Impact of viscous droplets on different wettable surfaces: Impact phenomena, the maximum spreading factor, spreading time and post-impact oscillation

Preparation of hyaluronic acid-loaded liquid-core hydrogel beads with acceptable mechanical properties and thermal stability

BACKGROUND

Hyaluronic acid liquid-core hydrogel beads (HA-LHB) is a good way for oral intake of HA. However, HA may affect the reaction-diffusion of sodium alginate (SA) and Ca2+ leading to poor mechanical properties, since HA is a polyanionic electrolyte having electrostatic effect and a certain spatial site-blocking effect.

RESULTS

The mechanical properties of HA-LHB were modified from bathing solution, core solution and secondary calcium bath time. The mechanical properties varied with the SA structure and concentration in bathing solution, where SA with high G (guluronic acid) segment compounded with SA with high M (mannuronic acid) segment at a mass ratio of 7:3 with a 11 g kg-1 concentration showed the best mechanical properties. The secondary calcium bath can greatly improve the mechanical properties due to the tight network formed by bidirectional crosslinking, and 15 min reaction reached the plateau if Ca2+ is sufficient. And the mechanical properties were positively correlated with calcium lactate concentration only at <70 g kg-1 in core solution, but the diffusion of Ca2+ was hindered by the tight gel network at higher concentrations. Moreover, the mechanical properties can be maintained during heat treatment, due to the rearrangement of alginate network structure.

CONCLUSION

Our results suggested that the problem of poor mechanical properties of LHB in the presence of high HA concentration can be avoided by process control, which may broaden the development of HA and popping boba market. © 2024 Society of Chemical Industry.

Defect by design: Harnessing the "petal effect" for advanced hydrophobic surface applications

HYPOTHESIS

In the interfacial wetting boundary, the superhydrophobic surface is often damaged, and the anisotropic wettability of its surface has attracted many researchers' attention. The "petal effect" surface has typical anisotropic wettability. We predict that under the dual conditions of structural defects and high impact velocity, the "petal effect" becomes more adhesive on the surface.

EXPERIMENTS

This study refers to the droplet state on rose petals, structural defects were constructed on the superhydrophobic surface. This paper studies the influence of macro-structural defects on the wettability change from natural to bionic "lotus effect" to "petal effect" in both static and dynamic angles.

FINDINGS

Macro defects significantly change the static contact angle of the superhydrophobic surface. The higher the impact velocity of the droplet, the higher the energy dissipation of the "petal effect" surface (DSHS), which improves the adhesion of the surface to the droplet and prolongs the contact time. It is found that the defect structure and high impact velocity will directly affect the deposition and desorption of droplets on the superhydrophobic surface, and they are both essential. This wetting dynamic law is very likely to be helpful in the quantitative design of defect structure scale for dynamic desorption of droplets on superhydrophobic surfaces.

Spreading dynamics of a droplet upon impact with a liquid film containing solid particles

This study examines how a deionized water droplet behaves when it centrally collides with a liquid film containing TiO2 nanoparticles at low impact velocities, aiming to understand how nanoparticles affect droplet spreading, in particular its maximum spreading diameter. Typically, we found that both the spreading velocity and dynamic contact angle of the droplet would be similarly affected by increasing TiO2 nanoparticle concentration. During retraction, the droplet's dimensionless spreading diameter oscillates, with more pronounced oscillations at higher nanoparticle concentrations. Moreover, both the droplet's maximum dimensionless rebound height and dynamic contact angle show similar trends with increasing TiO2 nanoparticle concentration. Interestingly, we proved that the influence of the solid-liquid interaction (Stokes force) on the fluid during the spreading process accounts for less than 2% of the surface energy when the droplet reaches its maximum spreading diameter, indicating a negligible effect on droplet spreading. We hypothesize that the droplet's initial energy is fully converted into surface energy and viscous dissipation at maximum spreading diameter, which involves viscous dissipation both between the fluid and the solid wall surface and the fluid and solid particle surface. Based on this, we developed a model for predicting the droplet's maximum spreading diameter that includes parameters associated with the solid particles. Compared to models in the literature that do not consider the effect of solid particles, our model aligns more closely with experimental data. The results indicate that adding solid particles leads to increased viscous dissipation, which in turn reduces the droplet's maximum spreading diameter.

Experimental investigation on the bouncing dynamics of a liquid marble during the impact on a hydrophilic surface

Liquid marbles are droplets coated by hydrophobic particles. At low Weber numbers (We), when impacting a hydrophilic surface, the marble may bounce on the substrate repeatedly without any rupturing until the quiescence condition is achieved. The marble bouncing has gained far less attention, although its rich underlying physics is due to the interaction between liquid core, hydrophobic grain, and surrounding air. Accordingly, this research experimentally scrutinizes the marble impact and subsequent bouncing on a hydrophilic surface for the first time. Additionally, the conversion of kinetic, gravitational potential, inertial, and surface energies occurring regularly during the impact is exhaustively surveyed. Moreover, the effect of Weber and gravitational Bond numbers (Bo) on the bouncing time, maximum spreading time, maximum spreading ratio, maximum elongation ratio, and maximum restitution are investigated, which characterize the marble impact and bouncing dynamics. This study is one of the limited investigations exploring the effects of the gravitational Bond number on the results. Dimensionless correlations are proposed for the mentioned parameters based on the experimental data. Furthermore, utilizing the simplifying theoretical presumptions, correlations are suggested based on the scale analysis for the spreading time and maximum spreading ratio. The results imply that the mentioned parameters behave differently at low and moderate Weber numbers, though the distinction is more pronounced in the case of the bouncing time, maximum spreading time and maximum spreading ratio. Although increasing with the Weber number when WeWecr. In addition, the maximum elongation ratio linearly grows with the Weber number.

Coupled Dynamics of Droplet Impact on a Flexible, Hydrophilic Cantilever Beam

We experimentally study the droplet impact on a flexible, hydrophilic cantilever beam. Droplets of water, water-glycerol (1:1 v/v), and glycerol were considered on a copper beam. Side visualization of the droplet impact on the cantilever was carried out by using a high-speed camera. We systematically vary cantilever stiffness to obtain a characteristic time scale of the beam dynamics, that is, shorter on the same order and longer than the characteristic time scale of droplet dynamics. Water droplet spreading reduces with an increase in the beam's flexibility, due to the "springboard effect". Results reveal that a threshold cantilever length exists beyond which the droplet vibration mode "locks-in" to the cantilever vibration mode. During lock-in, the bending energy of the beam increases with an increasing length or decreasing stiffness. The time-varying cantilever deflection exhibits an oscillatory, exponentially decaying response. However, in the case where both time scales are almost the same, we found a two-stage damping in the measurements: a fast, initial damping followed by a slower, damped response. We explain this damped response by the interplay of droplet and cantilever early dynamics. As expected, increasing the droplet viscosity dampens the magnitude of droplet spreading and displacement of the cantilever's tip due to a larger dissipation of kinetic energy in the bulk of the droplet. The decay is exponential in all cases, and the time taken to reduce the spreading and displacement is shorter with a larger viscosity. The damping coefficient is found to inversely scale with the cantilever length or mass. We corroborated the measurements with available analytical models, confirming the hypotheses used to explain the results. Overall, the present study provides fundamental insights into controlling the coupled dynamics of droplet and flexible substrates, with potential applications such as the design of efficient agricultural sprays and wings of microaerial vehicles.

Understanding and Utilizing Droplet Impact on Superhydrophobic Surfaces: Phenomena, Mechanisms, Regulations, Applications, and Beyond

Droplet impact is a ubiquitous liquid behavior that closely tied to human life and production, making indispensable impacts on the big world. Nature-inspired superhydrophobic surfaces provide a powerful platform for regulating droplet impact dynamics. The collision between classic phenomena of droplet impact and the advanced manufacture of superhydrophobic surfaces is lighting up the future. Accurately understanding, predicting, and tailoring droplet dynamic behaviors on superhydrophobic surfaces are progressive steps to integrate the droplet impact into versatile applications and further improve the efficiency. In this review, the progress on phenomena, mechanisms, regulations, and applications of droplet impact on superhydrophobic surfaces, bridging the gap between droplet impact, superhydrophobic surfaces, and engineering applications are comprehensively summarized. It is highlighted that droplet contact and rebound are two focal points, and their fundamentals and dynamic regulations on elaborately designed superhydrophobic surfaces are discussed in detail. For the first time, diverse applications are classified into four categories according to the requirements for droplet contact and rebound. The remaining challenges are also pointed out and future directions to trigger subsequent research on droplet impact from both scientific and applied perspectives are outlined. The review is expected to provide a general framework for understanding and utilizing droplet impact.

Singular jets during droplet impact on superhydrophobic surfaces

HYPOTHESIS

The impact of droplets is prevalent in numerous applications, and jetting during droplet impact is a critical process controlling the dispersal and transport of liquid. New jetting dynamics are expected in different conditions of droplet impact on super-hydrophobic surfaces, such as new jetting phenomena, mechanisms, and regimes.

EXPERIMENTS

In this experimental study of droplet impact on super-hydrophobic surfaces, the Weber number and the Ohnesorge number are varied in a wide range, and the impact process is analyzed theoretically.

FINDINGS

We identify a new type of singular jets, i.e., singular jets induced by horizontal inertia (HI singular jets), besides the previously studied singular jets induced by capillary deformation (CD singular jets). For CD singular jets, the formation of the cavity is due to the propagation of capillary waves on the droplet surface; while for HI singular jets, the cavity formation is due to the large horizontal inertia of the toroidal edge during the retraction of the droplet after the maximum spreading. Key steps of the impact process are analyzed quantitatively, including the spreading of the droplet, the formation and the collapse of the spire, the formation and retraction of the cavity, and finally the formation of singular jets. A regime map for the formation of singular jets is obtained, and scaling relationships for the transition conditions between different regimes are analyzed.

Damped Oscillatory Dynamics of a Drop Impacting over Oil-Infused Slippery Interfaces─Does the Oil Viscosity Slow it Down?

A liquid drop impacting on a soft surface is known to exhibit fascinating dynamics that is distinctive from its bounce-back atop a rigid surface. However, while the early spreading of the drop subsequent to its immediate impact with a lubricating liquid layer appears to be reasonably well understood, the later events of retraction and eventual stabilization appear to be poorly addressed. Here, we bring out the nontrivial confluence of the solid substrate wettability and the liquid layer viscosity toward modulating the post-collision dynamics of an impinging liquid drop on a viscous oil-infused surface during its later phase of settlement before arriving at an equilibrium state. Our results reveal that despite an intuitive analogy with the classical phenomenon of damped oscillation, the drop, during its later stages of motion, undergoes dynamical events that may be nontrivially dictated by not only the relative viscosity of the impacting drop and the liquid layer but also the intrinsic wettability of the solid substrate, governing its post-impact settlement via a sequel of spreading-retraction cycles. As a consequence, the viscous liquid layer, instead of providing additional damping, may nonintuitively reduce the effective viscous dissipation so as to hasten the drop's final settlement. These results may turn out to be critical in designing engineered surfaces for tuning the movement of drops in a preferential pathway, bearing decisive implications in the functionalities of liquid lenses, inkjet printing, spray coating and cooling, and several other emerging applications in the realm of lubricated fluidic interfaces.

Universality of Scaling Laws Governing Contact and Spreading Time Spans of Bouncing Liquid Marbles and its Physical Origin

The impact of liquid marbles coated with a diversity of hydrophobic powders with various solid substrates, including hydrophobic, hydrophilic, and superhydrophobic ones, was investigated. The contact time of the bouncing marbles was studied. Universal scaling behavior of the contact time tc as a function of the Weber number (We) was established; the scaling law tc = tc(We) was independent of the kind of powder and the type of solid substrate. The total contact time consists of spreading time and retraction time. It is weakly dependent on We and this is true for all kinds of studied powders and substrates. This observation hints to the surface tension/inertia spring model governing the impact. By contrast, the spreading time ts scales as [Formula: see text], n = 0.28 - 0.30 ± 0.002. We relate the origin of this scaling law to the viscous dissipation occurring within the spreading marbles. The retraction time tr grows weakly with the Weber number. The scaling law was changed at threshold values of We ≅ 15-20. It is reasonable to explain this change with the breaking of the Leidenfrost regime of spreading under high values of We.

Impinging blood droplets on different wettable surfaces: Impact phenomena, contact line motion, post-impact oscillation and dried stains

Understanding the underlying hydrodynamics of impinging blood droplets and finding out the physical parameters determining the bloodstain characteristics are of great importance in blood related forensic investigations. In this work, the impact of non-Newtonian blood droplets on solid surfaces ranging from lyophilic to superlyophobic was systematically investigated and compared to that of Newtonian droplets with a similar dynamic shear viscosity. We show that impinging blood droplets behave as low-viscosity Newtonian droplets in the short-time spreading, which is dominated by capillary and inertial forces, but their non-Newtonian viscoelasticity would notably affect the droplet retraction and post-impact oscillation occurring in large timescales. Whereas the strong liquid-solid adhesion and the non-Newtonian elongational viscosity hinder droplet recoiling and thus alter the impact phenomena on lyophobic and superlyophobic surfaces, the shear and elongational viscosities are coupled to result in higher damping coefficients of oscillating blood droplets after deposition, in comparison to that of impinging Newtonian droplets. The size of the dried bloodstain was found to be different from both the maximum spreading radius of the droplet that can reach during impact and the final radius of the deposited droplet after oscillation, and their correlations are highly dependent on the impact velocity and surface wettability. Moreover, the morphologic characteristics of the bloodstains would also be changed by varying either the impact velocity or the surface wettability. We envision that these findings can not only find applications in the bloodstain pattern analysis, but also provide useful information for medical diagnosis based on blood droplet test.

Impact Dynamics of a Droplet on Superhydrophobic Cylinders Structured with a Macro Ridge

Reducing the contact time of a droplet hitting a solid surface is crucial for many situations. In this work, the dynamic behavior of a low-viscosity droplet on a superhydrophobic surface, which consists of a cylindrical substrate and a macro ridge placed axially on the peak, was numerically investigated via the lattice Boltzmann method. The focus was given to the spreading and the detaching morphology of the droplet at the Weber number We = 0.84-37.8 and the cylinder-to-droplet radius ratio R* = 0.57-5.71. The ridge is found to redistribute the droplet mass and affect the impact outcomes, as well as the contact time. For each R*, a jug rebound, a stretched rebound straddling the ridge, and a split detachment occur sequentially with the increasing We. When R* does not exceed 1.71, the contact time decreases continuously with the increase in We. With R* being taken between 1.71 and 5.14, the contact time initially reduces with We and plateaus after We reaches 10.3. Once R* exceeds 5.14, the split droplets may present as a bestriding shape at We > 30.3 rather than the regular jug shape with a small We. The contact time would be decreased to a second plateau in this case. In most cases, the contact time can be shortened effectively for the droplet on a ridged cylinder compared with that of a smooth cylinder.

Electrowetting-Induced Coalescence of Sessile Droplets in Viscous Medium

Manipulating the coalescence of microdroplets has recently gained enormous attention in digital microfluidics and biological and chemical industries. Here, coalescence between two sessile droplets is induced by spreading them due to electrowetting. The electrocoalescence dynamics is investigated for a wide range of operating parameters such as electrowetting number, Ohnesorge number, driving frequency, and drop to surrounding medium viscosity ratio. Here, the characteristic time scale from the classical lubrication theory is modified with an additional driving and resisting force due to the electrostatic pressure force and liquid-liquid viscous dissipation, respectively. With the revised characteristic time scale, a universal bridge growth is shown between the two merging droplets following a 1/3 power law during early coalescence followed by a long-range linear variation. To ensure precise control on droplet coalescence, a geometric analysis is also performed to define the initial separation distance.

Spreading dynamics of microdroplets on nanostructured surfaces

HYPOTHESIS

Droplet spreading governs various daily phenomena and industrial processes. Insights about microdroplet spreading are limited due to experimental difficulties arising from microdroplet manipulation and substrate wettability control. For droplet sizes approaching the capillary length scale, the gravitational force plays an important role in spreading. In contrast, capillary and viscous forces dominate as the droplet size reduces to smaller length scales. We hypothesize that the dynamic spreading behavior of microdroplets whose radius is far lower than the capillary length differs substantially from established and well understood dynamics.

EXPERIMENTS

To systematically investigate the spreading dynamics of microdroplets, we develop contact-initiated wetting techniques combined with structuring-independent wettability control to achieve microdroplet (<500 μm) spreading on arbitrary surfaces while eliminating parasitic pinning effects (pining force ∼ 0) and initial impact momentum effects (Weber number ∼ 0).

FINDINGS

Our experiments reveal that the capillary-driven initial spreading of microdroplets is shorter, with significantly reduced oscillation dampening, when compared to millimeter-scale droplets. Furthermore, spreading along with capillary wave propagation results in coupling between the spreading velocity and dynamic contact angle at the contact line. These findings, along with our proposed microdroplet manipulation platform, may find application in microscale heat transfer, advanced manufacturing, and aerosol transmission studies.

Study on the Bouncing Behaviors of a Non-Newtonian Fluid Droplet Impacting on a Hydrophobic Surface

The control of a droplet bouncing on a substrate is of great importance not only in academic research but also in practical applications. In this work, we focus on a particular type of non-Newtonian fluid known as shear-thinning fluid. The rebound behaviors of shear-thinning fluid droplets impinging on a hydrophobic surface (equilibrium contact angle θ_eq ≈ 108°and contact angle hysteresis Δθ ≈ 20°) have been studied experimentally and numerically. The impact processes of Newtonian fluid droplets with various viscosities and non-Newtonian fluid droplets with dilute xanthan gum solutions were recorded by a high-speed imaging system under a range of Weber numbers (We) from 12 to 208. A numerical model of the droplet impact on the solid substrate was also constructed using a finite element scheme with the phase field method (PFM). The experimental results show that unlike the Newtonian fluid droplets where either partial rebound or deposition occurs, complete rebound behavior was observed for non-Newtonian fluid droplets under a certain range of We. Moreover, the minimum value of We required for complete rebound increases with xanthan concentration. The numerical simulations indicate that the shear-thinning property significantly affects the rebound behavior of the droplets. As the amount of xanthan increases, the high shear rate regions shift to the bottom of the droplet and the receding of the contact line accelerates. Once the high shear rate region appears only near the contact line, the droplet tends to fully rebound even on a hydrophobic surface. Through the impact maps of various droplets, we found that the maximum dimensionless height H_max^* of the droplet increases almost linearly with We as H_max^* ∼ αWe. In addition, a critical value H_max, c^* for the distinction between deposition and rebound for droplets on the hydrophobic surface has been theoretically derived. The prediction of the model shows good consistency with the experimental results.

Effects of surface acoustic waves on droplet impact dynamics

HYPOTHESIS

Surface acoustic waves (SAW) propagating along a solid surface can significantly affect the dynamics of droplet impact. Although droplet impact in presence of SAW has been attempted recently, here, we investigate the effects of surface wettability, droplet size, impact velocity, and SAW power on the impact and spreading dynamics along with post-impact oscillation dynamics of a drop.

EXPERIMENTS

Here, we study droplet impact on a surface exposed to traveling SAW produced using an interdigitated electrode patterned on a piezoelectric substrate. The effects of Weber number (We), surface wettability, and SAW power on the impact and spreading dynamics and post-impact oscillation dynamics are studied.

FINDINGS

Our study unravels that the interplay between capillary and viscous forces, and inertia forces arising due to pre-impact kinetic energy and SAW-induced bulk acoustic streaming underpins the phenomena. Remarkably, we find that the effect of SAW on droplet impact dynamics is predominant in the case of a hydrophilic (HPL) substrate at a higher SAW power and smaller We and hydrophobic (HPB) substrate irrespective of SAW power. Our study reveals that the maximum droplet spreading diameter increases with SAW power at smaller We for an HPL surface whereas it is independent of SAW power at higher We. Post-impact oscillation of a droplet over an HPL surface is found to be overdamped with a smaller amplitude compared to an HPB substrate, and a faster decay in oscillation amplitude is observed in the case of an HPB surface and higher We. Our study provides an improved understanding of droplet impact on a surface exposed to SAW that may find relevance in various practical applications.

Superhydrophobic Strategy for Nature-Inspired Rotating Microfliers: Enhancing Spreading, Reducing Contact Time, and Weakening Impact Force of Raindrops

Wind-dispersal of seeds is a remarkable strategy in nature, enlightening the construction of microfliers for environmental monitoring. However, the flight of these microfliers is greatly affected by climatic conditions, especially in rainy days, they suffer serious raindrop impact. Here, a hierarchical superhydrophobic surface is fabricated and a novel strategy is demonstrated that the superhydrophobic coating can enhance spreading while reduce contact time and impact force of raindrops, all of which are beneficial for the rotating microfliers. When the surface rotating speed exceeds a critical value, the effect of centrifugal force becomes considerable so that the droplet spreading is enhanced. The rotating superhydrophobic surface can rotate an impacting droplet by the tangential drag force from the air boundary layer, and the rotation of the droplet generates a negative pressure zone inside it, reducing the contact time by more than 30%. The impact force by the droplet on the rotating superhydrophobic surface also has a remarkable reduction of 53% compared to that on unprocessed hydrophilic surfaces, which helps maintain the flight stability of the microfliers. This work pioneers in revealing the droplet impact effect on rotating microflier surfaces and demonstrates the effectiveness of protecting microfliers with superhydrophobic coatings, which shall guide the manufacture and flight of microfliers in rainy conditions.

Penetration and ligament formation of viscoelastic droplets impacting on the superhydrophobic mesh

Spraying occurs by the impact of water droplets on the superhydrophobic wire meshes by liquid penetration during the spreading and recoiling. We have shown that adding a small amount of high molecular weight polymer (PEO) alters the ligaments formation and stabilizes them due to its high elasticity. Consequently, it suppresses droplet spray during droplet spreading and recoiling (recoil penetration). In the wide range of the impact velocities, the penetrated ligaments retracted back to the mesh after reaching the maximum length and eventually merged with the droplet on the mesh. The empirical fitting shows that the ligament evolution follows the parallel spring-dashpot model of Kelvin–Voigt. The additive polymer also changes the recoil penetration mechanisms from cavity collapse to cavity detachment due to the higher retraction velocity of the cavity near the mesh that is induced by the upward flow formed by the retraction of the ligaments to the mother droplet. A model based on mass conservation is proposed to calculate the variation of the maximum ligament size.

Droplet Impact on Asymmetric Hydrophobic Microstructures

Textured hydrophobic surfaces that repel liquid droplets unidirectionally are found in nature such as butterfly wings and ryegrass leaves and are also essential in technological processes such as self-cleaning and anti-icing. In many occasions, surface textures are oriented to direct rebounding droplets. Surface macrostructures (>100 μm) have often been explored to induce directional rebound. However, the influence of impact speed and detailed surface geometry on rebound is vaguely understood, particularly for small microstructures. Here, we study, using a high-speed camera, droplet impact on surfaces with inclined micropillars. We observed directional rebound at high impact speeds on surfaces with dense arrays of pillars. We attribute this asymmetry to the difference in wetting behavior of the structure sidewalls, causing slower retraction of the contact line in the direction against the inclination compared to with the inclination. The experimental observations are complemented with numerical simulations to elucidate the detailed movement of the drops over the pillars. These insights improve our understanding of droplet impact on hydrophobic microstructures and may be useful for designing structured surfaces for controlling droplet mobility.

Droplet Spreading Characteristics on Ultra-Slippery Solid Hydrophilic Surfaces with Ultra-Low Contact Angle Hysteresis

Dynamic interactions of the droplet impact on a solid surface are essential to many emerging applications, such as electronics cooling, ink-jet printing, water harvesting/collection, anti-frosting/icing, and microfluidic and biomedical device applications. Despite extensive studies on the kinematic features of the droplet impact on a surface over the last two decades, the spreading characteristics of the droplet impact on a solid hydrophilic surface with ultra-low contact angle hysteresis are unclear. This paper clarifies the specific role of the contact angle and contact angle hysteresis at each stage of the droplet impact and spreading process. The spreading characteristics of the droplet impact on an ultra-slippery hydrophilic solid surface are systematically compared with those on plain hydrophilic, hydroxylated hydrophilic, and plain hydrophobic surfaces. The results reveal that the maximum spreading factor (βmax) of impacting droplets is mainly dependent on the contact angle and We. βmax increases with the increase in We and the decrease in the contact angle. Low contact angle hysteresis can decrease the time required to reach the maximum spreading diameter and the time interval during which the maximum spreading diameter is maintained when the contact angles are similar. Moreover, the effect of the surface inclination angle on the spreading and slipping dynamics of impacting droplets is investigated. With the increase in the inclination angle and We, the gliding distance of the impacting droplet becomes longer. Ultra-low contact angle hysteresis enables an impacting droplet to slip continuously on the ultra-slippery hydrophilic surface without being pinned to the surface. The findings of this work not only show the important role of the surface wettability in droplet spreading characteristics but also present a pathway to controlling the dynamic interactions of impacting droplets with ultra-slippery hydrophilic surfaces.

How an Oxide Layer Influences the Impact Dynamics of Galinstan Droplets on a Superhydrophobic Surface

When exposed to air, gallium-based alloys rapidly form a thin oxide layer with viscoelasticity and high adhesion. Although previous work demonstrated that an oxide layer inhibits liquid metal droplet rebound, there is still a lack of a quantitative study to elaborate how an oxide layer affects the impact dynamics. To address this issue, we experimentally investigate Galinstan droplet impingement on a superhydrophobic CuO nanoblade surface and physically explain the difference in the dynamic characteristics of oxidized and unoxidized droplets. Experimental results show that the effect of an oxide layer becomes prominent during the retraction phase. The high adhesion significantly suppresses retraction and rebound, while the elastic response prevents a droplet from sufficiently stretching and maintains the stability of the morphology. More importantly, we systematically and quantitatively explore the influence of an oxide layer on several critical impact parameters, which contributes to a comprehensive understanding of the impact dynamics of liquid metal droplets. It is indicated that an oxide layer has little effect on the maximum spreading factor and spreading time, whereas it causes a 45% reduction of the restitution coefficient and a 36% increase in contact time. Notably, the scaling laws that describe the critical impact parameters of unoxidized droplets show good agreement with the ones known from ordinary Newtonian fluids.

Charging of drops impacting onto superhydrophobic surfaces

When neutral water drops impact and rebound from superhydrophobic surfaces, they acquire a positive electrical charge. To measure the charge, we analyzed the trajectory of rebounding drops in an external electric field by high-speed video imaging. Although this charging phenomenon has been observed in the past, little is known about the controlling parameters for the amount of drop charging. Here we investigate the relative importance of five of these potential variables: impact speed, drop contact area, contact line retraction speed, drop size, and type of surface. We additionally apply our previously reported model for sliding drop electrification to the case of impacting drops, suggesting that the two cases contain the same charge separation mechanism at the contact line. Both our experimental results and our theoretical model indicate that maximum contact area is the dominant control parameter for charge separation.

Contact Time of Droplet Impact on Inclined Ridged Superhydrophobic Surfaces

Superhydrophobic surfaces decorated with macrostructures have attracted extensive attention due to their excellent performance of reducing the contact time of impacting droplets. In many practical applications, the surface is not perpendicular to the droplet impact direction, but the impacting dynamics in such scenarios still remain mysterious. Here, we experimentally investigate the dynamics of droplet impact on inclined ridged superhydrophobic surfaces and reveal the effect of We_n (the normal Weber number) and α (the inclination angle) on the contact time τ. As We_n increases, τ first decreases rapidly until a platform is reached; if We_n continues to increase, τ further reduces to a lower platform, indicating a three-stage variation of τ in low, middle, and high We_n regions. In the middle and high We_n regions, the contact time is reduced by 30 and 50%, respectively, and is dominated by droplet spreading/retraction in the tangential and lateral directions, respectively. A quantitative analysis demonstrates that τ in the middle and high We_n regions is independent of We_n and α, while the range of middle and high We_n regions is related to α. When α < 30°, increasing α narrows the middle We_n region and enlarges the high We_n region; when α ≥ 30°, the two We_n regions remain unchanged. In addition, droplet sliding is hindered by the friction and is affected by the droplet morphology in the high We_n region. Overall, the synergistic effect of the surface inclination and macrostructures effectively promotes the detachment of impacting droplets on superhydrophobic surfaces, which provides guidance for applications of superhydrophobic surfaces.

Oscillation Dynamics of Drops on Immiscible Thin Liquid Films

While drop oscillation dynamics has been widely studied for many decades, the influence of a moving contact line on the oscillation modes of drops remains underexplored. Herein, we report the oscillation dynamics of drops on thin liquid films with different viscosities where lower viscosities provide a slipping surface and higher viscosities immobilize the contact line. A gently deposited drop onto an oil film undergoes shape oscillations due to capillarity, where the frequency, amplitude, and apparent contact angle are tracked via a high-speed camera. This study demonstrates that restraining the mobility of the drop contact line by increasing the viscosity of a thin oil film underneath the drop increases the extent of the drop oscillation time as well as affecting the natural frequency of the drop oscillation. The drop oscillation time was defined by the time at which the changes in the drop height dropped to values less than 1% of the equilibrium height. The experimental results for the first longitudinal mode oscillation frequencies as a function of the equilibrium contact angles for the pinning and slipping contact lines were in good agreement with previously reported numerical simulations and model predictions.

Surface acoustic wave-based generation and transfer of droplets onto wettable substrates

Fluid manipulation using surface acoustic waves (SAW) has been utilized as a promising technique in the field of microfluidics due to its numerous advantages, over other active techniques, such as low power requirement, facile fabrication methods, and non-invasive nature. Even though SAW-based generation of micron-sized droplets through atomization has been studied, the role of substrate wettability on the characteristics of the transferred droplets has not been explored to date. Here, we study the generation and effective transfer of micron-sized droplets using SAW onto wettable substrates whose water contact angles vary from 5° to 145°. The characteristics of transferred droplets after impacting the wettable substrates are characterized in terms of the contact line diameter and polydispersity index. A theoretical model is formulated to predict the initial average size of the transferred droplets on the wettable substrates of different contact angles. The variation of polydispersity and number density with contact angle is explained by considering droplet coalescence and bouncing. The relevance of the technique in biological assays is demonstrated by transferring droplets of streptavidin protein samples onto a substrate.

Investigation of surface acoustic wave-based generation and transfer of droplets onto wettable substrates is carried out and explained in terms of polydispersity index. Transfer of biomolecules is demonstrated to highlight the technique.

Effect of Viscosity on Bouncing Dynamics of Elliptical Footprint Drops on Non-Wettable Ridged Surfaces

An initial drop shape can alter the bouncing dynamics and significantly decrease the residence time on superhydrophobic surfaces. Elliptical footprint drops show asymmetric dynamics owing to a pronounced flow driven by the initial drop shape. However, the fundamental understanding of the effect of viscosity on the asymmetric dynamics has yet to be investigated, although viscous liquid drop impact on textured surfaces is of scientific and industrial importance. Here, the current study focuses on the impact of elliptical footprint drops with various liquid properties (density, surface tension, and viscosity), drop sizes, and impact velocities to study the bouncing dynamics and residence time on non-wettable ridged surfaces numerically by using a volume-of-fluid method. The underlying mechanism behind the variation in residence time is interpreted by analyzing the shape evolution, and the results are discussed in terms of the spreading, retraction, and bouncing. This study provides an insight on possible outcomes of viscous drops impinging on non-wettable surfaces and will help to design the desired spraying devices and macro-textured surfaces under different impact conditions, such as icephobic surfaces for freezing rain or viscous liquids.

Drop Impact on a Superhydrophilic Spot Surrounded by a Superhydrophobic Surface

The spatial variation in the wettability of a surface can have a significant effect on the spreading and retraction behavior of an impacting droplet and hence the overall impact dynamics. Although composite surfaces have proven applications, there is a lack of understanding of droplet impact on surfaces with a sudden jump in wettability. Here, we study the behavior of a liquid drop impacting a composite surface having a superhydrophilic (SHL) spot surrounded by a superhydrophobic (SHB) region. We find that the droplet exhibits different regimes: no-splitting, jetting, and splashing, depending upon the spot size (β_s) and the Weber number (We). At a smaller β_s, the behavior shifts from the stable to jetting regime and then to the splashing regime, with increasing We. We find that by increasing the value of β_s, one can avoid the undesirable splashing and jetting regimes and attain a stable regime even at a higher We. Our study reveals that β_s has a significant influence on the maximum spreading diameter β_max at a smaller We but a negligible effect at a higher We. We show that the dominance of capillary energy at a smaller We and viscous energy at a higher We underpins the phenomena. We employ an energy conservation approach to develop an analytical model to predict β_max on a composite SHL-SHB surface by considering the total energy of the system before the impact and at the maximum spread position. We find K = (Re^1/2/We) emerges as a key parameter in the model that accurately predicts the experimentally measured β_max. Our study reveals the existence of an inertia-viscous dominated regime at a smaller K and an inertia-capillary dominated regime at a larger K. The outcome of our study may find applications in stable and precise positioning of impacting droplets.

Spreading Dynamics of an Impinging Ferrofluid Droplet on Hydrophilic Surfaces under Uniform Magnetic Fields

This paper reports a numerical investigation on the spreading dynamics of an impinging ferrofluid droplet on solid hydrophilic surfaces (i.e., θ_w ≤ 60°) in the presence of uniform magnetic fields. A finite element method-based commercial solver is implemented to perform several numerical simulations, which uses a phase-field (PF) method to couple both the flow and magnetic fields. The results demonstrate that a uniform magnetic field is capable of controlling the spreading dynamics of an impinging droplet on hydrophilic substrates. Additionally, the application of a magnetic field results in the generation of a steady-state droplet shape with a reduced base diameter and an increased apex height at higher magnetic Bond numbers at the end of the spreading process. Moreover, as the viscosity of the droplet decreases, the droplet experiences an increase in its primary spreading diameter, which can be even reduced through the implementation of a vertical uniform magnetic field. Additionally, an oscillatory motion appears in a droplet during the spreading phenomenon at lower Ohnesorge numbers (i.e., Oh = 0.023), which is further sustained for a longer period of time in the relaxation phase with increased amplitudes in the case of an extremely low-viscosity droplet (i.e., Oh = 0.002) before attaining a final equilibrium shape. Furthermore, at Oh = 0.002, the droplet undergoes a breakup event after the impact for a short period of time, while the magnetic field induces an elastic behavior in a droplet at lower viscosities (i.e., Oh = 0.023) during the free fall under gravity.

The proper orthogonal decomposition: A powerful tool for studying drop oscillations

Liquid metal drops are released onto different wettable solid substrates. Their post-impact oscillations are recorded at 1000 images/s as soon as the triple line is at rest. The proper orthogonal decomposition (POD) is used to get and identify the frequencies involved. The POD is a technique widely used in the fluid dynamics community to study turbulent flows, but it is not used to determine droplet-free oscillation frequencies. The vertical and horizontal vibration frequencies of the sessile drop center of mass are successfully extracted from the images by POD. The first POD mode captures the vertical displacement frequency, and the second or third POD mode captures the horizontal displacement frequency of the drop center of mass. The spatial structure of the modes is the characteristic of the vertical and horizontal movement. Therefore, the POD can be used instead of the interface displacement tracking to determine the free oscillation frequencies of liquid metal drops and, more generally, of any vibrating sessile drops. As it is a standardized method, it can be used with confidence for routine measurements, especially for sensors.

Head-on Collision of Two Nanodroplets on a Solid Surface: A Molecular Dynamics Simulation Study

Most researchers focus on the collision of a single droplet with a solid surface, while it is common for a droplet to collide with a sessile droplet on a solid surface in reality. This study performed the head-on collision of two nanodroplets on a solid surface using the molecular dynamics simulation method. The effects of impact velocity, interaction intensity between solid and liquid atoms, and the solid fraction of the surface on the collision process are studied with independent simulation cases. The maximum spreading factor and the dimensionless maximum spreading time are recorded and calculated to describe the collision process quantitatively. The simulation results indicate that the maximum spreading factor depends more on the solid fraction than the interaction intensity since it does not fundamentally change the wetting state of the droplet at its maximum spreading state. Because of two different effects, the maximum dimensionless spreading time decreases first and then increases with the interaction intensity, and both effects weaken with the increase of impact velocity. As the solid fraction increases, the maximum spreading factor increases significantly at high impact velocity, and the maximum dimensionless spreading time first decreases and then increases because the wetting state of the coalescent droplet at the maximum spreading moment gradually changes from the Wenzel state to the Cassie state. In general, the initial wetting state of the sessile droplet and the wetting state of the coalescent droplet at the maximum spreading moment have important effects on the maximum spreading factor and the maximum spreading time. We establish a theoretical prediction model for the maximum spreading factor on a smooth surface based on energy conservation with quite good accuracy. This research has improved our understanding of the head-on collision process of two nanodroplets on a solid surface.

Droplet Impact on Surfaces with Asymmetric Microscopic Features

The impact of liquid drops on a rigid surface is central in cleaning, cooling, and coating processes in both nature and industrial applications. However, it is not clear how details of pores, roughness, and texture on the solid surface influence the initial stages of the impact dynamics. Here, we experimentally study drops impacting at low velocities onto surfaces textured with asymmetric (tilted) ridges. We found that the difference between impact velocity and the capillary speed on a solid surface is a key factor of spreading asymmetry, where the capillary speed is determined by the friction at a moving three-phase contact line. The line-friction capillary number Ca_f = μ_fV₀/σ (where μ_f,V₀, and σ are the line friction, impact velocity, and surface tension, respectively) is defined as a measure of the importance of the topology of surface textures for the dynamics of droplet impact. We show that when Ca_f ≪ 1, the droplet impact is asymmetric; the contact line speed in the direction against the inclination of the ridges is set by line friction, whereas in the direction with inclination, the contact line is pinned at acute corners of the ridges. When Ca_f ≫ 1, the geometric details of nonsmooth surfaces play little role.

Airflow-Assisted Impact of Drops of Various Viscosities: The Role of Viscous Dissipation, Normal Imposed Pressure, and Shear Flow of Air

The role of liquid viscosity on the spreading for an airflow-assisted impact of drops on a surface is investigated. The spreading diameter is found to increase with the Reynolds number of the airflow (Re_air) for a given viscosity and impact Weber number (We) compared to the still air. The increment is higher at a low We for viscous drops, whereas the effect of Re_air dominates at the intermediate We as the viscosity decreases. Two extra forces, the normal imposed pressure and shear force of air, act on the drop and influence the spreading along with the viscous dissipation. The drop's curvature decreases depending on the viscosity and impact velocity while spreading. Large-scale eddies near the drop-surface region are observed due to the separation of the incident airflow. The formation of eddies signifies low-pressure zones, which extract the trapped air, causing the spreading diameter of the viscous drop to increase at a low We. With the increase in the We, the lamella thickness of low-viscosity drops decreases and is pushed out by the air shear causing the spreading factor to increase. The boundary layer thickness is estimated using the energy balance method to predict the maximum spreading factor. The prediction compares well with the experimental one for higher viscosities. The accuracy improves when the effect of low pressure is incorporated. To confirm, the experimental spreading is compared with that obtained from three existing models, and one, which considers the influence, is observed to provide a better prediction.

Droplet impact on pillar-arrayed non-wetting surfaces

Droplet impact on pillar-arrayed polydimethylsiloxane (PDMS) surfaces with different solid fractions was studied. The lower and upper limits of Weber number, We, for complete rebound of impacting droplets decreased with decreasing solid fractions. Gaps were visible during the spreading and retraction processes of bouncing droplets on the surface with a solid fraction of 0.06 while no gaps were observed during the retraction process when We was greater than its upper limit, indicating that there existed a transition from the Cassie-Baxter wetting state to the Wenzel wetting state. Therefore, a novel model accounting for the penetration of a liquid into the cavities between the pillars was developed to predict the upper limit of the impact velocity of bouncing droplets. At high We, partial rebound was observed for surfaces with solid fractions of 0.50 and 0.20 while a sticky state was observed for the surface with a solid fraction of 0.06. Moreover, surface roughness has a great influence on the contact time of bouncing droplets. Besides, the maximum spreading parameter was found to follow a scaling law of We^1/4.

Analytical Consideration for the Maximum Spreading Factor of Liquid Droplet Impact on a Smooth Solid Surface

Based on the energy conservation approach, this study develops a universal model to predict the maximum spreading factor of liquid droplet impact on a smooth solid surface. Validated with the present simulations and experiments in the literature, this model effectively overcomes the limitation of previous models in the viscous regime and greatly reduces the computing errors from over 30% to below 6%. It is demonstrated that the underestimated maximum spreading factor by previous models results from the overestimation of viscous dissipation. By replacing the conventional model of spreading time, t_m = 8D₀/3U₀, with a more precise one, t_m = 1.47τ_iWe^-0.44, the formulation to compute the viscous dissipation of entire spreading is improved. Finally, we examine the applicability of present model in the capillary regime and good performance is also shown.

Viscoelasticity and elastocapillarity effects in the impact of drops on a repellent surface

We investigate freely expanding viscoelastic sheets. The sheets are produced by the impact of drops on a quartz plate covered with a thin layer of liquid nitrogen that suppresses shear viscous dissipation as a result of the cold Leidenfrost effect. The time evolution of the sheet is simultaneously recorded from top and side views using high-speed cameras. The investigated viscoelastic fluids are Maxwell fluids, which are characterized by low elastic moduli, and relaxation times that vary over almost two orders of magnitude, thus giving access to a large spectrum of viscoelastic and elastocapillary effects. For the purposes of comparison, Newtonian fluids, with viscosity varying over three orders of magnitude, are also investigated. In this study, dmax, the maximal expansion of the sheets, and tmax the time to reach this maximal expansion from the time at impact, are measured as a function of the impact velocity. By using a generalized damped harmonic oscillator model, we rationalize the role of capillarity, bulk elasticity and viscous dissipation in the expansion dynamics of all investigated samples. In the model, the spring constant is a combination of the surface tension and the bulk dynamic elastic modulus. The time-varying damping coefficient is associated to biaxial extensional viscous dissipation and is proportional to the dynamic loss modulus. For all samples, we find that the model reproduces accurately the experimental data for dmax and tmax.

Axial spreading of droplet impact on ridged superhydrophobic surfaces

HYPOTHESIS

Due to the complex hydrodynamics of droplet impact on ridged superhydrophobic surfaces, quantitative droplet spreading characteristics are unrevealed, limiting the practical applications of ridged superhydrophobic surfaces. During droplet impacting, the size ratio (the ratio of the ridge diameter to the droplet diameter) is an important factor that affects droplet spreading dynamics.

EXPERIMENTS

We fabricated ridged superhydrophobic surfaces with size ratios ranging from zero to one, and conduct water droplet impact experiments on these surfaces at varied Weber numbers. Aided by the numerical simulations and theoretical analysis, we illustrate the droplet spreading dynamics and reveal the law on the maximum axial spreading coefficient.

FINDS

The results show that the droplet spreading and retraction dynamics on ridged superhydrophobic surfaces are significantly asymmetric in the axial and spanwise directions. Focusing on the maximum axial spreading coefficient, we find it decreases first and then increases with increasing size ratios, indicating the existence of the critical size ratio. The maximum axial spreading coefficient can be reduced by 25-40% at the critical size ratio compared with that on flat surfaces. To predict the maximum axial spreading coefficient, two theoretical models are proposed respectively for size ratios smaller and larger than the critical size ratio.

Visible-light harvesting innovative W6+/Yb3+/TiO2 materials as a green methodology photocatalyst for the photodegradation of pharmaceutical pollutants

In this work, we report on the synthesis of a new-age reusable visible-light photocatalyst using a heterojunction nanocomposite of W⁶⁺/Yb³⁺ on a mixed-phase mesoporous network of monolithic TiO₂. The structural properties of the monolithic photocatalysts are characterized using p-XRD, SEM-EDAX, TEM-SAED, XPS, PLS, UV-Vis-DRS, FT-IR, micro-Raman, TG-DTA, and N₂ isotherm analysis. The electron microscopic analysis reveals a mesoporous network of ordered worm-like monolithic design, with a polycrystalline mixed-phase (anatase/rutile) TiO₂ composite, as indicated by diffraction studies. The UV-Vis-DRS analysis reveals a redshift in the light absorption characteristics of the mixed-phase TiO₂ monolith as a function of W⁶⁺/Yb³⁺ co-doping. It is observed that the use of (8.0 mol%)W⁶⁺/0.4 (mole%)Yb³⁺ co-doped monolithic TiO₂ photocatalyst, with an energy bandgap of 2.77 eV demonstrates superior visible-light photocatalysis, which corroborates with the PLS studies in terms of voluminous e^-/h⁺ pair formation. The practical application of the photocatalyst has been investigated through a time-dependent dissipation of enrofloxacin, a widely employed antimicrobial drug, and its degradation pathway has been monitored by LC-MS-ESI and TOC analysis. The impact of physio-chemical parameters such as solution pH, sensitizers, drug concentration, dopant/codopant stoichiometry, catalyst quantity, and light intensity has been comprehensively studied to monitor the process efficiency.

How different freezing morphologies of impacting droplets form

HYPOTHESIS

Freezing morphologies of impacting water droplets depend on the interaction between droplet spreading and solidification. The existing studies showed that the shape of frozen droplets mostly is of spherical cap with a singular tip, because of much shorter timescale of the droplet spreading than that of the solidification. Here, we create the experimental conditions of extended droplet spreading and greatly enhanced heat transfer for fast solidification, thereby allowing to study such droplet freezing process under the strong coupling of the droplet spreading and solidification.

EXPERIMENTS

We design experiments that a room-temperature water droplet impacts on a subcooled superhydrophilic surface in an enclosure chamber filled with nitrogen gas. We thoroughly investigate the freezing processes of impacting droplets under the effects of impact velocity and substrate temperature. Both the droplet impact dynamics and solidification are studied with a high-speed camera.

FINDINGS

We observed five different freezing morphologies which depend on the droplet impact velocity and substrate temperature. We found that the formation of diverse morphologies results from the competitive timescales related to droplet solidification and impact hydrodynamics. We also develop a phase diagram based on scaling analysis and show how freezing morphologies are controlled by droplet impact and freezing related timescales.