Droplet Impact Dynamics Research Articles

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.

On the dynamics of head-on collision of sessile droplets on the traveling substrate

In this work, the dynamics of the head-on collision of two sessile water droplets, namely the moving droplet and pinning droplet, on a traveling substrate was experimentally investigated. Unlike the traditional scenario of sessile droplets collision, the traveling substrate propelled the moving droplet attached to it to move at a certain speed. The results revealed that there are only two distinct regimes of collision consequences: coalescence without separation and separation with separation. A series of time-resolved photographic images mapping all the collision regimes in the parameter space of Capillary number and size ratio were used to identify the controlling factors for different collision results. The breakup of the receding meniscus in separation regime was discussed in detail as it is caused by the change of the droplet morphology. The findings indicated that the length of the receding meniscus played a significant role in the droplet impact dynamics, and when it exceeded about 8.2 mm, the receding meniscus broke up. Furthermore, it was demonstrated that the sum of the volume of initial pinning droplet’s receding meniscus and the volume of the moving droplet before collision is equal to the volume of the receding meniscus at its maximum length after collision. The critical Capillary number/size ratio for the transition between these two regimes was derived based on the volume principle before and after the collision. The model-predicated results show good agreement with the experiments. The findings could contribute to a better understanding of the droplet collision dynamics and the optimization of the anti-icing, self-cleaning and inkjet printing devices.

Energy exchange during the early phase of droplet impact onto a dry surface

This study investigates droplet impact dynamics on a rigid substrate using droplets of water and water–glycerol mixtures. Experiments are conducted in the Weber number range of 179–929, and the corresponding Reynolds numbers are in the range of 5253–12 090. The profile of the droplet interface is studied. Assuming self-similarity in the internal flow at the interface of the droplet, the profiles are scaled using appropriate scales. It is observed that the profiles of the droplet interface (at different points of time) collapse close to each other when plotted in this manner. This observation serves as an experimental evidence to the self-similarity of the internal flow in this phase. Based on this fact, we make an estimate of kinetic energy at early stages of droplet impact. The surface energy is also estimated by assuming axisymmetry in the droplet profile obtained through back-light imaging. We observe that a considerable amount of the kinetic energy is lost during the early stages of droplet impact. We believe that an accurate estimation of this deficit in kinetic energy at an early stage of impact will be necessary to account in the energy based models for droplet impact.

The effect of vibration on droplet dynamics and heat transfer of spray cooling

The heat transfer mechanism of spray cooling under vibration has yet to be revealed, so it is crucial to deeply analyze the droplet impingement dynamics and heat transfer mechanism under vibration. However, there is still a gap in analyzing how vibration quantitatively affects droplet impingement dynamics and heat transfer performance. To fill this research gap, this paper will employ high-speed cameras to quantitatively analyze droplets' dynamics and heat transfer properties under various vibrational conditions. The results demonstrate that droplet spreading is enhanced at high-frequency conditions, but the enhancement decreases with the reduction in amplitude. Under high amplitude conditions, droplets gain additional inertial forces to overcome adhesive forces, causing oscillation in the three-phase contact line of the droplets, which significantly consumes the kinetic energy of droplet spreading, thereby suppressing droplet spreading. Vibration overall suppresses droplet spreading; at an amplitude of 0.2 mm and frequency of 80 Hz, the spreading enhancement factor is merely 4 %. Moreover, the droplet's heat transfer rate, heat flux, heat transfer coefficient, and cooling efficiency all increase with the rise in vibrational frequency but are all subdued by the amplitude. Compared to a static surface, vibration suppresses droplet heat transfer but can facilitate droplet heat transfer under low amplitude and high-frequency conditions. At an amplitude of 0.2 mm, the maximum heat transfer enhancement factor (HTEF) is 16 %. At an amplitude of 0.8 mm and frequency of 10 Hz, the minimum HTEF is −44 %. This research undoubtedly brings innovative insights into spray droplet impact dynamics and heat transfer and can provide valuable guidance for related industrial 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.

Droplet impact on a rapidly spinning superhydrophobic surface: Shortened contact time and reduced collision force

Despite extensive research on the impact of motionless superhydrophobic surfaces, the understanding of droplet impact behavior on spinning superhydrophobic surfaces had been limited and not adequately explored. Here, we used the template method to create a low-cost, low-adhesion, and highly water-repellent layered superhydrophobic surface. By employing a combination of experimental observations and simulation techniques, we successfully determined the contact time and collision force. Building upon these findings, our study further delved into the dynamics of droplet impact on both the center and eccentric of a spinning superhydrophobic surface. In the case where the droplet impacted at a distance of 5 mm from the center of rotation, we observed a significant reduction in contact time by 36.4 % and a decrease in the maximum collision force by 22.5 %. This could be attributed to the spinning motion of the superhydrophobic surface, which exerted frictional force on the droplet. Our findings provided a strong theoretical foundation for achieving better water repellency by combining spinning solids with superhydrophobic surfaces.

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 dynamics on superhydrophobic surfaces with convex hemispherical shapes

Functional solid surfaces that can realize rapid shedding of liquid droplets have received significant research interest due to their close relevance to many industrial applications. Droplet impact on superhydrophobic surfaces with point-like protrusions has been demonstrated to take off as rings, which alters droplet impact dynamics and thus reduces contact time compared to flat surfaces. However, the essential role of the size ratio of protrusion-to-droplet (λ) for droplets impinging on such surface is rarely considered. Here, we numerically investigate droplet impact on superhydrophobic surfaces with convex hemispherical shapes using a phase-field model coupled with dynamic contact angles. The postimpact outcome regimes occurring for varied λ and Weber number (We) values, spanning 0 ≤ λ ≤ 1.44 and 0.69 ≤ We ≤ 33.68, are mapped on a We−λ diagram. Three distinct dynamic behaviours of droplet impact are identified: contactless bouncing, conventional bouncing, and ring bouncing. Detailed comparative analyses of these impact outcomes are also presented, including the evolution of droplet morphology, impact force, maximum impact pressure, pressure distribution, and velocity vector distribution. The results reveal a previously unknown phenomenon in contactless bouncing, where the impact force exhibits an initial increase followed by a subsequent decrease, while the maximum impact pressure remains approximately constant. Annular rotating retraction results in a longer contact time. Breakup occurs near the necked area, inducing a part of the droplet to depart from the surface as a jet. In addition, it is observed that the dimensionless maximum wetting area becomes independent of the λ and follows a scaling law of 0.67We3/5 if the We exceeds 2.75. Ring bouncing exclusively occurs within the range of 0.24 ≤ λ ≤ 0.96 and We ≥ 24.74, resulting in an approximate 50 % reduction in non-dimensional contact time compared to conventional bouncing. These findings favor the understanding of the underlying mechanisms governing droplet impact and thereby provide available guidance to the design of superhydrophobic surfaces.

Numerical study of supercooled water droplet impacting on cold superhydrophobic surface under electric field

The process of ice formation on outdoor electrical equipment is determined by the impact of supercooled droplets on the cold surface under an electric field. Clarifying the impact-freezing of a supercooled droplet under an electric field is important for designing anti-icing surfaces in the power industry. Here, we developed a coupled electro-solidification model by combining the volume of fluid (VOF) method, a dynamic contact angle model, the two-phase electrohydrodynamic (EHD) model, the modified enthalpy solidification method and the nucleation effect. Then, the impact dynamics of a water droplet on a cold superhydrophobic surface under an electric field were studied numerically. The effects of the electric field intensity, Weber number, initial droplet temperature and conductivity on the spreading factor βm and the freezing fraction αad are analyzed. By specifically considering the effect of the electric field enhancing the water to freeze, the bottom filament is successfully recreated in the simulation. This phenomenon was first reproduced in our simulation, and it would significantly increase the probability of icing on the cold surface under the electric field, even on the superhydrophobic surface. Finally, based on the numerical results and published experimental data, we fit the freezing fraction relation of the supercooled water droplet impinging on cold superhydrophobic surface under the electric field, which can be used to predict the icing growth and prevention of icing on transmission lines. The numerical model developed here can also be directly used to simulate ice growth and guide the design of anti-icing surfaces in power transmission systems.

Compound Droplet Impact on a Thin Hydrophobic Cylinder.

The impact of compound droplets on solid surfaces is a ubiquitous phenomenon that pervades both the natural and technological fields. A comprehensive understanding of the dynamics of the droplet impact on solid surfaces is therefore of paramount importance for a broad range of applications. In this study, we investigate the impact of a water-in-oil compound droplet on a thin hydrophobic cylindrical surface, with regard to the Weber number and cylinder dimensions. Owing to the prewetting effect of the oil, the droplet completely engulfs the cylinder during impact. The ensuing breakups of oil and water engender various unique impact outcomes, which are depicted via a phase map. The phase boundaries are described by analyzing the gravitational and drag forces exerted by the cylinder. A threshold value of the Weber number is found beyond which its effect on the azimuthal spreading process becomes less obvious. The distinctive axial spreading processes of oil and water are illustrated through high-speed imaging from both front and side perspectives, revealing that droplet oscillation is critically influenced by the Weber number. Our work elucidates the impact dynamics of compound droplets on curved surfaces, providing pivotal insights into related thermal management, droplet printing, and coating fabrication applications.

Molecular dynamics simulations of droplet coalescence and impact dynamics on the modified surfaces: A review

The effective control of droplet coalescence and impact behaviors on solid surfaces plays a crucial role in various fields, such as material science, environmental science, energy, biomedicine, agriculture, and aerospace. This review aims to summarize recent advancements in the understanding of coalescence and impact dynamics of droplets under different conditions using molecular dynamics (MD) simulations. We highlight diverse approaches that enable the achievement of controllable coalescence and impact behaviors through the manipulation of surface properties, droplet properties, and coalescence and impact conditions. These approaches encompass adjustments in surface structures, surface morphology, and surface wettability, as well as the manipulation of droplet size, viscosity, and components, and the control of initial shape setting and impact velocity. Furthermore, we also introduce the dynamics associated with the coexistence of these two behaviors. Importantly, this review is expected to provide valuable insights for both industrial and technological applications, particularly in the areas of self-cleaning surfaces and microfluidics.

Numerical investigation of droplet impact dynamics on Janus-textured heated substrates

Janus-textured substrates refer to surfaces with heterogeneous topographies, which have received particular attention recently due to their potential application in manipulating droplet-bouncing behaviors [Li et al., Nat. Phys. 12, 606–612 (2016)]. In this paper, the droplet impact dynamics on the Janus-textured heated substrates are numerically investigated with an improved thermal lattice Boltzmann method. A comprehensive parametric study is conducted by varying the wettability, the Jakob number, the Weber number, and the surface topographies. With different control parameters, three distinct boiling regimes are observed, i.e., the contact boiling regime, the transition boiling regime, and the film boiling regime (Leidenfrost state). To reveal the underlying physics, the distributions of the unbalance Young's force, the thermophoretic force, and the vapor pressure difference in the system are theoretically analyzed. As for the self-propulsion behaviors, it is find that the droplet tends to move toward the denser side (area with more pillar arrays) for the contact boiling regime. However, when the droplet is under the Leidenfrost state, its bouncing dynamics depend on the combined effects of the Weber number and the wettability, and a decrease in wettability induces the droplet to migrate toward the sparser side (area with fewer pillar arrays). These physical insights enrich the fundamental understanding of the droplet-bouncing dynamics on heated substrates and also provide guidelines for designing advanced surfaces to manipulate the droplet-bouncing behavior.

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.

Hypergolic ignition response to oxidizer droplet properties

The hypergolic ignition response to oxidizer droplet properties is an important consideration for oxidizer injector design in hybrid rocket motors. Hence, the present work focused on hypergolic ignition characterization as a function of droplet properties and impact dynamics for a promising propellant. The propellant for the present work consisted of rocket grade hydrogen peroxide (RGHP) as oxidizer, high-density polyethylene (HDPE) as fuel and sodium borohydride (NaBH4) as the hypergolic additive embedded in the HDPE matrix. This propellant was chosen for this detailed study since it showed promising results in prior studies, exhibiting low (<10 ms) ignition delays. For this work, in a drop-test setup, RGHP droplet diameters between 1.90±0.11 mm and 4.35±0.26 mm were dropped on the HDPE + NaBH4 fuel samples at velocities between 0.3 m/s to 1.93 m/s. The ensuing ignition event was studied using both visible and infrared high-speed imaging. Post-impact droplet parameters were determined to enable a deeper analysis of observed phenomena. While ignition delay was the focus of this work, flame spread areas and heat release were also studied. Higher impact velocities generally led to lower ignition delays while splashing oxidizer drops increased probability of larger flame areas and higher heat release. Additionally, the initial ignition/heat release event was found to originate in a small region at the thinnest area of the post-impact droplet. Surface temperature measurements were also performed using infrared imaging. The data suggested that the initial heat release was found to be likely due to RGHP-NaBH4 reaction with no contribution from RGHP decomposition. Regression and random forest machine learning analysis found ignition delay depended strongly on the minimum post-impact drop layer thickness. Based on the data analysis, a simple mathematical model was developed whose results matched experimentally observed trends. The study is expected to further understanding of the processes that control hypergolic ignition in addition to aiding rocket engineers design better oxidizer feed systems. Novelty and SignificanceThis work constitutes a novel in-depth study on the influence of drop impact properties on hypergolic ignition. Using innovative techniques, this work is the first to show the overwhelming importance of residual droplet layer thickness on ignition delay. Additionally, a simple mathematical model based on that finding performed well against experimental data which is of substantial significance, given the complex and multi-parametric nature of hypergolic ignition. Finally, the work establishes that operating in the splashing regime enhances heat release and flame spread. The candidate propellant for this work was hydrogen peroxide and high-density polyethylene with embedded NaBH4. However, the findings of this study are likely generalizable over a range of solid-liquid hypergolic propellants involving solid fuels with embedded energetic materials, of which there are many. The findings of this work can enhance understanding of hypergolic ignition in addition to aiding in better rocket injection system design.

Numerical study on dynamics of oblique hollow droplet impact on a liquid film

Numerical study on dynamics of oblique hollow droplet impact on a liquid film

Freezing behaviors of an impacting droplet on subcooled hydrophobic surfaces

The solidification of impacting water droplets on cold substrates wildly exists in nature and engineering devices, which would significantly affect their performances. The freezing mechanisms of impacting water droplets on hydrophobic surfaces are not well understood. In this work, we explore the freezing behaviors of impacting water droplets on a cold hydrophobic surface in the regime where the interaction between the droplet impact dynamics and solidification is strong. We observe six different freezing morphologies on hydrophobic surfaces via tuning the substrate temperature and impact velocity. The diverse freezing morphologies are resulted from the competition of timescales associated with the solidification and droplet impact dynamics. The final freezing area on surfaces shows a non-monotonic variation with impact height when Ts = -38° C. We thus developed a model to predict the final freezing area, which agrees well with the experimental results.

Droplet impact dynamics on shallow pools

When a fast droplet impacts a pool of the same fluid, a thin ejecta sheet that dominates the early-time dynamics emerges within the first few microseconds. Fluid and impact properties are known to affect its evolution; we experimentally reveal that the pool depth is a critical factor too. Whilst ejecta sheets can remain separate and subsequently fold inwards on deeper pools, they instead develop into outward-propagating lamellae on sufficiently shallow pools, undergoing a transition that we delineate by comprehensively varying impact inertia and pool depth. Aided by matching direct numerical simulation results, we find that this transition stems from a confinement effect of the pool base on the impact-induced pressure, which stretches the ejecta sheet to restrict flow into it from the droplet on sufficiently shallow pools. This insight is also applied to elucidate the well-known transition due to Reynolds number.

Impact and wetting of polysilazane droplets on a metal surface

Spray coating with liquid polymers is a crucial step in producing polymer-derived ceramic (PDC) coatings before curing the precursor. However, the interactions between polymer droplets and target surfaces during the spray coating process have not been adequately characterized in existing literature. This experimental study aims to comprehensively examine the previously unknown droplet impact dynamics for a specific ceramic precursor, Polysilazane, on Inconel surfaces. The diameter of Polysilazane droplets was kept constant, while their impact velocity was varied to achieve different impact conditions. The same parameter range was also explored with water, water-glycerol, and ethanol droplets for comparison purposes. High-speed videos were captured to observe the instantaneous impact process, while low-speed videos were recorded at specific instances to document the gradual wetting process at later stages. The investigation revealed unique spreading dynamics of Polysilazane droplets, including smooth contact angle variation during the transition from impact to lateral spreading, absence of delayed wetting, no formation of wavy structures on the droplet interface during spreading, and no retraction process within the studied conditions (Weber number up to 1200). Conversely, Polysilazane displayed similarities in the normalized spreading curves with other liquids. Additionally, the maximum spread factor of Polysilazane could be well predicted using existing universal scaling models designed for different liquid types. Lastly, Polysilazane exhibited a distinctive post-impact wetting process that persisted for an extended duration. The wetting dynamics of Polysilazane could be effectively described by an empirical exponential law originally developed for partial wetting systems.

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.

Hydrodynamic behavior of liquid flow in a rotating packed bed

Rotating Packed Bed (RPB) technology has emerged as a promising technology for reducing carbon footprint of various petrochemical processes by leveraging the HiGee field-induced mass transfer enhancement and allow for better capture of greenhouse gases. Despite its potential, there are still significant challenges that hinder the effective utilization of RPB technology in process intensification. Specifically, the hydraulics of liquid and gas phases within RPB packings present a significant challenge. In this study, 2D – VOF approach is employed to study the behavior of liquid droplets impacting on single rotating wire and on a whole rotating wire mesh within a Rotating Packed Bed (RPB). A comprehensive computational fluid dynamics (CFD) model is developed to analyze the influence of rotating speed, liquid velocity, and droplet diameter on the dynamics of liquid droplets. The boundaries of splashing – no splashing and dripping – capture breakup modes were validated for a single rotating wire and identified for wire mesh in RPBs by constructing the corresponding regime maps. This is achieved thanks to a new data processing algorithm that applies the principle of neighborhood aggregation. The proposed data processing algorithm helps reconstruct the regime maps for the various breakup phenomena within RPBs. The results show that the splashing mechanism reproduces higher-velocity detached daughter droplets, while the momentum-induced dripping mechanism results in low velocity daughter droplets. The results also reveal that the deposited liquid film with the wires has a key role in enhancing the splashing phenomena in RPBs. The radial distribution of diameter and velocity of liquid droplets in RPB is also analyzed in light of the droplet impact dynamics. The increase in the average liquid velocity with radial direction was attributed to the increase of splashed drops, which led to a bigger number of high-velocity droplets. The conclusions of this study can be used to help improve the dynamics of the two-phase flow within RPBs through a better packing design and flow conditions.