Critical Weber Number Research Articles

Dynamic behavior and maximum width of impact droplets on single-pillar superhydrophobic surfaces

Superhydrophobic surfaces with excellent water repellence show huge potential in diverse application fields such as self-cleaning and energy harvesting. This potential of superhydrophobic surfaces can be further improved by adding various micro- or macro- structures on the superhydrophobic surfaces. Pillar is a typical structure, while the droplet impact dynamics on the surfaces with a single pillar remain unclear due to the lack of related studies. Here, we experimentally explore the droplet impact behaviors on the superhydrophobic surfaces with a single pillar of different sizes. The effects of Weber number and the pillar-to-droplet diameter and height ratios on the contact state between the droplet and solid surface (including the pillar and the substrate) and the maximum width are investigated in detail. As the Weber number increases, the impact droplets exhibit three outcomes in sequence: failing to touch the substrate, touching the substrate without liquid fingers, and droplet breakup with liquid fingers. The critical Weber number for touching the substrate and forming liquid fingers is affected by the pillar-to-droplet diameter and height ratios. The increasing pillar size decreases the maximum width factor of impact droplets, which is smaller than that on the flat superhydrophobic surface under the same Weber number. A theoretical model based on energy conversation is developed for calculating the maximum width factor on the single-pillar superhydrophobic surfaces, which agrees well with experimental results and yields a ±10 % prediction deviation. This work provides useful guidance for the design and application of structures on superhydrophobic surfaces.

Splashing behavior of impacting droplets on grooved superhydrophobic surfaces

During water droplet impingement onto a rice-leaf-inspired grooved superhydrophobic surface, the unidirectional textures can reduce the solid–liquid contact time through modifying the droplet impact dynamics. The influence of the groove geometry on the splashing of impacting droplets is still unrevealed. In this study, we experimentally identify the droplet bouncing and splashing regimes on grooved superhydrophobic surfaces of varying parameters. Asymmetric spreading and retracting of droplets are observed on the surfaces, accompanied by obvious liquid jets generated within the grooves. As the impact velocity increases, secondary droplets are ejected from the rim of the liquid jets, which is the onset of droplet splashing on the grooved superhydrophobic surfaces. We find that the critical Weber number for the splash of liquid jets decreases with the groove width but increases with the droplet diameter. Scaling analysis is performed to model the splashing criteria and explain its dependence on groove parameters and droplet properties. This research advances the understanding of droplet splashing dynamics on textured superhydrophobic surfaces, which is promising for some agricultural and industrial applications.

Drop breakup and entrainment in the updraft

AbstractThis study aims to investigate the characteristics of gas–liquid countercurrent contact processes. In spray towers or other applications, several drops containing pollutants are entrained by the updraft flue gas, which can easily cause environmental pollution. Traditionally, this drop entrainment phenomenon is alleviated by increasing the diameter of the drops. However, the breakup of a large drop would also cause drop entrainment to become serious, a process referred to as secondary atomization. Herein, we propose the boundary of three drop modes in the updraft: drop falling mode, reverse entrainment mode, and breakup entrainment mode. The critical Weber number (We) is the key dimensionless number marking the beginning of the drop breakup. The ratio of the drag force to gravity and We are proposed as criteria for the drop entrainment.

Droplet behavior in overexpanded supersonic two-phase jets

The interaction of liquid droplets generated by spray atomization with high-speed co-flowing gas is of interest in various applications including fuel injection, spray cooling, and surface coating. The underlying processes involve interactions between the droplets themselves, and with the carrier gas. Additionally, they are influenced by shock and expansion waves present in high-speed flows, accompanied by resulting velocity and pressure fluctuations. Non-intrusive diagnostics including Shadowgraphy and Phase Doppler Particle Anemometry, along with flow simulations, are used to study droplet behavior, characterized by size and velocity changes, as a finely atomized spray is propelled by a carrier gas through a supersonic, overexpanded jet structure. Measurements of droplet size and velocity are correlated to the shock train structure of the overexpanded jet and further to gas velocity as obtained from simulation results. While the shock structure is observed to be unaffected by spray injection, periodic increases and decreases are observed in average droplet size. Analysis using gas flow field obtained from simulations, estimated critical Weber numbers for droplet breakup and timescales for droplet dynamics, compared to residence time in the flow, suggests that droplet size changes can be attributed to alternating coalescence and breakup. The two-dimensional flow structure involving converging and diverging sections as well as a spread in droplet sizes likely promote coalescence and breakup processes leading to periodic variation in droplet SMD. The streamwise variations of gas velocity along the centerline caused by the shock train are not noticed in the droplet velocity, which can be explained by the high Stokes number causing droplets at the centerline to behave as ballistic particles moving through the shock structure. Experimental measurements, simulation results, and their subsequent analyses show that droplet collision and coalescence regimes established in previous work for ambient conditions show deviations when subject to high-speed gas flow conditions.

Study of the secondary droplet breakup mechanism and regime map of Newtonian and power law fluids at high liquid–gas density ratio

This work reports the numerical investigation of the secondary breakup of non-Newtonian droplets at different Weber Weg and Ohnesorge Ohl numbers. As part of this work, an in-house coupled level set volume of fluid solver is developed based on OpenFOAM libraries. It uses improved curvature calculation techniques like smoothening and the closest point search method. Flow is assumed to be axisymmetric. Approximately 95 different cases were simulated to investigate the effect of Weg and Ohl numbers on secondary breakup for Newtonian, shear-thinning, and shear-thickening fluids. Ohl varies from 10−3 to 101, and, correspondingly, Weg varies from 101 to 103. The non-Newtonian rheology is modeled as a power-law fluid, and the power-law index n ranged from 0.2–1.8. The present work describes the flow field near the droplet and the effects of non-Newtonian parameters and viscosity on the flow field. The various aspects of droplet dynamics like droplet deformation ratio y, deformation rate ẏ, and coefficient of pressure Cp are studied and compared with the internal flow theory. A generalized relation for critical Weber number Weg,cr is proposed for both Newtonian and non-Newtonian fluids and is shown in a phase diagram plot to map the different regimes of secondary droplet breakup.

Simulation Analysis on the Jet Flow Field of a Single Nozzle Spraying for a Large Ship Outer Panel Coating Robot

A mathematical model of the cavity flow of the fan nozzle, a mathematical model of jet atomisation, and a simplified physical model of the equivalent entity are established. A simulation of the spraying flow at different spraying pressures is carried out using a 0.48 calibre nozzle as a case study, and compared with experimental data; error results between 4.3% and 7.5% indicate the simulation means used are reliable and the simulation model is valid. The simulation means include using the effective simulation model to further explore the evaluation index of atomisation characteristics; in the critical Weber number on the impact of atomised particles, analysis of the impact of the critical Weber number on the diameter of atomised particles and the speed of movement, and determining the critical Weber number; atomisation spraying effect, for atomisation pressure on atomised particle diameter, speed of movement, impact kinetic energy, deposition rate, and liquid film growth, etc. The results show that, in the existing high-pressure airless spraying equipment within the range of permissible pressure 6~16 MPa, with the increase in atomisation pressure, the better the atomisation effect of the paint, the better the atomised particle spraying adhesion deposition rate of the paint, and the better the overall spraying effect.

Deformation and acceleration of water droplet in continuous airflow

The present work investigates the deformation and acceleration of water droplets in continuous airflow. The numerical approach is based on the level set method for capturing the liquid–gas interface and the projection method for solving the three-dimensional incompressible Navier–Stokes equations. The effects of the incoming airflow velocity (10–100 m/s), initial droplet diameter (20–100 μm), and supercooling on water droplet deformation are investigated. The results indicate that the droplet enters the breakup regime at a critical Weber number of 10, which agrees with the published literature. A dimensionless deformation factor L is defined to describe the droplet deformation. The results confirm that the extreme values of L increase with increasing Weber number during droplet movement. Two models are proposed to predict the minimum deformation factor and the corresponding dimensionless time. The effect of supercooling on water droplet deformation is analyzed, and it is found that the deformation factor of supercooled droplets is lower than that of room-temperature droplets, while supercooled water droplets exhibit greater acceleration. Furthermore, based on the numerical results, a model governed by the Weber number and the Ohnesorge number is proposed for predicting droplet acceleration.

Liquid Droplet Impact Over Hydrophobic Mesh Surfaces and Assessment of Weber Number Dependent Characteristics

Abstract Impacting droplets and droplet ejection from hydrophobic mesh surfaces have interest in biomedicine, heat transfer engineering, and self-cleaning of surfaces. The rate and the size of newborn droplets can vary depending on the droplet fluid properties, Weber number, mesh geometry, and surface wetting states. In this study, impacting water droplets onto hydrophobic mesh surface is investigated and impact properties including, spreading, rebounding, and droplet fluid penetration and ejection rates are examined. Droplet behavior is assessed using high recording facilities and predicted in line with the experiments. The findings reveal that the critical Weber number for droplet fluid penetrating/ejecting from mesh screen mainly depends on the droplet fluid capillary length, and hydrophobic mesh size. The contact time of impacting droplet over mesh surface reduces with increasing droplet Weber number, which opposes the case observed for impacting droplets over flat hydrophobic surfaces. The restitution coefficient attains lower values for impacting droplets over mesh surfaces than that of flat surfaces. The rate and diameter of the ejected droplet from the mesh increases as droplet Weber increases. At the onset of impact, streamline curvature is formed inside droplet fluid, which creates a stagnation zone with radially varying pressure at the droplet fluid mesh interface. This reduces the ejected droplet diameter from mesh cells as mesh cells are located away from the impacting vertical axis.

Toward Surfaces with Droplet Impact Robustness and Low Contact Angle Hysteresis

AbstractSuperhydrophobic surfaces show excellent water repellent performance. However, liquid impalement occurs when a droplet impacts on the surface at high velocity. To achieve higher resistance to liquid impalement at the same scale, a dense array of structures or structures with pinning at the structures top are typically used, but they also lead to increased contact angle hysteresis and higher energy dissipation. Changing the structure side wall shape can help to maintain low hysteresis and withstand high impact energy at the same scale. Droplet contact angle, contact angle hysteresis and droplet impact experiments are performed on both conical and cylindrical pillar surfaces. Comparing conical and cylindrical pillar structures with the same pitch and height, it is found that cylindrical pillars exhibit higher critical Weber number but result in larger contact angle hysteresis and larger liquid residue size when above a critical Weber number. A proper design of conical structures can maintain large contact angle, low hysteresis, strong resistance to impalement, higher number of bouncing and smaller liquid residue size. In addition, the critical Weber number for the conical structures in this work is higher than micro‐patterned pillar surfaces at the same pitch range, implying that we improve the anti‐wetting performance further.

Experimental Correlation for Splashing Condition of Droplets on Solid Substrates

Droplet splashing behaviors of water-ethanol binary mixture liquids on roughened solid surfaces were experimentally observed in order to investigate the effects of surface tension, viscosity, and wettability/surface roughness on the splashing occurrence. The range of the droplet volumes was from 1.7 μL to 32.6 μL. The ranges of the surface tension and the viscosity were from 21.1 mN/m to 71.9 mN/m, and from 1 mPas to 2.91 mPas, respectively. The surface roughness range was from 0.03 μm to 1.25 μm for Ra. The present experimental data were evaluated on the basis of the existing models. Resulting from these experiments, a simple model using the Ohnesorge number evaluated by the capillary length was proposed and the accuracy of the predicted critical values such as the critical Weber and Reynolds numbers were discussed. The result indicated that the liquid properties and the quantification of the surface condition such as surface roughness are important factors for the prediction of the splashing behavior.

Fluidics of an immiscible drop impact onto a hot oil film

Droplet rapid phase transition during its impact over a hot immiscible oil film is studied experimentally, which is of paramount importance in fire extinguishing, forensics, internal combustion engines, and various accident scenarios in the industries. The impact of a cold methanol droplet on a hot mustard oil film and its repercussions are analyzed from high-speed images for a temperature range relevant from the thermodynamic and heat transfer perspective. The interfacial temperature of the hot oil film has been varied through the saturation temperature, Leidenfrost point, superheat limit, and critical temperature, for methanol. A regime map has been proposed to characterize fluidic observations on Weber number and non-dimensional average temperature plane. Violent cavity crater explosions have been observed above a critical Weber number ranging 70–80 for average interfacial temperature higher than the critical point of methanol due to direct contact between the droplet and base of the petridish.

Crown evolution kinematics of a camellia oil droplet impacting on a liquid layer

The phenomenon of droplet impact on an immiscible liquid is encountered in a variety of scenarios in nature and industrial production. Despite exhaustive research, it is not fully clear how the immiscibility of the liquid on which a droplet impacts affects the crown evolution. The present work experimentally investigates the evolution kinematics of a crown formed by the normal impact of a camellia oil droplet on an immiscible water layer. Based on discussion of dynamic impact behaviors for three critical Weber numbers (We), the radius of the crown and its average spreading velocity are compared with those of previous theoretical models to discuss their applicability to the immiscible liquid. The evolution kinematics (morphology and velocity) are analyzed by considering the effects of the We and layer thickness. Furthermore, the ability of crown expansion in radial and vertical directions is characterized by a velocity ratio. The results show that our experimental crown radius still follows a square-root function of evolution time, which agrees with the theoretical predictions. The dimensionless average spreading velocity decreases with We and follows a multivariate power law, while the dimensionless average rising velocity remains constant. The velocity ratio is shown to linearly increase with We, demonstrating that the rising movement in crown evolution gradually enhances with We. These results are helpful for further investigation on the droplet impact on an immiscible liquid layer.

Phenomena of single water droplet impacting a heptane layer on water pool

The behavior of single water drop impacting an oil layer on the deep water pool was recorded using a high-speed camera. Heptane was used as the target liquid layer on the water pool. A particular phenomenon of double crown can be observed. The formation of double crown is not only related to the impact Weber number of the water droplet, but also the thickness of the oil layer. The critical Weber number for the formation of double crown decreases sharply as the decrease of the oil layer thickness. With the increase of Weber number and the decrease of oil layer thickness, there are four typical phenomena: single crown-jet, single crown-bubble, double crown-bubble and double crown-jet. Moreover, the effects of oil layer thickness and impact Weber number on surface bubble lifetime and the geometry size of crown, crater and jet were quantitatively analyzed.

Cavity Detachment from a Wedge with Rounded Edges and the Surface Tension Effect

Cavity flow around a wedge with rounded edges was studied, taking into account the surface tension effect and the Brillouin–Villat criterion of cavity detachment. The liquid compressibility and viscosity were ignored. An analytical solution was obtained in parametric form by applying the integral hodograph method. This method gives the possibility of deriving analytical expressions for complex velocity and for potential, both defined in a parameter plane. An expression for the curvature of the cavity boundary was obtained analytically. By using the dynamic boundary condition on the cavity boundary, an integral equation in the velocity modulus was derived. The particular case of zero surface tension is a special case of the solution. The surface tension effect was computed over a wide range of the Weber number for various degrees of cavitation development. Numerical results are presented for the flow configuration, the drag force coefficient, and the position of cavity detachment. It was found that for each radius of the edges, there exists a critical Weber number, below which the iterative solution process fails to converge, so a steady flow solution cannot be computed. This critical Weber number increases as the radius of the edge decreases. As the edge radius tends to zero, the critical Weber number tends to infinity, or a steady cavity flow cannot be computed at any finite Weber number in the case of sharp wedge edges. This shows some limitations of the model based on the Brillouin–Villat criterion of cavity detachment.

Secondary breakup of water and surrogate fuels: Breakup modes and resultant droplet sizes

Secondary breakup of water and single-component surrogates of diesel such as n-dodecane and n-hexadecane, has been experimentally investigated in the present study. The experimental arrangement involves injection of mono-disperse droplets of the test liquid into an air jet issuing from a contoured nozzle. The mono-disperse droplet generator (MDG) is used to produce liquid droplets of diameter around 200 ± 4-µm, which is close to those found in practical sprays. The aerodynamic Weber number (We) is varied by changing the air-jet velocity. In the present study, apart from the most-reported regimes namely bag breakup, bag and stamen breakup, shear breakup and catastrophic breakup - two more regimes, viz. dual-bag breakup and multi-bag breakup regimes, have also been observed. The dual bag regime occurs in the Weber number range of 30 to 46 followed by the multi-bag regime in the Weber number of 46 to 80. These two regimes have been very rarely reported in the technical literature. The temporal droplet deformation observed in the present study during bag regime and bag and stamen regime is observed to match well with data reported in the literature. The size of core droplet in the bag and stamen mode is observed to increase with Weber number and after a Weber number of 30 it is of sufficient size for its Weber number to be above the critical Weber number. This core droplet undergoes a subsequent breakup resulting in dual-bag breakup mode. Variation of SMD of resultant droplets is measured and reported for all the breakup modes ranging from We = 10 up to 500 and data at some salient points is observed to match well with data from literature. Detailed droplet probability distributions for bag, bag and stamen, dual bag and multi-bag regimes has been reported. A tri-modal droplet size distribution is observed in bag and bag and stamen breakup regimes, where the first peak corresponding to film, second peak corresponding to rim and the third corresponding to nodes on the rim and stamen. The rim, nodes and stamen of the bag is observed to contribute up to around 90% of mass from the parent droplet. With increase in Weber number, the droplet distribution transforms in to a bi-modal distribution. The droplet size distribution resulting from water breakup is different from those of the other two liquids in the larger droplet size range due to the higher surface tension of water. The experimental data presented is useful to validate computational models in terms of their capability to predict the droplet deformation dynamics, resultant droplet sizes and distribution with water and diesel fuel surrogates such as n-dodecane and n-hexadecane.

Experimental Study on Droplet Splash and Receding Breakup on a Smooth Surface at Atmospheric Pressure.

Droplet impact on a smooth solid surface at atmospheric pressure was experimentally studied and physically interpreted. A particular emphasis of the study is on the effects of liquid viscosity on the transition between droplet deposition (or droplet spreading without breakup) and droplet disintegration (including droplet splash and receding breakup). Specifically, the critical Weber number separating droplet deposition from droplet disintegration decreases and then increases with increasing Ohnesorge number (Oh). The splash in the low-Oh region and the receding breakup in the high-Oh region were analyzed qualitatively based on the unbalanced forces acting on the rim of the spreading or receding liquid film. A semiempirical correlation of droplet deposition/disintegration thresholds is proposed and well fits the experimental results from previous and present studies over a wide range of liquid viscosity.

A study of transition from periodic dripping to jetting in the presence of an electric field

A liquid is issued from the outlet of the capillary tube vertically, and drop formation may be in the form of periodic dripping, dripping faucet and jetting, which usually depends on flow rate or Weber number. We consider the critical Weber number (WeC=ρV02D/σ) at which the transition from periodic dripping to jetting occurs in the presence of an electric field, where high-resolution images are recorded. The necking time is mainly related to nozzle diameter and surface tension, and independent of electric potential and flow rate (in a reasonable range).The first threshold limit decreases with an increase in electric potential, where the dripping faucet is clearly affected and the point of drop detachment gradually increases. When the drop formation is in the form of dripping faucet, the transition from dripping faucet to jetting regime is enhanced by electric potential, where a sudden transition could be observed in an extremely limited range of liquid flow rate. The critical criterion (Weber number) is presented to determine the transition from dripping to jetting in the presence of an electric field. The critical Weber number is in a reasonable agreement with the experiment, although the predicted results are quantitatively divergent with experimental data.

Vortex-interface interactions in two-dimensional flows

This work focuses on the basic interactions between a vortex and an interface separating two incompressible fluids. Specifically, we investigate how vorticity produced at an interface influences the dynamics of this very same interface and how the produced vorticity engenders small scales and small droplets. A critical Weber number Wec(1) exists discriminating the conditions upon which the interface rolls up around the vortex significantly. In addition, we show that a second critical Weber number Wec(2) appears. For Weber numbers below this value, the dynamic response of the interface only depends slightly on the Reynolds number. For Weber numbers above Wec(2), the vorticity layers generated by the interface itself trigger a combined Rayleigh–Taylor and Kelvin–Helmholtz instability that leads to the appearance of extremely small structures with a characteristic size that strongly depends on the Reynolds number.

Parametric study of deformation and breakup of non-Newtonian droplet

In this paper deformation and breakup of a non-Newtonian shear thinning droplet are studied parametrically. The effects of physical and geometrical properties are investigated by means of numerical methods. The flow is simulated in the range of 716 up to 2864 for Reynolds number and 8.5 to 70 for the Weber number. The VOF numerical method is used for capturing the droplet deformation and Carreau model is used to simulate non-Newtonian physical properties. The results are compared with those exist in literature. It is found that various non-Newtonian parameters of the fluid properties do affect the critical Weber number and the deformation of the droplet.

Numerical studies on bubble dynamics in an unsteady turbulence of the venturi bubble generator applied to TMSR

In the online fission gas removal system applied to TMSR, the venturi bubble generator was developed to produce the dispersed bubbles from the reactor coolant. It is essential to establish the critical condition of bubble breakup for the bubble generation. Numerical simulations of the bubble dynamics in an unsteady turbulent flow in the bubble generator are performed with Volume-of-fluid (VOF) and Large-eddy-simulation (LES). The flow fields with similar turbulent characteristics in the bubble generator are established in the cavity to track the bubble dynamics. The dynamic boundary conditions are set to simulate the bubble dynamics in the two patterns of flow including shearing flow and rotational flow. The critical Weber number of the bubble ranges from 0 to 10. Weber number is always fluctuating in a certain range before bubble breakup. The dynamic characteristics of the bubble shape factor in this complex unsteady flow can be modeled by a one-dimensional damped oscillator model. The bubble oscillation in unsteady turbulence can be predicted by combining the dimensionless number of time and the Weber number.