Dynamics Of Water Droplets Research Articles

Surface-deformability dependent contact time of bouncing droplets on sessile soap bubbles

HypothesisThe curvature of the free-standing liquid film is expected to modify its surface deformability, thereby affecting droplet bouncing dynamics and possibly tuning the liquid repellency performance in practical applications. ExperimentsIn this study, the bouncing dynamics of water droplets on sessile soap bubbles with different curvatures has been experimentally investigated using high-speed camera. FindsTo resist the impacting droplets, the soap bubbles is observed to show two types of deformation: the geometrical deformation caused by the total impacting force and the pressure distribution induced deformation from the droplet dynamics. The variation trend of the contact time of the droplet with the impact velocity is found to be highly dependent on the surface deformability of the soap bubble. This trend becomes non-monotonic when the soap bubble is large and more deformable. The decreasing contact time with increasing impact velocity can be well captured by a phenomenological model of coupled springs. The increasing contact time for the large soap bubbles at high impact velocities is due to the further compression of the soap bubble by the recoiling droplet, leading to the decoupling of the above two types of bubble deformation.

CFD simulation of the interaction between water droplets on the GDL of a low temperature PEM FC in conditions of air cross-flow

Abstract Droplet dynamics in low temperature proton exchange membrane fuel cells (LT-PEMFCs) are significantly important with respect to water management and removal. Three main phenomena are linked to water generation/transport in a LT-PEMFC: H2O production on the cathode side, electro-osmotic drag (anode to cathode) and back diffusion (cathode to anode). The excess/lack of water, depending on membrane humidity, strongly affects LT-PEMFC performance, involving its instability. In this work CFD simulation of droplets was performed when they were deposited in tandem on the gas diffusion layer (GDL) and subjected to 15 m/s parallel air flow. The volume of fluid (VOF) method was adopted and droplets with diameters that range from 0.3 mm to 0.8 mm were considered. Simulations demonstrate that deformations, oscillations and sliding of droplets were affected by their relative size and position. Results can contribute to define predictive models of water droplet dynamics on the GDL surface and their detachment towards the FC gas channel.

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.

Effect of Microchannel Curvature on Water Droplet Dynamics in a Highly Viscous Flow

Effect of Microchannel Curvature on Water Droplet Dynamics in a Highly Viscous Flow

Experimental insight into dynamics of water droplet impacting on solid surface and theoretical prediction for maximum spreading coefficient at low Weber number

The hydrodynamics of a droplet impacting solid surface at low Weber number has been studied comprehensively by using a high-speed camera and a theoretical approach based on the improved models of surface energy and viscous dissipation. The impact process is elucidated by analyzing quantitatively the interface evolution of droplet impact solid surface, and the effects of glycerol solution concentration, surfactant concentration, impact velocity, and wall contact angle on spreading width and rebounding height are extensively investigated, respectively. Four stages, namely, approaching, spreading, retracting and stabilizing stages are identified visually during a complete droplet collision. Increasing the concentration of glycerol solution can simultaneously reduce droplet spreading width and rebounding height. However, improving surfactant concentration or enhancing impact velocity can promote droplet spread but hinder its rebound. Decreasing wall contact angle is beneficial to droplet propagation, whereas disadvantageous to droplet rebound. Both surface energy and viscous dissipation are accurately considered based on a real geometric shape and an improved spreading time at the maximum spreading, and thus a novel theoretical formula for the maximum spreading coefficient of droplet impacting at low Weber number has been developed and proved to have a higher prediction accuracy than the previous models under present experimental conditions.

Rebound characteristics of a water droplet impacting on a superhydrophobic cone

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°.

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.

Effects of heterogenous wettability on evaporation from a simulated soil pore: Stick-slip evaporative mode and contact line motion

The Ogallala Aquifer, a primary irrigation water source in the High Plains region of the United States, is declining, thereby necessitating new water conservation strategies. This paper investigates the impact of mixed wettability on the evaporation dynamics of a 10-µl sessile water droplet placed within simulated soil pores comprised of hydrophobic Teflon beads (CA ∼ 108°) and hydrophilic glass (CA ∼ 41°) beads with 2.38-mm diameters, where homogeneous and heterogenous (i.e., mixed hydrophobicity and hydrophilicity) wettability configurations were investigated. Experiments were performed in an environmental chamber where the relative humidity and temperature were 60% ± 0.1% RH and 20 ± 0.4 °C, respectively. Wettability influenced evaporation times, with homogeneous hydrophobic pores (i.e., three Teflon beads) and heterogenous one glass, two Teflon pores having the longest average evaporation times of 40 and 39 min, respectively. Homogeneous hydrophilic pores (i.e., three glass beads) and heterogenous two glass, one Teflon pores exhibited evaporation times of 34 min. Evaporation times for heterogenous combinations trended based on the predominant wettability. Contact angles and the projected length of contact were analyzed from videos to capture pinning and depinning during evaporation. For many cases including hydrophobicity, contact angles were less than 90°, and in some configurations, water would be pinned on a Teflon bead, whereas depinning (i.e., moving) on a glass bead. Stick-slip evaporation was observed, where the evaporating droplet switched between constant contact radius and constant contact area evaporative modes to minimize droplet surface energy. The results suggest wettability alterations in agricultural settings may reduce evaporation.

Behavior of small water droplets in a highly viscous flow in a converging and diverging channel

Understanding the evolution of water droplets moving in a highly viscous bulk flow (e.g., bitumen) has attracted increasing attention in the context of numerous separation technologies due to various issues relating to the environment (re-use of water) and engineering failures (corrosion of pipelines). With this in mind, the main objectives of this work are to explore the dynamics of water droplets with a diameter of seven micrometers, moving in highly viscous bitumen flowing through a smoothly converging and diverging 11-micron channel using three-dimensional (3D) and two-dimensional (2D) droplet-resolved simulations and to adjust an existing population balance model (PBM) to predict geometry-driven coalescence for different flow rates. The Eulerian–Eulerian (EE) method coupled with a new PBM is used to predict the behavior of water droplets with a diameter of 7 μm. Numerical simulations were carried out for various capillary numbers (0.1<Ca<3) and compared with the volume of fluid method combined with the level-set function (CLSVOF). Adaptive mesh refinement (up to six levels) was used in 3D and 2D CLSVOF simulations, producing interface cells measuring up to 30 nm. Good agreement was observed between EE-PBM and CLSVOF models. For comparison, we show the results of 2D CLSVOF simulations. This new PBM model can be used to predict water–oil separation in new cascade-formed geometries to enhance the coalescence of water droplets in highly viscous bulk flows.

Unraveling the role of vaporization momentum in self-jumping dynamics of freezing supercooled droplets at reduced pressures

Supercooling of water complicates phase change dynamics, the understanding of which remains limited yet vital to energy-related and aerospace processes. Here, we investigate the freezing and jumping dynamics of supercooled water droplets on superhydrophobic surfaces, induced by a remarkable vaporization momentum, in a low-pressure environment. The vaporization momentum arises from the vaporization at droplet’s free surface, progressed and intensified by recalescence, subsequently inducing droplet compression and finally self-jumping. By incorporating liquid-gas-solid phase changes involving vaporization, freezing recalescence, and liquid-solid interactions, we resolve the vaporization momentum and droplet dynamics, revealing a size-scaled jumping velocity and a nucleation-governed jumping direction. A droplet-size-defined regime map is established, distinguishing the vaporization-momentum-dominated self-jumping from evaporative drying and overpressure-initiated levitation, all induced by depressurization and vaporization. Our findings illuminate the role of supercooling and low-pressure mediated phase change in shaping fluid transport dynamics, with implications for passive anti-icing, advanced cooling, and climate physics.

Experimental analysis of water-droplet–fiber interaction on a mechanically excited hydrophobic fiber

In this study, the dynamics of a single water droplet on a mechanically excited single fiber are investigated fundamentally. By utilizing state-of-the-art high-speed camera technology, the droplet's motion is captured with exceptional temporal resolution, enabling a detailed analysis of its position, size, and kinetics. We can identify distinct motion patterns of a droplet adhering to the fiber, which can exhibit either a static, a tilting, or swinging motion. The swinging and tilting motion can be overlaid with a higher-frequency deformation in response to the fiber excitation. Additionally, we examine the detachment of the droplet from the fiber as well as for the first time the (periodic) reattachment resulting from the mechanical excitation. The used droplet volumes are smaller, and the excitation shown here is greater than the excitation acceleration previously investigated in single fiber studies. Insights into droplet–fiber interactions can provide a better understanding of the mechanisms occurring in coalescence filters in harsh environments, which cannot be observed in situ with high temporal and spacial resolution in a full-scale filter due to the lack of optical access.

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.

Numerical investigation on rebound dynamics of supercooled water droplet on cold superhydrophobic surface

The rebound dynamics of a microscale supercooled water droplet on cold superhydrophobic surface is numerically studied. A three-dimensional numerical model based on level set method and Enthalpy-Porosity model is developed to study the impacting-freezing behaviors of supercooled water droplet. The retraction rate and the morphology evolution of the supercooled water droplet are focused on. The accuracy of the adopted numerical model is validated via the well agreement with the experimental results. Four different regimes are observed for the impacting-freezing process: fully rebound, satellite rebound, breakup and fully adhesion. The numerical results indicate that the retraction rate is decreased with the cold surface temperature. The heat transfer rate between water droplet and surface is increased with the impact velocity, droplet diameter and supercooled degree of cold surface. The evolution of droplet morphology reveals the competitive relationship between droplet impact dynamics and solidification. Regarding the fully rebound regime, the rebound length increases with the Reynolds number. For the situations that rebound with satellite droplet, with the increase of the impact velocity, the generation of satellite droplet is delayed, while the size of satellite droplet is increased.

Experimental investigation on the dynamics of a single water droplet impacting wood surface

The dynamic characteristics of water mist droplets hitting the wood surface is one of the important factors affecting the fire extinguishing performance. However, the spreading dynamics between water droplets and wood surfaces during the impacting process have not been adequately characterized in existing literature. This study experimentally investigates the dynamic process of a single water droplet with changing Weber numbers from 66.7 to 1268.5 impacting different solid wood surface from the perspective of fire suppression. Typical impacting phenomena, the phenomena distribution, the droplet spreading dynamics and the maximum spread factor have been analyzed and discussed. Typical phenomena including no splash, transition from no splash to prompt splash, and prompt splash with varying Weber number are observed for the wood surface. The typical phenomena distribution can be distinguished by lgWe and lgRe and the result shows that lgWe < 2.11, 2.11 < lgWe < 2.42, and lgWe > 2.42 correspond to the phenomena of no splash, transition from no splash to prompt splash and prompt splash respectively. The spreading time can be predicted by the expression of ts/(ρRmax3/σ)0.5=6.52∗We-0.92. By analyzing the maximum spreading factor, the model βmax∝(We/Oh)0.198 is found to present good predictions for wood surfaces.

Laser-induced, single droplet fragmentation dynamics revealed through megahertz x-ray microscopy

The fragmentation dynamics of single water droplets from laser irradiation is studied with megahertz frame rate x-ray microscopy. Owed to the nearly refraction-free and penetrating imaging technique, we could look into the interior of the droplet and reveal that two mechanisms are responsible for the initial explosive fragmentation of the droplet. First, reflection and diffraction of the laser beam at the droplet interface result in the formation of laser ray caustics that lead to non-homogeneous heating of the droplet, locally above the critical temperature. Second, homogeneous cavitation in the droplet that is likely caused from shockwaves reflected as tension waves at the acoustic soft boundaries of the droplet. Further atomization occurs in three stages, first a fine sub-micrometer sized mist forms on the side of the droplet posterior to laser incidence, then micrometer sized droplets are expelled from the rim of an expanding liquid sheet, and finally into droplets of larger size through hole and ligament formation in the thinning liquid sheet where ligaments pinch off.

Investigation of droplet impact dynamics on textured cylindrical hydrophobic surfaces

In this experimental investigation, a study of water droplet dynamics has been performed on a semi-hierarchical textured cylindrical target. Three different textures, viz. cycloid, sawtooth, and triangular, with amplitude of 300 µm and time-period of 600 and 800 µm, were fabricated on a Nickel-Titanium alloy through the Wire Electrical Discharge Turning process. The contact angle of the textured samples improved drastically compared to the as-received samples and was related to the roughness factor (r). The spreading in the axial direction has been studied for the various textures, and it was observed that the textures significantly reduce the maximum spreading diameter compared to the smooth cylinders. Furthermore, the experimental investigation revealed splashing in the case of textured samples and deposition in the case of as-received samples at α ≥ 38.8, indicating r, along with diameter ratio, D* , plays a critical role in determining the splashing zone. Accordingly, a regime map has been plotted between r and α, and a critical curve in the form of hyperbolic function was observed. The average velocity of spreading and receding was calculated, and the spreading velocity was 3–5 times higher than the receding velocity. Finally, a model has been developed based on data-driven machine learning, which was in good agreement with the previous experimental investigations.

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.

Liquid Water Transport Characteristics and Droplet Dynamics of Proton Exchange Membrane Fuel Cells with 3D Wave Channel

Water management is a crucial aspect in the efficient functioning of proton exchange membrane fuel cells (PEMFCs). The presence of a two-phase flow, consisting of water and reactive gas, in the channel of the PEMFC is of utmost importance for effective water management. This study focuses on investigating the removal of liquid water in 3D wave channels and 2D straight channels using the volume of fluid method. The study analyzes the dynamic behavior of droplets emerging from the gas diffusion layer (GDL) into the channel under the influence of gas flow. The study also explores the effects of droplet growth, deformation, detachment, force, and pore size on critical water behavior and water content in the channel. The results indicate that the 3D wave channel is more effective in removing liquid water compared to the 2D straight channel. It is observed that increasing the velocity facilitates the discharge of liquid water. However, excessively high velocities lead to parasitic power losses. Furthermore, while larger pore sizes in the GDL are not advantageous for PEMFC performance, a moderate increase in pore size aids in the discharge of liquid water. The knowledge gained through this study deepens the understanding of droplet dynamics in PEMFC gas channels and assists in optimizing the design and operational conditions of these channels.

Dynamics and heat transfer of water droplets impacting on heated surfaces: The role of surface structures in Leidenfrost point

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 with 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 that supports the droplet and increases Leidenfrost point from 188 ℃ (for bare aluminum surface) to 428 ℃. A higher Leidenfrost point over 500 ℃ (the maximum heating temperature) is achieved by 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. The prediction of present model shows good agreement with the 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.