Precise control of droplet rebound behavior on superhydrophobic surfaces is essential for various industrial applications like anti-icing and self-cleaning. However, current studies still lack a comprehensive understanding of this phenomenon. Herein, we conduct a numerical investigation on the rebound dynamics of water droplets impacting on superhydrophobic conical cones under various Weber numbers and cone angles. A phase diagram illustrating impact outcome transitions from non-impalement to impalement and ring bouncing is presented. A semi-empirical model is proposed to identify the impalement transition by correlating critical Weber number with cone angle. While ring bouncing reduces contact time by up to 47% compared to flat surfaces, it is a transient regime due to low rebound velocity, causing the liquid ring to recontact the cone and eventually rebound from the cone tip in a conventional manner with a prolonged contact time. We also observe attractive phenomena upon ring bouncing, including periodically oscillating radial extension and rapid rotation. Shorter contact times in conventional bouncing are achieved at larger cone angles and lower Weber numbers by minimizing radial expansion and falling distance. Furthermore, a theoretical model that accurately predicts the contact time of ring bouncing is developed. It is demonstrated that rebound velocities in both conventional and ring bouncing rise as cone angle decreases, attributed to reduced viscous dissipation and surface energy. Notably, in conventional bouncing, rebound velocity increases by 63% on average compared to flat surfaces when the cone angle is 60°.

Triboelectric nanogenerator (TENG) has been seen as one of the most promising energy harvesting technologies. However, there are an irreconcilable contradiction between low friction and high electrical output performance of the TENG. Here, we have devised a macroscale liquid superlubric triboelectric nanogenerator based on solid- liquid-solid structure, leveraging the concept of liquid superlubricity technology, resulting in a remarkable increase in both the open circuit voltage and short-circuit current by 53.0 % and 58.4 %, respectively. This huge increase in electrical output performance is accompanied by a 99.1 % reduction in friction coefficient (approximate to 0.0025) and 99.993 % reduction in wear rate (approximate to 0.76x10-- 7 mm3/N & sdot;m), 3 /N & sdot;m), when compared to those of a lubricant-free triboelectric nanogenerator. This work delves into the lubrication and charge transfer mechanisms. The liquid superlubricity technology achieves friction reduction through a hybrid mechanism combining boundary and hydrodynamic lubrication. And the high outputs arise from the charges transfer at solid-liquid interface. The triboelectric charges generated by the friction pair are transferred from solid to the lubricating liquid. Meanwhile, the lubricating liquid promotes electron transfer and contributes additional electrons. Our work provides profound insights into the lubrication and charge transfer mechanisms at solid-liquid interfaces, and addresses the paradox of high output and low friction in TENGs.

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.

The recent discovery of Leidenfrost droplet trampolining deviates from the traditionally accepted steady-state assumption and updates our understanding of Leidenfrost droplet state. However, the conditions of trampolining and its effect on heat transfer have not been fully understood. To address these issues, this study numerically investigates the dynamic behavior and heat transfer characteristics of Leidenfrost droplets under varying liquid viscosity and droplet size. A regime map for Leidenfrost droplet state with respect to Bond number and Ohnesorge is presented. Particularly, an unreported oscillation regime is discovered between equilibrium regime and trampolining regime. The results indicate that low viscosity and moderate droplet size favor the observation of trampolining. Besides, the oscillating droplet is modeled via a mass-spring-damper system in both equilibrium and oscillation regimes, with damping coefficient, spring constant and oscillation period quantitatively correlated with liquid viscosity and droplet size by simple scaling laws. In the trampolining regime, an intriguing phenomenon is observed as the maximum vapor layer thickness demonstrates two local maxima with increasing droplet size. We also quantitatively unravel that reducing liquid viscosity and increasing droplet size can lead to a thicker vapor layer thickness, thus inhibiting the heat transfer to the droplet.

In this work, we experimentally investigated the coalescence-induced irregular particle-droplet removal phenomenon. We chose graphite and iron particles, common contaminant dust in HTR-PM, with large density and irregular (non-spherical) shapes at the sub-millimeter scale. It is found that the coalescence mechanism achieves excellent performance in droplet jumping enhancement and particle removal. The maximum transport height of graphite particles was 0.55mm, and the maximum transport height of iron particles was 0.40mm. It is revealed that since the particles always sunk at the bottom of the droplet, their maximum transport height was related to the droplet departure velocity. Besides, irregular particles enhanced the droplet departure velocity. The droplet departure velocity with all graphite particles and part of iron particles was higher than that without particles. The maximum dimensionless departure velocity is 0.35(graphite) and 0.29(iron), 40% and 16% higher than droplet jumping with no particles. Notably, it is illustrated that the mechanism of droplet jumping enhancement with particles was similar to that with macrostructures, which reduced the viscous dissipation and improved the velocity consistency of droplets by shortening the duration of the merge stage and prolonging the duration of the contact stage. This study provided an efficient method for irregular particle removal and opened up a new possible research direction for dust removal and aerosol removal in nuclear industry applications.

Electrowetting presents a powerful technique for manipulating droplets, but its potential to enhance post-impact droplet rebound remains insufficiently understood and underutilized. In this study, we realize the regulation of rebound enhancement and suppression in impacting Galinstan and water droplets using square pulse electrowetting techniques. We numerically investigate the effects of pulse width, surface wettability, and liquid properties on rebound characteristics and demonstrate a phase diagram of rebound modes. Our findings reveal that a moderate pulse width facilitates rebound enhancement, whereas excessively small or large pulse widths lead to rebound suppression. Notably, a fascinating bubble entrapment phenomenon is identified under moderate pulse width, resulting in a distinctive tooth-like rebound shape and secondary liquid–solid contact. Contrary to conventional beliefs, we discover that the optimal rebound velocity occurs at approximately 1.5 times the spreading time, rather than solely at one spreading time. Through unraveling the energy conversion mechanism, we attribute this deviation to the trade-off between additional surface energy and total energy loss. Furthermore, this study highlights that compared to water droplets, the ultra-high surface tension of Galinstan increases additional surface energy while diminishing the viscous effect, leading to heightened rebound velocity, reduced contact time, and an expanded range of pulse widths for rebound enhancement.

Inhibiting the Leidenfrost effect has drawn extensive attention due to its detrimental impact on heat dissipation in high-temperature industrial applications. Although hierarchical structures have improved the Leidenfrost point to over 1000 °C, the current performance of single-scale structures remains inadequate. Herein, we present a facile high-temperature treatment method to fabricate superhydrophilic nickel foams that demonstrate ultrafast droplet permeation within tens of milliseconds, elevating the Leidenfrost point above 500 °C. Theoretical analysis based on the pressure balance suggests that these remarkable features arise from the superhydrophilic property, high porosity, and large pore diameter of nickel foams that promote capillary wicking and vapor evacuation. Compared to solid nickel surfaces with a Leidenfrost temperature of approximately 235 °C, nickel foams nucleate boiling at high superheat, triggering an order of magnitude higher heat flux. The effects of the pore diameter and surface temperature on droplet permeation behaviors and heat transfer characteristics are also elucidated. The results indicate that droplet permeation is dominated by inertial and capillary forces at low and high superheat, respectively, and moderate pore diameters are more conducive to facilitating droplet permeation. Furthermore, our heat transfer model reveals that pore diameter plays a negligible role in the heat flux at high surface temperatures due to the trade-off between effective thermal conductivity and specific surface area. This work provides a new strategy to address the Leidenfrost effect by metal foams, which may promise great potential in steel forging and nuclear reactor safety.

Hypothesis Although extensive research has been conducted on the dynamic wetting of Newtonian fluids, limited insights have been gained for viscoelastic fluids, particularly on engineered surfaces. We hypothesize that differences in dynamic wetting on microstructured surfaces exist between such fluids, which may be attributed to variations in viscosity and elasticity as well as changes in the microscopic morphology of the moving contact line. Experiments To systematically investigate the wetting differences between Newtonian and viscoelastic fluids on microstructured surfaces, we conducted forced wetting experiments of glycerol-water and carboxymethyl cellulose aqueous solutions on microstructured polytetrafluoroethylene surfaces through a modified Wilhelmy plate method. Findings Results demonstrated an apparent difference in the relationship between the dynamic contact angle and moving velocity with different microstructured surfaces for Newtonian and viscoelastic fluids. The power-law exponent between the capillary number and cubic of the dynamic contact angle increases with the strengthening of shear thinning and elastic effects. In contrast, this exponent is rarely influenced by the scale of microstructured surfaces, particularly in highly viscous regions where viscous force dominates. In addition, viscosity affects the viscous bending and distance that liquid molecules jump at the contact line. These findings have potential applications in coating complex fluids on engineered surfaces.

Macrostructures exhibit excellent performance in coalescence-induced droplet jumping enhancement. Previous velocity prediction models were mainly established for flat plain surface, which usually set up the balance relationship between excess surface energy, kinetic energy and dissipation. But these models are no longer appropriate in macrostructure cases due to great variation of oscillational kinetic energy and gravitational potential energy caused by textures. In this work, coalescence-induced droplet jumping on macrostructures was investigated numerically on flat, sidewall, string, ridge and egg shape substrates. An energy conversion model based on energy efficiency rather than energy balance was established for departure velocity by proposing three sub-efficiencies to evaluate jumping enhancement. In this model, oscillational kinetic energy was distinguished from dissipation, gravitational potential energy induced by macrostructures were considered, and the real droplet morphology were used to calculate surface energy. By dividing the whole droplet jumping process into merge and contact stage, the influence of macrostructures on duration of each stage was closely connected to the macrostructure effects on dissipation and kinetic energy conversion. Pressure and velocity distributions near the macrostructure were also discussed to further explore the mechanism for droplet jumping enhancement. Further, the significant increase of initial surface energy for egg case points out a possible new approach to enhance jumping velocity. This model helps us understand the determinants of jumping enhancement with macrostruc-tures and it also applies to flat plain.

Condensation heat transfer enhancement has received increased attention in nuclear engineering in the past few years. Coalescence-induced droplet jumping is a spontaneous dewetting phenomenon, which may promote dropwise condensation. It not only further enhances condensation heat transfer, but also is consistent with passive characteristic of nuclear design without extra heat exchange area. In this paper, a stepped-structure surface was designed, with five different heights (0mm, 0.4mm, 0.8mm, 1.2mm, 1.6mm). We experimentally studied coalescence and departure process of two water droplets with fixed droplet size (R=0.8mm). Stepped-structure surface exhibited excellent performance with strong horizontal droplet transport ability and high energy efficiency, whose jumping direction is ranging from ~6.2° to ~90°, maximum non-dimension velocity v* = 0.65 and maximum energy efficiency η = 34.9%. By disassembling η into three sub-efficiencies, one correlates to step height and two correlate to duration of merge stage and contact stage, we analyzed mechanism of jumping enhancement. Results showed that largely changed duration of merge stage and contact stage is the main reason of high energy efficiency, while step height had little influence on it. Stepped-structure surface provides a new solution for breaking the condensation limit.

Textured surface has shown great potential in inhibiting Leidenfrost phenomenon for the thermal management of high heat flux devices. Although diverse textured surfaces have been designed to achieve multi-fold increases in Leidenfrost point, the dominant physical mechanism of different surface structures remains elusive. In this study, three aluminum-based surfaces including bare aluminum surface, superhydrophilic micro/nanostructured surface, superhydrophilic macro-pillar arrayed surface are fabricated by simple, low-cost methods. The effects of surface structures at various scales on Leidenfrost point and the dynamic characteristics of water droplets are elucidated. The experimental results indicate that micro/nanostructures cause intermittent liquid-solid contact and trigger more vapor dispersion into micro/nanocavities. A thicker vapor layer generated above micro/nanostructures reduces the vapor pressure for pushing droplet upward and increases Leidenfrost point from 188 ℃ (for bare aluminum surface) to 428 ℃. A higher Leidenfrost point over 500 ℃ (the maximum heating temperature) is achieved on the macro-pillar arrayed surface due to strong capillary wicking and high permeability. Theoretical models that integrate the influence of surface structures on Leidenfrost point are established through balancing vapor pressure with capillary pressure and gravitational pressure. Prediction results are shown good agreement with experimental results. Impact and heat transfer regime maps are also provided, where a unique explosive bouncing with a significant reduction in contact time and an extended temperature span of transition boiling are observed on structured surfaces. Furthermore, macrostructures are found to induce a larger and longer liquid-solid contact, thus demonstrating an excellent cooling capability in the transition boiling.

This study numerically investigates the bouncing characteristics of impacting droplets on superhydrophobic sub-millimeter parallel grooves by the level-set method. Once the Weber number (We) is increased to a critical value (Wec), a unique petal-like droplet bouncing off the parallel grooves without horizontal retraction is found, dramatically reducing the contact time (tc) by up to ∼75%. Such a bouncing mode is attributed to the rectification of capillary energy stored in the penetrated liquids into upward motion. To achieve controllable petal bouncing, the coupling effects of impact velocity and surface geometric characteristics on tc and Wec are elucidated from the perspective of timescale, momentum, and energy. The numerical results indicate that narrowing the center-to-center spacing contributes to shortening tc and slowing down the growth of tc with We. In contrast, the effect of ridge height is negligible. By establishing the model of emptying time, the relationships of tc with impact velocity and geometric parameters are quantitatively identified. Furthermore, along with the strengthened anisotropic property, a large center-to-center spacing promotes the conversion of horizontal momentum into vertical momentum and suppresses the increment of surface energy, thus inducing the reduction in Wec. Distinct from known anisotropic surfaces in the previous work, the anisotropic property of parallel-grooved surface plays an opposite role in shortening tc. Finally, incorporating the energy balance approach, a semi-empirical model is developed to predict Wec, exhibiting good agreement with present simulation. This work provides physical insights into petal bouncing and inspires the design of textured surfaces to reduce contact time.

HYPOTHESIS:The unbalanced capillary force provided by wettability patterns, non-uniform/asymmetric microtextures enables directional droplet transport, while macrotextures have shown potentials in reducing the contact time. Inspired by these findings, we design millimeter superhydrophobic stepped surfaces to simultaneously achieve highly steerable directional bouncing and contact time reduction of impacting droplets. EXPERIMENTS:The stepped surfaces are fabricated by computerized numerical control, chemical oxidation, hydrophobic treatment. Systematic impact experiments are conducted under Weber number ranging from 10.5 to 20.5, two step heights (0.5 mm and 1.0 mm) and extensive impact positions. FINDINGS:Compared with known microtextured surfaces, the stepped surfaces exhibit excellent performance with the maximum lateral movement distance about 8 times of droplet radius, controllable rebound angle ranging from ∼ 32° to ∼ 90° and up to ∼ 30 % reduction in contact time. Particularly, we divide the directional bouncing characteristics into six regimes and attribute the variation of rebound velocity by the synergistic effects of viscous dissipation, excess surface energy, excess kinetic energy. It is demonstrated that the contact time is reduced by liquid mass redistribution and asymmetry enhancement. Predictive models of contact time that incorporate the coupling effects of impact position, impact velocity and step height are also established.

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.

HYPOTHESIS:Droplet spreading governs various daily phenomena and industrial processes. Insights about microdroplet spreading are limited due to experimental difficulties arising from microdroplet manipulation and substrate wettability control. For droplet sizes approaching the capillary length scale, the gravitational force plays an important role in spreading. In contrast, capillary and viscous forces dominate as the droplet size reduces to smaller length scales. We hypothesize that the dynamic spreading behavior of microdroplets whose radius is far lower than the capillary length differs substantially from established and well understood dynamics.EXPERIMENTS:To systematically investigate the spreading dynamics of microdroplets, we develop contact-initiated wetting techniques combined with structuring-independent wettability control to achieve microdroplet (<500 μm) spreading on arbitrary surfaces while eliminating parasitic pinning effects (pining force ∼ 0) and initial impact momentum effects (Weber number ∼ 0).FINDINGS:Our experiments reveal that the capillary-driven initial spreading of microdroplets is shorter, with significantly reduced oscillation dampening, when compared to millimeter-scale droplets. Furthermore, spreading along with capillary wave propagation results in coupling between the spreading velocity and dynamic contact angle at the contact line. These findings, along with our proposed microdroplet manipulation platform, may find application in microscale heat transfer, advanced manufacturing, and aerosol transmission studies.

The initial spreading of glycerol and silicon oil droplets on smooth, corrugated, and orthogonal surfaces is numerically investigated by an effective, sharp-interface modeling method. In this study, the temporal evolution of spreading radius during the initial phase is scaled by R/R0 = C(t/τi)α for inertial regime and R/R0 = C(t/τμ)α for the viscous regime. We focus on exploring how wettability, liquid properties, and substrate topography influence the exponent α and coefficient C. Instead of discussing the effects of density, viscosity, and surface tension separately, we use the Ohnesorge number Oh = μ/(ρD0γ)1/2 to unify the combined influence of liquid properties. The results show that in the inertial regime (Oh ≪ 1), α is determined by wettability and the capillary wave is observed to propagate along the droplet interface, whereas in the viscous regime (Oh ≫ 1), α is determined by Oh and no capillary wave is observed. Consequently, both qualitative (propagation of capillary wave) and quantitative (Ohnesorge number) criteria to distinguish the two distinct regimes are provided. Regarding the coefficient C, it is found to increase with the increasing hydrophilicity and decreasing Oh in the inertial regime. A larger C is also observed in orthogonal microgrooves with wider gap or narrower width. Besides, the hydrophobicity and hydrophilicity can be enhanced by the corrugated surfaces, inducing a higher and lower α on hydrophilic and hydrophobic corrugated surfaces, respectively. Meanwhile, some interesting phenomena are also observed, such as the faster contact line velocity on the inside of a single corrugation and the “stick-jump” advancing mode of the contact line on orthogonal surfaces.

Electrowetting-induced detachment of liquid droplets has application prospects in selfcleaning and digital microfluidics. Although several models have been provided to estimate the critical condition for jumping droplet, there is still a lack of a comprehensive understanding of the energy conversion during detachment process and an accurate prediction of the jumping velocity. In this study, an analytical model adopting the energy balance approach is derived to predict the jumping velocity of an electrowetting-actuated droplet. Our main contribution is to reformulate the models of four energy components including the surface energy, kinetic energy, gravitational potential energy at detachment, as well as the viscous dissipation of entire recoiling. The necessity to correct these energy components has also been physically explained. On the one hand, the droplet morphology at detachment is not spherical but a balloonlike shape, leading to the underestimated surface energy and gravitational potential energy. On the other hand, the previous model that assumes a constant velocity gradient in the bulk results in the overestimated viscous dissipation. Moreover, the kinetic energy of jumping droplet cannot be simply characterized by a rigid body model because of the non-negligible radial velocity. According to the statistics, the correction of the viscous dissipation term contributes the most to reducing prediction error, approaching -90%, while the relative errors introduced from other three energy terms are comparable, approaching -20%. By testing the prediction results against both present simulations and the experiments in the literature, it is validated that the present model successfully identifies the influence of liquid properties, droplet size, surface wettability, and applied voltage on jumping velocity. The results indicate that the increase in the droplet size causes a nonmonotonic change in jumping velocity, which first increases due to the weakened viscous dissipation, then decreases due to the prominent influence of gravity.

This study adopts the phase-field method to investigate the dynamics of droplet impact on spherical surfaces at various Reynolds numbers Re and Weber numbers We. Five liquids are studied in the present simulation, which expands the research scope of viscosity (1-970 mPa.s) and surface tension (20-500 mN/m) compared with previous works. The temporal evolution of the spreading factor beta and the dimensionless center thickness h* is systematically analyzed. The results indicate that beta(proportional to)(max)We(alpha) suggested by previous works does not apply to viscous fluids. Thus, we adopt the impact factor P = We/Re-0.8, which has been used to study droplet impact on flat surfaces, to decide the dominating force of beta(max) for impact on spheres. We first find that beta(max).Reb exists in the viscous regime (P > 1), whereas beta(proportional to)(max)We(alpha) mainly exists in the capillary regime (P < 1). Although the fluid properties of incident droplets vary widely, the variation in h* with dimensionless time tau always has three distinct phases. The first phase follows h* = 1-tau, and the second phase basically conforms to h*alpha tau (-1.6). The minimum dimensionless center thickness h* min scales as Re-c. Furthermore, the exponents a, b, and c are found to be strongly related to the diameter ratio of spheres and droplets, and prediction models of the three exponents are proposed.

Based on the energy conservation approach, this study develops a universal model to predict the maximum spreading factor of liquid droplet impact on a smooth solid surface. Validated with the present simulations and experiments in the literature, this model effectively overcomes the limitation of previous models in the viscous regime and greatly reduces the computing errors from over 30% to below 6%. It is demonstrated that the underestimated maximum spreading factor by previous models results from the overestimation of viscous dissipation. By replacing the conventional model of spreading time, tm = 8D0/3U0, with a more precise one, tm = 1.47τiWe-0.44, the formulation to compute the viscous dissipation of entire spreading is improved. Finally, we examine the applicability of present model in the capillary regime and good performance is also shown.

It is fundamentally significant to predict the maximum spreading of liquid droplets impact on textured surfaces. However, relevant work is very limited. Considering the effects of contact line pinning and liquid penetration into textures, a theoretical model to predict the maximum spreading factor on concentric ring-textured surfaces is developed. Validated with numerical simulations conducted by an effective, sharp-interface, continuum level modeling method, this model has shown a good predicting performance. It is demonstrated that in the viscous regime, the viscous dissipation arising from liquid penetration into textures has a considerable effect on the maximum spreading factor, whereas the effects of the contact line pinning and surface energy are negligible. Meanwhile, as viscous dissipation becomes more dominant, the effect of texture gap on maximum spreading is less visible. The phase diagram of the wetting state at maximum spreading is also provided. We indicate that the intermediate wetting state is favorable under small Reynolds number and narrow texture gap, while the partial wetting state is supported under the opposite conditions.