Coalescence-Induced Self-Propulsion of Droplets on Superomniphobic Surfaces

Damping the jump of coalescing droplets through substrate compliance

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

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

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

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.

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%.

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

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

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.

High-Efficiency Directional Ejection of Coalesced Drops on a Circular Groove

Coalescence-induced drop jumping has received significant attention in the past decade. However, its application remains challenging as a result of the low energy conversion efficiency and uncontrollable drop jumping direction. In this work, we report the high-efficiency coalescence-induced drop jumping with tunable jumping direction via rationally designed millimeter-sized circular grooves. By increasing the surface-droplet impact site area and restricting the oscillatory deformation, the energy conversion efficiency of the jumping droplet reaches 43.5%, 600% as high as the conventional superhydrophobic surfaces. The droplet jumping direction can be tuned from 90° to 60° by varying the principal curvature of the circular groove, while the energy conversion efficiency remains unchanged. We show through theoretical analysis and numerical simulations that the directional jumping mainly originates from reallocation of droplet momentum enabled by the asymmetric liquid bridge impact. Our study demonstrates a simple yet effective method for fast, efficient, and directional droplet removal, which warrants promising applications in jumping droplet condensation, water harvesting, anti-icing, and self-cleaning.

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.

Investigation of Coalescence-Induced Droplet Jumping on Mixed-Wettability Superhydrophobic Surfaces

Coalescence-induced droplet jumping has received more attention recently, because of its potential applications in condensation heat transfer enhancement, anti-icing and self-cleaning, etc. In this paper, the molecular dynamics simulation method is applied to study the coalescence-induced jumping of two nanodroplets with equal size on the surfaces of periodic strip-like wettability patterns. The results show that the strip width, contact angle and relative position of the center of two droplets are all related to the jumping velocity, and the jumping velocity on the mixed-wettability superhydrophobic surfaces can exceed the one on the perfect surface with a 180° contact angle on appropriately designed surfaces. Moreover, the larger both the strip width and the difference of wettability are, the higher the jumping velocity is, and when the width of the hydrophilic strip is fixed, the jumping velocity becomes larger with the increase of the width of the hydrophobic strip, which is contrary to the trend of fixing the width of the hydrophobic strip and altering the other strip width.

Ultimate jumping of coalesced droplets on superhydrophobic surfaces

HYPOTHESIS

Jumping of coalesced droplets on superhydrophobic surfaces (SHSs) is widely used for enhanced condensation, anti-icing/frosting, and self-cleaning due to its superior droplet transport capability. However, because only a tiny fraction (about 5%) of the released excess surface energy during coalescence can be transformed into jumping kinetic energy, the jumping is very weak, limiting its application.

METHODS

We experimentally propose enhanced jumping methods, use machine learning to design structures that achieve ultimate jumping, and finally combine experiments and simulations to investigate the mechanism of the enhanced jumping.

FINDING

We find that a more orderly flow inside the droplets through the structure is the key to improve energy transfer efficiency and that the egg tray-like structure enables the droplet to jump with an energy transfer efficiency 10.6 times higher than that of jumping on flat surfaces. This energy transfer efficiency is very close to the theoretical limit, i.e., almost all the released excess surface energy is transformed into jumping kinetic energy after overcoming viscous dissipation. The ultimate jumping enhances the application of water droplet jumping and enables other low surface energy fluid such as R22, R134a, Gasoline, and Ethanol, which cannot jump on a flat surface, to jump.

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.

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.

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.

The Effect of the Initial State of the Droplet Group on the Energy Conversion Efficiency of Self-Propelled Jumping

The essential characteristic of the self-propelled jumping droplet is the jumping velocity, which determines its application value in heat transfer enhancement, antifrosting, self-cleaning, and so on. The jumping velocity is directly related to the energy conversion efficiency (i.e., the ratio of jumping kinetic energy surface energy released by coalescence to surface energy released by coalescence) and it is affected by the initial state of droplets but there is no unified theory to describe the relationship between the initial state of droplets and the energy conversion efficiency. In this paper, the projection of the initial chemical potential and the final chemical potential difference of droplets in the direction of jumping is defined as jumping potential by theoretical analysis of the chemical potential evolution. The effects of droplet number, distribution, and radius ratio on energy conversion efficiency can be synthetically characterized by jumping potential. The larger the jumping potential is, the higher the energy conversion efficiency is. Finally, the rationality and universality of the jumping potential are verified by numerical simulations and comparison with previous studies. The jumping potential can explain phenomena that cannot be explained in previous studies and can provide a synthesis critical value of droplet jumping.

Hemocompatibility of Super-Repellent surfaces: Current and Future

Virtually all blood-contacting medical implants and devices initiate immunological events in the form of thrombosis and inflammation. Typically, patients receiving such implants are also given large doses of anticoagulants, which pose a high risk and a high cost to the patient. Thus, the design and development of surfaces with improved hemocompatibility and reduced dependence on anticoagulation treatments is paramount for the success of blood-contacting medical implants and devices. In the past decade, the hemocompatibility of super-repellent surfaces (i.e., surfaces that are extremely repellent to liquids) has been extensively investigated because such surfaces greatly reduce the blood-material contact area, which in turn reduces the area available for protein adsorption and blood cell or platelet adhesion, thereby offering the potential for improved hemocompatibility. In this review, we critically examine the progress made in characterizing the hemocompatibility of super-repellent surfaces, identify the unresolved challenges and highlight the opportunities for future research on developing medical implants and devices with super-repellent surfaces.

Superomniphobic Surfaces with Improved Mechanical Durability: Synergy of Hierarchical Texture and Mechanical Interlocking

Due to their unique functionality, superomniphobic surfaces that display extreme repellency toward virtually any liquid, have a wide range of potential applications. However, to date, the mechanical durability of superomniphobic surfaces remains a major obstacle that prevents their practical deployment. In this work, a two-layer design strategy was developed to fabricate superomniphobic surfaces with improved durability via synergistic effect of interconnected hierarchical porous texture and micro/nano-mechanical interlocking. The improved mechanical robustness of these surfaces was assessed through water shear test, ultrasonic washing test, blade scratching test, and Taber abrasion test.

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.

Coalescence-induced jumping of droplets on superomniphobic surfaces with macrotexture

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

Enhancement of Coalescence-Induced Nanodroplet Jumping on Superhydrophobic Surfaces

Coalescence-induced droplet self-jumping on superhydrophobic surfaces has received extensive attentions over the past decade because of its potential applications ranging from anti-icing materials to self-sustained condensers, in which a higher jumping velocity v_j is always expected and favorable. However, the previous studies have shown that there is a velocity limit with v_j ≤ 0.23 u_ic for microscale droplets and v_j ≤ 0.127 u_ic for nanoscale droplets, where u_ic is referred to as the inertial-capillary velocity. Here, we show that the jumping velocity can be significantly increased by patterning a single groove, ridge, or more hydrophobic strip, whose size is comparable with the radius of coalescing droplets, on a superhydrophobic surface. We implement molecular dynamics simulations to investigate the coalescence of two equally sized nanodroplets (8.0 nm in radius) on these surfaces. We found that a maximum v_j = 0.23 u_ic is achieved on the surface with a 1.6 nm high and 5.9 nm wide ridge, which is 1.81 times higher than the nanoscale velocity limit. We also demonstrate that the presence of groove, ridge, and strip alters coalescence dynamics of droplets, leading to a significantly shortened coalescence time which remarkably reduces viscous dissipation during coalescence; thus, we believe that the present approach is also effective for microscale droplet jumping.