Enhanced Coalescence-Induced Droplet-Jumping on Nanostructured Superhydrophobic Surfaces in the Absence of Microstructures

Single Condensation Droplet Self-Ejection from Divergent Structures with Uniform Wettability

Coalescence-induced condensation droplet jumping has been extensively studied for anti-icing, condensation heat transfer, water harvesting, and self-cleaning. Another phenomenon that is gaining attention for potential enhancements is the self-ejection of individual droplets. However, the mechanism underlying this process remains elusive due to cases in which the abrupt detachment of an interface establishes an initial Laplace pressure difference. In this study, we investigate the self-ejection of individual droplets from uniformly hydrophobic microstructures with divergent geometries. We design, fabricate, and test arrays of truncated, nanostructured, and hydrophobic microcones arranged in a square pattern. High-speed microscopy reveals the dynamics of a single condensation droplet between four cones: after cycles of growth and stopped self-propulsion, the suspended droplet self-ejects without abrupt detachments. Through analytical modeling of the droplet in a conical pore as an approximation, we describe the slow isopressure growth phases and the rapid transients driven by surface energy release once a dynamic configuration is reached. Microcones with uniform wettability, in addition to being easier to fabricate, have the potential to enable the self-ejection of all nucleated droplets with a designed size, promising significant improvements in the aforementioned applications and others.

Nanorough Is Not Slippery Enough: Implications on Shedding and Heat Transfer

Lowering droplet-surface interactions via the implementation of lubricant-infused surfaces (LISs) has received important attention in the past years. LISs offer enhanced droplet mobility with low sliding angles and the recently reported slippery Wenzel state, among others, empowered by the presence of the lubricant infused in between the structures, which eventually minimizes the direct interactions between liquid droplets and LISs. Current strategies to increase heat transfer during condensation phase-change relay on minimizing the thickness of the coating as well as enhancing condensate shedding. While further surface structuring may impose an additional heat transfer resistance, the presence of micro-structures eventually reduces the effective condensate-surface intimate interactions with the consequently decreased adhesion and enhanced shedding performance, which is investigated in this work. This is demonstrated by macroscopic and optical microscopy condensation experimental observations paying special attention at the liquid-lubricant and liquid-solid binary interactions at the droplet-LIS interface, which is further supported by a revisited force balance at the droplet triple contact line. Moreover, the occurrence of a condensation-coalescence-shedding regime is quantified for the first time with droplet growth rates one and two orders of magnitude greater than during condensation-coalescence and direct condensation regimes, respectively. Findings presented here are of great importance for the effective design and implementation of LISs via surface structure endowing accurate droplet mobility and control for applications such as anti-icing, self-cleaning, water harvesting, and/or liquid repellent surfaces as well as for condensation heat transfer.

Interplay of Drop Shedding Mechanisms on High Wettability Contrast Biphilic Stripe-Patterned Surfaces

To improve the rate of DWC, numerous studies have adjusted the distribution of drops through biphilic surface patterning and wettability gradients to control the nucleation and drop shedding rates on the condensing surface, yet the connection between drop shedding mechanisms and surface wettability patterning remains unclear. Moreover, wettability patterning places geometric bounds on the governing forces (i.e., gravity, capillary, and inertia), which drive the droplet shedding mechanisms. Thus, the subsequent influence of droplet distribution along the DWC regions on the shedding mechanisms may not be known a priori. In this study, the area fraction, ADWC, of the DWC and also the DWC region width, LN, were varied between 10 and 50% and 0.5-1.5 mm, respectively, to probe the dominant droplet shedding mechanisms on a high wettability contrast surface (i.e., the contact angle on the DWC was 159 ± 3.4° and the hysteresis 9 ± 3.6°, whereas the FWC was nearly perfectly wetting). Humid air was introduced inside a custom-built chamber with the upright steady-state condensation imaged by both real-time and high-speed imaging techniques. We found that the droplet shedding mechanisms changed with increasing LN where the sliding drop radii are reduced with LN while the jumping drop radii remained unchanged with LN. The maximum drop size for shedding also decreased by 13%, which we attribute to the secondary droplet inertia, which helps gravity overcome the capillary retention force. Lastly, although many studies have probed DWC enhancements via surface wettability patterning, an optimal combination of ADWC and LN provided in this study significantly aids in the improvement of future DWC-based condensers and water collector applications.

Superhydrophobic Surface Designing for Efficient Atmospheric Water Harvesting Aided by Intelligent Computer Vision

Atmospheric water harvesting (AWH) is a possible solution for the current water crisis on the Earth, and the key process of AWH has been widely applied in commercial dehumidifiers. To improve the energy efficiency of the AWH process, applying a superhydrophobic surface to trigger coalescence-induced jumping could be a promising technique that has attracted extensive interest. While most previous studies focused on optimizing the geometric parameters such as nanoscale surface roughness (<1 μm) or microscale structures (10 μm to a few hundred μm range), which might enhance AWH, here, we report a simple and low-cost approach for superhydrophobic surface engineering, through alkaline oxidation of copper. The prepared medium-sized microflower structures (3-5 μm) by our method could fill the gap of the conventional nano- and microstructures, simultaneously act as the preferable nucleation sites and the promoter for the condensed droplet mobility including droplet coalescence and departure, and eventually benefit the entire AWH performances. Moreover, our AWH structure has been optimized with the aid of machine learning computer vision techniques for droplet dynamic analysis on a micrometer scale. Overall, the alkaline surface oxidation and medium-scale microstructures could provide excellent opportunities for superhydrophobic surfaces for future AWH.

Dropwise Condensate Comb for Enhanced Heat Transfer

Dropwise condensation on superhydrophobic surfaces could potentially enhance heat transfer by droplet spontaneous departure via coalescence-induced jumping. However, an uncontrolled droplet size could lead to a significant reduction of heat transfer by condensation, due to large droplets that resulted in a flooding phenomenon on the surface. Here, we introduced a dropwise condensate comb, which consisted of U-shaped protruding hydrophilic stripes and hierarchical micro-nanostructured superhydrophobic background, for a better control of condensation droplet size and departure processes. The dropwise condensate comb with a wettability-contrast surface structure induced droplet removal by flank contact rather than three-phase line contact. We showed that dropwise condensation in this structure could be controlled by designing the width of the superhydrophobic region and height of the protruding hydrophilic stripes. In comparison with a superhydrophobic surface, the average droplet radius was decreased to 12 μm, and the maximum droplet departure radius was decreased to 189 μm by a dropwise condensate comb with 500 μm width of a superhydrophobic region and 258 μm height of a protruding hydrophilic stripe. By controlling the droplet size and departure on hierarchical micro-nanostructured superhydrophobic surfaces, it was experimentally demonstrated that both the heat transfer coefficient and heat flux could be enhanced significantly. Moreover, the dropwise condensate comb showed a maximum heat transfer coefficient of 379 kW m^-2 K^-1 at a low subcooling temperature, which was 85% higher than that of a superhydrophobic surface, and it showed 113% improvement of high heat flux or heat transfer coefficient when it was compared with that of the hierarchical micro-nanostructured superhydrophobic surface at a high subcooling temperature of ∼10.6 K. This work could potentially transform the design and fabrication space for high-performance heat transfer devices by spatial control of condensation droplet size and departure processes.

Preferred Mode of Atmospheric Water Vapor Condensation on Nanoengineered Surfaces: Dropwise or Filmwise?

Condensing atmospheric water vapor on surfaces is a sustainable approach to addressing the potable water crisis. However, despite extensive research, a key question remains: what is the optimal combination of the mode and mechanism of condensation as well as the surface wettability for the best possible water harvesting efficacy? Here, we show how various modes of condensation fare differently in a humid air environment. During condensation from humid air, it is important to note that the thermal resistance across the condensate is nondominant, and the energy transfer is controlled by vapor diffusion across the boundary layer and condensate drainage from the condenser surface. This implies that, unlike condensation from pure steam, filmwise condensation from humid air would exhibit the highest water collection efficiency on superhydrophilic surfaces. To demonstrate this, we measured the condensation rates on different sets of superhydrophilic and superhydrophobic surfaces that were cooled below the dew points using a Peltier cooler. Experiments were performed over a wide range of degrees of subcooling (10-26 °C) and humidity-ratio differences (5-45 g/kg of dry air). Depending upon the thermodynamic parameters, the condensation rate is found to be 57-333% higher on the superhydrophilic surfaces compared to the superhydrophobic ones. The findings of the study dispel ambiguity about the preferred mode of vapor condensation from humid air on wettability-engineered surfaces and lead to the design of efficient atmospheric water harvesting systems.

3D Solar Evaporation Enhancement by Superhydrophilic Copper Foam Inverted Cone and Graphene Oxide Functionalization Synergistic Cooperation

Solar evaporation has become a promising and sustainable technique for harvesting freshwater from seawater and wastewater. However, the applicability and efficacy of solar evaporation need further improvement to achieve high production closer to theoretical limits in compact systems. A 3D (three-dimensional) hierarchical inverted conical solar evaporation is developed, which consists of a 3D copper foam skeleton cone decorated with micro-/nano-structures functionalized with graphene oxide, fabricated via easy and scalable wet oxidation, impregnation, and drying at room temperature. The proposed configuration empowers high-efficiency solar absorption, continuous liquid film spreading and transport, enhanced interfacial local evaporation, and rapid vapor diffusion through the pores. More notably, the 3D conical evaporator realizes thermal localization at the skeleton interface and allows evaporation to occur along the complete structure with unimpeded liquid and vapor rapid diffusion. The solar-thermal evaporation efficiency under 1-Sun is as high as 93% with a maximum evaporation rate per unit area of 1.71 kg·m^-2 ·h^-1 . This work highlights the benefits of synergistic cooperation of an easily scalable 3D hierarchical functiomicro-/nano-structured copper foam skeletons and functionalized graphene oxide for high-efficient solar evaporation of interest to numerous applications.

Binary mixture droplet wetting on micro-structure decorated surfaces

Liquid surface tension as well as solid structure play a paramount role on the intimate wetting and non-wetting regimes and interactions between liquids droplets and solid substrates. We hypothesise that the coupling of these two variables, independently addressed in the past, eventually offer a wider range of understanding to the surface science and interfacial communities. In this work, intrinsically hydrophobic micro-pillared surfaces varying in the spacing between structures, and pure ethanol, pure water and their binary mixtures (as well as acetone-water and ethylene glycol-water mixtures) are utilised, accessing a wide range of substrate solid fractions and liquid surface tensions experimentally. Wettability measurements are carried out at different azimuthal directions to exemplify the wetting/non-wetting behaviour as well as the droplet asymmetry function of both liquid composition and structure spacing. Our findings reveal that high water concentration droplets, i.e., high surface tension fluids, sit in the Cassie-Baxter regime while partial non-wetting Wenzel or mixed-mode regimes with enhanced droplet asymmetry ensuing for medium and high ethanol concentrations, i.e., low surface tension fluids, below certain micropillar spacing. Beyond micropillar spacing s ≥ 40 µm, the impact of the surface structure on the droplet shape is negligible, and droplets adopt a similar contact angle and circular shape as on a flat smooth hydrophobic surface. Wetting and non-wetting regimes are then supported by classical wetting theories and equations. A wetting regime map for a wide range of surface tension fluids and/or their mixtures on a wide domain of solid fractions is then proposed.

Bioinspired self-cleaning surface with microflower-like structures constructed by electrochemically corrosion mediated self-assembly

Developing facile and low-cost methods for the fabrication of bioinspired self-cleaning surfaces is of significant importance but still very challenging. In this work, we present a simple facile and low-cost...

Condensation of Humid Air on Superhydrophobic Surfaces: Effect of Nanocoatings on a Hierarchical Interface

Vapor condensation is a well-known phase-change phenomenon observed in nature as well as in different industrial applications. Superhydrophobic surfaces (SHSs) with low hysteresis can efficiently drain off the condensate and rejuvenate the nucleation sites further. In this work, three distinct SHSs were fabricated by nanocoating three hydrophobic agents, viz., perfluoro-octyl-triethoxy-silane (PFOTS), perfluoro-octanoic-acid (PFOA), and commercial Glaco solution on a hierarchical aluminum surface. The surface morphology of all surfaces was investigated, and its effects on the wetting, droplet departure, and overall heat-transfer coefficient (HTC) during condensation phenomena in the humid air (>95% noncondensable gases) were analyzed. The contact angle hysteresis of all three surfaces was very low (∼5°); however, different wetting behaviors were observed during the condensation, depending on the adhesion of the condensate drop with nanoscale textures in the microcavities. Dropwise condensation (DWC) was observed in silane and Glaco-coated surfaces. A gravity-assisted sweeping mechanism removed the condensate from the silane-coated surface. In contrast, the condensate was ejected out of the plane of the Glaco-coated surface by droplet jumping. The PFOA-coated surface has shown DWC initially and floods in the later stages due to highly pinned condensed droplets. This study reports an enhancement of ∼35 to ∼110% in the HTC for the SHS-exhibiting gravity-assisted sweeping mechanism compared to the droplet-jumping mechanism. The present work will provide substantial insights into the fabrication of efficient hierarchical interfaces for water-energy nexus applications.

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.

Condensation Behavior of Hierarchical Nano/Microstructured Surfaces Inspired by Euphorbia myrsinites

In nature, many extant species exhibit functionalized surface structures during evolution. In particular, wettability affects the functionalization of the surface, and nano/microstructures have been found to enable functions, such as droplet jumping, thereby making self-cleaning, antifog, antibacterial, and antireflection surfaces. Important efforts are underway to understand the surface structure of plant leaves and establish rational design tools for the development of new engineering materials. In this study, we focused on the hierarchical nano/microstructure of the leaves of Euphorbia myrsinites (hereinafter, E. myrsinites), which has a hierarchical shape with microsized papillae, covered with nanosized protruding wax, and observed the condensation behavior on the leaf surface. Si is vertically etched via reactive ion etching (RIE) to artificially mimic the hierarchical nano/microstructures on the leaves of E. myrsinites. We made four types of artificial hierarchical structures, with micropillars having pillar diameters of 5.6 and 16 μm (pillar spacing of 20 and 40 μm, respectively) and heights of 6.5 and 19.5 μm, and nanopillars formed on the surface. The optical observation with a microscope revealed a very high density of condensed droplets on the artificial surface and a stable jumping behavior of droplets of 10 μm or more. Furthermore, in the samples with a micropillar diameter of 5.6 μm and a micropillar height of 19.5 μm, the droplets that had jumped and fallen thereupon bounced off, thereby preventing reattachment. As a result, no droplets of 35 μm or more could exist even after 10 min. In addition, it was clear that a small underlying droplet of less than 10 μm was generated at the bottom of the relatively large secondary droplet existing on the large micropillar of 16 μm, and a frequent coalescence of the droplets occurred. This study revealed the phenomenon of condensation on the surface of plants as well as made it possible to improve the heat exchange process by significantly promoting the heat transfer of condensation using artificial surfaces.

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.

Dropwise Condensation on a Hierarchical Nanopillar Structured Surface

Nanopillar structure processing has been performed on condensation surfaces to control wettability and achieve a high heat transfer coefficient via dropwise condensation and jumping droplets. Modified dry etching was performed using gold (Au) nanoparticles generated by annealing Au as a mask. High-aspect-ratio nanopillar processing was also performed to produce uniform pillar surfaces and novel hierarchical pillar surfaces. A uniform nanopillar surface with pillars having diameters of 20-850 nm and a hierarchical pillar surface with thick pillars having diameters ranging from 100 to 860 nm and thin pillars with diameters ranging from 20 to 40 nm were mixed and fabricated. Condensation experiments were performed using the noncoated nanopillar surfaces, and the condensation behaviors on the silicon (Si) surfaces were observed from above using a microscope and from the side using a high-speed camera. On the uniform surface US-3 and the hierarchical surfaces HS-1 and HS-2, droplet jumps were observed frequently in the droplet size range of 20-50 μm. In contrast, as the droplet size increased to 50 μm or more, the number of jumps observed decreased as the droplet size increased. The frequency of droplet jumps on the hierarchical surfaces from the start of condensation to approximately 2 min was higher than that on the uniform surfaces, although the density of droplet formation on the hierarchical surfaces was not relatively large. On the basis of the observation of droplet behavior from the side surface, we identified that the primary jump was due to the coalescence of droplets adhering to the surface and that the subsequent jump was caused by the droplet coalescence when the jump droplets were reattached. The primary jump occurrence rate was high on all pillar surfaces.

Breaking Droplet Jumping Energy Conversion Limits with Superhydrophobic Microgrooves

Coalescence-induced droplet jumping has the potential to enhance the performance of a variety of applications including condensation heat transfer, surface self-cleaning, anti-icing, and defrosting to name a few. Here, we study droplet jumping on hierarchical microgrooved and nanostructured smooth superhydrophobic surfaces. We show that the confined microgroove structures play a key role in tailoring droplet coalescence hydrodynamics, which in turn affects the droplet jumping velocity and energy conversion efficiency. We observed self-jumping of individual deformed droplets within microgrooves having maximum surface-to-kinetic energy conversion efficiency of 8%. Furthermore, various coalescence-induced jumping modes were observed on the hierarchical microgrooved superhydrophobic surface. The microgroove structure enabled high droplet jumping velocity (≈0.74U) and energy conversion efficiency (≈46%) by enabling the coalescence of deformed droplets in microgrooves with undeformed droplets on adjacent plateaus. The jumping velocity and energy conversion efficiency enhancements are 1.93× and 6.67× higher than traditional coalescence-induced droplet jumping on smooth superhydrophobic surfaces. This work not only demonstrates high droplet jumping velocity and energy conversion efficiency but also demonstrates the key role played by macroscale structures on coalescence hydrodynamics and elucidates a method to further control droplet jumping physics for a plethora of applications.

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.

Self-Enhancement of Coalescence-Induced Droplet Jumping on Superhydrophobic Surfaces with an Asymmetric V-Groove

Coalescence-induced droplet jumping on superhydrophobic surfaces have recently received significant attention owing to their potential in a variety of applications. Previous studies demonstrated that the self-jumping process is inherently inefficient, with an energy conversion efficiency η ≤ 6% and dimensionless jumping velocity V_j* ≤ 0.23. To realize a quick removal of droplets, increasing effort has been devoted to breaking the jumping velocity limit and inducing droplets sweeping. In this work, we used superhydrophobic surfaces with an asymmetric V-groove to experimentally achieve an enhanced coalescence-induced jumping velocity V_j* ≈ 0.61, i.e., more than 700% increase in energy conversion efficiency compared with droplets jumping on flat superhydrophobic surfaces, which is the highest efficiency reported thus far. Moreover, the enhanced jumping direction shows a deviation as high as 60° from the substrate normal. The induced in-plane motion is conducive to remove a considerable number of droplets along the sweeping path and significantly increase the speed of droplet removal. Numerical simulation indicated that the jumping enhancement is a joint effect resulting from the impact of the liquid bridge on the corner of the V-groove and the suppression of droplet expansion by the sidewall of the V-groove. The transient variation of the droplet velocity and the driving force of the coalescing droplets on a surface with and without the asymmetric V-groove were revealed and discussed. Furthermore, effects of groove angle, droplet pair positions, and size mismatches on the jumping velocity and direction have been studied. The novel mechanism of simultaneously increasing the coalescence-induced droplet jumping velocity and changing the jumping direction can be further studied to enhance the efficiency of various applications.

Rationally designed surface microstructural features for enhanced droplet jumping and anti-frosting performance

The accretion of frost on heat exchanging surfaces through the freezing of condensed water in cold and humid environments significantly reduces the operating efficiency of air-source heat pumps, refrigerators and other cryogenic equipment. The construction of hierarchical micro-nanostructured SHSs, with the ability to timely remove condensed water before freezing via self-propelled droplet jumping, serves as a promising anti-frosting strategy. However, the actual relationship between microstructural features and water removal capability through droplet jumping is still not clear, hindering the further optimization of anti-frosting SHSs. Herein, a series of aluminum SHSs with different micro-cone arrays is designed and fabricated via ultrafast laser processing and chemical etching. The effect of microstructural features on water removal capability is elucidated by statistically analyzing the condensation process. As compared to nanostructured SHSs with the micro-cone size ranging from 10 to 40 μm, the water removal through droplet jumping is remarkably enhanced from 3.42 g m-2 to as much as 13.91 g m-2 over 10 minutes of condensation experiments due to the effective transition of condensed microdroplets from the initial high-adhesion partial wetting (PW) state to low-adhesion Cassie state, leading to significantly reduced water accumulation and improved anti-frosting performance. However, a further increase in the micro-cone size decreased the water removal amount due to greater droplet adhesion to the surface, which results in higher chances for immobile coalescence and the formation of large droplets. Herein, by rationally tuning the size scale of the structured micro-cones, the optimal SHSs display the least water accumulation and render excellent frosting delay of over 90 minutes under simulated harsh operating conditions.

Departure Velocity of Rolling Droplet Jumping

Droplet jumping phenomenon widely exists in the fields of self-cleaning, antifrosting, and heat transfer enhancement. Numerous studies have been reported on the static droplet jumping while the rolling droplet jumping still remains unnoticed even though it is very common in practice. Here, we used the volume of fluid (VOF) method to simulate the droplet jumping induced by coalescence of a rolling droplet and a stationary one with corresponding experiments conducted to validate the correctness of the simulation model. The departure velocity of the jumping droplet was the main concerned here. The results show that when the center velocity of the rolling droplet (V₀ = ωR, where ω is the angular velocity of the rolling droplet and R is the droplet radius) is fixed, the vertical departure velocity satisfies a power law which can be expressed as V_z,depar = aR^b. When the droplet radius is fixed, the vertical departure velocity first decreases and then increases if the center velocity exceeds a critical value. Interestingly, the critical center velocity is demonstrated to be approximately 0.76 times the capillary-inertial velocity, corresponding to a constant Weber number of 0.58. Different from the vertical departure velocity, the horizontal departure velocity is basically proportional to the center velocity of the rolling droplet. These results deepen the understanding of the droplet jumping physics, which shall further promote related applications in engineering fields.

Large-scale efficient water harvesting using bioinspired micro-patterned copper oxide nanoneedle surfaces and guided droplet transport

As the Earth's atmosphere contains an abundant amount of water as vapors, a device which can capture a fraction of this water could be a cost-effective and practical way of solving the water crisis. There are many biological surfaces found in nature which display unique wettability due to the presence of hierarchical micro-nanostructures and play a major role in water deposition. Inspired by these biological microstructures, we present a large scale, facile and cost-effective method to fabricate water-harvesting functional surfaces consisting of high-density copper oxide nanoneedles. A controlled chemical oxidation approach on copper surfaces was employed to fabricate nanoneedles with controlled morphology, assisted by bisulfate ion adsorption on the surface. The fabricated surfaces with nanoneedles displayed high wettability and excellent fog harvesting capability. Furthermore, when the fabricated nanoneedles were subjected to hydrophobic coating, these were able to rapidly generate and shed coalesced droplets leading to further increase in fog harvesting efficiency. Overall, ∼99% and ∼150% increase in fog harvesting efficiency was achieved with non-coated and hydrophobic layer coated copper oxide nanoneedle surfaces respectively when compared to the control surfaces. As the transport of the harvested water is very important in any fog collection system, hydrophilic channels inspired by leaf veins were made on the surfaces via a milling technique which allowed an effective and sustainable way to transport the captured water and further enhanced the water collection efficiency by ∼9%. The system presented in this study can provide valuable insights towards the design and fabrication of fog harvesting systems, adaptable to arid or semi-arid environmental conditions.

Numerical Simulation of Jumping Droplet Condensation

Jumping droplet condensation has been shown to enhance heat transfer performance (≈100%) when compared to dropwise condensation by reducing the time-averaged droplet size (≈10 μm) on the condensing surface. Here, we develop a rigorous, three-dimensional numerical simulation of jumping droplet condensation to compute the steady-state time-averaged droplet size distribution. To characterize the criteria for achieving steady state, we use maximum radii (R_max) tracking on the surface, showing that R_max settles to an average in time once steady state is reached. The effects of the minimum jumping radius (0.1-10 μm), maximum jumping radius, apparent advancing contact angle (150-175°), and droplet growth rate were investigated. We provide a numerical fit for the droplet size distribution with an overall correlation coefficient greater than 0.995. The heat transfer performance was evaluated as a function of apparent contact angle and hydrophobic coating thickness, showing excellent agreement with prior experimentally measured values. Our simulations uncovered that droplet size mismatch during coalescence has the potential to impede the achievement of steady state and describe a new flooding mechanism for jumping droplet condensation. Our work not only develops a unified numerical model for jumping droplet condensation that is extendable to a plethora of other conditions but also demonstrates design criteria for nonwetting surface manufacture for enhanced jumping droplet condensation heat transfer.

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.

Dropwise Condensation on Multiscale Bioinspired Metallic Surfaces with Nanofeatures

Nonwetting surfaces engineered from intrinsically hydrophilic metallic materials are promising for self-cleaning, anti-icing, or condensation heat transfer applications where the durability of commonly applied hydrophobic coatings is an issue. In this work, we fabricate and study the wetting behavior and the condensation performance on two metallic nonwetting surfaces with varying number and size of roughness tiers without the need for further hydrophobic coating procedure. On one hand, the surface resembling a rose petal exhibits a sticky nonwetting behavior as drops wet the microscopic roughness features with consequent enhanced drop adhesion, which leads to filmwise condensation. On the other hand, the surface resembling a lotus leaf provides super-repellent nonwetting behavior prompting the continuous nucleation, growth, and departure of spherical drops in a dropwise condensation fashion. On a lotus leaf surface, the third nanoscale roughness tier (created by chemical oxidation) combined with ambience exposure prompts the growth of drops in the Cassie state with the benefit of minimal condensate adhesion. The two different condensation behaviors reported are well supported by a drop surface energy analysis, which accounts for the different wetting performance and the surface structure underneath the condensing drops. Further, we coated the above-mentioned surfaces with polydimethylsiloxane, which resulted in filmwise condensation due to the smoothening of the different roughness tiers. Continuous dropwise condensation on a hierarchical bioinspired lotus leaf metallic surface without the need for a conformal hydrophobic coating is hence demonstrated, which offers a novel path for the design and manufacture of noncoated metallic super-repellent surfaces for condensation phase change applications, among others.

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.

Bio-inspired antifogging PDMS coupled micro-pillared superhydrophobic arrays and SiO2 coatings

In this work, inspired by some typical creatures from nature with superhydrophobic surfaces, a bio-inspired antifogging PDMS is designed and fabricated successfully using UV lithography and a template method. First, we fabricated an SU-8 layer with a bio-inspired micro-pillared array (MPA) using traditional UV lithography. Then, it was used as a template to fabricate a PDMS film (PF). After that, it was chemically modified with SiO2 coatings. It was found that the PF coupled with sprayed SiO2 coatings and a MPA have a higher water contact angle (CA) of 158° and a lower contact angle hysteresis (CAH) of less than 2°. Water drops can be separated from this bio-inspired PDMS surface within 86.8 ms. More importantly, this film's antifogging property is superior, with a recovery time of less than 13 s, which is significantly superior to that of the flat PF and the PF with the MPA. Afterwards, FTIR was applied to analyse the surface chemistry features and suggested that the bio-inspired PF has extremely low surface tension. So, it can be confirmed that an excellent superhydrophobic antifogging property has been achieved on the surface of the PF. Meanwhile, the microscopic and macroscopic dynamic movement behaviour of the fog drops was further observed. Then, the underlying antifogging mechanism was also revealed. These properties mainly benefit from the coupling effect of intermolecular attraction of droplets, chemical compositions (nanometre roughness SiO2) and the physical structures (MPA). The investigations offer a promising way to handily design and fabricate multiscale hierarchical structures on polymers and other materials. More importantly, these findings suggest great potential value for specific antifogging applications in display devices, transport, agricultural greenhouses, food packaging and solar products, especially in continuous harsh fogging conditions.

Hierarchical Superhydrophobic Surfaces with Micropatterned Nanowire Arrays for High-Efficiency Jumping Droplet Condensation

Self-propelled droplet jumping on nanostructured superhydrophobic surfaces is of interest for a variety of industrial applications including self-cleaning, water harvesting, power generation, and thermal management systems. However, the uncontrolled nucleation-induced Wenzel state of condensed droplets at large surface subcooling (high heat flux) leads to the formation of unwanted large pinned droplets, which results in the flooding phenomenon and greatly degrades the heat transfer performance. In this work, we present a novel strategy to manipulate droplet behaviors during the process from the droplet nucleation to growth and departure through a combination of spatially controlling initial nucleation for mobile droplets by closely spaced nanowires and promoting the spontaneous outward movement of droplets for rapid removal using micropatterned nanowire arrays. Through the optical visualization experiments and heat transfer tests, we demonstrate greatly improved condensation heat transfer characteristics on the hierarchical superhydrophobic surface including the higher density of microdroplets, smaller droplet departure radius, 133% wider range of surface subcooling for droplet jumping, and 37% enhancement in critical heat flux for jumping droplet condensation, compared to the-state-of-art jumping droplet condensation on nanostructured superhydrophobic surfaces. The excellent water repellency of such hierarchical superhydrophobic surfaces can be promising for many potential applications, such as anti-icing, antifogging, water desalination, and phase-change heat transfer.