Impact Dynamics Of Water Droplets Research Articles

Numerical and theoretical modeling of water droplet impact on hydrophilic and superhydrophobic cones

The phenomenon of droplet impingement on solid surfaces is prevalent in various natural and industrial contexts. Research on impact dynamics on conical surfaces keeps emerging, with superhydrophobic cones receiving more attention than hydrophilic ones. This study systematically investigates water droplet impact dynamics on both hydrophilic and superhydrophobic cones using a two-phase numerical solver under different Weber numbers (We) and cone angles (φ). Three distinct phases are identified in the We–φ map to describe the different outcomes on each type of cones. Generally, deposition occurs ultimately on hydrophilic cones, whereas rebounding is observed on superhydrophobic ones. The maximum spreading area βAmax on hydrophilic cones depends only slightly on φ but consistently increases with We, following a scaling law of We0.5 at higher We. In contrast, on superhydrophobic cones, βAmax increases significantly with both We and φ, and the exponent in the scaling laws of βAmax with respect to We increases notably as φ increases. Three characteristic times are defined to describe important motion states on both types of cones. Corresponding scaling laws for each time with We are established. Two theoretical models are developed to predict the maximum spreading position for droplets on hydrophilic cones and the rebound position on superhydrophobic cones, respectively. Gravitational potential energy is included in the energy budget for both models, and an auxiliary viscous dissipation due to spontaneous spreading is accounted for the hydrophilic case. Satisfactory agreement between the theoretical and numerical results is achieved.

Highly-efficient low-voltage electrodeposition of superhydrophobic diamond-like carbon films from N-methyl pyrrolidone

N-methyl pyrrolidone was proposed as a new carbon source for efficiently preparing the diamond-like carbon (DLC) films by a one-step electrodeposition technique at a low voltage. The responses of surface morphology, microstructure and surface wettability of the DLC films on the variation of the area ratio of anode to cathode were investigated in terms of current density in the process of electrodeposition. Especially, the dynamic behaviors of water droplets impacting on one of the superhydrophobic DLC films were studied in detail as a function of Weber number and inclined angle. Results revealed that either a larger or a smaller area ratio than 1.56 could facilitate the formation of hierarchical structure with more hydrocarbon features, which is in favor of creating superhydrophobicity with low surface adhesion. Further, it was found that a competitive strategy between deformation and movement depending on Weber number and inclined angle, where the movement is balanced by sliding with rolling, dominates the impact dynamics of water droplets. This work provides new insight and explanation for the efficient electrodeposition of DLC films at low voltage and the dynamic evolution of impacting droplets on the inclined superhydrophobic surface.

Dynamics of a Water Droplet Impacting an Ultrathin Layer of Oil Suspended on a Pool of Water

This study investigates water droplets impacting a two-layered pool, consisting of a deep pool of water above which an ultrathin a suspended layer of silicone oil is present. Initially, the difference between the impact dynamics of water droplets on ultrathin and thick layers of oil were studied. It was found that the existence of an ultrathin layer of oil changes the impact characteristics such how aggressively the jet rises, how the dimensions of the impact impression change, and how the jets are broken down on their tops. Then, in a series of experiments on ultrathin layers of oil, the droplet size, the velocity of the droplets upon impact, and the viscosity of the oil layers were changed to observe and measure the characteristic dimensions of the formed craters and the jets. It was observed that when the viscosity of oil layers decreased to a minimum of 1 (cSt), the jet height and crater sizes increased to their maximum value. In addition to the effect of the oil viscosity, it was found that the droplet size and the release heights of the droplets were in the next orders of significance in determining the impact dynamics. The impacts were also characterized qualitatively by specifically looking into the crown and crater formations, pinch-off modes in jets, and number of formed secondary droplets. As well as the quantitative conclusion, it was found that the major affecting parameter in changing each of these qualities was the viscosity of the suspended oil layer.

Impact dynamics of water droplets on oil-covered dielectrowetting substrate: Effects of oil film thickness and surface wettability

Droplet impacting on solid or liquid film is a ubiquitous phenomenon in relevant processes such as spray cooling and inkjet printing on primer layers. In this study, the dynamics of water droplets impacting a solid substrate covered by a silicon oil film is investigated under the influences of the surface wettability of the dielectrowetting substrate (69.3°-117.4°) and the thickness of the silicon oil film (7.79–21.8 μm) at We=6.81. A phase diagram is established, which reflects the relationships between the impact dynamic behavior, equilibrium contact angle, and the oil film thickness. The maximum spreading factor βmax and maximum out-of-plane height Hmax/D0 for rebound of sub-droplet behaviors was smaller than 13 % and greater than 3 times than those droplet deposition behaviors, respectively. Finally, the retraction dynamics of the droplet after reaching its maximum spreading diameter is analyzed and discussed based on retraction rate γw=vr/Dmax=σw(cosθrmin-cosθeq)/fkDmax through the force balance at the three-phase contact line. Results of the study indicate that the surface wettability of the dielectrowetting substrate and thickness of the silicon oil film significantly affect the impact dynamics of water droplets on a solid substrate covered by the silicone oil film, especially in the retraction stage. This study sheds new light on controlling the dynamic impact of the droplets on silicon oil films, which is of importance to the control or optimization of processes such as inkjet printing on a primer layer.

Water droplet impact dynamics comparison on solid and hollow square micropillared substrates

We experimentally investigate microliter-sized water droplet impact on solid and hollow square micropillared polydimethylsiloxane substrates. Micropillared substrates with different values of pitch (34, 47, and 62 μm) and hole sizes (0, 3, 6, and 10 μm) of pillars are fabricated using soft lithography following direct laser writer maskless photolithography. We observe that hollow micropillared substrates exhibit increased hydrophobicity as compared to the solid micropillared substrates. Interestingly, we find that hydrophobicity is further enhanced as the hole size is increased. To understand the impact dynamics, we perform high-speed visualization to acquire the transient evolution of the impacting droplets. Based on the impact velocity (0.22–0.62 m/s), pitch, and hole size, we identify various regimes, namely, non-bouncing, partial bouncing, and complete bouncing. At a given impact velocity and pitch value, non-bouncing and bouncing regimes are observed for solid and hollow micropillared substrates, respectively. We find that the hollow micropillared substrate exhibits higher values for capillary pressure, impalement pressure, and the energy barrier associated with the Cassie–Baxter to Wenzel transition toward the impacting droplets. This is due to a decrease in the solid fraction owing to the incorporation of circular holes in pillars. The analysis shows the energy loss due to viscous dissipation decreases with an increase in hole size, which enhances the bouncing fate possibility. The fundamental insights gained from this study can be effectively leveraged by modulating the surface morphology to realize the desired droplet impact characteristics for various potential applications such as self-cleaning and energy harvesting.

Droplet impacting on pillared hydrophobic surfaces with different solid fractions

HypothesisThe solid fraction of the substrate is expected to influence the bouncing behavior of an impinging droplet, thereby affecting spreading and contact time. Hence, it should be possible to alter the velocity and pressure distribution of impacting droplet, and also affect the impact velocity for droplet penetration right upon impact. SimulationsWe systematically investigate the impact dynamics of water droplets on pillared hydrophobic surfaces with different solid fractions using phase-field simulations. The velocity and pressure distributions of impacting droplets on pillared hydrophobic surfaces with varied Weber numbers and solid fractions are studied. In addition, the influences of the solid fraction on the bouncing behaviors of the impinging droplet, such as the maximum wetting spreading, the maximum impacting depth, and the contact time, are also investigated to further understand the impact event. FindingsWe show that a three-peak pressure profile appears on the top of the pillared hydrophobic surface during droplet impact by varying the solid fraction of the surface. The first peak is generated by the impact of the droplet itself, while the second peak arises from the droplet recoil impact associated with the dynamic properties of the jet. Moreover, we identify a hitherto unknown third pressure peak related to the hydrodynamic singularity that emerges due to the convergence of the fluid during the droplet rebound. This solid fraction-dependent impacting behavior reveals the intricate interplay between droplet dynamics and the underlying surface characteristics, providing valuable insights into the design and optimization of micro/nano structured hydrophobic surfaces for various applications.

Droplet impact on a microhole through a partially wetting surface

In this study, we thoroughly investigate the impact dynamics of water droplets on a partially wetting substrate with a single hole. By conducting experiments using de-ionized water droplets and high-speed imaging, we observe various outcomes, including downward jetting without pinch-off, jetting with single and multiple pinch-offs, and the intriguing emergence of an upward jet during droplet recoil. A regime map is constructed to establish the relationship between the dynamics of the jet and the Weber number. We find the small amount of liquid leakage through the hole has a negligible effect on the maximum spreading of the droplet. We analyze the behavior of the downward jet resulting from droplet impact in terms of its length, speed, and breakup characteristics. The scaling relation between the maximum jet length before its breakup and the Weber number is derived and compared with experimental data. We find that the growth of the downward jet length follows a consistent power-law relationship with time regardless of impact velocity, while the maximum jet velocity scales linearly with the impact velocity, confirming the hydrodynamic focusing theory. The size of the head satellite droplet formed during the jet pinch-off process remains nearly constant across different Weber numbers. Additionally, we investigate the volume of ejected liquid through the microhole, observing an initial increase with the Weber number followed by a saturation point. The occurrence of the upward jet during droplet recoil is a significant finding, and we analyze its diameter, height, and velocity in relation to the Weber number.

Water droplets impact dynamics on laser engineered superhydrophobic ceramic surface

The development of superhydrophobic surfaces is significant due to the industrial applications in various fields, from energy to biomedical implants. The surface morphology and chemistry primarily govern the characteristics of the interface between the water droplet and the surfaces. Herein, a combination of laser patterning and low-pressure technique has been adopted to generate the superhydrophobic TiN surface. The superhydrophobic surface was subjected to wetting property and chemical analysis with respect to the surface geometry. The impact dynamics of water droplets at the laser-patterned superhydrophobic surface have been studied. The droplet impacts result in finger formation at the start of the spreading, and the droplets formed at the tip of fingers detached from the rim during the retraction. The resulting fragmentation favors decreased travel distance and time required for recoiling the water droplets. The fragmentation during the recoiling results from modified hydrodynamics induced by the surface morphology and wetting property. The laser-processed hierarchical surface structures are a potential method to reduce the contact time at the solid-liquid interface.

Temperature-dependent droplet impact dynamics of a water droplet on hydrophobic and superhydrophobic surfaces: An experimental and predictive machine learning–based study

• Droplet impact on microstructured surfaces (hydrophobic/superhydrophobic) at different temperatures has been studied. • Effect of velocity, droplet diameter, temperature, surface wettability and roughness on impact dynamic are evaluated. • Using three machine-learning algorithms, an innovative method for predicting droplet impact dynamic is presented. Heightening the water repellency of surfaces can serve anti-icing purposes by removing water drops before they freeze and adhere to a surface. Here we study the impact dynamics of water droplets on silicone rubber surfaces—ranging from hydrophobic to superhydrophobic—at −20, −10, and 25 °C. We evaluate the influence of static contact angle, contact angle hysteresis, surface roughness, temperature, impacting velocity, and droplet diameter on droplet behavior (e.g., deposition, bouncing, splash). Minor effect of temperature on droplet dynamics on microstructured surfaces for a wide range of Weber and Reynolds numbers is observed. Experimental observations show that full bouncing only occurs on superhydrophobic surfaces with a CA > 160° and a CAH < 2° at temperatures above 0 °C for We < 110 and Re < 5000. Increasing the impact velocity of the droplet on rough surfaces heightens the probability of splashing. This experimental data is then coupled with machine-learning techniques (logistic regression, decision tree, and random forest) to comprehensively investigate droplet impact behavior on hydrophobic and superhydrophobic surfaces at various temperatures. We predict the behavior probability of impacting droplets on surfaces as a function of Weber number, Reynolds number and surface features (static contact angle, contact angle hysteresis, temperature, and surface roughness). Our experimental results and machine learning–based predictions are highly consistent, demonstrating that machine learning can effectively predict droplet motion on hydrophobic and superhydrophobic silicone rubber surfaces at different temperatures.

Contact time of impacting droplets on a superhydrophobic surface with tunable curvature and groove orientation

Regulating the impact dynamics of water droplets on a solid surface is of great significance for some practical applications. In this study, the droplet impingement on a flexible superhydrophobic surface arrayed with micro-scale grooves was investigated experimentally. The surface was curved into cylindrical shapes with certain curvatures from two orthogonal directions, where axial and circumferential grooves were formed, respectively. The effects of curvature diameter and Weber number, as well as the orientation of grooves on droplet spreading and retracting dynamics were analyzed and explained. Results show that the circumferential grooves promote the spreading of a droplet in the azimuthal direction, where the droplet rebounds from the surface with a stretched shape. This mechanism further reduces the contact time of impacting droplets on the superhydrophobic surface compared to the other curving mode.

Wetting, Adhesion, and Droplet Impact on Face Masks.

In the present pandemic time, face masks are found to be the most effective strategy against the spread of the virus within the community. As aerosol-based spreading of the virus is considered as the primary mode of transmission, the interaction of masks with incoming droplets needs to be understood thoroughly for an effective usage among the public. In the present work, we explore the interactions of the droplets over the most commonly used 3-ply surgical masks. A detailed study of the wetting signature, adhesion, and impact dynamics of water droplets and microbe-laden droplets is carried out for both sides of the mask. We found that the interfacial characteristics of the incoming droplets with the mask are very similar for the front and the back side of the mask. Further, in an anticipated attempt to reduce the adhesion, we have tested masks with a superhydrophobic coating. It is found that a superhydrophobic coating may not be the best choice for a regular mask as it can give rise to a number of smaller daughter droplets that can linger in air for longer times and can contribute to the transmission of potential viral loads.

Further Step toward a Comprehensive Understanding of the Effect of Surfactant Additions on Altering the Impact Dynamics of Water Droplets.

The addition of surfactants to pure water for specific applications has made controlling the impact dynamics of surfactant-laden droplets a complex phenomenon. This work investigates the influence of the molecular weight (MW), concentration, and ionic nature of the surfactants as well as the substrate surface characteristics on the impact dynamics of surfactant-laden droplets using a high-speed camera at 10 000 frames per second. Sodium dodecyl sulfate, hexadecyltrimethylammonium bromide, and n-decanoyl-n-methylglucamine were used as anionic, cationic, and nonionic surfactants, respectively. We used hydrophilic glass slides, hydrophobic polytetrafluoroethylene, and superhydrophobic alkyl ketene dimer (AKD) as substrates. The results show that the efficiency of the surfactant addition in increasing the maximum spreading diameter is significantly influenced by the molecular weight and ionic nature of the solutions as well as the nonwettability of the substrate. Among all of the surfaces examined, the concentration and ionic nature of the solutions were found to be more dominant parameters in determining the energy dissipation in the retraction phase of the droplet impact on the superhydrophobic AKD surfaces. As the concentration decreases or positive charges are present in the solution, it is more likely to observe a similar retraction dynamic to pure water when the droplet hits the superhydrophobic AKD having negatively charged surface sites. Finally, in terms of the impact outcomes of the surfactant-laden droplets on the superhydrophobic AKD, it is shown that the influence of the surfactant addition is more noticeable at lower Weber numbers, where the droplet tries to rebound by overcoming the energy loss that occurred in the spreading.

Oblique droplet impact on superhydrophobic surfaces: Jets and bubbles

Previous studies revealed that the perpendicular impact of low-viscosity droplets on sufficiently lyophobic surfaces would stimulate a liquid jet during droplet recoiling, and in some cases, it is accompanied with the entrapment of an air bubble. However, whether such free-surface flow phenomena occur in oblique droplet impact and how surface inclinations influence the dynamics remain open questions. Herein, we perform a comparative investigation on the perpendicular and oblique impact dynamics of water droplets on superhydrophobic surfaces. We show that the inclinations of the target surface do not influence the jet emission and the bubble entrapment in droplet impact. The jetting phenomena, which are triggered by the collapse of the air cavity, can be classified into three types of scenarios, and the jet velocity scales with its size according to two power laws as suggested by the scaling analyses in the previous studies. On the other hand, the air bubble entrapment is caused by the asymmetric cavity collapse when the recoiling speed of the droplet top is close to that of the bottom, and the bubble size can be reduced by the rising jet from the cavity bottom. We also show that some entrapped bubbles on inclined surfaces would move to the droplet surface and eventually burst, shooting out another thin jet. The correlation between the jet velocity and the bubble size is compared with different empirical scaling laws in the literature.

Impact Dynamics of Aqueous Polymer Droplets on Superhydrophobic Surfaces

Controlling the impact of water droplets on nonwetting surfaces is difficult due to their superior liquid repellency. Herein, we experimentally demonstrate that the impact dynamics of water droplets on superhydrophobic surfaces can be effectively altered by adding a very small amount of high molecular weight polymer. The presence of polymer chains in water enhances droplet–surface interactions and liquid viscoelasticity, which couple with the hydrodynamic effect and thus affects the dynamic behaviors of impinging droplets. Whereas various impact phenomena with altered transitional boundaries in the phase diagram have been observed for droplets of aqueous polymer solutions at low concentrations, only deposition was identified for aqueous polymer droplets with high concentrations. Nevertheless, the polymer addditive does not influence droplet spreading but siginificantly slows down droplet retraction and increases the contact time of rebounding droplets on the superhydrophobic surface. Moreover, the induced...

Developing a non-optical platform for impact dynamics analysis on nanostructured superhydrophobic surfaces using a quartz crystal microbalance

Quantitative analysis of water droplet behavior under dynamic conditions is one of the critical challenges for applications of wettability-controlled surfaces. Currently, various optical analysis techniques have been employed to analyze impact dynamics. Despite the convenience of direct observation of water droplets, most of these techniques have limited applicability to microscopic and quantitative investigations. In an effort to overcome these limitations, here, we suggest a complementary analysis platform using a quartz crystal microbalance (QCM) to study impact dynamics. A high-speed camera and QCM were applied together to study the behavior of water droplets that impact wettability-controlled surfaces with various We numbers (Weber number). For these experiments, ZnO nanowire surfaces were prepared and chemically modified by alkyl-thiol molecules with various carbon chain lengths (C0–C12) to control the surface energy. For nanowire surfaces with high surface energies (C0–C6) and for the lowest surface energy sample (C18), both methods exhibited highly consistent impact dynamics, showing stable wetting and dewetting properties, respectively. In addition to these apparent behaviors, QCM was further able to provide detailed microscopic information regarding the penetration and deformation of water droplets in a quantitative way based on acoustic sensing. More interestingly, QCM was able to determine the metastable water repellency of a C12-modified surface with a high We number, which could not be detected by the high-speed camera. These results suggest the significant potential of QCM as a new platform to analyze the impact dynamics of water droplets via quantitative, microscopic investigations.

Remarkably facile fabrication of extremely superhydrophobic high-energy binary composite with ultralong lifespan

In the 21st century, it is bound to become an important trend for the assembly of novel micro/nano functional materials with long lifespan in the real world by using facile techniques. In this report, the concept of using a low-cost and convenient method of electrophoretic assembly and further surface functionalization by perfluoroalkyltriethoxysilane (FAS-17) modification to obtain superhydrophobic nanoscale composite coatings (e.g. Al/Bi2O3) and its first demonstration are reported. The resulting low-energy coatings with nanoparticles distributed homogeneously in nanoscale and abundant rough reticular structures possess almost perfect superhydrophobic properties with a water contact angle (WCA) of ca.170° and a negligible roll-off angle. The water droplet impact dynamics is analyzed by a high-speed photography in detail. Additionally, the superhydrophobicity and exquisite heat release performance of the products keep almost unchanged after ultra-long exposure time and high relative humidity (>90%), respectively, indicating the excellent stability and great resistance to changeable environment and wide application potential in fields of surface chemistry, materials science and engineering, physics, etc. This study provides an effective general strategy for the design and development of superhydrophobic functional composites with wide application for different experimental and industrial purposes.

Dual dimensional nanostructures with highly durable non-wetting properties under dynamic and underwater conditions

Non-wetting states with high durability under both dynamic and underwater conditions are very desirable for practical applications of superhydrophobic surfaces in various fields. Despite increasing demands for this dual stability of non-wetting surfaces, studies investigating both the impact dynamics and underwater stability are very rare. In the current study, we performed water droplet impact dynamics and underwater stability studies using ZnO/Si hierarchical nanostructures (HNs) as a model system. The effects of the surface structure on the non-wetting states under dynamic conditions were first studied by comparing various surface structures, such as ZnO nanowires (NWs), Si microposts (MPs), ZnO/Si HNs with controlled MP interspacings, and lotus leaf (LL). The growth of ZnO NWs on Si MPs drastically improves the non-wetting properties of Si MPs under dynamic conditions. The transition of wetting states from the Cassie-Baxter state to the Wenzel state occurs on ZnO/Si HNs as the impact velocity increases. Measurement of the critical We number during transition enables us to determine the important parameters of wetting pressure using a simple model. Moreover, compared to Si MPs, ZnO NWs, and LL, our ZnO/Si HNs exhibit dramatically increased air pocket lifetimes under underwater conditions, which is due to the enhanced capillary pressure originating from the dual dimensional hierarchical structure. Our study indicates that optimally designed hierarchical surfaces have remarkably high durability non-wetting states under both dynamic and underwater conditions, expanding the potential application of non-wetting surfaces.

The icephobicity comparison of polysiloxane modified hydrophobic and superhydrophobic surfaces under condensing environments

Four polydimethylsiloxane (PDMS) coatings with different surface free energies have been prepared and applied to smooth and roughened aluminum plates to form hydrophobic and superhydrophobic surfaces. Their surface wettability in terms of water contact angle (CA), sliding angle (SA) and water droplet impact dynamics was studied under an ambient (50% relative humidity, RH at 25°C) and three different condensing environments (low, highly and extremely condensing, i.e. 30%, 60% and 90% RH at −10°C). In addition, the surface ice adhesion was investigated under the extremely condensing condition. Different PDMS coatings on either smooth or roughened surfaces displayed a very similar impact to static and dynamic wettability under the ambient environment. However, the water impact behavior and ice adhesion under the extremely condensing condition between the hydrophobic and superhydrophobic surfaces are significantly different. One of the superhydrophobic surfaces (R2180) demonstrated an excellent water repelling capability to retard ice accumulation, and reduced ice adhesion strength even under the extremely condensing condition, and thus will be a good candidate for ice-phobic applications. This excellent ice-phobic property is attributed to the low surface free energy of the coating, which effectively prevents the water condensation inside the cavities of the hierarchical superhydrophobic structures and thus maintains “air cushion” on the solid/water interface, indicated by a very low solid-liquid contact area increase after surface is exposed to this condensing weather condition. This result demonstrates that the “air cushion” in a superhydrophobic surface could be maintained even under an extremely condensing condition by carefully selection of coating composition with a very low surface free energy.

Wettability and impact dynamics of water droplets on rice (Oryza sativa L.) leaves

We investigated the wettability and impact dynamics of water droplets on rice leaves at various leaf inclination angles and orientations. Contact angle, contact angle hysteresis (CAH), and roll-off angle (α roll) of water droplets were measured quantitatively. Results showed that droplet motion exhibited less resistance along the longitudinal direction. Impact dynamic parameters, such as impact behaviors, maximum spreading factor, contact distance, and contact time were also investigated. Three different impact behaviors were categorized based on the normal component of Weber number irrespective of the inclination angle of the rice leaf. The asymmetric impact behavior induced by the tangential Weber number was also identified. Variation in the maximum spreading factor according to the normal Weber number was measured and compared with theoretical value obtained according to scaling law to show the wettability of the rice leaves. The contact distance of the impacting droplets depended on the inclination angle of the leaves. Along the longitudinal direction of rice leaves, contact distance was farther than that along the transverse direction. This result is consistent with the smaller values of CAH and α roll along the longitudinal direction.

Impact dynamics of water droplets on Cu films with three-level hierarchical structures

Three Cu films with different three-level hierarchical structures were fabricated using a one-step electric brush-plating technique. Impact dynamics of water droplets on three Cu films was investigated. In the absence of surface chemical modification, the Cu films showed static hydrophobicity and even superhydrophobicity. Under dynamic impact, the two hydrophobic Cu films were wetted partially, whereas the superhydrophobic Cu film exhibited considerably robust water-repellency in a wide range of Weber number. Analysis based on the pressure balance relation revealed that the considerably robust water-repellency of the superhydrophobic Cu film arises from the damping role of the varied height and shape of the micro-protrusions in lowering the water hammer pressure, the delaying role of the submicro-bumps on the side of the micro-protrusions in preventing the penetration process of the depinned water–air interface and the critical surface hydrophobization role of the nano-scale structure in changing the wetting property of the basal surface of the Cu film from hydrophilicity to hydrophobicity.