Search Results (45)

Superhydrophobic surfaces with arrayed pillar structures have huge application prospects in various industrial fields, such as self-cleaning, waterproofing, anti-corrosion, and anti-icing. The knowledge gap regarding the liquid–solid interaction between impacting droplets and microstructured surfaces must be addressed to guide the practical engineering applications more effectively. In this study, the effects of the stationary and horizontally moving superhydrophobic micro-pillar surfaces on the droplet impact dynamic behavioral characteristics are investigated numerically, focusing on the droplet morphology, spreading diameter, contact time, and energy conversion. Based on the numerical simulation results, new prediction correlations of the dimensionless maximum spreading diameter for droplets impacting stationary and horizontally moving micro-pillar surfaces are proposed. Moreover, significant rolling phenomena occur when droplets impact horizontally moving micro-pillar surfaces, which leads to an increase in viscous dissipation and forms a competitive mechanism with the asymmetric spreading–retraction process of the droplets. Two different stages are recognized according to the analysis of the contact time and velocity restitution coefficient. This study may provide new insights into understanding the dynamic behavior of droplets on microstructured surfaces. Full article

In spray application contexts, plant leaves are bent and twisted upon droplet impact, which has a significant impact on the droplet’s impact behavior and its deposition effect on the leaves. This study examines the impact behavior of droplets on flexible pepper leaves and develops a mathematical model for droplet spreading and rebound, integrating the effects of leaf bending and torsion via energy conservation and cantilever beam theory. The energy required for leaf bending and twisting due to droplet impact was estimated in accordance with Hooke’s law. The droplets attained their maximum spreading diameter 4 ms post-impact on flexible pepper leaves, with droplet retraction occurring significantly faster on flexible leaves than on rigid ones, resulting in a return to steady state in half the duration required by rigid leaves. This study aims to establish a scientific foundation for optimizing pesticide application strategies and selecting parameters for spraying equipment in pepper production. Full article

The effects of substrate roughness and impact angle on the spreading behavior of Polyvinylidene Fluoride (PVDF) slurry droplets during the spraying process using a dispersing disk are investigated, aiming to enhance the quality of lithium-ion battery separators. In this study, through theoretical modeling and simulation analysis, mathematical expressions for the maximum spreading coefficient and the final shrinking coefficient of the droplets are derived. A simulation model for droplet impact and diffusion on the substrate surface is established based on the Lattice Boltzmann Method (LBM) and the Lagrangian function. Simulation results indicate that the maximum spreading coefficient of the droplet decreases with increasing substrate roughness and impact angle, while the final shrinking coefficient increases with substrate roughness but decreases as the impact angle increases. Finally, spray coating experiments for lithium-ion battery separators are conducted, and the results show that as the surface roughness and impact angle of the substrate increase, the average diameter of the droplets decreases, thereby validating the accuracy of the simulation results. Full article

Ice accretion from the impingement of supercooled water droplets on the rotating components of aero-engines reduces engine efficiency and poses significant in-flight safety risks. In the present study, we experimentally investigate the impact of water droplets on the center of a rotating disk to gain insights into the icing mechanisms on these components. The effects of impact velocity and disk rotation speed on dynamic behaviors are systematically explored by visualizing the phenomena and quantitatively analyzing the evolution of droplet diameters during long time durations. Three distinct regimes of impact dynamics are identified based on the final states: stable rotation, stable ring, and ring ejection. The experimental results reveal that the spreading phase is primarily governed by inertial effects, with minimal influence from disk rotation, while the latter significantly affects the retraction phase. The maximum spreading factor increases with the impact velocity and shows little dependence on rotation, and the spreading time remains nearly unchanged. Scaling laws for the maximum and equilibrium spreading factors as functions of the Weber number and rotational Bond number are established. While the maximum spreading factor increases with impact velocity on static disks, the retraction time decreases as both the impact velocity and rotation speed increase. Full article

Closeness is a measure that quantifies how quickly information can spread from a given node to all other nodes in the network, reflecting the efficiency of communication within the network by indicating how close a node is to all other nodes. For a graph G, the subset S of vertices of $V\left(G\right)$ is called vertex cut of G if the graph $G-S$ becomes disconnected. The minimum cardinality of S for which $G-S$ is either disconnected or contains precisely one vertex is called connectivity of G. A graph is called k-connected if it stays connected even when any set of fewer than k vertices is removed. In communication networks, a k-connected graph improves network reliability; even if up to $k-1$ nodes fail, the network remains operational, maintaining connectivity between devices. This paper aims to study the concept of closeness within n-vertex graphs with fixed connectivity. First, we identify the graphs that maximize the closeness among all graphs of order n with fixed connectivity k. Then, we determine the graphs that achieve the maximum closeness within all k-connected graphs of order n, given specific fixed parameters such as diameter, independence number, and minimum degree. Full article

The wetting behaviors of Al-Si-Cu-Mg-Zn brazing materials on 5083 aluminum alloy substrate were investigated through changing the proportion of Mg from 0 to 2 wt.%. The experimental results showed that the welding process goes through the three following stages: slow spreading, fast spreading, and stabilizing. The wettability of the brazing material was improved effectively, and the porosity of the interfacial layer was reduced, with the addition of Mg. With Mg content at 1 wt.%, the wetting diameter reached a maximum value of 20.46 mm. The reaction mechanism of the wetted interfacial layer between the brazing material and substrate alloy was illustrated with dynamic data, provided through experimentation and simulated thermodynamic calculation, and showed that the wetting behavior of the resultant Al-7.5Si-15Cu-1Mg-5Zn brazing material was dominated primarily by a diffusion reaction from elemental magnesium. Full article

The temperature field distribution of high-speed double-helical gears under oil injection lubrication is investigated by obtaining heat flux density and convective heat transfer coefficients through theoretical calculations and CFD (computational fluid dynamics) simulations. Based on the CFD method, fluid simulations are performed to obtain the distribution of lubricating oil on the surface of the double-helical gears, the velocity streamline diagram of the lubricating oil, and the convective heat transfer coefficients of different surfaces of the gears. The friction heat flux density is calculated using Hertzian contact theory and theoretical formula of heat generation. The double-helical gears’ steady-state temperature field simulation uses this heat flux density as a boundary condition. The correctness of the calculation method is verified through experiments. The study shows that increasing the jet velocity allows the jet to reach the tooth surface more effectively, improving the cooling effect and reducing the maximum gear temperature. However, the relationship between the jet velocity and the minimum gear temperature is non-linear. Within a certain range, increasing the jet diameter makes the jet wider, and the area covered by the lubricating oil becomes larger as the jet spreads around the gear teeth, enhancing the cooling effect. An increase in gear speed leads to an increase in frictional heat flux density; moreover, the high-velocity airflow generated by the increased speed reduces the amount of lubricant entering the mesh zone, which in turn causes the maximum temperature of the gears to continue to rise. Full article

The process of atomizing aluminum alloy powder using a rotating disk was studied by numerical simulation and experimental verification. The motion characteristics of the molten metal thin liquid film and the evolution law of atomization into droplets were systematically studied with different disk shapes and speeds. The results showed that the slippage of the liquid film on the surface of the spherical disk was smaller, the liquid film spread more evenly, and the velocity distribution was more uniform. Under the same working condition, the boundary diameter of the continuous liquid film on the spherical disk was 21–29% larger, and the maximum liquid film velocity increased by approximately 19%. In other words, the liquid film obtained more energy at the same rotational speed, the energy utilization rate was higher, and the liquid filaments produced by the splitting region of the disk surface were finer and greater in number. The data showed that the average thickness of the liquid film on the surfaces of different disk shapes was more affected by the speed of the flat disk, and the thickness on the spherical disk was relatively stable and uniform, but the difference in thickness between the two disk shapes decreased from 4.2 μm to 0.3 μm when the speed increased from 10,000 rpm to 60,000 rpm. In particular, the influence of the disk shape on the liquid film thickness became smaller when the speed increased to a certain range. At the same time, the characteristics of the liquid film during the spreading movement of molten metal on the disk and the mechanisms of the primary and secondary breakage of the liquid film were obtained through this simulation study. Full article

Given the problem that droplets cannot stay on the surfaces of leaves and wet them effectively, resulting in high levels of pesticide input and environmental pollution, this work studied the dynamic behaviors of droplets with different diameters (400–550 um) falling on the surfaces of wheat leaves from different heights (2–16 cm) using contact angle-measuring instruments and a high-speed camera. The VOF method in Fluent software was used to establish a numerical model of droplets impacting the surfaces of wheat leaves. The results show that with an increase in the initial diameter and initial velocity of a droplet, the maximum diameter of the droplet during the spreading process also gradually increases. After a droplet impacts a wheat leaf, the droplet-spreading diameter first increases and then decreases. The maximum droplet spreading rate, βmax, increases with an increase in the Weber number, βmax $\in W{e}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$, which is consistent with the existing theory. The results of this study lay a foundation for studying the spread of droplets on the surfaces of leaves, which is conducive to improving the rate of pesticide utilization. Full article

The effect of coal hydrophilic particles in water-glycerol drops on the maximum diameter of spreading along a hydrophobic solid surface is experimentally studied by analyzing the velocity of internal flows by Particle Image Velocimetry (PIV). The grinding fineness of coal particles was 45–80 μm and 120–140 μm. Their concentration was 0.06 wt.% and 1 wt.%. The impact of particle-laden drops on a solid surface occurred at Weber numbers (We) from 30 to 120. It revealed the interrelated influence of We and the concentration of coal particles on changes in the maximum absolute velocity of internal flows in a drop within the kinetic and spreading phases of the drop-wall impact. It is explored the behavior of internal convective flows in the longitudinal section of a drop parallel to the plane of the solid wall. The kinetic energy of the translational motion of coal particles in a spreading drop compensates for the energy expended by the drop on sliding friction along the wall. At We = 120, the inertia-driven spreading of the particle-laden drop is mainly determined by the dynamics of the deformable Taylor rim. An increase in We contributes to more noticeable differences in the convection velocities in spreading drops. When the drop spreading diameter rises at the maximum velocity of internal flows, a growth of the maximum spreading diameter occurs. The presence of coal particles causes a general tendency to reduce drop spreading. Full article

The dynamic contact behavior between multi-component droplets and the surface of iron ore dust was taken as the research object, analysis of the maximum spreading coefficient, maximum acting diameter, maximum acting area, and maximum bouncing height of solid-liquid contact, from a microscopic perspective, using high-speed photography and image analysis and processing technology. The experimental results indicate that (1) with the particle size of dust particles decreases, the solid-liquid contact behavior sequentially manifests as spread immediately after broken, retraction, negative bounce, primary bounce, and secondary bounce. (2) When the surface tension of the droplets decreases from 55.5 to 34.8 mN/m, the maximum spreading diameter of the droplet has increased by 30% to 40%, the maximum bounce heights (coefficients) decreased by 100%, 57.14%, and 53.57%, respectively, the maximum spreading coefficient of the droplet exhibits no obvious pattern. (3) With decreasing droplet surface tension, the unidirectional acting diameter and the maximum acting area increase when the dust surface size is over 100 μm. When the surface particle size is less than 100 μm, there is no significant change in the unidirectional acting diameter and maximum acting area despite decreasing surface tension. Thus, droplet diffusion is mainly influenced by particle size. These findings contribute to enhancing the theory of water mist dust removal and improving dust removal efficiency. Full article

The dynamic behaviors of water droplets on a slippery surface are significant to practical anti-icing applications. Herein, the impact and sliding behavior of water droplets on lubricant-infused surfaces (LISs) were investigated with a high-speed camera. LISs were prepared by infusing perfluoropolyether oils into anodized porous surfaces. The results show that the maximum spreading diameter and retraction velocity of the impact droplet increased with the We number. For LIS-100, the spreading factor at 2.5 ms increased from 2.00 to 3.88 with We increasing from 30 to 267. Low-viscosity lubricant facilitated the retraction speed and rebound of droplet impact on the surface, while high-viscosity lubricant contributed to the lubricant stability of the LIS. Additionally, high inclination angle (θ) facilitated the rapid shedding of water droplets on the surface. The velocity increased rapidly from 1.04 to 4.66 mm/s with θ increasing from 15° to 45°. The LIS prepared with low-viscosity lubricant had a high sliding velocity, and the sliding velocity of water droplets on LIS-100 was about seven times faster than that on LIS-104. This work reveals the impacting law of water droplets on LISs and provides useful information for the design of LISs under drop impact conditions. Full article

The phenomenon of steam–water direct contact condensation has significance in a wide range of industrial applications. Superheated steam was injected upward into a cylindrical water vessel. Visual observations were conducted on a turbulent steam jet to determine the dimensionless steam jet length compared to the steam nozzle exit diameter and the steam maximum swelling ratio as a function of steam mass flux at the nozzle exit, with a gas steam flux ranging from 295–883 kg/m²s. The Reynolds number based on the steam jet’s maximum expansion ranged from 41,000 to 93,000. Farther above of the condensation region, the jet evolved as a single-phase heated plume, surrounded by ambient water. Mean axial central velocity profiles were determined against the steam mass flux ranging from 295–883 kg/m²s to observe the exponential drop in the mean axial velocity as the vertical distance increased. The radial velocity distribution within the spread of the jet was determined to be self-similar, and the radial distribution of the velocity profile followed the Gaussian function, after the proper scaling of the vertical distance and the axial mean velocity. Full article

The dynamic of droplet spreading on a free-slip surface was studied experimentally and numerically, with particularly interest in the impacts under relatively small droplet inertias ($We\le 30$). Our experimental results and numerical predictions of dimensionless droplet maximum spreading diameter ${\beta }_{max}$ agree well with those of Wildeman et al.’s widely-used model at $We>30$. The “1/2 rule” (i.e., approximately one half of the initial kinetic energy $E_{k0}$ finally transferred into surface energy) was found to break down at small Weber numbers ($We\le 30$) and droplet height is non-negligible when the energy conservation approach is employed to estimate ${\beta }_{max}$. As We increases, surface energy and kinetic energy alternately dominates the energy budget. When the initial kinetic energy is comparable to the initial surface energy, competition between surface energy and kinetic energy finally results in the non-monotonic energy budget. In this case, gas viscous dissipation contributes the majority of the dissipated energy under relatively large Reynolds numbers. A practical model for estimating ${\beta }_{max}$ under small Weber numbers ($We\le 30$) was proposed by accounting for the influence of impact parameters on the energy budget and the droplet height. Good agreement was found between our model predictions and previous experiments. Full article

Shell is a typical biomineralized inorganic–organic composite material. The essence of scallop deshelling is caused by the fracture failure at the interface of the organic and inorganic–organic matter composites. The constitutive equations were solved so that the stress distributions of the adductor in the radial, circumferential, and axial directions were obtained as σ_r = σ_θ = P, σ_z = 2(2 − ν)P/(2ν − 1), and the shear stress was τ_zr = 0. Using the method of finite element simulation analysis, the stress distribution laws at different interface states were obtained. The experimental results show that when the amplitude is constant, the undulation period is smaller than the diameter of the adductor or the angle between the bus of the adductor, and the reference horizontal plane gradually decreases, so the interface is more likely to yield. After the analysis, the maximum stress for the yielding of the scallop interface was about 247 MPa, and the whole deshelling process was gradually spread from the outer edge of the interface to the center. The study analyzed the scallop organic–inorganic material interface from the perspective of mechanics, and the mechanical model and simulation analysis results were consistent with the parameter optimization results, which can provide some theoretical basis for the composite material interface failure and in-depth research. Full article