Dynamic behavior of water droplets impacting on the superhydrophobic surface: Both experimental study and molecular dynamics simulation study

The impacting phenomenon of nanodroplets has received much attention due to their importance in various industrial applications. The oblique impingement of single droplets is well understood; however, the effect of oblique angle on impacting the dynamics of multiple droplets at the nanoscale is very limited. To address this gap, we perform molecular dynamics (MD) simulations to study the impacting dynamics of binary nanodroplets with various oblique angles (αob) and Weber numbers (We). Using MD simulations, we directly capture the detailed morphological evolution of the impacting binary droplets with various given conditions. Compared to the oblique impingement of a single droplet, the evolution of impacting binary droplets involves two novel dynamic characteristics: the asymmetric dynamics with droplet preferential spreading in the y direction and the rotating of the coalescing droplet. The mechanisms underlying are well studied. The asymmetric dynamics is a result of the velocity gradient of the outer edge of the spreading droplet, and the rotating effect is due to the change in angular momentum induced by surface force. The analysis and study of these phenomena have never been mentioned in previous studies of single droplet. Finally, we investigate the effect of αob and We on normalized moving distance (L/Dsin) and contact time (tc). This work paves the way for offering a comprehensive understanding of the oblique impingement of binary nanodroplets.

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.

The impact dynamics of double unequal-sized droplets impacting superhydrophobic surfaces are investigated via lattice Boltzmann method (LBM) simulations. The simulations capture the spreading and receding dynamics of unequal-sized droplets on superhydrophobic surfaces, and reveal the influences of the radius ratio of the droplets (K), the droplet spacing (L*), and the Weber number. The radius ratio and the droplet spacing significantly affect the contact time. The contact time increases with the radius ratio when 1.2 < K < 2.1, as the increasing radius ratio leads to the intensification of the asymmetry in the impact processes that causes more intense internal collisions and energy dissipation; while it remains unchanged when 2.1 ≤ K ≤ 3.0, since the larger droplet dominates the morphological evolution and the contact time is equivalent to that of a single droplet. Besides, the contact time decreases with the droplet spacing when 1.2 ≤ L* ≤ 1.6, as the coalescence strength decreases with the increase of droplet spacing, leading to less viscous dissipation; while the contact time increases when 1.6 < L* ≤ 2.0, since the increasing droplet spacing causes the increase of the degree of separation of droplets during rebound, which reduces the kinetic energy for rebound provided by the smaller droplet. Our work demonstrates the key physics governing the impact dynamics of unequal-sized droplets impacting superhydrophobic surfaces, key for enhanced antifrosting/icing, self-cleaning, and water/energy harvesting.

Superhydrophobic coating has a great application prospect in self-cleaning and oil-water separation but remains challenging for large-scale preparation of robust and weather-resistant superhydrophobic coatings via facile approaches. Herein, this work reports a scalable fabrication of weather-resistant superhydrophobic coating with multiscale rough coral reef-like structures by spraying the suspension containing superhydrophobic silica nanoparticles and industrial coating varnish on various substrates. The coral reef-like structures effectively improves the surface roughness and abrasion resistance. Rapid aging experiments (3000h) and the outdoor building project application (3000 m2 ) show that the sprayed superhydrophobic coating exhibits excellent self-cleaning properties, weather resistance, and environmental adaptability. Moreover, the combined silica-coating varnish-polyurethane (CSCP) superhydrophobic sponge exhibits exceptional oil-water separation capabilities, selectively absorbing the oils from water up to 39 times of its own weight. Furthermore, the molecular dynamics (MD) simulation reveals that the combined effect of higher surface roughness, smaller diffusion coefficient of water molecules, and weaker electrostatic interactions between water and the surface jointly determines the superhydrophobicity of the prepared coating. This work deepens the understanding of the anti-wetting mechanism of superhydrophobic surfaces from the perspective of energetic and kinetic properties, thereby paving the way for the rational design of superhydrophobic materials and their large-scale applications.

Summary Dynamics of droplet impact on solid surfaces is of great importance in many engineering applications such as ink-jet printing and rapid spray cooling of hot surfaces. In this study, the lattice kinetic scheme based on the lattice Boltzmann method for immiscible two-phase fluids [Inamuro (2006)] is applied to such micro-fluid problems. The present method enables us to perform stable calculations of two-phase flows with large density ratios of up to 1000. The boundary condition based on the wetting potential that is calculated according to a prescribed static contact angle is used on solid surfaces [Briant, Papatzacos, and Yeomans (2002)]. First, the dynamic behavior of a single droplet impinging on a horizontal wall is investigated for various Weber numbers. The dynamic contact angle, the contact line velocity, and the wet length are calculated, and found to be in good agreement with available experimental data. Next, the collision of a falling droplet with a stationary droplet on a solid surface is investigated. The behavior of the droplets and the mixing process during their collision are simulated for various impact velocities and several static contact angles on the solid surface. It is seen that mixing occurs around the rim of the coalescent droplet owing to the circular flows. Also, the relation between the mixing rate of the primary coalescent droplet and Weber number is obtained. Finally, adherence and bouncing of liquid droplets impacting on dry surfaces are examined for several Reynolds numbers based on the droplet diameter. These calculated results indicate that the present method can be a promising numerical approach to investigation of microscale droplet dynamics on solid surfaces.

Steam condensation with non-condensable gas exists widely in petro-chemical, power plant and seawater desalination processes. Super-hydrophobic surfaces with high contact angle could be an promising condensing surface to promote DWC and enhance heat transfer. As pure steam condensing droplet completely occupies micro/nano-structures of super-hydrophobic surfaces, super-hydrophobic function becomes “invalid”. For stream-air mixture vapor, the non- condensable gas would occupy the micro/nano-structures instead of water. Droplets form Cassie or transition wetting mode, holding or partly holding super-hydrophobic feature. Inclination angle of the tube can influence the shape, size and dynamic characteristics of the condensing droplets, thus changing the heat transfer performance. Therefore, for getting deeply insights of the effect of the non-condensable gas on condensation heat transfer, it is necessary to study the condensing drops characteristics on super-hydrophobic tube for different inclined angles. According to dropwise condensation model, increasing contact angle hysteresis, departure droplet size, sweeping period would reduce the condensation heat transfer efficiency. In this paper, dropwise condensation is performed on super-hydrophobic copper tube, departure droplet size, sweeping period and the phenomenon of contact angle hysteresis are thoroughly studied and are compared with the case of hydrophobic surface or pure steam to explore the influence of inclined angle and surface wettability on droplet dynamics to achieve condensation heat transfer enhancement. The experimental result shows: (1) On the top of copper tube, for the condensation of steam with 10% non-condensable gas, the contact angle hysteresis on super-hydrophobic surface is smaller than that on hydrophobic surface. Compared with pure steam condensation on super-hydrophobic surface, the contact angle hysteresis of mixed steam is smaller because the non- condensable gas fills the micro/nano-structures. However, on the middle and bottom parts of the tube, the contact angle hysteresis on super-hydrophobic surface is greater than that on hydrophobic surface for the condensation of both pure steam and mixed steam. This phenomenon indicates that the contact angle hysteresis is determined by surface wettability instead of inclination angle. (2) The departure droplet size on super-hydrophobic surface increases with the inclination angle and the opposite trend is found on hydrophobic surface. With the increase of inclination angle, the support force provided by the tube would increase and change direction. So the wettability of the surface and departure droplet size would be changed. (3) The sweeping period of droplet on super-hydrophobic surface is longer because the micro/nano-structures increase the adhesion between the surface and the droplets. With the increase of the inclination angle, the sweeping period decreased slightly, shorter than the sweeping time when the tube is vertical. The sweeping period of vapor with non-condensable gas condensation is greater than that of pure steam. The presence of non-condensable gas increases thermal resistance, thus slowing down the drop growth rate and increasing the sweeping period. To sum up, on the top of copper tube, the contact angle hysteresis on super-hydrophobic surface is smaller than that on the hydrophobic surface. However, the totally opposite trend is found on the middle and bottom parts of the tube. The departure droplet size on super-hydrophobic surface increases with the inclination angle. The sweeping period of droplet on super-hydrophobic surface is longer. This work offers a new avenue to further enhance heat transfer of condensation with non-condensable gas.

Reducing the contact time of an impacting droplet is highly desirable in various industrial fields including anti-icing. With the straightforward upscaling advantage, singularities on superhydrophobic surfaces can induce an annular rebound with a limited reduction in contact time. To break this limitation and further reduce contact time, this study focuses on optimizing the singularity number and arrangement. The effects of the singularity number and dimensionless spacing (l* scaled by the droplet diameter) on the dynamic and contact time characteristics of a droplet impacting the superhydrophobic surface are experimentally studied under varying Weber numbers (We). The experimental results indicate that in comparison to the single singularity, two singularities with l* < 1.0 can generate two liquid rings with four lateral liquid subunits due to the impalement at the high We region. Owing to the reduced equivalent diameter of the subunit, increasing We results in a gradually decreased contact time and accordingly breaks the limitation. However, the liquid film cannot be pierced at l* > 1.0 with a limited reduction. Considering the further reducing potential at l* < 1.0, four singularities are explored without a further reduced contact time due to the formed central liquid film. Using an additional central singularity, the central liquid film is pierced promoting its annular rebound. In consequence, five singularities significantly break the limitation in contact time, particularly a 61.7% reduction to the superhydrophobic flat surface at l* < 1.0.

Droplet impact on superhydrophobic surfaces is central to applications such as self-cleaning, waterproofing, and heat-transfer enhancement. However, the coupled roles of droplet geometric asymmetry and substrate macroscopic curvature in rebound dynamics remain unclear. This study employs the Volume-of-Fluid (VOF) framework to study ellipsoidal droplets impacting a superhydrophobic cylindrical surface, varying rotation angle (φ, defined as the angle between the droplet’s major axis and the cylinder axis), aspect ratio (AR), and Weber number (We). Rotation angle is identified as a dominant control parameter: small φ promotes rebound and shortens contact time, whereas large φ increases residence time. A robust transition from rebound promotion to suppression occurs at φ = 60°–75° across the investigated We and AR ranges. We further show that the rebound height-to-width ratio (Λ) provides a simple visual indicator for contact-time trends. Based on these insights, we propose an empirical model incorporating a geometric asymmetry parameter (P), predicting contact time within ±10% and agreeing well with published data.

Superhydrophobic surface has wide application in self-cleaning, anti-pollution, anti-adhesion, drag reduction, but the stable and efficient manufacture of bionic superhydrophobic surfaces is a challenge. We have reproduced the microscopic structure of natural plants and achieved superhydrophobic surface preparation without chemical modification by mechanical process. This program need many experiments to generate processing parameters based on the bionic surface structure. To solve this problem, based on the natural Green Bristlegrass superhydrophobic surface, an optimized bio-inspired striped configuration was presented and the computational fluid dynamics approach was integrated into the fabrication, which was estimated the superhydrophobicity of bio-inspired surface. The volume of fluid (VOF) model and the Level Set function were used to determine the position of the interface during the liquid impact process by solving the change of the volume fraction of each phase in the mixed fluid, thus tracking the gas-liquid phase interface. According to the simulation of striped surface structure, we have processed the bionic samples successfully and they showed an excellent superhydrophobic property, the contact angle was 154° ± 2° and the sliding angle was <5°. The contact time of bionic sample was 12.8 ms. This article used the VOF simulation method to evaluate the design and parameters of the structure, so that the selection of processing parameters were more optimized. Furthermore, the study was essential to access the bio-inspired design and fabrication procedure of superhydrophobic surface.

Frosting is common found natural phenomenon in late autumn or early spring, which sometimes brings unwanted effects or even disaster to human. With the development of science and technology, frosting may to some extend be mitigated by hydrophobic surfaces. Micro-Nanostructure was gained via chemical etching on aluminium surface. The surface was further modified by low surface energy polymer coating to form a very thin nano-layer on the surface. A kind of fluoroalkylsilane is used as the coating polymer. After fluorination treating, the aluminium surface become super hydrophobic with water contact angles more than150°. The surface was observed to be configured with plateaus and caves of micro-Nanoscale. In subcooled environments, frosting experiment was carried out on the surface of aluminium rods and aluminium sheets using humidifier to supply the water droplets. The comparison of the quantity of frost formed on the super-hydrophobic and untreated aluminium surfaces was conducted in the present work. And the quantity of frost formed on aluminium surfaces of different contact angles was compared. The results show that super-hydrophobic aluminium surfaces have obvious advantages in inhibiting frost. Besides, the contact angle has evident influences on restraining frost. Therefore, super-hydrophobic surfaces may serve as an effective means in decreasing the accumulation of frost on outside solid surfaces.

Cisplatin uptake and release assessment from hydrogel synthesized in acidic and neutral medium: An experimental and molecular dynamics simulation study

The dynamics of liquid droplet impact on a super-hydrophobic surface was investigated experimentally and theoretically. The reactions of Newtonian droplet impact on a super-hydrophobic surface at low impact velocities (0-1.7m/s) and low Weber numbers (0 - 200) were revisited. The work further extended the investigation to non-Newtonian drops such as shear-thickening cornstarch and shear-thinning blood. The spreading dynamics of pure water, milk, 15wt.% cornstarch colloidal solution and healthy rabbit blood drops were studied by experiments and compared to the previous reported theoretical models. While the Roisman's model agreed well with the Newtonian drop spreading, a large deviation was observed in the experiments with non-Newtonian drops, especially of blood. Further theoretical analysis revealed the effects of the blood shear thinning properties on the droplet spreading. With the knowledge of the experimental spreading dynamics, we developed a rim instability theory to explain the fingering behavior by modifying the classical Rayleigh-Plateau instability. Our model accurately predicted the fingering behavior of water, milk and cornstarch drops, but over-estimated the blood droplet fingering at high impact Weber numbers (greater than 105). Based on the preliminary theoretical analysis, the shear thinning of blood, caused by the red blood cells deformability, was believed as the reason for the deviations in fingering. Following the discussions of spreading and fingering, the stability of the liquid jet was investigated experimentally where the jet breakup modes as well as mode transition were introduced. The jet evolution maps were created for water, milk and cornstarch droplets based on the experiments. Similar to the spreading and fingering, the extraordinary stability of the blood droplet was observed in jetting and was coined as 'shear-thinning inertia-driven stability'. The investigations on jetting filled the vacuum in research on droplet impact. Furthermore, our work initiated the research on the dynamics of blood droplet impact. The 'shear-thinning inertia-driven stability' creates a connection between the blood dynamics and the red blood cells deformability which suggests an important potential application: early diagnosis of blood diseases.

The effect of droplet dynamics on electric output of a PVDF (Polyvinylidene fluoride) cantilever is investigated through conducting in-laboratory experiments towards the raindrop energy harvesting (REH) applications. The droplet-substrate interaction affects the voltage output by several key factors, such as the droplet diameter, the impact velocity and the regime transition of droplet dynamics. The splash of droplet is shown to be dominant in voltage generation in an open circuit condition which is determined by the Weber number (We). The high-speed camera capturing technique allows the acquisition of both the droplet dynamic behaviors and the displacement of PVDF cantilever by means of which the effect on electric output can be comprehensively investigated. Results show that for single droplet impact, cantilever with a hydrophilic surface produces slightly higher voltage than that with a Super-hydrophobic (SH) surface; whereas for multiple droplet impacts, the SH surface performs better producing constant voltage amplitude and oscillating time. In this case, the accumulated water layer on hydrophilic surface attenuates the peak voltage successively especially when splash occurs. This work reveals the unneglectable effect of droplet dynamics on voltage output from an REH device. It may lay the foundation for improving energy conversion efficiency in terms of impact efficiency concerning the energy transfer from kinetic energy of droplet to vibration energy of a PVDF cantilever.

Dynamic characteristics of impacting binary nanodroplets on solid surfaces: From hydrophobic to superhydrophobic

An outlook on tunable superhydrophobic nanostructural surfaces and their possible impact on ice mitigation