Droplet Rebound Research Articles

On the bounce: developing reduced models for air–liquid interactions in droplet rebounds

Impact dynamics have long fascinated due to their ubiquity in everyday phenomena, from rain droplets splashing on windscreens to stone-skimming on the surface of the ocean. Impacts are characterized by rapid changes over disparate length scales, which make them expensive or sensitive to capture experimentally and computationally. Here, reduced mathematical models come to the fore, offering a way to get significant physical insight at reduced cost. In this volume, Phillips & Milewski (J. Fluid Mech., 2024) develop a mathematical model allowing for air–water interactions in the low-impact speed regime, in which an impactor bounces or rebounds rather than splashes. Their model offers a reliable way to capture air effects in bouncing, with a range of potential applications including hydrodynamic-quantum analogues and biomimetic water walkers.

Spreading and rebound of viscoelastic droplets on surfaces with hybrid wettability

Understanding viscoelastic droplet impact dynamics on solid surfaces is crucial for various industrial applications, including fuel injection, spray coating, inkjet printing, and microfluidics. This study investigates the behavior of a viscoelastic droplet impacting a solid substrate with different wettability properties characterized by different wall contact angles (WCA): hydrophilic (10°), hydrophobic (160°), and a hybrid surface that combines both properties (10°–160°). This study integrates the Oldroyd-B viscoelastic model with a dynamic contact angle framework to examine the effects of WCA and fluid relaxation time on droplet spreading and rebound behaviors. The findings reveal that surface wettability significantly influences droplet behavior during the spreading and rebound stages, affecting wetted area and droplet shape. On hydrophilic surfaces, droplets exhibit typical rebound behavior with partial attachment, while hydrophobic surfaces induce spreading with smaller contact areas and increased rebound. Notably, hybrid surfaces induce complex, asymmetric droplet dynamics markedly different from surfaces with homogeneous wettability. Increasing a droplet's relaxation time enhances spreading and reduces droplet deformation during the maximum rebound stage, particularly on the hydrophobic part of hybrid surfaces. In contrast, reduced relaxation times result in an increase in the height of the droplet during the rebound stage.

Influence of laser-fabricated surface features on droplet spreading, rebound behaviour, and ice adhesion on superhydrophobic surfaces

Influence of laser-fabricated surface features on droplet spreading, rebound behaviour, and ice adhesion on superhydrophobic surfaces

Molecular dynamics study of nanodroplet impact on superhydrophobic surfaces with varying inclination angles

The dynamic behavior of nanodroplets impacting solid surfaces has significant applications in fields such as anti-icing, self-cleaning, and nanotechnology. However, research on nanodroplet impacts on inclined superhydrophobic surfaces remains limited. In this study, molecular dynamics simulations are employed to systematically investigate the impact of nanodroplets on superhydrophobic surfaces with varying inclination angles. The study reveals the underlying mechanisms of droplet rebound modes, contact time, and sliding distance. The results demonstrate that droplet rebound behavior can be categorized into three modes: regular rebound, cavity rebound, and splashing rebound. The occurrence of these modes is governed by both the Weber number and the surface inclination angle. An analysis of contact time shows a three-phase variation: contact time decreases rapidly at low speeds, remains relatively stable at moderate speeds, and decreases significantly at high speeds. Notably, in the moderate-speed range, the formation of cavity rebound increases contact time, a phenomenon not commonly observed in previous studies on flat surfaces. Additionally, this study derives a theoretical formula for droplet sliding distance based on the Lennard-Jones potential and verifies it through simulations, demonstrating the competition between inertial forces and intermolecular interactions during sliding. The research not only presents a phase diagram of nanodroplet impact outcomes but also contributes novel theoretical insights into contact time and sliding behavior, providing a solid theoretical foundation for optimizing nanodroplet behavior in industrial applications.

Experimental insights into droplet behavior on Van der Waals and non-Van der Waals liquid-impregnated surfaces

Droplet impact is a fascinating phenomenon that occurs when a liquid droplet collides with a surface. It is not only a fundamental area of scientific inquiry but also has practical implications across many industries and natural systems. The dynamics during droplet impact on liquid-impregnated surfaces (LIS) are of special interest because the properties of the surface and impregnated liquid may significantly change the impact outcome. We present a detailed study of the impact and subsequent retraction of liquid droplets on a liquid-impregnated surface using high-speed imagery. Square-shaped textures with varying post-spacings of 5, 20, and 30 μm on a silicon wafer were fabricated and functionalized using octadecyltrichlorosilane. Two different lubricants, silicone oil and hexadecane, were infused to investigate how their properties affect impact dynamics. Droplet impacts were investigated on these surfaces across a broad range of Weber numbers, i.e., (28–495). Additionally, we measured the stability of the LIS surface by calculating spreading coefficients and contact angles. The experiments revealed that the properties of the infused oil play an insignificant role in droplet dynamics, including spreading, rebound, and unique phenomena related to oil interaction with surface textures. This study provides insights into the intricate dynamics of droplet interactions with LIS, offering valuable contributions to understanding surface-wetting phenomena.

Visualization and quantitative study on film boiling heat transfer of a salt droplet on the hydrophobic substrate

A droplet impacts on high temperature surface may lead to film boiling. Hydrophobic coating used for corrosion prevention is easy to cause film boiling at low temperature, which results in a remarkable decrease in evaporation efficiency and heat transfer coefficient. However, there is a lack of quantitative visual experimental data on the flow field around the droplet to understand the heat transfer characteristics during film boiling. In this study, schlieren photography combined with high-speed imaging technology is used to observe the evolution process of a droplet impact, rebound, oscillation, and stable boiling. The effects of temperature on lifetime, vapour velocity and heat transfer coefficient of a salt droplet with different concentrations are studied for aluminum and Teflon surfaces. The distribution characteristics of vapour velocity are quantitatively analyzed using cross-correlation algorithm, and the calculation formulas of heat transfer coefficient under nucleate and film boiling modes are proposed. It is found that increasing the concentration of a salt droplet can improve the heat transfer coefficient during film boiling. This work will provide a theoretical basis for the improvement of heat exchanger efficiency in areas such as sea water spray cooling.

Lubrication-mediated rebounds off fluid baths

We present herein the derivation of a lubrication-mediated (LM) quasi-potential model for droplet rebounds off deep liquid baths, assuming the presence of a persistent dynamic air layer which acts as a lubricating pressure transfer. We then present numerical simulations of the LM model for axisymmetric rebounds of solid spheres and compare quantitatively to current results in the literature, including experimental data in the low-speed impact regime. In this regime the LM model has the advantage of being far more computationally tractable than direct numerical simulation (DNS) and is also able to provide detailed behaviour within the micro-metric thin lubrication region. The LM system has an interesting mathematical structure, with the lubrication layer providing a free-boundary elliptic problem mediating the drop and bath free-boundary evolutionary equations.

Ultrafast bounce of particle-laden droplets

The rebound of liquid droplets on solid surfaces exhibits behavior reminiscent of elastic spheres, albeit with distinct contact dynamics. While the rapid detachment of droplets from surfaces holds significant relevance for various applications, previous endeavors relying on engineered surfaces can only reduce the contact time to several milliseconds, primarily due to capillary effects dominating droplet bounce. Here, we present ultrafast rebound by designing heterogeneous core-shell droplets encapsulating a particle (DEP), which achieves an unprecedentedly short contact time of 0.3 ms and 0.05 ms with polydimethylsiloxane and glass particles, respectively. This remarkable contact-time reduction is universally applicable to diverse systems, including both water and oil droplets, elastic and rigid particles, super-repellent and superlyophilic surfaces, and is effective across a wide range of impact velocities. Beyond exhibiting liquid-like dynamics, DEP manifests solid-like behavior owing to asynchronized motions between the particle and the droplet, which effectively breaks down the dominance of capillarity. With systematic experimental and analytical studies, we delineate contact times in three bouncing regimes and identify critical conditions governing regime transitions. DEP amalgamates the bouncing dynamics of both solids and liquids, offering a robust and versatile strategy for tailoring contact time to suit diverse applications involving solid-liquid composite systems.

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.

Probing the contact time of droplet impacts: From the Hertz collision to oscillation regimes.

Droplet rebound on nonwetting surfaces is a common phenomenon. However, the underlying physics regulating the contact time remains unclear. In this work, we investigate droplet impacts on superamphiphobic surfaces through experiments and theoretical analyses. By analyzing the spreading and retraction of droplet impinging processes over a wide range of Weber numbers (We), it is revealed that droplet impacts experience three regimes as We is varied, which are denoted as the Hertz collision (We<1), transition (1<We<10), and oscillation (We>10) regimes. In the Hertz collision regime, the droplet impinging process is temporally symmetric, i.e., the spreading time, t_{S}, and the retraction time, t_{R}, are almost the same. Furthermore, t_{S} and t_{R} decrease with increasing We and follow a power-law dependence, which is different from previous theories. In the transition regime, t_{S} remains dominated by the Hertz collision, while t_{R} is governed by droplet oscillation. In the oscillation regime, t_{S}, t_{R}, and the total contact time, t_{C}, become independent of We. These three regimes are valid for both monophase and compound droplets. The findings in this work advance the understanding and offer a clear picture of droplet impact dynamics.

An Eco-friendly β-cyclodextrin/Stilbene-Integrated supramolecular material Realizes the effective treatment of bacterial diseases via enhancing the biofilm eradication and Agrochemical bioavailability

Bacterial biofilm-associated diseases have become the leading challenge for global food security. The inherently dense biofilm matrix provides bacteria with violent resistance to the host immune response and chemical attack. Current antimicrobials with weak biofilm-targeting options and inadequate foliar adhesion severely degrade the disruptor-biofilm interactions. To tackle these issues, the host–guest supramolecular technique was employed to optimize a bactericidal stilbene-decorated ingredient (StA8) by β-cyclodextrin (β-CD). Thus, a potent supramolecular bactericidal material (StA8@β-CD), owning both enhancive biofilm eradication and excellent foliar deposition properties, was successfully fabricated. This inclusion effectively disrupts pre-formed biofilms of Xanthomonas oryzae pv. oryzae (Xoo) and definitely kills planktonic and biofilm-enclosed bacteria. After aged Xoo cells for 48 h, subsequent StA8@β-CD treatment provides excellent biofilm eradication rate of 82.8 % at 15.68 μg mL−1. Mechanism researches disclose that StA8@β-CD inhibits exopolysaccharides (EPS) production, the transcription of swimming-associated genes, bacterial quorum sensing, and cellulase/amylase activity, all pivotal for biofilm formation and bacterial virulence. Also, this self-assembled material dramatically relieves droplet splash and rebound on hydrophobic rice leaves, thereby improving efficient utilization of agrochemicals. Combining these advantages, in vivo anti-Xoo experiments reveal that StA8@β-CD has excellent control efficiency of 50.8 % at 200 μg mL−1, quite superior to the thiodiazole-copper-20 %SC formulation (34.5 %). Besides, StA8@β-CD exhibits broad-spectrum bioactivities against citrus and kiwifruit cankers with outstanding control efficacies of 73.3 % and 73.7 %, respectively. This attempt provides a new direction for the exploitation of multipurpose supramolecular bactericidal materials.

Achieving wide temperature range of gentle film boiling on textured hydrophobic tool surfaces

Hydrophobic tool surfaces have become a hot topic in recent years due to their significant advantages such as anti-adhesion and friction reduction. However, enhancing hydrophobicity would inadvertently decrease the Leidenfrost point of droplets, which diminishes the heat transfer efficiency and compromises manufacturing quality. This issue presents a considerable challenge and underscores the critical need to understand the boiling dynamics when droplets encounter heated hydrophobic surfaces. Herein, we propose a kind of textured hydrophobic tool surface based on laser processing and hydrophobic coating technology, which could achieve gentle film boiling across a wide temperature range. The raised micropillars protect hydrophobic coating with excellent abrasion resistance and stabilizes the droplets in the gentle film boiling regime under harsh conditions. The primary rationale behind this advancement is the reduction in the critical temperature for film boiling and the elevation of the critical temperature for droplet rebound. We have developed a predictive model for the Leidenfrost point, which has been experimentally validated to determine the wall temperature necessary for achieving the gentle film boiling regime. In addition, we found that the textured hydrophobic surface can still inhibit the bouncing and spreading of droplets at high temperatures. This study not only deepens our understanding of the effects of droplets on heated surfaces but also has the potential to improve manufacturing performance by consistently maintaining the hydrophobic properties of tool surfaces during cutting operations.

Hydrogel Embedding Enables Enhanced Leaf Deposition and Bioavailability of Fe-Based Engineered Nanoparticles.

Nanofertilizers comprising engineered nanoparticles (ENPs) have great potential in sustainable agriculture due to their strong capabilities of improving crop yields. As an effective fertilization strategy, foliar spraying could lead to broken and splashed ENP droplets, resulting in inaccurate leaf targeting and potential environmental contamination. Herein, we propose embedding Fe-based ENPs into a supramolecular hydrogel to effectively enhance the deposition amount on leaves and thus the bioavailability. The proper rheological properties of the hydrogel droplets and their robust interaction with soybean leaf simultaneously reduce the droplet rebound and fragmentation, especially under elevated impact speeds, resulting in up to 168.9% more droplet deposition compared to the ENP suspension. Computational fluid dynamics simulation analysis suggests that the contact angle is a key sensitive factor influencing the dynamic deposition behavior of the hydrogel droplet. A 15% reduction in the contact angle results in a 14% reduction of the highest bouncing height. The incorporation of ENPs enhances the viscous dissipation rate by 7.4% in comparison with pure hydrogel droplets. The hydrogel embedding also causes a 1.5-fold increase in ENP uptake compared to that of the ENP suspension. The hydrogel embedding delivers a reduction of 80% in the ENP application amount, compared to ENP suspensions, while achieving a 28% increase in the fresh weight of soybean seedlings. This work provides an effective method to enhance the deposition of ENPs during foliar application.

Experimental study on the influence of surface properties on droplet collision dynamics, from adhesion to rebound to breakup

Liquid droplet impact on dry surfaces often results in bouncing or breakup beyond a certain threshold. Surface contact angles, especially dynamic ones present during impact, significantly affect this process. Our experimental study underscores that advancing and receding contact angles influence droplet behaviors like rebounding and different types of breakup. This discovery provides new insights and criteria for understanding liquid droplet impact on surfaces. Special characteristics were found in the breakup on microstructured surfaces: the size of fractured droplets notably decreases, and the spreading–breakup occurs more easily and earlier. Additionally, microstructured surfaces reduce contact time to some extent. Furthermore, the uniqueness of oblique impacts is mainly reflected in how they lower the threshold of the receding contact angle for rebound. Studying the correlations and differences in droplet rebound and breakup related to these surface characteristics will contribute to improving research on liquid–solid interactions and the design of hydrophobic surfaces, including microstructured surfaces.

A novel coaxial air-R134a spray cooling for heat transfer enhancement of laser dermatology

Efficient cooling is essential in laser dermatology to prevent thermal damage, but current methods are often hindered by thermal barrier film deposition. This study presents coaxial air-R134a spray cooling for heat transfer enhancement and deposited-film mitigation. Surface temperature was measured using a TFTC thermocouple, while heat flux was estimated through the improved Duhamel theorem. High-speed camera visualization with the Mie-scattering technique captured the spray and film behavior. The results showed uniform and effective cooling via transient surface heat transfer and film behaviors. The boiling curve identified three distinct cooling phases: transition boiling, nucleate boiling, and single-phase film deposition. Airflow adjustments not only enhance the heat transfer coefficient but also control spray dynamics, droplet rebounding, and film spreading. Self-organizing maps revealed that medium-to-high nozzle spacing (y/D) reduces surface temperature and increases the heat transfer coefficient. Film resistance time is minimized by either high airflow and low y/D or low airflow and high y/D. For critical heat flux, low y/D and airflow are optimal. A y/D = 32 and 60 L/min airflow provided appropriate operating conditions. However, airflow increased frost deposition during off-duty, suggesting moisture-free air in the future.

Numerical and experimental investigation of the supercooled large droplets icing of rotating spinner

The icing of aero-engine rotating components is more complex than traditional aircraft icing. A three-dimensional numerical method was developed based on the Eulerian method to study the supercooled large droplets icing of a rotating spinner. Typical dynamic behaviours of supercooled large droplets, such as deformation, breakup, rebound, and splashing, were considered. An icing thermodynamic model applicable to a rotating spinner was established by considering the effects of pressure gradient, air shear force, and centrifugal force on the flow of the water film. Meanwhile, an ice wind tunnel experiment on supercooled large droplets icing of a rotating spinner was carried out. The results showed that the maximum relative deviation of the simulated icing thickness at the cone tip is no more than 15% compared with the experimental result, and the icing thickness on the surface of the rotating spinner is basically consistent with the experimental result. Based on the three-dimensional numerical method developed in this study, the effects of the rotational speed, inflow velocity, and inflow temperature on the supercooled large droplets icing of a rotating spinner were investigated. As the rotational speed increases, the rebound and splashing of supercooled large droplets becomes more obvious, leading to an increase in the mass loss coefficient and a decrease in the collected mass of water droplets on the surface of the rotating spinner. Consequently, the icing thickness at the tail of the rotating spinner decreases with an increase in the rotational speed. Since the liquid water content in the environment is relatively low, water droplets freeze immediately after impacting the surface of the rotating spinner and rime ice is usually formed. When the inflow temperature is relatively high, overflow water exists and glaze ice is formed near the tip of the rotating spinner. The findings of this study can provide valuable support for the design and verification of anti-icing systems for aero-engine rotating spinner.

Publisher's Note: “Droplet impact and rebound dynamics on superhydrophobic surfaces” [Phys. Fluids 36, 072103 (2024)

Publisher's Note: “Droplet impact and rebound dynamics on superhydrophobic surfaces” [Phys. Fluids <b>36</b>, 072103 (2024)

Experimental study on the dynamics of a liquid nitrogen droplet impacting a surface under Leidenfrost conditions

Liquid nitrogen droplet impacting a superheated surface is a fundamental phenomenon of liquid nitrogen spray cooling, whereas the mechanisms behind which are still unclear. We designed and developed a visual experimental system to investigate the dynamics of a liquid nitrogen droplet impacting a superheated surface under cryogenic conditions. The impact dynamics of the liquid nitrogen droplet at the Leidenfrost state are captured, and the effects of Weber number (We) and surface temperature on the spreading and rebound characteristics of the droplet are analyzed. The findings show that the droplet exhibits spreading, retraction and rebound at a low We. Droplet spreading and rebound characteristics are mainly affected by We while insensitive to surface temperature. The maximum spreading coefficient exhibits a power-law increase with We, while the maximum rebound coefficient shows an upward and then downward trend with We. The dimensionless maximum spreading time, dimensionless residence time, and dimensionless maximum rebound time show power-law increase with We. Corresponding fitting correlations for these factors for liquid nitrogen droplets are also proposed. This study contributes to an in-depth understanding of the impact dynamics of cryogenic liquid droplet under cryogenic conditions.

An analysis of the contact time of nanodroplets impacting superhydrophobic surfaces with square ridges

Reducing the contact time between liquid droplets and solid surfaces is important in numerous engineering applications. Mechanisms for reducing the contact time have been extensively studied. However, there is still a lack of systematic research on the mechanisms governing the changes in the contact time of nanodroplets impacting superhydrophobic surfaces with square ridges. Additionally, there has been relatively little examination of the differences between nanodroplets and macroscopic droplets in this scenario. In this work, we investigate the impact of nanodroplets on both superhydrophobic planes and superhydrophobic surfaces with square ridges. When nanodroplets impact a superhydrophobic plane, we find that the droplet contraction time determines the total contact time. When nanodroplets impact superhydrophobic surfaces with square ridges, we find for the first time that the critical factor determining its contact time is the detachment time of the droplet from the square ridges as it lifts off. Compared to millimeter-sized droplets, nanodroplets exhibit stronger adhesion to solid surfaces. Additionally, we propose for the first time that nanodroplets are more resistant to deformation and splitting. We define the Weber number (We) at which the droplet rebounds as the critical rebound Weber number (We), and use this to evaluate the effect of square ridges on improving droplet rebound. We observe that a moderate increase in the square ridge height is beneficial to reducing the contact time. By altering the square ridge width, we find that a narrower ridge is more favorable for reducing the contact time and for facilitating droplet splitting.

Dynamic behaviors of shear-thinning droplet impacting on a spherical particle surface

Non-Newtonian droplet impact is common in nature and industry. The viscosity of non-Newtonian liquids changes with shear stress, leading to different impact behaviors compared to Newtonian liquids. This study prepared shear-thinning solutions by adding HPMC polymer into deionized water and investigated its impact dynamics on hydrophobic spherical surface. The evolution patterns of droplet spreading factor, film thickness, and dynamic contact angle are investigated under different impact conditions. The results show that addition of polymers increases the energy dissipation during impact and suppresses droplet rebound from spherical surface compared to Newtonian droplet with similar viscosity. The droplet-impacting process is distinguished into three phases: (I) initial deformation, (II) inertia-dominated, and (III) viscosity-dominated phases. The temporal evolution of film thickness in Phases I and II is fitted by simple equations. In addition, an empirical formula that integrates Weber and Reynold numbers is proposed to predict the maximum spreading factor of HPMC droplets.