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

Fundamental Limits of the Spatial Control of Heterogeneous Nucleation on Biphilic Surfaces

Condensation of water vapor on nonwetting surfaces, termed dropwise condensation, leads to rapid droplet removal and significantly improves heat transfer compared to wetting surfaces. However, the spatial distribution of heterogeneous nucleation sites during dropwise condensation is random. Furthermore, the low surface energy of the nonwetting substrate reduces the nucleation rate as predicted by classical nucleation theory. To achieve higher nucleation rates, biphilic surfaces having low nucleation energy barriers that rely on spatial heterogeneity of surface chemistry have been developed. Here, we use a robust method to create biphilic surfaces on flat and micropillar samples having various dimensions (pillar lengths: 10-15 μm, pillar heights: 0-15 μm) by utilizing lift-off microfabrication. Our fabrication approach leads to hydrophilic pillar tops and hydrophobic pillar sides and surrounding basal areas. To study water vapor condensation on the biphilic surfaces, we utilized optical microscopy in a controlled temperature and humidity environment. Interestingly, our studies show that while the majority of nucleation (≈100%) occurred only on the hydrophilic areas (pillar tops) for small pillar center-to-center spacing (pitch), the spatial control of heterogeneous nucleation broke down when the pitch increased. For larger pitches, we observed the nucleation of water droplets on the hydrophobic base in conjunction with hydrophilic pillar tops. Using theoretical models of vapor diffusion coupled with heat transfer and three-dimensional (3D) numerical simulations, we show that nucleation initiation on hydrophilic pillar tops leads to the formation of dry zones, preventing nucleation on hydrophobic regions. However, with increasing pitch, part of the hydrophobic region no longer feels the presence of the vapor depletion zone, resulting in subsequent nucleation at defect sites on the hydrophobic regions at the base. Our study offers insights into the fundamental limitations of biphilic condensation and offers avenues for their further improvement for applications such as boiling, icing, evaporation, and condensation.

Hierarchical Structure with Microcrater Covered with Nanograss Enhancing Condensation and Its Antifrosting/Anti-Icing Performance Inspired by Euphorbia helioscopia L

Over an extended period of evolution and natural selection, a multitude of species developed a diverse array of biological interface features with specific functions. These biological structures provide a rich source of inspiration for the design of bionic structures on superhydrophobic surfaces. Understanding the functional mechanism of plant leaves is of paramount importance for the advancement of new engineering materials and the further promotion of engineering applications of bionic research. The hierarchical structure of microcrater-covered nanograss (MCNG) on the surface of E. helioscopia L. leaf provided the inspiration for the bionic MCNG surface, which was successfully prepared on a copper substrate by hybrid laser micromachining technology and chemical etching. The combined action of texture structure and surface chemistry resulted in a contact angle of 169° ± 1° for MCNG surface droplets and a rolling angle of less than 1°. Notably, the condensation-induced adhesion force does not augment with the increase of the temperature difference, which facilitated the shedding of hot droplets from the surface. The microscope observation revealed a high density of condensed droplets on the MCNG surface and the tangible jumping behavior of the droplets. The fabricated MCNG also demonstrated excellent antifrost/anti-icing abilities in low-temperature and high-humidity environments. Finally, the study confirmed the exceptional mechanical durability and reusability of the MCNG surface through various tests, including scratch damage, sandpaper wear, water flow impact and flushing, and condensation-drying cycle tests. The nanograss can be effectively protected within the microcrater structure. This research presents a promising approach for preventing and/or removing unwanted droplets in numerous engineering applications.

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.

Coalescence-Induced Self-Propelled Particle Transport with Asymmetry Arrangement

We experimentally investigated the coalescence-induced droplet-particle jumping phenomenon on a submillimeter scale in symmetric and asymmetric particle arrangements with poly(methyl methacrylate) (PMMA) particles and stainless steel (SS) particles. Coalescence-induced droplet-particle jumping exhibited excellent capability and interesting behavior for both droplet jumping enhancement and particle transport. The particle increased the normalized droplet jumping velocity from 0.250 for no particle case to 0.315 and 0.320 for symmetric and asymmetric particle cases. Compared with similar-sized macrostructures fixed between droplets, better jumping performance with particles may be attributed to avoiding the work of adhesion during droplet-macrostructure separation. Besides, all particles always sunk at the bottom in the symmetric cases, while the stick mode for PMMA particles and sink, wander, and jet modes for SS particles appeared in the asymmetry cases. We revealed that the asymmetric particle arrangement induces an unbalanced surface tension force, which may provide a driving force in the vertical direction. Additionally, a small enough resistive force caused by hydrophobic particles is another necessary condition for the wonder and jet mode. Finally, we realized a significantly superior particle transport in the asymmetric SS particle cases with maximum particle height reaching ∼2.1 mm, ∼12.4 times the particle radius, the most significant vertical self-propelled transport distance currently.

Emergent Collective Motion of Self-Propelled Condensate Droplets

Recently, there is much interest in droplet condensation on soft or liquid or liquidlike substrates. Droplets can deform soft and liquid interfaces resulting in a wealth of phenomena not observed on hard, solid surfaces (e.g., increased nucleation, interdroplet attraction). Here, we describe a unique collective motion of condensate water droplets that emerges spontaneously when a solid substrate is covered with a thin oil film. Droplets move first in a serpentine, self-avoiding fashion before transitioning to circular motions. We show that this self-propulsion (with speeds in the 0.1-1  mm s^{-1} range) is fueled by the interfacial energy release upon merging with newly condensed but much smaller droplets. The resultant collective motion spans multiple length scales from submillimeter to several centimeters, with potentially important heat-transfer and water-harvesting applications.

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.

Exploration of Sweeping Effect: Droplet Coalescence Jumping of a Rolling and Static Droplet

The sweeping effect of merged droplets plays a key role in enhancing application performance due to the continuing coalescence caused by the horizontal jumping velocity. Most studies focused on static droplet coalescence jumping, while moving droplet coalescence is poorly understood. In this work, we experimentally and numerically study the coalescence of a rolling droplet and a static one. When the droplet radius ratio is larger than 0.8, as the dimensionless initial velocity increases and the vertical jumping velocity first decreases and then increases. The critical dimensionless initial velocity Vc* corresponding to the minimum vertical jumping velocity could be estimated as 0.9 ( r s 2 r m 2 ) . When the droplet radius ratio is smaller than 0.8, the dimensionless initial velocity has a positive effect on the vertical jumping velocity. The mechanism of the vertical jumping velocity can be attributed to two parts: liquid bridge impact and retraction of the merged droplet. The squeezing effect generated by the initial velocity between the two droplets promotes the growth of the liquid bridge and enhances the impact effect of the liquid bridge but weakens the upward velocity accumulation caused by the retraction of the merged droplets. However, different from the vertical jumping velocity, the horizontal jumping velocity is approximately proportional to the dimensionless initial velocity. The outcome of our work elucidates a fundamental understanding of a rolling droplet coalescing with a static one.

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.

Investigation of factors enhancing droplets spreading on leaves with burrs

Introduction

Spread effect is one of the aspects on deposition quality evaluation of pesticide droplets. It could be affected by many factors such as the microstructure of the target plant leaf surface, physical features of the droplets, and the concentration of spray additives.

Methods

In this study, using a high-speed photography system, 2.3% glyphosate ammonium salt solution with different concentration of the additive was applied to investigate the impact process of single droplet deposition on the plant leaf surface with burrs. Effect of droplet sizes and velocities on spreading area and dynamic deposition procedure was analyzed using image processing programs.

Results

The diffusion factor in the process of droplet spreading was changed over time. The occurrence of bubbles in the droplets was observed in the results. With the bubble generation, the droplet diameter expands and a better diffusion effect is obtained. As a result, better spreading effect was obtained as the droplet diameter was expanded with the generation of bubbles. The significant effects of each physical property of droplets on droplet spreading and the interaction effects between the influencing factors were analyzed. A significant correlation was found between additive concentration, droplet impact velocity, droplet diameters and droplet spreading area. All interactions of concentration:velocity, concentration:diameter, velocity:diameter, and concentration:velocity:diameter had a significant effect on the spreading area of droplets. The study of the factors influencing the process of pesticide droplet impact on the leaf surface contributes to the efficient use of pesticides. Thus, the consumption of pesticides and the resulting impact on the environment can be reduced.

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.

Not All Sizes of Dust can be Removed by Jumping Condensates on Superhydrophobic Surfaces

It is well known that superhydrophobic surfaces (SHSs) possess self-cleaning ability, either by impacting or rolling water droplets or by self-propelled jumping condensate. However, contaminants that are present in the air are various. Is it possible that these contaminants can all be removed from SHSs by jumping condensate? In this study, hydrophilic SiO₂ micro- or nanoparticles with diameters larger than, comparable to, and smaller than the width of the nanogaps of the SHS were first filled in the nanogaps or suspended on the nanostructures with the help of ethanol, and the resulting SHS was exposed to condensing water vapor. Direct observation through microscopy showed that jumping condensation was still obvious on the SHS that were capped or filled with micro- or nanoparticles. Scanning electron microscopy (SEM) imaging demonstrated that following jumping condensation, particles that possessed diameters significantly smaller or larger than the width of the nanogaps were both removed from the SHS. However, most particles possessing diameters comparable to the width of the nanogaps remained on the SHS. This confirms for the first time that not all contaminants or dust can be removed from an SHS by self-propelled jumping condensate. Furthermore, the study also simply demonstrates that vapor condensation occurs within the nanogaps of the SHS. This study is helpful in further understanding the mechanism of the self-cleaning caused by jumping condensate and exploring the initial formation of condensate droplets on the SHS.

Out-of-Plane Biphilic Surface Structuring for Enhanced Capillary-Driven Dropwise Condensation

Rapid and sustained condensate droplet departure from a surface is key toward achieving high heat-transfer rates in condensation, a physical process critical to a broad range of industrial and societal applications. Despite the progress in enhancing condensation heat transfer through inducing its dropwise mode with hydrophobic materials, sophisticated surface engineering methods that can lead to further enhancement of heat transfer are still highly desirable. Here, by employing a three-dimensional, multiphase computational approach, we present an effective out-of-plane biphilic surface topography, which reveals an unexplored capillarity-driven departure mechanism of condensate droplets. This texture consists of biphilic diverging microcavities wherein a matrix of small hydrophilic spots is placed at their bottom, that is, among the pyramid-shaped, superhydrophobic microtextures forming the cavities. We show that an optimal combination of the hydrophilic spots and the angles of the pyramidal structures can achieve high deformational stretching of the droplets, eventually realizing an impressive "slingshot-like" droplet ejection process from the texture. Such a droplet departure mechanism has the potential to reduce the droplet ejection volume and thus enhance the overall condensation efficiency, compared to coalescence-initiated droplet jumping from other state-of-the-art surfaces. Simulations have shown that optimal pyramid-shaped biphilic microstructures can provoke droplet self-ejection at low volumes, up to 56% lower than superhydrophobic straight pillars, revealing a promising new surface microtexture design strategy toward enhancing the condensation heat-transfer efficiency and water harvesting capabilities.

Numerical Investigation on Coalescence-Induced Jumping of Centripetal Moving Droplets

Coalescence-induced droplet jumping could promote self-removal of droplets, which has broad potential in related fields such as heat-transfer enhancement, self-cleaning, energy harvesting, electricity generation, radiative cooling, and antifrosting/icing. In practical applications, droplets often have initial velocity under external forces. In this work, the coalescence-induced jumping of centripetal moving droplets on a superhydrophobic plane is experimentally observed using a high-speed photography platform, and the effects of the initial velocity of the moving droplet on jumping velocity, energy conversion, and droplet morphology are numerically investigated. Results show that the jumping velocity decreases and then increases as the We number of the moving droplet increases. The main source of the total kinetic energy of the coalesced droplet switches from the released surface energy to the initial kinetic energy of the moving droplet with the increasing We number, but the proportion of the jumping kinetic energy to the total kinetic energy decreases. Besides, the initial velocity of the moving droplet intensifies the droplet deformation and accelerates the process of coalescence-induced jumping. Through theoretical analysis, it is found that the jumping velocity is affected by two mechanisms: the deformation intensification and the liquid bridge impact enhancement.

Fabrication of Metallic Superhydrophobic Surfaces with Tunable Condensate Self-Removal Capability and Excellent Anti-Frosting Performance

Laser fabrication of metallic superhydrophobic surfaces (SHSs) for anti-frosting has recently attracted considerable attention. Effective anti-frosting SHSs require the efficient removal of condensed microdroplets through self-propelled droplet jumping, which is strongly influenced by the surface morphology. However, detailed analyses of the condensate self-removal capability of laser-structured surfaces are limited, and guidelines for laser processing parameter control for fabricating rationally structured SHSs for anti-frosting have not yet been established. Herein, a series of nanostructured copper-zinc alloy SHSs are facilely constructed through ultrafast laser processing. The surface morphology can be properly tuned by adjusting the laser processing parameters. The relationship between the surface morphologies and condensate self-removal capability is investigated, and a guideline for laser processing parameterization for fabricating optimal anti-frosting SHSs is established. After 120 min of the frosting test, the optimized surface exhibits less than 70% frost coverage because the remarkably enhanced condensate self-removal capability reduces the water accumulation amount and frost propagation speed (<1 μm/s). Additionally, the material adaptability of the proposed technique is validated by extending this methodology to other metals and metal alloys. This study provides valuable and instructive insights into the design and optimization of metallic anti-frosting SHSs by ultrafast laser processing.

Coalescence-Induced Bubble Departure: Effects of Dynamic Contact Angles

Coalescence-induced bubble departure is a common phenomenon in boiling and gas evolution reactions, which has significant impacts on the heat/mass transport. In this work, we systematically investigate the effects of dynamic contact angles on the coalescence and departure processes of two equal-sized bubbles. A critical contact angle (θ_cr) of 76° is determined for an ideal surface on the basis of a surface energy analysis, beyond which the coalesced bubble does not depart from the wall. Using 3D multi-relaxation-time (MRT) lattice Boltzmann simulations, we demonstrate that the advancing contact angle mainly governs the movement of the outer side of the contact lines, and the increase of the advancing contact angle may delay or even prevent the departure of the coalesced bubble. On the other hand, the receding contact angle dominates the motion of the inner side of the contact lines, and the decrease of the receding contact angle facilitates the departure of the coalesced bubble. We identify a regime map for the coalescence-induced bubble departure with respect to the contact angles, which includes four regions: the all-departure region, the advancing contact angle dominated region, the receding contact angle dominated region, and the nondeparture region. Numerically simulated critical contact angles that separate the above-mentioned regions agree well with theoretical analyses. The results of this study will contribute to the manipulation of bubble behaviors and the optimal design of working surfaces in a variety of energy systems involving boiling and gas-evolving reaction processes.

Particulate-Droplet Coalescence and Self-Transport on Superhydrophobic Surfaces

Particulate transport from surfaces governs a variety of phenomena including fungal spore dispersal, bioaerosol transmission, and self-cleaning. Here, we report a previously unidentified mechanism governing passive particulate removal from superhydrophobic surfaces, where a particle coalescing with a water droplet (∼10 to ∼100 μm) spontaneously launches. Compared to previously discovered coalescence-induced binary droplet jumping, the reported mechanism represents a more general capillary-inertial dominated transport mode coupled with particle/droplet properties and is typically mediated by rotation in addition to translation. Through wetting and momentum analyses, we show that transport physics depends on particle/droplet density, size, and wettability. The observed mechanism presents a simple and passive pathway to achieve self-cleaning on both artificial as well as biological materials as confirmed here with experiments conducted on butterfly wings, cicada wings, and clover leaves. Our findings provide insights into particle-droplet interaction and spontaneous particulate transport, which may facilitate the development of functional surfaces for medical, optical, thermal, and energy applications.

Coalescence-Induced Droplet Jumping on Honeycomb Bionic Superhydrophobic Surfaces

Condensation-induced jumping of droplets on superhydrophobic surfaces has received extensive attention because of its great potential for applications in areas such as condensation enhancement and self-cleaning. However, the jumping efficiency of droplets on flat superhydrophobic surfaces is very low, and there is no reliable means of achieving efficient droplet jumping on large scales, which greatly limits its application. To this end, we developed a class of honeycomb bionic superhydrophobic surfaces (HBSS) that enable reliable and efficient droplet jumping on a large scale for the first time and performed experimental and simulation studies on droplet condensation and jumping on this kind of surface. Condensation experiments show that condensate droplets on HBSS can be effectively positioned under the influence of gravity and the uniformity of the droplet diameter is ensured, laying the foundation for achieving efficient jumping. The shape and geometric parameters of HBSS have a significant impact on the droplet jumping efficiency, and the maximum dimensionless jumping velocity of droplet jumping was experimentally measured to be 0.747, corresponding to an efficiency of about 45.25%. Combining with the results of simulation calculations, we found that the surface structure of HBSS can promote more of the excess surface energy to net upward kinetic energy along an extremely efficient and simple pathway (direct conversion), thus achieving an energy conversion efficiency of over 45%.

Microscale Confinement and Wetting Contrast Enable Enhanced and Tunable Condensation

Dropwise condensation represents the upper limit of thermal transport efficiency for liquid-to-vapor phase transition. A century of research has focused on promoting dropwise condensation by attempting to overcome limitations associated with thermal resistance and poor surface-modifier durability. Here, we show that condensation in a microscale gap formed by surfaces having a wetting contrast can overcome these limitations. Spontaneous out-of-plane condensate transfer between the contrasting parallel surfaces decouples the nanoscale nucleation behavior, droplet growth dynamics, and shedding processes to enable minimization of thermal resistance and elimination of surface modification. Experiments on pure steam combined with theoretical analysis and numerical simulation confirm the breaking of intrinsic limits to classical condensation and demonstrate a gap-dependent heat-transfer coefficient with up to 240% enhancement compared to dropwise condensation. Our study presents a promising mechanism and technology for compact energy and water applications where high, tunable, gravity-independent, and durable phase-change heat transfer is required.

Laplace Pressure Difference Enhances Droplet Coalescence Jumping on Superhydrophobic Structures

Coalescence-induced droplet jumping has great prospects in many applications. Nevertheless, the applications are vastly limited by a low jumping velocity. Conventional methods to enhance the droplet coalescence jumping velocity are enabled by protruding structures with superhydrophobic surfaces. However, the jumping velocity improvement is limited by the height of protruding structures. Here, we present rationally designed limitation structures with superhydrophobic surfaces to achieve a dimensionless jumping velocity, V_j^* ≈ 0.64. The mechanism of enhancing the jumping velocity is demonstrated through the study of numerical simulations and geometric parameters of limitation structures, providing guidelines for optimized structures. Experimental and numerical results indicate that the mechanism consists of the combined action of the velocity vectors' redirection and the Laplace pressure difference within deformed droplets trapped in limitation structures. On the basis of previous research on the mechanisms of protruding structures and our study, we successfully exploited those mechanisms to further improve the jumping velocity by combining the limitation structure with the protruding structure. Experimentally, we attained a dimensionless jumping velocity of V_j^* ≈ 0.74 with an energy conversion efficiency of η ≈ 48%, breaking the jumping velocity limit. This work not only demonstrates a new mechanism for achieving a high jumping velocity and energy conversion efficiency but also sheds lights on the effect of limitation structures on coalescence hydrodynamics and elucidates a method to further enhance the jumping velocity based on protruding structures.

Exploring the Role of Initial Droplet Position in Coalescence-Induced Droplet Jumping: Lattice Boltzmann Simulations

Coalescence-induced droplet jumping on superhydrophobic surfaces with different initial positions was numerically simulated using the 2D multi-relaxation-time (MRT) Lattice Boltzmann method (LBM). Simulation results show that for coalesced droplets with radii close to the structure length scale, the change of initial droplet positions leads to a significant deviation of jumping velocity and direction. By finely tuning the initial droplet positions on a flat-pillared surface, perpendicular jumping, oblique jumping, and non-jumping are successively observed on the same structured surface. Droplet morphologies and vector diagrams at different moments are considered. It is revealed that the asymmetric droplet detachment from the structured surface leads to the directional transport of liquid mass in the droplet and further results in the oblique jumping of the coalesced droplet. In order to eliminate the influence of initial droplet position on droplet jumping probability, a surface with pointed micropillars is designed. It is demonstrated that compared to flat-topped micropillars, a surface with pointed micropillars can suppress the initial droplet position effects and enhance droplet jumping probability. Furthermore, the effect of droplet/structure scale on droplet jumping is investigated. The influence of initial positions on coalescence-induced droplet jumping from the refined surface can be ignored when the droplet scale is larger than three times the structure scale. This study illustrates the role of initial droplet position in coalescence-induced droplet jumping and provides guidelines for the rational design of structured surfaces with enhanced droplet self-shedding for energy and heat transfer applications.

How an Oxide Layer Influences the Impact Dynamics of Galinstan Droplets on a Superhydrophobic Surface

When exposed to air, gallium-based alloys rapidly form a thin oxide layer with viscoelasticity and high adhesion. Although previous work demonstrated that an oxide layer inhibits liquid metal droplet rebound, there is still a lack of a quantitative study to elaborate how an oxide layer affects the impact dynamics. To address this issue, we experimentally investigate Galinstan droplet impingement on a superhydrophobic CuO nanoblade surface and physically explain the difference in the dynamic characteristics of oxidized and unoxidized droplets. Experimental results show that the effect of an oxide layer becomes prominent during the retraction phase. The high adhesion significantly suppresses retraction and rebound, while the elastic response prevents a droplet from sufficiently stretching and maintains the stability of the morphology. More importantly, we systematically and quantitatively explore the influence of an oxide layer on several critical impact parameters, which contributes to a comprehensive understanding of the impact dynamics of liquid metal droplets. It is indicated that an oxide layer has little effect on the maximum spreading factor and spreading time, whereas it causes a 45% reduction of the restitution coefficient and a 36% increase in contact time. Notably, the scaling laws that describe the critical impact parameters of unoxidized droplets show good agreement with the ones known from ordinary Newtonian fluids.

Tunable and Robust Nanostructuring for Multifunctional Metal Additively Manufactured Interfaces

Novel processing phenomena coupled with various alloying materials used in metal additive manufacturing (AM) have opened opportunities for the development of previously unexplored micro-/nanostructures. A rationally devised structure nanofabrication strategy of AM surfaces that can tailor the interface morphology and chemistry has the potential for many applications. Here, through an understanding of grain formation mechanisms during AM, we develop a facile method for tuning micro-/nanostructures of one of the most used AM alloys and rationally optimize the morphology for applications requiring low surface adhesion. We demonstrate that optimized AM structures reduce the adhesion of impaling water droplets and significantly delay icing time. The structure can also be altered and optimized for antiflooding jumping-droplet condensation that exhibits significant enhancement in heat transfer performance in comparison to nanostructures formed on conventional Al alloys. In addition to demonstrating the potential of functionalized AM surfaces, this work also provides guidelines for surface-structuring optimization applicable to other AM metals.

How Coalescing Bubbles Depart from a Wall

Bubble evolution plays a fundamental role in boiling and gas-evolving electrochemical systems. One key stage is bubble departure, which is traditionally considered to be buoyancy-driven. However, conventional understanding cannot provide the full physical picture, especially for departure events with small bubble sizes commonly observed in water splitting and high heat flux boiling experiments. Here, we report a new regime of bubble departure owing to the coalescence of two bubbles, where the departure diameter can be much smaller than the conventional buoyancy limit. We show the significant reduction of the bubble base area due to the dynamics of the three-phase contact line during coalescence, which promotes bubble departure. More importantly, combining buoyancy-driven and coalescence-induced bubble departure modes, we demonstrate a unified relationship between the departure diameter and nucleation site density. By elucidating how coalescing bubbles depart from a wall, our work provides design guidelines for energy systems which can largely benefit from efficient bubble departure.

How Superhydrophobic Grooves Drive Single-Droplet Jumping

Rapid shedding of microdroplets enhances the performance of self-cleaning, anti-icing, water-harvesting, and condensation heat-transfer surfaces. Coalescence-induced droplet jumping represents one of the most efficient microdroplet shedding approaches and is fundamentally limited by weak fluid-substrate dynamics, resulting in a departure velocity smaller than 0.3u, where u is the capillary-inertia-scaled droplet velocity. Laplace pressure-driven single-droplet jumping from rationally designed superhydrophobic grooves has been shown to break conventional capillary-inertia energy transfer paradigms by squeezing and launching single droplets independent of coalescence. However, this interesting droplet shedding mechanism remains poorly understood. Here, we investigate single-droplet jumping from superhydrophobic grooves by examining its dependence upon surface and droplet configurations. Using a volume of fluid (VOF) simulation framework benchmarked with optical visualizations, we verify the Laplace pressure contrast established within the groove-confined droplet that governs single-droplet jumping. An optimal departure velocity of 1.13u is achieved, well beyond what is currently available using condensation on homogeneous or hierarchical superhydrophobic structures. We further develop a jumping/non-jumping regime map in terms of surface wettability and initial droplet volume and demonstrate directional jumping under asymmetric confinement. Our work reveals key fluid-structure interactions required for the tuning of droplet jumping dynamics and guides the design of interfaces and materials for enhanced microdroplet shedding for a plethora of applications.

Life Span of Slippery Lubricant Infused Surfaces

Since their discovery a decade ago, slippery liquid infused porous surfaces (SLIPSs) or lubricant infused surfaces (LISs) have been demonstrated time and again to have immense potential for a plethora of applications. Of these, one of the most promising is enhancing the energy efficiency of both thermoelectric and organic Rankine cycle power generation via enhanced vapor condensation. However, utilization of SLIPSs in the energy sector remains limited due to the poor understanding of their life span. Here, we use controlled conditions to conduct multimonth steam and ethanol condensation tests on ultrascalable nanostructured copper oxide structured surfaces impregnated with mineral and fluorinated lubricants having differing viscosities (9.7 mPa·s < μ < 5216 mPa·s) and chemical structures. Our study demonstrates that SLIPSs lose their hydrophobicity during steam condensation after 1 month due to condensate cloaking. However, these same SLIPSs maintain nonwetting after 5 months of ethanol condensation due to the absence of cloaking. Surfaces impregnated with higher viscosity oil (5216 mPa·s) increase the life span to more than 8 months of continuous ethanol condensation. Vapor shear tests revealed that SLIPSs do not undergo oil depletion during exposure to 10 m/s gas flows, critical to condenser implementation where single-phase superheated vapor impingement is prevalent. Furthermore, higher viscosity SLIPSs are shown to maintain good stability after exposure to 200 °C air. A subset of the durable SLIPSs did not show change in slipperiness after submerging in stagnant water and ethanol for up to 2 weeks, critical to condenser implementation where single-phase condensate immersion is prevalent. Our work not only demonstrates design methods and longevity statistics for slippery nanoengineered surfaces undergoing long-term dropwise condensation of steam and ethanol but also develops the fundamental design guidelines for creating durable slippery liquid infused surfaces.

Effect of Viscosity on Bouncing Dynamics of Elliptical Footprint Drops on Non-Wettable Ridged Surfaces

An initial drop shape can alter the bouncing dynamics and significantly decrease the residence time on superhydrophobic surfaces. Elliptical footprint drops show asymmetric dynamics owing to a pronounced flow driven by the initial drop shape. However, the fundamental understanding of the effect of viscosity on the asymmetric dynamics has yet to be investigated, although viscous liquid drop impact on textured surfaces is of scientific and industrial importance. Here, the current study focuses on the impact of elliptical footprint drops with various liquid properties (density, surface tension, and viscosity), drop sizes, and impact velocities to study the bouncing dynamics and residence time on non-wettable ridged surfaces numerically by using a volume-of-fluid method. The underlying mechanism behind the variation in residence time is interpreted by analyzing the shape evolution, and the results are discussed in terms of the spreading, retraction, and bouncing. This study provides an insight on possible outcomes of viscous drops impinging on non-wettable surfaces and will help to design the desired spraying devices and macro-textured surfaces under different impact conditions, such as icephobic surfaces for freezing rain or viscous liquids.

Superhydrophobic materials used for anti-icing Theory, application, and development

The accumulation of ice will reduce the performance of the base material and lead to all kinds of damage, even a threat to people's life safety. Recent increasing studies suggest that superhydrophobic surfaces (SHSs) originating from nature can remove impacting and condensing droplets from the surface before freezing to subzero temperatures, and it can be seen that hydrophobic/SH coating has good freezing cold resistance. But such anti-icing performances and developments in practical applications are restricted by various factors. In this paper, the mechanism and process of surface icing phenomenon are introduced, as well as how to prevent surface icing on SHS. The development of SH materials in the aspect of anti-icing in recent years is described, and the existing problems in the aspect of anti-icing are analyzed, hoping to provide new research ideas and methods for the research of anti-icing materials.

Fabrication Optimization of Ultra-Scalable Nanostructured Aluminum-Alloy Surfaces

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

Synergistic dispersal of plant pathogen spores by jumping-droplet condensation and wind

Plant pathogens are responsible for the annual yield loss of crops worldwide and pose a significant threat to global food security. A necessary prelude to many plant disease epidemics is the short-range dispersal of spores, which may generate several disease foci within a field. New information is needed on the mechanisms of plant pathogen spread within and among susceptible plants. Here, we show that self-propelled jumping dew droplets, working synergistically with low wind flow, can propel spores of a fungal plant pathogen (wheat leaf rust) beyond the quiescent boundary layer and disperse them onto neighboring leaves downwind. An array of horizontal water-sensitive papers was used to mimic healthy wheat leaves and showed that up to 25 spores/h may be deposited on a single leaf downwind of the infected leaf during a single dew cycle. These findings reveal that a single dew cycle can disperse copious numbers of fungal spores to other wheat plants, even in the absence of rain splash or strong gusts of wind.

Scalable Slippery Omniphobic Covalently Attached Liquid Coatings for Flow Fouling Reduction

Fouling and accretion have negative impacts on a plethora of processes. To mitigate heterogeneous nucleation of a foulant, lowering the surface energy and reducing surface roughness are desired. Here, we develop a multilayer coating to mitigate solution-based heterogeneous fouling for internal flows. The first layer is a sol-gel silicon dioxide (SiO₂) coating, which acts as a corrosion barrier, creates the surface chemistry needed for covalent bonding of the slippery omniphobic covalently attached liquid (SOCAL), and ensures an atomically smooth (<1 nm) interface. The second layer bonded to SiO₂ is SOCAL, which further reduces the nucleation rate due to its low surface energy (<12 mJ/m²). The presence of a consistent sol-gel SiO₂ base coating to bind to the SOCAL enables application to various metallic substrates. The coating is solid, making it more durable when compared to alternative slippery liquid-infused surfaces (LIS) that suffer from lubricant loss. To demonstrate performance and scalability, we apply our coating to the internal walls of aluminum (Al) tubing and test its fouling performance in a flow-fouling setup with single-phase flow of synthetic seawater. The seawater consists of saturated calcium sulfide (CaSO₄), and fouling is characterized in both laminar and turbulent flow regimes (Reynolds numbers 1030 to 9300). Our coating demonstrated a reduction in salt scale fouling by 95% when compared to uncoated Al tubes. Furthermore, we show our coating to withstand turbulent flow conditions, mechanical abrasion loading, and corrosive environments for durations much longer than LIS. Our work demonstrates a coating methodology applicable to a variety of metal substrates and internal passages to achieve antifouling in single-phase flows.

Optimization Strategy to Inhibit Droplets Rebound on Pathogen-Modified Hydrophobic Surfaces

The deposition and retention of pesticide sprays on the surface of hydrophobic plant leaves is a major agricultural challenge, and the deposition of hydrophobic surfaces caused by plant leaf diseases is also a major agricultural problem. Many recent studies have focused on evaluating the effect of adding surfactants to water rather than to pesticide solutions to increase the deposition and retention of spray liquids. Here, we report a strategy to solve the problem of deposition and retention by studying the impact of the behavior of pesticide droplets with added surfactants and performing kinetic analysis on cucumber leaves with powdery mildew. The reduction in the bounce and splash of the pesticide droplets was analyzed by combining the pinning site formed in the retraction stage and the viscous dissipation in the rebound stage. In the practical application of the pesticide spray, we can clearly see that the bounce, splash, and powdery mildew spore ejection decreased when surfactants were added to the pesticide spray that was used on the cucumber leaves, and the adhesion and retention increased. The proposed comprehensive method is helpful for understanding the interactions between pesticide spray droplets and the surface of cucumber leaves with powdery mildew.

Enhancement and Guidance of Coalescence-Induced Jumping of Droplets on Superhydrophobic Surfaces with a U-Groove

Coalescence-induced droplet jumping has received considerable attention owing to its potential to enhance performance in various applications. However, the energy conversion efficiency of droplet coalescence jumping is very low and the jumping direction is uncontrollable, which vastly limits the application of droplet coalescence jumping. In this work, we used superhydrophobic surfaces with a U-groove to experimentally achieve a high dimensionless jumping velocity V_j^* ≈ 0.70, with an energy conversion efficiency η ≈ 43%, about a 900% increase in energy conversion efficiency compared to droplet coalescence jumping on flat superhydrophobic surfaces. Numerical simulation and experimental data indicated that a higher jumping velocity arises from the redirection of in-plane velocity vectors to out-of-plane velocity vectors, which is a joint effect resulting from the redirection of velocity vectors in the coalescence direction and the redirection of velocity vectors of the liquid bridge by limiting maximum deformation of the liquid bridge. Furthermore, the jumping direction of merged droplets could be easily controlled ranging from 17 to 90^° by adjusting the opening direction of the U-groove, with a jumping velocity V_j^* ≥ 0.70. When the opening direction is 60^°, the jumping direction shows a deviation as low as 17^° from the horizontal surface with a jumping velocity V_j^* ≈ 0.73 and corresponding energy conversion efficiency η ≈ 46%. This work not only improves jumping velocity and energy conversion efficiency but also demonstrates the effect of the U-groove on coalescence dynamics and demonstrates a method to further control the droplet jumping direction for enhanced performance in applications.

Unraveling the Interaction of Water-in-Oil Emulsion Droplets via Molecular Simulations and Surface Force Measurements

Water-in-oil emulsions widely exist in various chemical and petroleum engineering processes, and their stabilization and destabilization behaviors have attracted much attention. In this work, molecular dynamic (MD) simulations were conducted on the water-in-oil emulsion droplets with the presence of surface-active components, including a polycyclic aromatic compound (VO-79) and two nonionic surfactants: the PEO₅PPO₁₀PEO₅ triblock copolymer and Brij-93. At the surface of water droplets, films were formed by the adsorbate molecules that redistributed during the approaching of the droplets. The redistribution of PEO₅PPO₁₀PEO₅ was more pronounced than that of Brij-93 and VO-79, which contributed to lower repulsion during coalescence. The interaction forces during droplet coalescence were also measured using atomic force microscopy. Jump-in phenomenon and coalescence were observed for systems with VO-79, Brij-93, and a low concentration of Pluronic P123. The critical force before jump-in was lowest for the low concentration of Pluronic P123, consistent with the MD results. Adhesion was measured when separating water droplets with a high concentration of Pluronic P123. By correlating theoretical simulations and experimental force measurements, this work improves the fundamental understanding on the interaction behaviors of water droplets in an oil medium in the presence of interface-active species and provides atomic-level insights into the stabilization and destabilization mechanisms of water-in-oil emulsion.

Tailoring silicon for dew water harvesting panels

Dew water, mostly ignored until now, can provide clean freshwater resources, just by extracting the atmospheric vapor available in surrounding air. Inspired by silicon-based solar panels, the vapor can be harvested by a concept of water condensing panels. Efficient water harvesting requires not only a considerable yield but also a timely water removal from the surface since the very beginning of condensation to avoid the huge evaporation losses. This translates into strict surface properties, which are difficult to simultaneously realize. Herein, we study various functionalized silicon surfaces, including the so-called Black Silicon, which supports two droplet motion modes-out-of-plane jumping and in-plane sweeping, due to its unique surface morphology, synergistically leading to a pioneering combination of above two required characteristics. According to silicon material's scalability, the proposed silicon-based water panels would benefit from existing infrastructures toward dual functions of energy harvesting in daytime and water harvesting in nighttime.

Atmospheric Corrosion Protection Performance and Mechanism of Superhydrophobic Surface Based on Coalescence-Induced Droplet Self-Jumping Behavior

The coalescence-induced droplet self-jumping behavior on the superhydrophobic surface (SHS) provides a new way to achieve atmospheric corrosion protection. This work controls the droplet self-jumping behavior by regulating the SHS's surface energy and analyzes the relevant mechanism from the energy perspective, revealing the key pathway by which the surface energy impacts the droplet self-jumping behavior. On this basis, the electrochemical impedance spectroscopy testing technique is used to evaluate the effect of the droplet self-jumping behavior on the SHS corrosion protection performance, and the SHS atmospheric corrosion protection mechanism based on the coalescence-induced droplet self-jumping behavior is revealed. This study provides theoretical guidance for the development of SHS-based anticorrosion protection.

Solar anti-icing surface with enhanced condensate self-removing at extreme environmental conditions

The inhibition of condensation freezing under extreme conditions (i.e., ultra-low temperature and high humidity) remains a daunting challenge in the field of anti-icing. As water vapor easily condensates or desublimates and melted water refreezes instantly, these cause significant performance decrease of most anti-icing surfaces at such extreme conditions. Herein, inspired by wheat leaves, an effective condensate self-removing solar anti-icing/frosting surface (CR-SAS) is fabricated using ultrafast pulsed laser deposition technology, which exhibits synergistic effects of enhanced condensate self-removal and efficient solar anti-icing. The superblack CR-SAS displays superior anti-reflection and photothermal conversion performance, benefiting from the light trapping effect in the micro/nano hierarchical structures and the thermoplasmonic effect of the iron oxide nanoparticles. Meanwhile, the CR-SAS displays superhydrophobicity to condensed water, which can be instantly shed off from the surface before freezing through self-propelled droplet jumping, thus leading to a continuously refreshed dry area available for sunlight absorption and photothermal conversion. Under one-sun illumination, the CR-SAS can be maintained ice free even under an ambient environment of -50 °C ultra-low temperature and extremely high humidity (ice supersaturation degree of ∼260). The excellent environmental versatility, mechanical durability, and material adaptability make CR-SAS a promising anti-icing candidate for broad practical applications even in harsh environments.

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.

Droplet Evaporation Dynamics of Low Surface Tension Fluids Using the Steady Method

Droplet evaporation governs many heat- and mass-transfer processes germane in nature and industry. In the past 3 centuries, transient techniques have been developed to characterize the evaporation of sessile droplets. These methods have difficulty in reconciling transient effects induced by the droplet shape and size changes during evaporation. Furthermore, investigation of evaporation of microdroplets residing on wetting substrates, or fluids having low surface tensions (<30 mN/m), is difficult to perform using established approaches. Here, we use the steady method to study the microdroplet evaporation dynamics of low surface tension liquids. We start by employing the steady method to benchmark with water droplets having base radii (20 ≤ R_b ≤ 260 μm), apparent advancing contact angle (45° ≤ θ_a,app ≤ 162°), surface temperature (30 < T_s < 60 °C), and relative humidity (40% < ϕ < 60%). Following validation, evaporation of ethanol (≈22 mN/m), hexane (≈18 mN/m), and dodecane (≈25 mN/m) were studied for 90 ≤ R_b ≤ 400 μm and 10 < T_s < 25 °C. We elucidate the mechanisms governing the observed behavior using heat and mass transport scaling analysis during evaporation, demonstrating our steady technique to be particularly advantageous for microdroplets, where Marangoni and buoyant forces are negligible. Our work not only elucidates the droplet evaporation mechanisms of low surface tension liquids but also demonstrates the steady method as a means to study phase change processes.

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.

Laplace Pressure Driven Single-Droplet Jumping on Structured Surfaces

Droplet transport on, and shedding from, surfaces is ubiquitous in nature and is a key phenomenon governing applications including biofluidics, self-cleaning, anti-icing, water harvesting, and electronics thermal management. Conventional methods to achieve spontaneous droplet shedding enabled by surface-droplet interactions suffer from low droplet transport velocities and energy conversion efficiencies. Here, by spatially confining the growing droplet and enabling relaxation via rationally designed grooves, we achieve single-droplet jumping of micrometer and millimeter droplets with dimensionless jumping velocities v* approaching 0.95, significantly higher than conventional passive approaches such as coalescence-induced droplet jumping (v* ≈ 0.2-0.3). The mechanisms governing single-droplet jumping are elucidated through the study of groove geometry and local pinning, providing guidelines for optimized surface design. We show that rational design of grooves enables flexible control of droplet-jumping velocity, direction, and size via tailoring of local pinning and Laplace pressure differences. We successfully exploit this previously unobserved mechanism as a means for rapid removal of droplets during steam condensation. Our study demonstrates a passive method for fast, efficient, directional, and surface-pinning-tolerant transport and shedding of droplets having micrometer to millimeter length scales.

Evaporation-Crystallization Method to Promote Coalescence-Induced Jumping on Superhydrophobic Surfaces

Biphilic surfaces exhibit outstanding condensation efficiency compared to surfaces having homogeneous wettability. Especially, hydrophilic patterns on a superhydrophobic substrate significantly promote the coalescence-induced jumping of condensed droplets by increasing the nucleation rate of condensation, thus enhancing the condensation efficiency drastically. However, the application of biphilic surfaces in practical industries remains challenging because controlling the size and spacing of the hydrophilic spots on large and complex surfaces is difficult. In this study, we have achieved heterogeneous wettability using the evaporation-crystallization method, which can be applied to various surfaces as required by industries. The crystals generated using the evaporation-crystallization process drastically increased the number density of condensed droplets on a superhydrophobic surface (SHS), so the developed biphilic surface increased the cumulative volume of jumping droplets by up to 63% compared to that on a conventional superhydrophobic surface. Furthermore, the condensation dynamics on the biphilic surface were analyzed with the classical nucleation theory and the Ohnesorge number. The analysis results indicated that the generated hydrophilic crystals can reduce the nucleation energy barrier and decrease the available excessive surface energy of coalesced droplets on the biphilic surface; this implies that the size distribution of the crystals determines the condensation dynamics. In sum, this study not only introduced an effective surface tailoring approach for enhancing condensation but also provided insights into the design of optimum biphilic surfaces for various conditions, creating new opportunities to widen the applicability of biphilic surfaces in practical industries that exploit condensation.

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.

Delayed Frost Growth on Nanoporous Microstructured Surfaces Utilizing Jumping and Sweeping Condensates

Self-propelled jumping of condensate droplets (dew) enables their easy and efficient removal from surfaces and is essential for enhancing the condensation heat transfer coefficient and for delaying the frost growth rate on supercooled surfaces. Here, we report the droplet-jumping phenomenon using nanoporous vertically aligned carbon nanotube (VA-CNT) microstructures grown on smooth silicon substrates and coated with poly-(1H, 1H, 2H, 2H-perfluorodecylacrylate) (pPFDA). We also report droplet-sweeping phenomenon on horizontally mounted surfaces, concluding that the frost surface coverage area and the frost growth rates observed with the droplet-sweeping phenomenon are much lower than those that are observed with the droplet-jumping phenomenon alone. We also investigate the fundamentals of droplet-jumping and the frost growth phenomena using line-shaped, hollow-cylindrical, and cylindrical microstructures, comparing the frost surface coverage area and the ice-bridging times during condensation-frosting, prolonged condensation-frosting, and direct-frosting. We find that the closely spaced thin line-shaped microstructures and hollow-cylindrical microstructures are optimal for frost coverage reduction because of their ability to exhibit droplet-jumping and droplet-sweeping phenomena. We observe that adding nonuniform roughness on top of the microstructures leads to jumping-associated droplet-sweeping on supercooled surfaces. Here, we report the evaporation of an already frozen droplet because of freezing of a supercooled condensate droplet in its close vicinity, enabling the Cassie-Baxter state frost growth and enhancing defrosting efficiency. Finally, we discuss the dynamic defrosting behavior of the pPFDA-coated VA-CNT microstructures, concluding that the small gaps (spacings) between the microstructures not only enable dewetting transitions of droplets but also promote the Cassie-Baxter state frost formation.

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.

Spontaneous dewetting transition of nanodroplets on nanopillared surface

The spontaneous dewetting transition (SDT) of nanoscale droplets on the nanopillared surface is studied by molecular dynamics simulations. Three typical SDT modes, i.e. condensing, merging and coalescing with flying droplets are observed, and the underlying physical mechanism is clearly revealed by the potential energy analysis of droplets. We find that there exists a dimensionless parameter of the relative critical volume of droplet C _cri which completely controls the SDT of nanodroplets. Furthermore, the C _cri remains constant for geometrically similar surfaces, which indicates an intrinsic similarity of nanoscale SDT. The effect of pillar height, diameter and spacing on SDT has also been studied and it is likely to occur on the surface with longer, wider and thicker pillars, as well as pillars with cone-like shape and larger hydrophobicity. These results should be useful for a complete understanding of the nanoscale SDT and shed light on the design of smart superhydrophobic 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.

Precursor-Film-Mediated Thermocapillary Motion of Low-Surface-Tension Microdroplets

In contrast to microdroplet condensation with high contact angles, the one with low contact angles remains unclear. In this study, we investigated dynamics of microdroplet condensation of low-surface-tension liquids on two flat substrate surfaces by using reflection interference confocal microscopy. Spontaneous migration toward relatively larger droplets was first observed for the microdroplets nucleated on the hydrophilic quartz surface. The moving microdroplets showed a contact angle hysteresis of ∼0.5°, which is much lower than the values observed on typical flat substrates and is within the range observed on slippery lubricant-infused porous surfaces. Because the microdroplets on the hydrophobic polydimethylsiloxane surface did not move, we concluded that the ultrathin precursor film is formed only on the hydrophilic surface, which reduces a resistive force to migration. Also, reduced size of droplets promotes the thermocapillary motion, which is induced by a gradient in local temperature inside a small microdroplet arising due to the difference in size of adjacent droplets.

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.