Droplet Impact Research Articles

Investigation on droplet spreading and energy conversion process on solid surface with low impinging velocity

Accurately and quantitatively tracking the droplet impinging and spreading process in theory is of paramount importance for informing and advancing engineering application. However, the existing models have problems such as large energy calculation deviations and imprecise shape hypotheses, which lead to significant theoretical errors and require in-depth correction. In this paper, a numerical model based on the laminar flow equation coupled phase field method and the dynamic contact angle model involved in the droplet impinging and spreading process is first developed and validated. The morphology and parameters of droplet spreading at various conditions and the role and influence of gravitational potential energy are further investigated. Subsequently, a semi-empirical modified spoon-like model grounded in numerical outcomes and attempting to overcome traditional assumptions limitations is advanced, with its practical applicability rigorously discussed. Results show that the droplet spreading process basically undergoes “round sphere”, “round cap”, and “pancake-like /cylinder-like” to “shallow bottomed round tray”. Changes in Weber number (We) and equilibrium contact angle (θe) marginally alter the duration, spreading size, and droplet morphology characteristics in each process. The impact of gravitational potential energy is notably modulated by process parameters, exhibiting an increase with escalating droplet diameter and density, while decreasing in response to heightened initial droplet velocity and surface tension coefficients. Conversely, it remains largely invariant to changes in droplet viscosity and equilibrium contact angle. The consideration of shape factor and viscosity modification factor allows the surface energy and viscous dissipation energy to be accurately defined, making the proposed semi-empirical modified spoon-like model exhibit good performance, for all 65 studied cases the relative errors of droplet maximum spreading length factor (βmax) and center thickness (h) fall essentially within the 5% and 10% interval respectively.

Droplet impact behavior on a hydrophobic plate with a wettability-patterned orifice: A lattice Boltzmann study

Droplet impact behavior on a hydrophobic plate with a wettability-patterned orifice: A lattice Boltzmann study

Droplet impact dynamics on the surface of super-hydrophobic BNNTs stainless steel mesh.

The 'gas‒liquid‒solid' mechanism annealing method was used to create a superhydrophobic boron nitride nanotube (BNNT) stainless steel mesh in a tube furnace at 1250°C in an NH3 environment. Fe powder was used as a catalyst, and B:B2O3 = 4:1 was used as the raw material. The water droplets on the surface of the superhydrophobic material had a contact angle of approximately 150° and a slide angle of approximately 3°. By using molecular dynamics (MD) simulation technology, a three-dimensional braided physical model of nanodroplets and superhydrophobic BNNT mesh surfaces with the same contact angle and rolling angle was prepared via the function weaving method. The Weber number (We) was used as the entrance point to establish the relationship between macroscale experimental studies and nanoscale MD simulation analysis on the basis of these efforts. A study was conducted on the dynamic behaviour of droplets impacting a superhydrophobic BNNT filter surface. We suggest that the wettability, substrate structure, and impact velocity are connected to the impact dynamic behaviour of droplets on the basis of the data obtained at various scales. The findings demonstrate that when the droplet impact velocity increases, several droplet phenomena-such as impact-rebound, impact-spread-rebound, and impact-spread-breaking-polymerisation-spatter-appear on the substrate surface sequentially. The mechanism of impact behaviour at various scales is explained in light of these events. Furthermore, a better theoretical model is proposed to assess the droplet wetting transition at the nanoscale. This model accurately predicts the boundary Weber number that starts the wetting transition. Moreover, the connections among the impact velocity, spreading diameter, and contact time (or We) are examined. The tendencies found via MD simulations match the outcomes of the experiments. Our discoveries and outcomes broaden our understanding of how droplet impact affects the dynamic behaviour of superhydrophobic surfaces. A scientific foundation for examining the dynamic behaviour of droplets is provided by combining simulations and experiments.

Clinching 1/2 scaling: Deciphering spreading data of droplet impact

Clinching 1/2 scaling: Deciphering spreading data of droplet impact

Flow behavior and heat transfer characteristics of liquid film on vertical hot surface by inclined jet impingement

In this study, the flow behavior and heat transfer characteristics of the liquid film on the hot wall by inclined jet impingement are experimentally studied in detail. The effects of jet parameters, such as jet inclination angle, impingement distance, jet Reynolds number (Rej), and nozzle diameter are explored. The liquid film flow is visualized using a high-speed camera, and the surface temperature and heat flux are obtained by solving the inverse heat conduction problem. The results indicate that the liquid film shape is strongly affected by jet inclination angle but is almost unaffected by other parameters. As the inclination angle increases, the liquid film shape changes from elliptical to fusiform. In addition, the onset, enhancement, and disappearance of boiling cause the expansion and contraction of liquid film. The splashing rate is barely affected by jet parameters and remains within the range of 80–95 % under all conditions. The propagation of wetting fronts exhibits anisotropy. Except for the impingement distance, the position of wetting fronts along y-axis direction displays a high dependence on all parameters. The Rej and nozzle diameter have a significant effect on the heat flux at the impingement point and parallel flow zone, while the jet inclination angle and impingement distance only effect the impingement point. The visualization image proves that the droplet impingement pattern is the main reason for the increase in heat flux at higher impingement distances. Optimizing jet parameters can promote the wall to enter the rapid cooling stage in advance and increase maximum heat flux, thereby improving the maximum cooling capacity of the jet. Finally, an empirical equation is proposed to predict the maximum Nusselt number.

Methyl ricinoleate droplet impact on a high temperature stainless steel surface: Dynamic behavior and heat transfer

The rapid and uniform heating of the feedstock plays a key role in pyrolysis processes. Dispersing methyl ricinoleate (MR) into spray droplets can improve the heating speed and uniformity in the pyrolysis process, which is of great benefit to the yield of the target product. This article describes the results and mechanisms of single MR droplet impacting on a heated stainless steel surface at different temperatures (385 ∼ 520 °C). Two non-contact measurement techniques, including a high-speed camera and a thermal infrared imager, were used to record the dynamic behavior and heating effects of the MR droplet on the heated surface at different temperatures, respectively. Four representative impingement states were observed during droplet impact: adhesion rebound, adhesion rebound with breakup, bouncing, and bouncing with breakup. As a result, a comprehensive map was created, based on a dimensionless analysis, describing the relationships between the typical states. Regarding the quantitative analysis, the maximum spreading factor and the dimensionless droplet residence time were linearly related to the 0.336 and 0.389 powers of the Weber number, respectively. By calculating the average heat flux of a droplet, it was found that it is related to the stainless steel surface temperature, the droplet saturation temperature, and the Reynolds number. The transient temperature at the surface of the MR droplet was measured to quantify the effectiveness of the heating. This study could provide a theoretical basis for the regulation and optimization of MR pyrolysis conditions.

Analysis of the interfacial evolution characteristics of hollow droplet impact on a liquid pool

The impact dynamics of a hollow droplet on a liquid pool have significant implications across various industrial applications. This study employs numerical simulations to explore the dynamic evolution of the interface during the impact of a hollow droplet on a liquid pool. The investigation focuses on the effects of varying the hollow ratio Dr and liquid pool depth h* while maintaining a constant volume of liquid within the droplet shell. The findings reveal that both the hollow ratio Dr and pool depth h* critically influence the formation of ejecta + lamella, and vortex rings after the impact of a hollow droplet on a liquid pool. The confinement effect of the pool bottom can influence the evolution of the splashing, while the internal air in the hollow droplet can absorb a part of the impact energy during the collision. Specifically, at shallow pool depths, the interface primarily evolves into ejecta + lamella structures, whereas at greater pool depths, vortex ring formation is predominant. Furthermore, an increase in the hollow ratio leads to a reduction in the critical pool depth hc* at which the transition between these interfacial modes occurs. These findings indicate that, in practical applications involving the impact of hollow droplets on liquid pools, sufficient attention should be given to the pool depth. This enhances our understanding of the bottom pressure, droplet impact, and vortex formation, which is of significant relevance to related industrial technologies.

Exploring mechanisms of asymmetric droplet impact dynamics on roughness gradient surface

Droplet impact on surfaces with varying roughness and wettability is a common phenomenon in both natural and industrial environments. While previous studies have primarily examined asymmetric droplet rebound driven by impact velocity or Weber number, the influence of surface structure and associated impact mode transitions has received less attention. In this study, molecular dynamics simulations and detailed analyses are employed to investigate the mechanisms governing droplet rebound on nanopillar arrays with gradient distributions. Results reveal that nanopillar height significantly influences rebound direction, with two distinct directional transitions occurring as the height increases. Additionally, the effects of surface structure and Weber number on impact patterns, rebound velocity, and contact time are systematically evaluated, with contact angle calculations shedding light on the underlying force mechanisms. A phase diagram is developed to illustrate the relationship between rebound direction, Weber number, and nanopillar height. The study further extends the analysis to substrates with bidirectional gradient distributions, demonstrating consistency with single-directional gradient results and validating the broader applicability of the findings. This research provides critical insights into droplet dynamics on roughness gradient surfaces, emphasizing the role of nanopillar height and impact mode in controlling droplet behavior and highlighting potential applications in the design of structured array surfaces.

Dynamic impact analysis of solution droplets in frost-free air-source heat pumps: Transition from droplets to liquid film

This study investigates the dynamic propagation of solution droplets in frost-free air source heat pump systems, focusing on calcium chloride and ethylene glycol solutions. The research examines three key stages: droplet impact on a surface, collision with stationary droplets, and impact on a stabilized liquid film. Key findings include that increased surface contact angle and solution concentration inhibit droplet spreading, while higher impact velocity enhances it. Droplet retraction is influenced by surface tension and adhesion, with calcium chloride droplets showing variable retraction and ethylene glycol droplets consistently retracting less as concentration increases. Collisions with stationary droplets lead to behaviors such as merging, spreading, and rebound, with higher velocity accelerating these processes. In the final impact stage, a stable liquid film formation results in crown sputtering and oscillation, where sputtering height is inversely related to concentration but increases with impact velocity. These insights contribute to optimizing droplet management in air treatment systems.

Bouncing dynamics of a droplet impacting onto a superhydrophobic surface with pillar arrays

A superhydrophobic surface (SHS) patterned with pillar arrays has been demonstrated to achieve excellent water repellency and is highly effective for self-cleaning, anti-icing/frosting, etc. However, the droplet impact dynamics and the related mechanism for contact time (tc*) reduction remain elusive, especially when different arrangements of pillar arrays are considered. This study aims to bridge this gap by exploring a droplet impinging on an SHS with square pillar arrays in a cuboid domain. This fluid dynamics problem is numerically simulated by applying the lattice Boltzmann method. The influences of the droplet diameter (D*), the Weber number (Wew), and the pillar spacing and height (s* and h*) on the droplet dynamics and tc* are investigated. The numerical results show that the droplet can exhibit different bouncing patterns, normal or pancake bouncing, depending on Wew, s*, and h*. Pancake bouncing usually occurs when Wew ≥1.28, h*≥1, and s* ≈ 1, yielding a small tc*. Among all cases, a small tc* can be attained when the conversion rate of kinetic energy to surface energy (ΔĖsur*) right after the impacting exceeds a critical value around 0.038. This relation broadens that given in A. M. Moqaddam et al. [J. Fluid Mech. 824, 866–885 (2017)], which reported that the large total change of surface area renders small tc*. Furthermore, the maximum impacting force remains nearly the same in all cases, regardless of the bouncing patterns.

On-the-fly clustering for exascale molecular dynamics simulations

Computational resources have experienced exponential growth in the last decades enabling the simulation of complex physical problems at the cost of a massive increase in data storage. This is especially true for N-body simulations now reaching billions or trillions particles in certain cases. To overcome the drawbacks of data storage on disk for post-processing purposes, on-the-fly analysis has gained momentum but still represents a challenge in both its implementation and efficiency without impacting the simulation engine performances. This work provides a new in-situ procedure for features detection in massive N-body simulations, leveraging state-of-the-art techniques from various fields. Based on a discrete-to-continuum paradigm shift, particles and their respective physical quantities are projected onto a 3D regular grid before applying image analysis algorithms to group voxels based on specific user-defined criteria. A significant extension to the hybrid parallelism of connected component analysis within the image processing community is also introduced in the present study. Traditionally operating in shared memory parallelism, this extension now incorporates both distributed and shared memory approaches. The implementation is carried out within the exaStamp classical Molecular Dynamics code, a variant of the open-source exaNBody platform (see section 6). This adaptation allows for the on-the-fly analysis of multi-billion atoms samples with at most a 1.3% overhead. In addition, the entire framework is benchmarked up to 32768 cores. The applicability of the present approach is demonstrated on the case of a spall fracture in a tantalum sample as well as high velocity impact of a tin droplets on a rigid surface.

Effect of liquid droplet impingement on electrochemical passivation behavior of 321 stainless steel in 0.5 wt.% NaCl solution

Effect of liquid droplet impingement on electrochemical passivation behavior of 321 stainless steel in 0.5 wt.% NaCl solution

Analyzing rain erosion using a Pulsating Jet Erosion Tester (PJET): Effect of droplet impact frequencies and dry intervals on incubation times

Accelerated laboratory testing is essential to understand the rain erosion behavior of coated samples applied to the leading edge surface of a wind turbine blade. This study investigates the impact of droplet impact frequencies and dry intervals on the incubation time for damage on polyurethane-coated samples using a Pulsating Jet Erosion Tester (PJET). A novel theoretical model for water slug volume is introduced, allowing for a more accurate comparison across different impact velocities and frequencies. The effect of dry intervals on coating performance is quantified, revealing that longer dry intervals and shorter pre-dry rain exposure can significantly increase the number of impacts a coating can withstand before damage. The study challenges the traditional continuous impingement testing by demonstrating that dry intervals can extend incubation time by a factor of three to five. Additionally, this paper proposes a recalibrated approach to PJET testing, which better mimics the cyclic nature of real-world rainfall, leading to improved predictive models for material degradation. The findings emphasize the importance of considering the visco-elastic behavior of coatings and the role of intermittent rain exposure in erosion testing, offering invaluable insights for designing future PJET test parameters.

Experimental investigation of the impact and freezing processes of supercooled water droplet on different cold curved surfaces

The impact of supercooled water droplets (SCWD) on aircraft cold surfaces constitutes a major cause of aircraft icing, posing a considerable threat to flight safety. Developing a safe, efficient, and energy-efficient anti-icing method necessitates an in-depth investigation of the icing mechanism of SCWD impacting cold curved surfaces. This study experimentally investigates the freezing behavior of SCWD on cold surfaces with diverse curvatures. The results show that the water droplet spreading factor (WDSF) significantly increases as surface curvature ranges from 0 to 125 while simultaneously decreasing the freezing time. Furthermore, the ice ring morphology from droplet freezing transitions from a raised crown shape to a concave cake shape at the center. Changing the impact position of droplet resulted in a marked increase in WDSF, a substantially reduced freezing time, and the emergence of strip icicles at the lower part. Additionally, this study examines the effects of Weber number (We = 459–650) and impact surface temperature (Tw = −30 °C–0 °C) on the impact freezing process. An increase in We leads to a higher WDSF and reduced freezing times, while lower surface temperatures decelerate droplet retraction, thereby shortening freezing time. At surface temperatures below −25 °C, Tw results in droplets splashing upon impact and rapidly freezing during the spreading stage. The findings of this research provide experimental insights crucial for developing aircraft anti-icing technology.

Numerical investigation of droplet impacting, spreading and penetration on porous substrates

The behavior of droplets impacting porous surfaces, including spreading and penetration, plays a critical role in various engineering applications, yet the underlying mechanisms governing the interaction between these processes remain unclear. In this study, the complex interplay between droplet spreading and penetration on porous media was comprehensively investigated using the Level Set method. The droplet evolutions outside and inside the porous substrate influenced by droplet size, impact velocity, porosity, particle diameter, surface tension, and dynamic viscosity were explored. The results indicate that increases in droplet size and velocity lead to a simultaneous increase in both spreading factor and penetration depth. Higher values of porosity, particle diameter, and surface tension facilitated droplet penetration, despite at the expense of impeding droplet spreading on porous surfaces. Droplet size and surface tension exhibited less pronounced effects on penetration depth, particularly during the early stages. The spreading factor exhibited a non-monotonic trend with viscosity, initially increasing and subsequently decreasing, while the penetration depth decreased accordingly. Moreover, a larger spreading diameter corresponds to an expanded penetration width. A correlation was proposed to predict the maximum spreading factor based on Weber number, Reynolds number, and Darcy number, which can predict 83 % data in literature with deviations within ±20 %. This study provides new insights into the droplet dynamics on porous media and offers practical guidance for optimizing relevant engineering applications.

Solidification process of hollow metal droplets impacting a substrate

Recently, there has been a renewed interest in hollow droplet impact, as the internal bubble makes a difference in the spreading morphology during thermal spraying and three-dimensional printing. This paper is dedicated to the solidification process of a hollow metal droplet impacting a cold substrate. The influence of initial impact velocity and substrate temperature on the spreading process is numerically investigated by employing a phase-field method coupled with a solidification model. Solidification was shown to strongly alter droplet spreading and the flow state of the center liquid column. To describe the flow state of the center liquid column, three patterns, namely ‘no-jet’, ‘transition region’, and ‘counter-jet’ are defined. The simulation results show that the formation of the center counter-jet is inhibited by the solidification layer when Péclet number Pe<357, where Pe is the ratio of convection rate to diffusion rate. In addition, the critical Pe at which the phenomenon of counter-jet occurs gradually rises with the substrate temperature falling. Finally, a quantitative analysis of the maximum spreading diameter is proposed by establishing an energy conservation equation. The predicted diameters are in good agreement with the simulated results. It allows us to provide a general expression for the hollow droplets' maximum spreading diameter, using the impact and temperature parameters.

Dynamics of water droplet impact on a textured heated and tilted surface

The study reports the experimental results of dynamics of water droplet impact on smooth and rough tilted substrates made of stainless steel with different temperature of the surfaces. The influence of the direction of the texture and the temperature of the surface on the characteristics of droplet impact and sliding was studied. The tilt angle of the substrate was varied over a wide range. The Weber number was 100.It was established that the temperature of the surface did not influence the droplet/surface interaction modes. However, at the tilt angle of the substrate more than 20°, the surface temperature began to have an effect on the characteristics of the droplet sliding. The distance a water droplet travelled on the surface from the moment of contact with the substrate to the moment it came to a complete stop (droplet pinning) increased. The greatest influence of the temperature and tilt angle of the surface was observed when the droplet slid over the substrate in the direction not along but across the scratches. In this case, the distance a water droplet travelled on the surface increased significantly.

Bionic Fluorine-Free Multifunctional Photothermal Surface for Anti/de/Driving-Icing and Droplet Manipulation.

Due to safety concerns associated with ice accumulation, there is a need to develop a durable surface with anti/de-icing properties. Inspired by Gecko skin and Nepenthes, a superhydrophobic photothermal surface (SH-PS) with micro-nano hierarchical structure based on carbon nanotube composites is prepared by one-step laser method. It can be switchable to a slippery photothermal surface (S-PS) by injecting silicone oil. S-PS can effectively delay icing at -20 °C/-30 °C, and maintain excellent dynamic anti-icing capabilities following 28 times supercooled droplet impact (-30 °C). Under near-infrared (NIR) irradiation, S-PS exhibits high-efficiency photothermal deicing and excellent ice droplet control capabilities. Furthermore, S-PS also exhibits remarkable droplet manipulation capabilities under NIR irradiation, even anti-gravity transport (8°) and programmable track manipulation. Notably, after 20m abrasion, the S-PS still maintains good performances of anti/de-icing and droplet manipulation after infusing lubricant. All these excellent performances can promote its application in a wider range of fields.

Frozen Patterns in Viscoelastic Droplets Impacting on a Subcooled Surface.

The impact of droplets on a cold surface is ubiquitous in nature and various industrial applications, ranging from the icing of supercooled droplets on aircraft to the solidification of ink droplets in 3D printing. However, our understanding of the impact dynamics of droplets of complex fluids on cold surfaces is still very limited. Here, we experimentally study the spreading and frozen patterns of viscoelastic polymer droplets falling onto a subcooled substrate. We observe that the maximum spreading diameter of post-impact droplets decreases with increasing the subcooling temperature and the polymer concentration. Remarkably, all experimental data for spreading collapse into a universal curve, following the classic theory that accounts for inertial, capillary, and viscous forces. Unexpectedly, we find that, in contrast to the case of pure fluids, which exhibits three frozen modes, only two distinct modes, namely, freezing and hierarchical cracking, can be observed for polymer droplets. Finally, based on the undercooling temperature and polymer concentration, we construct a phase diagram for characterizing the morphologies of all frozen patterns. We expect that our findings may have implications in understanding the solidification of complex fluids on cold surfaces, for instance, in the fields of spray coating, inkjet printing, and additive manufacturing.

Spatio-temporal reconstruction of droplet impingement dynamics by means of color-coded glare points and deep learning

Abstract The present work introduces a deep learning approach for the three-dimensional reconstruction of the spatio-temporal dynamics of the gas-liquid interface on the basis of monocular images obtained via optical measurement techniques.&amp;#xD;The method is tested an evaluated at the example of liquid droplets impacting on structured solid substrates.&amp;#xD;The droplet dynamics are captured through high-speed imaging in an extended shadowgraphy setup with additional glare points from lateral light sources that encode further three-dimensional information of the gas-liquid interface in the images.&amp;#xD;A neural network is trained for the physically correct reconstruction of the droplet dynamics on a labelled dataset generated by synthetic image rendering on the basis of gas-liquid interface shapes obtained from direct numerical simulation.&amp;#xD;The employment of synthetic image rendering allows for the efficient generation of training data and circumvents the introduction of errors resulting from the inherent discrepancy of the droplet shapes between experiment and simulation. &amp;#xD;The accurate reconstruction of the three-dimensional shape of the gas-liquid interface during droplet impingement on the basis of images obtained in the experiment demonstrates the practicality of the presented approach.&amp;#xD;The introduction of glare points from lateral light sources in the experiments is shown to improve the reconstruction accuracy, which indicates that the neural network learns to leverage the additional three-dimensional information encoded in the images for a more accurate depth estimation.&amp;#xD;By the successful reconstruction of obscured areas in the input images, it is demonstrated that the neural network has the capability to learn a physically correct interpolation of missing data from the numerical simulation.&amp;#xD;Furthermore, the physically reasonable reconstruction of unknown gas-liquid interface shapes for drop impact regimes that were not contained in the training dataset indicates that the neural network learned a versatile model of the involved two-phase flow phenomena during droplet impingement.