, 2) An overview of recent research on superomniphobicity and dropwise condensation of low surface tension substances, and 3) Suggested materials and surface structures for dropwise CO₂ condensation based on the two first parts.

Breath Figures under Electrowetting: Electrically Controlled Evolution of Drop Condensation Patterns

We show that electrowetting (EW) with structured electrodes significantly modifies the distribution of drops condensing onto flat hydrophobic surfaces by aligning the drops and by enhancing coalescence. Numerical calculations demonstrate that drop alignment and coalescence are governed by the drop-size-dependent electrostatic energy landscape that is imposed by the electrode pattern and the applied voltage. Such EW-controlled migration and coalescence of condensate drops significantly alter the statistical characteristics of the ensemble of droplets. The evolution of the drop size distribution displays self-similar characteristics that significantly deviate from classical breath figures on homogeneous surfaces once the electrically induced coalescence cascades set in beyond a certain critical drop size. The resulting reduced surface coverage, coupled with earlier drop shedding under EW, enhances the net heat transfer.

Facile Fabrication of Durable Copper-Based Superhydrophobic Surfaces via Electrodeposition

Superhydrophobic surfaces have myriad industrial applications, yet their practical utilization has been limited by their poor mechanical durability and longevity. We present a low-cost, facile process to develop superhydrophobic copper-based coatings via an electrodeposition route, that addresses this limitation. Through electrodeposition, a stable, multiscale, cauliflower shaped fractal morphology was obtained and upon modification by stearic acid, the prepared coatings show extreme water repellency with contact angle of 162 ± 2° and roll-off angle of about 3°. Systematic studies are presented on coatings fabricated under different processing conditions to demonstrate good durability, mechanical and underwater stability, corrosion resistance, and self-cleaning effect. The study also presents an approach for rejuvenation of slippery superhydrophobic nature (roll-off angle <10°) on the surfaces after long-term water immersion. The presented process can be scaled to larger, durable coatings with controllable wettability for diverse applications.