Low Weber Number Research Articles

Characteristics of entrapped jet and cavity instability following the water entry of a superhydrophobic sphere

Following the impact of a superhydrophobic sphere on water, the formation of a stable-streamlined gas cavity undergoes several stages characterized by impact load slamming, cavity flow forming, cavity collapse, and unstable cavity. The former three stages have been extensively investigated. However, limited attention has been given to the post-collapse instability of the gas cavity. In the present study, a systematic experiment is conducted to investigate the evolution of the cavity subsequent to the water entry of a superhydrophobic sphere. The pattern of cavity collapse significantly influences the dynamic characteristics of the downward liquid jets entering the cavity. The liquid jets entrapped in the cavity behave as liquid films composed of tiny individual cavities generated with cavity collapse. Deep sealing with a relatively low Weber number consistently promotes the onset of jet penetration, whereas surface sealing results in droplet penetration. The repulsion of entrapped liquid films from the inner rim of the sphere plays a pivotal role in stimulating the periodic instability experienced by the descending gas cavity. The obtained conclusions shed light on the dynamics of the liquid films entrapped in a gas cavity and the cavity stability.

Non-circular pressure swirl nozzles injecting into stagnant air

As far as we are aware, all the previous studies have focused on circular injectors. Here, the effect of non-circular orifice shape on pressure swirl injector was investigated experimentally. For this purpose, three injectors; circular, square and rectangular were manufactured. The nozzles had the same cross-sectional area. Water was used as the working fluid and tests were conducted at room temperature and pressure. The Weber number varied from 484 to 1936. Flow parameters of the swirl jets were obtained by an in-house image processing code. The measured parameters were: discharge coefficient, spray angle, breakup length, lateral spread, SMD of drops and wavelength of surface waves formed on the cone. The influence of nozzle shape on all these parameters are discussed.A new breakup regime morphology for non-circular pressure swirl nozzles was defined. At lower Weber numbers, the air core was trapped inside the liquid sheet and relatively large ligaments were formed and separated from the edges (fiber breakup regime). As the Weber number was increased Rayleigh-Taylor instability produced cell-like structures near the nozzle exit. These cell-like structures eventually broke up at the thickened edges of the cells and formed Christmas tree like structures (Christmas tree regime). We found that all the measured flow parameters can best be correlated as a function of Reynolds number and Weber number based on liquid sheet thickness at nozzle exit. All these correlations were reported. Breakup length and lateral spread were heavily influenced by the breakup regime. In fiber breakup regime the breakup length and lateral spread increased with increasing Weber number. However, in Christmas tree (cellular) breakup regime, breakup length and lateral spread decreased with increasing Weber number.

Droplet–jet collision following the monodispersedly dripping of coaxial binary droplets above a pool surface

In the present study, the collision between a falling droplet and a rising Worthington jet was experimentally studied. The event is followed by the monodispersedly dripping of coaxial binary droplets into a quiescent pool of glycerol solution. Different concentrations of the solution are considered. Unique droplet–jet collision characteristics are observed when the dripping flow rate is manipulated to release binary droplets. When the first droplet impacts the pool, a significant disturbance is imposed onto the pool, forming a deep crater followed by a Worthington jet. The second droplet is timed to collide with the rising jet to create a unique mushroom-shaped droplet–jet collision. Two jet pinch-off modes (tip pinch-off and no pinch-off) and four distinct collision regimes (partial rebounding, end-pinching, elongated, and clotted central jet collision) are recognized. Liquid viscosity and jetting mode significantly influence the collision dynamics and splattering characteristics. To achieve partial rebounding collision at low Weber number, a high-impact coefficient incorporating characteristic dimensions of the droplets and the Worthington jet is required, whereas a low-impact coefficient is required at high Weber number to attain clotted jet collision. The overall end-pinching phenomenon occurs due to the interaction between liquid flow toward the jet tip and the retraction of the tip, which causes the jet neck diameter to decrease on a capillary timescale. As the impact parameter decreases, the Worthington jet is inhibited, and the mushroom-shaped collision splash spreading is suppressed.

ANALYSIS OF THE DYNAMICS AND FREEZING OF WATER DROPLETS ON METAL SURFACES

This article investigates the effects of substrate temperature, tilt angle, and droplet size on droplet impact dynamics and freezing using a Motionpro high-speed camera and a DSA-30 droplet surface analyzer. The temperature of the substrate was changed from the ambient temperature of 21°C to -13°C, and three droplet sizes (<i>D</i><sub>0</sub> = 2.57, 3.02, and 3.54 mm) were studied. The results show that some air gets trapped under the liquid film during the impact process due to insufficient escape time, resulting in the interior of the droplet being in an unstable state. Simultaneously, due to the low surface energy of the substrate, liquid droplets exhibit a rebound effect upon impact with the ambient temperature substrate, reaching their maximum height and forming a dumbbell-like shape. Furthermore, the rebound height decreases rapidly with the decrease in substrate temperature. A change in substrate temperature had no significant effect on the droplet spreading process, but decreasing substrate temperature increased the viscous forces, thereby suppressing the droplet retraction and oscillation processes, ultimately leading to longer droplet freezing times. Additionally, at low Weber numbers (<i>We </i>< 250), the droplet dimensionless parameters exhibited a similar trend with respect to dimensionless time or temperature.

Rebound dynamics of two droplets asymmetrically impacting single-ridge superhydrophobic surfaces

On a single-ridge superhydrophobic surface, the rebound dynamics of double droplet impacts is investigated via lattice Boltzmann method (LBM) simulations, where one droplet is on the left of macro-ridges, whereas the other droplet being on the top of macro-ridges, leading to the asymmetrical impact of double droplets. The simulation results show that under different impact conditions of various Weber numbers, that is, at low, moderate and high Weber numbers, the rebound regime of double droplet impacts always consists of the complete-coalescence-rebound (CCR), partial-coalescence-rebound (PCR) and coalescence-split-rebound (CSR) regimes. Under these three rebound regimes, the contact time of double droplet impacts is always reduced by the increased We, as the center-to-center distances in the horizontal and vertical directions, Lx and Lz, are constant. At constant Lx and We, the contact time of double droplet impacts on single-ridge superhydrophobic surfaces is increased by the increased Lz because of the earlier formation of liquid bridges at larger Lz. But under different impact conditions of various center-to-center distances in the horizontal direction, that is, at the increased Lx, the rebound regime of double droplet impacts is not always composed of the CCR, PCR and CSR regimes at low, moderate and high Weber numbers. At constant We and Lz, both coalescence strength and rebound regime are significantly affected by the increased Lx for double droplet impacts. So that the contact time of double droplet impacts on singe-ridge superhydrophobic surfaces depends on the center-to-center distance in the horizontal direction, that is, in the x- direction.

Contact Time of Droplet Impact on Superhydrophobic Cylindrical Surfaces with a Ridge.

This study investigates whether adding ridges to a superhydrophobic cylindrical surface can reduce contact times compared to those of ridged flat or cylindrical surfaces, inspired by the shortened contact time achieved by adding ridges to flat surfaces. The study focuses on studying azimuthal ridges on the cylinder through experimentation, emphasizing the impact dynamics and contact time characteristics under varying We (Weber number) and D* (dimensionless droplet diameter). Within the ultralow Weber number range (ULWR), low Weber number range (LWR), and medium Weber number range (MWR), the contact time is longer than on ridged flat surfaces. In the high Weber number range (HWR), the opposite is observed: increased inertial forces lead to the rupture of the liquid film above the ridges due to Rayleigh-Plateau instability. As a result, the primary droplet splits into two sections with curvature effects promoting its recoiling and rebounding. This study introduces a criterion, defined as C = We/D*, and finds that when C exceeds 2.42, not only is the contact time shorter than on ridged flat or cylindrical surfaces, but it also further decreases with an increase in We or a decrease in D*. The contact time characteristics observed in the HWR offer potential applications in areas such as anti-icing.

Flow and Heat-Transfer Characteristics of Droplet Impingement on Hydrophilic Wires.

It is a common phenomenon that droplets collide with wires in industrial production, and their flow and heat-transfer behavior significantly impact the production efficiency. This article presents an experimental and numerical study on the impact of pure water droplets on hydrophilic stainless-steel wires. The dynamic behavior and solid-liquid heat-transfer law of droplet impacting the wire are emphatically analyzed. The impact position of the droplets has a significant effect on their morphology. Under the condition of low Weber number (We), eccentric impacts tend to cause droplets to separate from the wire. Additionally, both We and wire/droplet size ratio have noticeable effects on the droplet morphology. The smaller the We, the larger the wire/droplet size ratio, and the easier it is for droplets to be captured by wires. Conversely, as We increases and the wire-to-droplet size ratio decreases, some droplets become detached from the wire, primarily exhibiting a single-film falling mode. Furthermore, the impact morphology of droplets is influenced by the Ohnesorge number (Oh). The higher the Oh, the more inclined the droplet to develop a double-film falling mode. There is obvious field synergy in the process of droplet impacting on wire. The maximum heat flux is located at the three-phase contact line, while the minimum heat flux is observed at the bubble interface. The impact position of droplets influences the temperature distribution, although its impact on the magnitude of temperature variation is minimal.

Gas entrapment and pore formation in metal droplet-based 3D printing

Gas entrapment behavior during metal droplet deposition tends to form pore defects and discourages interfacial bonding between droplets, resulting in lower densities and poorer performance of printed components. Moreover, the gas entrapment process is influenced by the interaction of gas-liquid two-phase flow and non-isothermal solidification, which makes the interfacial behavior of droplets challenging to identify. Therefore, gaining insight into the gas entrapment behavior and pore formation mechanism at the bottom of molten droplets is essential. This paper established a model of two-dimensional axisymmetric numerical by combining the fluid volume tracking method and heat transfer solidification model. Single metal molten droplet deposition experiments verified the accuracy of the model. The evolution of solid phase fraction, velocity field, pressure field, and contact surface heat flux during the deposition of the molten droplet at low Weber numbers (0.1-10) was investigated comprehensively. The mechanisms of gas entrapment and pore formation were revealed. The effects of molten droplet impact velocity, contact angle, and surface tension on the gas film evolution process and pore morphology were further investigated. The results show that decreasing the droplet impact velocity causes capillary waves to contact the substrate surface and form local solidification, allowing the gas disk to evolve into central and two peripheral pores. Moreover, the pore breaks away from the substrate and remains inside the droplet when decreasing the droplet contact angle to 50°. Furthermore, the rate of gas disk retraction decreases as surface tension reduces, which may accentuate the resistance effect of the contact surface solidification layer on the gas disk retraction, thus changing the final morphology of the pores. These findings elucidate the mechanism of pore formation at the bottom of molten metal droplets and further understand the interfacial behavior of droplets in 3D-printed metal structures.

Contact-time reduction of viscous droplets impacting a grooved superhydrophobic surface

Adding a macroscale groove structure to the superhydrophobic surface makes the water droplet to bounce in a petal shape and dramatically reduces the contact time of the water droplet. Most studies on petal bouncing have been conducted on water droplets without considering the effects of viscosity. In this study, the bouncing dynamics of glycerol/water droplets impacting a grooved hydrophobic surface were investigated by changing the viscosity and impact speed of the droplets. As the viscosity of the droplets increased, the Weber number range in which petal bouncing occurred decreased. Petal bouncing was observed in up to 50 wt. % glycerol/water droplets with a viscosity approximately six times that of water. In the low Weber number region (We < 25), as the viscosity of the droplet increased, a sufficient amount of capillary energy was not stored in the fluid penetrating the grooved structure, owing to the viscous dissipation of the fluid. In contrast, in the moderate-Weber-number region (25 < We < 40), the impact energy of the droplet became sufficiently large to overcome the viscous force of the fluid, enabling spreading and retraction along the bottom of the structure. This caused a discrepancy between the time at which the retraction of the fluid above the structure started and the time for the fluid to penetrate and empty the structure, resulting in a transition from petal bouncing to conventional rebound. The critical Weber number for petal bouncing was calculated using the energy-balance approach, and the results were similar to the experimentally observed values.

Impact and freezing coupling processes of supercooled water droplets on cold superhydrophobic spheres at low Weber numbers

While the previous studies discussed the impact and freezing coupling processes of supercooled water droplets on cold superhydrophobic convex spheres at medium or high Weber numbers (We > 10), the cases on convex and concave spheres at low Weber numbers (We ≤ 10) are numerically studied. A numerical model using the VOF (Volume of Fluid) method and solidification-melting model is established and validated by comparing the calculated results with the experimental data in reference. The influences of the Weber number, supercooling degree, and sphere diameter (characterized by the sphere-to-droplet diameter ratio) on the dynamic behaviors, including the droplet profile, the spreading area and arc angle, and the final outcomes, are explored. As the Weber number increases and the supercooling degree decreases, the impact droplet yields a higher retraction speed and tends to rebound from the cold spheres more easily. The influence of the diameter ratio at low Weber numbers is distinct from that at medium Weber numbers. With the increase of the diameter ratio, the maximum spreading area factor on the convex sphere increases while that on the concave sphere decreases. The final droplet outcome transits from adhesion to rebound when the surface shape continuously changes from concave to convex. The rebound-adhesion morphology maps in terms of the Weber number and diameter ratio are obtained at various supercooling degrees. The rebound region of the convex sphere in the morphology map is wider than that of the concave sphere, and the adhesion region of the morphology map expands with a greater supercooling degree. A smaller diameter ratio yields a smaller critical Weber number between rebound and adhesion regions on the convex sphere but a greater one on the concave sphere. The innovation and optimization of the anti-icing surface may obtain theoretical reference and guidance from the above findings.

The effect of a temperature-dependent viscosity on cooling droplet-droplet collisions

A detailed understanding of the collision dynamics of liquid droplets is relevant to natural phenomena and industrial applications. These droplets could experience temperature changes altering their physical properties, which affect the droplet collisions. As viscosity is one of the relevant physical properties, this study focuses on the effect of temperature on viscosity, with an Arrhenius temperature dependence, of collisions of two equal-sized droplets using the Volume of Fluid Method. The results show that the higher temperature of the droplets leads to an effectively lower viscosity, leading to increased interface oscillations. This leads to the onset of separation at lower Weber numbers as expected. The local cooling droplets will create a local viscosity profiles, which results in the formation of a ridge upon combination of droplets. In addition, the collision outcomes sometimes cannot be explained solely on basis of an effective viscosity, undermining the usefulness of existing collision regime maps.

Microfluidic Droplet-Generation Device with Flexible Walls.

Controlling droplet sizes is one of the most important aspects of droplet generators used in biomedical research, drug discovery, high-throughput screening, and emulsion manufacturing applications. This is usually achieved by using multiple devices that are restricted in their range of generated droplet sizes. In this paper, a co-flow microfluidic droplet-generation device with flexible walls was developed such that the width of the continuous (C)-phase channel around the dispersed (D)-phase droplet-generating needle can be adjusted on demand. This actuation mechanism allowed for the adjustment of the C-phase flow velocity, hence providing modulated viscous forces to manipulate droplet sizes in a single device. Two distinct droplet-generation regimes were observed at low D-phase Weber numbers, i.e., a dripping regime at high- and medium-channel widths and a plug regime at low-channel widths. The effect of channel width on droplet size was investigated in the dripping regime under three modes of constant C-phase flow rate, velocity, and Capillary number. Reducing the channel width at a constant C-phase flow rate had the most pronounced effect on producing smaller droplets. This effect can be attributed to the combined influences of the wall effect and increased C-phase velocity, leading to a greater impact on droplet size due to the intensified viscous force. Droplet sizes in the range of 175-913 µm were generated; this range was ~2.5 times wider than the state of the art, notably using a single microfluidic device. Lastly, an empirical model based on Buckingham's Pi theorem was developed to predict the size of droplets based on channel width and height as well as the C-phase Capillary and Reynolds numbers.

A study on the solidification shapes of molten metal droplet impacting at low weber number

In uniform molten metal micro droplet deposition manufacturing (UDDM), the control of droplet solidification shape is essential to meet the forming requirements in different application scenarios to achieve a high forming quality. However, although the prediction of droplet solidification shape has been clearly mastered in a high Weber number application scenario such as thermal spray, droplets generally impact on a substrate at a low Weber number level of 2–10 in UDDM, where the droplet will solidify into various shapes under different processing parameter combinations. Here, to uncover the differentiation mechanism and establish a prediction strategy of the geometric shape of a solidified droplet during print process, the impact events under common forming conditions were systematically investigated by numerical and experimental methods. The solidification shapes of the droplets were roughly assorted into three major categories and a subtype. Results indicate that the solidification shapes are very sensitive to the footprint diameter of the droplet, thereafter an empirical formula for which was derived. On this basis, a mapping of droplet solidification shape to droplet footprint diameter was further developed, which was experimentally verified to be accurate and effective. This work shares a panorama of the solidification shapes of molten droplets impacting at low Weber number. It provides a convenient approach to automatically recognize the contour of a solidified droplet only through measuring the droplet footprint diameter, and more than that, lays a way to artificially tailor the droplet morphology in printing.

Effect of temperature difference between impinging droplet and cold superhydrophobic surface on its dynamic behavior

The phenomenon of water droplets impacting on cold surfaces and freezing is common in various fields and has numerous detrimental effects. Meanwhile, superhydrophobic surfaces have received a lot of attention in terms of preventing icing. Therefore, it is important to investigate the dynamic behavior of water droplets impacting on superhydrophobic surfaces in a supercooled environment under different temperature conditions in order to prevent icing. In this study, the dynamic behavior of water droplets impacting on superhydrophobic surfaces in a supercooled environment is visualized using a high-speed camera, and the effect of the temperature difference between the droplet and the cold surface on the dynamic behavior of the impacting droplet is emphatically investigated. The dynamic characteristics of the droplet were also analysed in terms of dimensionless contact diameter, dimensionless droplet height, contact time and energy balance. The results show that the change in properties of the droplet is mainly reflected in the change in viscosity. At low Weber number, the change in viscosity has little effect on the dimensionless contact diameter and contact time but has a significant effect on the dimensionless height of the droplet during retraction. Of particular note is the fact that when the droplet temperature is constant, a decrease in the surface temperature leads to a significant slowing down of the droplet retraction process on the superhydrophobic surface and a significant increase in the contact time. However, a phenomenon contrary to intuition has been observed, namely that a similar situation occurs with increasing droplet temperature when the surface temperature is constant. This behaviour of the droplets is related to the possible existence of liquid-phase condensation processes in the microstructure, and we have also analysed theoretically the conditions under which condensation occurs. This study could contribute to the development of anti-icing technology.

Splashing of droplet under the vibration effect of flexible membrane

The impact dynamics of a droplet falling onto a substrate is significant in various applications such as inkjet printing, spray coating, and bioprinting. Generally, several factors, such as the fluid properties (e.g. viscosity or surface tension) and substrate characteristics (e.g. surface roughness or flexibility) govern whether falling droplets spread or splash. In this study, we experimentally investigate droplet impact dynamics on a thin, flexible membrane for various Weber numbers (230 < We < 600) and membrane stiffnesses, which can be controlled by the applied tensile force. In addition, the effect of membrane vibration on impact behavior is considered. In the high Weber number regime, splashing is dominant, regardless of the membrane stiffness. In contrast, in the low Weber number regime, a transition between splashing and deposition is observed, depending on the membrane stiffness. In short, flexible membrane vibration induces droplet splashing despite the insufficient kinetic energy of the droplet. Increasing the stiffness of the membrane contributes to the suppression of droplet splashing by minimizing membrane vibration.

Effect of the Weber number on the coalescence of relatively moving droplets in an electric field: A molecular dynamics study

Herein, the movement of two non-centric droplets in hexane was studied using a molecular dynamics method to understand the microscopic coalescence mechanism of droplets with an initial velocity in an electric field. Unlike previous studies, this study overcame the limitations in experimental conditions and conventional analytical tools to understand the mechanism of droplet coalescence under the coupling effect of electric and velocity fields at the molecular level. This has implications for the development of inkjet printing technology and microfluidics. The analysis of droplet trajectories and centroid distances revealed that the Weber number can be divided into three ranges according to the three modes of droplet behaviour: incomplete coalescence, complete coalescence and non-coalescence. At a low Weber number (We < 1), the inhomogeneous distribution of ions in droplets causes the fragmentation of droplets that are not completely coalesced. The interaction energy and weak interaction analysis shows that hydrogen bonds between water molecules are the strongest, followed by van der Waals interactions, which is very prominent in the first and second coordination layers. Hexane and water molecules exhibit van der Waals interactions. As the Weber number increases from 0 to 5, the total interaction energy between two droplets increases, and the number of hydrogen bonds increases. A decrease in the total interaction energy, number of hydrogen bonds, radial distribution function and coordination number in a single droplet shows that increasing the Weber number loosens the single droplet and simultaneously promotes the coalescence of two droplets. However, when We > 5, the total interaction energy and number of hydrogen bonds between droplets are zero, and the two droplets do not merge. This is because the angle between the electric field and centreline of the droplets is so large that the electric field cannot horizontally act upon the droplets. This study provides a fundamental guide for studying the mechanism of droplet coalescence under the coupling effect of electric and flow fields.

An adaptive multi-resolution SPH approach for three-dimensional free-surface flow with fluid impacting

This paper presents a new adaptive multi-resolution smoothed particle hydrodynamics (SPH) approach for simulating three-dimensional free surface flows with fluid impacting. The governing equations for multi-resolution SPH are derived based on the finite particle method (FPM) particle interpolation, which is an alternative SPH formulation for improving interpolation accuracy in the non-uniform particle distribution. A variable kernel length related to the volume of neighbor particles is proposed to control the numerical instability due to the multi-resolution scheme. In adaptive particle refinement (APR), a concept named as continuously-variable characteristic length (CCL) for each particle is defined to determine the splitting or merging scheme and then build a smoothing non-uniform particle distribution. Three-dimensional examples are conducted to validate the presented new APR approach, and the capability and numerical efficiency of the proposed numerical model are verified through solving free-surface flow problems with middle and low Weber numbers. After validation, a refined simulation of droplet impacting is conducted using the proposed adaptive multi-resolution SPH approach. The results show that the proposed SPH could well adapt to the large deformation of three-dimensional free-surface flow, and only provide a refinement near the free-surface domain.

Contact time of nanodroplets obliquely impacting nanopillar-arrayed superhydrophobic surfaces: A molecular dynamics study

On nanopillar-arrayed superhydrophobic surfaces, the contact time of oblique nanodroplet impacts is for the first time investigated via molecular dynamics simulations. Here, oblique nanodroplet impacts are triggered by nanodroplets impacting superhydrophobic surfaces under various impact angles, α. The simulation results show that owing to the non-axisymmetry of spreading factors on nanopillar-arrayed superhydrophobic surfaces, the contact time of oblique nanodroplet impacts is always less on nanopillar-arrayed rather than smooth superhydrophobic surfaces under same impact angles. As the impact angle is increased from 5° to 65°, that is, under different impact conditions, the non-axisymmetry is more remarkable as α &amp;gt; 35° instead of α &amp;lt; 35° at the low, medium, and high normal Weber numbers, Wen. Hence, the contact time is sharp as α &amp;gt; 35° and then slowly reduced as α &amp;lt; 35° at the low, medium, and high Wen, at which the drastically increased sliding length as α &amp;gt; 35° further promotes the rapid reduction in contact time. As the impact angle is constant at 35°, the non-axisymmetry is more remarkable as h/w &amp;lt; 1 instead of h/w &amp;gt; 1 as the aspect ratio of nanopillars, h/w, is increased, that is, under different surface conditions. Hence, the contact time is sharp as h/w &amp;lt; 1 and then slowly reduced as h/w &amp;gt; 1 at the low, medium, and high Wen, at which the drastically reduced sliding length as h/w &amp;gt; 1 further hinders the rapid reduction in contact time.

Universal scaling of droplet retraction dynamics on vibrating surfaces

Over the past decade, extensive efforts have been made in the study of droplet impact, especially on stationary surfaces, owing to its direct applications in thermal cooling, self-cleaning, and power generation. However, many practical applications, such as ultrasonic cleaning, aerosolized drug delivery, and vibration-assisted welding, involve the direct interaction of droplets with vibrating surfaces, on which droplets undergo spreading and retraction. Distinct from stationary surfaces where the retraction behaviors, such as the retraction velocity and rate, are mainly governed by the surface wettability and droplet inertia, the retraction behaviors on vibrating surfaces become complicated due to the vibration velocity, which dictates the outcomes of droplet impact, such as the pinning, bouncing, gyrating, and jetting. Here, we revealed the synergistic effect of droplet inertia and vibration velocity on droplet retraction. We found that the droplet retraction behaviors on both stationary and vibrating surfaces could be characterized by a universal scaling law, allowing us to analyze and predict the maximum droplet retraction velocities. Moreover, we found that the maximum retraction rate increased with the maximum spreading radius at low Weber numbers. We demonstrated that the droplet retraction dynamics at both low Weber numbers and high Weber numbers could be unified into one integrated model, which indicates the decisive role of the maximum droplet spreading in droplet retraction dynamics.

Enhancing droplet rebound on superhydrophobic cones

Understanding the underlying hydrodynamics and developing strategies to control bouncing droplets on superhydrophobic surfaces are of fundamental and practical significance. While recent efforts have mainly focused on regulating the contact time of bouncing droplets, less attention was given to manipulating droplet rebound from the perspective of energy optimization, which determines the long-term successive dynamics. Here, we investigate the impact of water droplets on superhydrophobic cones at low Weber numbers, where ideally complete rebounds arise. In sharp contrast to flat superhydrophobic surfaces, an impinging droplet on a cone-shaped superhydrophobic surface undergoes almost inversion-symmetric spreading and retracting processes with prolonged contact time, and more strikingly, it rebounds with a higher restitution coefficient. Such enhanced droplet rebound is beyond the prediction of existing theoretical models, in which the viscous boundary layer was recognized as the dominant channel of energy dissipation and, thus, an increase in the contact time would result in a lower restitution coefficient; nevertheless, numerical simulations have confirmed the increase in the restitution coefficient. The quantitative energy and flow field analyses of our numerical results reveal that the suppression of the boundary layer in early impact and the weakening of the viscous flow near the moving edge in the subsequent impact phases, which were not accounted for yet in existing theoretical models, are the causes for the enhancement of droplet rebound on superhydrophobic cones.