Effect of a Superhydrophobic Surface Structure on Droplet Jumping Velocity

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.

Dynamics of Droplet Coalescence on Hydrophobic Fibers in Oil: Morphology and Liquid Bridge Evolution

Although droplet self-jumping on hydrophobic fibers is a well-known phenomenon, the influence of viscous bulk fluids on this process is still not fully understood. In this work, two water droplets' coalescence on a single stainless-steel fiber in oil was investigated experimentally. Results showed that lowering the bulk fluid viscosity and increasing the oil-water interfacial tension promoted droplet deformation, reducing the coalescence time of each stage. While the total coalescence time was more influenced by the viscosity and under-oil contact angle than the bulk fluid density. For water droplets coalescing on hydrophobic fibers in oils, the expansion of the liquid bridge can be affected by the bulk fluid, but the expansion dynamics exhibited similar behavior. The drops begin their coalescence in an inertially limited viscous regime and transition to an inertia regime. Larger droplets did accelerate the expansion of the liquid bridge but had no obvious influence on the number of coalescence stages and coalescence time. This study can provide a more profound understanding of the mechanisms underlying the behavior of water droplet coalescence on hydrophobic surfaces in oil.

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.