Droplet Weber Number Research Articles

Experimental Study of Liquid Spray Mode of Twin Fluid Atomizer Using Optical Diagnostic Tool

Twin fluid atomizers allow for two different spray forming modes, flow focusing and flow blurring, depending on the operating, geometric, and thermophysical properties of the working liquids. In flow focusing mode, the liquid jet breaks outside the injector, whereas in flow blurring mode, the liquid jet breaks inside the atomizer. Operating conditions are believed to play an essential role in determining the size and velocity of droplets with specific geometric and fluid properties. This work investigates the effect of air flow rate and liquid flow rate on spray characteristics by varying them independently. The geometric parameters, height (H = 0.3 mm) and orifice diameter (D = 1.5 mm) of the atomizer are kept constant (with H/D = 0.2). Spray mode is identified using high-speed images. Phase Doppler particle analyzer is used to measure droplet size and velocity simultaneously. Regardless of liquid flow rate, flow focusing mode is observed at low air flow rate and flow blurring mode is observed at high air flow rate. In general, flow blurring mode produced smaller droplets at higher velocities than flow focusing mode. The Joint probability distribution function of droplet size and velocity shows unimodal near the exit of the atomizer and bimodal distribution around 50 mm downstream due to the completion of the secondary breakup around that position and the subsequent loss of momentum due to the resistance of the surrounding air from the injector outlet. Flow focusing mode showed that sauter mean diameter and mass median diameter tend to increase initially due to coalescence of the spray and begin to decrease due to secondary breakup. The joint probability distribution of droplet Weber number and the droplet Reynolds number indicate that the flow blurring spray produced finer and faster droplets than the flow focusing spray. Overlapping of two Gaussians representing smaller and larger droplets best fits the droplet probability distribution as compared to lognormal or gamma or beta distribution.

Impingement behaviour of single ethanol droplet on a liquid film of glycerol solution

Research on single drop impact, especially in the past two decades, has been motivated by a need for better predictive capability in many industries. However, there are few reports in the literature describing the case of single droplet impinging on liquid films with different physicochemical properties. In this study, laser-induced fluorescence (LIF) methods were used to clarify the impingement behaviour of millimetre-sized single ethanol droplets onto films of different concentrations of glycerol solution. The impingement behaviour is found to differ depending on the Weber number of the incident droplet and the viscosity and the thickness of the liquid film. New results on coalescence/splash thresholds criteria are obtained taking into account the incident droplet Weber number and liquid film characteristics. In addition, the formation mechanism and composition of secondary droplets and crown structures after collision are analysed. For the crown structure parameters, we found that the evolution of the crown height over time is affected by the combination of droplet and liquid film characteristics. The maximum height and diameter of the crown are proportional to the Weber number of the incident droplet, and these parameters can be predicted by the combination of the incident droplet Weber number and the liquid film Ohnesorge number.

Droplet Precise Self‐Splitting on Patterned Adhesive Surfaces for Simultaneous Multidetection

AbstractPrecise separation and localization of microdroplets are fundamental for various fields, such as high‐throughput screening, combinatorial chemistry, and the recognition of complex analytes. We have developed a droplet self‐splitting strategy to divide an impacting droplet into predictable microdroplets and deposit them at preset spots for simultaneous multidetection. No matter exchange was observed between these microdroplets, so they could be manipulated independently. Droplet self‐splitting was attributed to anisotropic liquid recoiling on the patterned adhesive surface, as influenced by the droplet Weber number and the width of the low‐adhesive stripe. A quantitative criterion was also developed to judge the droplet self‐splitting capability. The precise separation and distribution of microdroplets enabled simultaneous arrayed reactions and multiple analyte detection using one droplet of sample.

Design and development of a coating device: Multiple-droplet drop-casting (MDDC-Alpha).

We report the development of a coating device (multiple-droplet drop-casting), which releases multiple droplets simultaneously or with a short time-lag (<10 ms) using a multi-channel syringe pump to achieve deposition of large-area (up to ∼100 cm2) and patterned coatings. The device exhibits the following features and characteristics: simple, low-cost, and scalable; adaptive to various solution-processed materials; insensitive to small contaminations/impurities; minimizes material waste; and can create patterns (printing). The demonstration of the device performance was carried out by fabricating coatings using four strategic model solutions, namely, carbon nanotube ink, graphene oxide ink, [poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate)] PEDOT:PSS solution, and n-methyl-2-pyrrolidone diluted methylammonium lead iodide (CH3NH3PbI3)-based light harvesting perovskite. We investigated the effect of release height (droplet velocity or Weber number) and the film area on the film characteristics. The results show that the device yields reproducible and uniform films on the order of micrometers in thickness and ∼1 μm in roughness.

Experiment study of droplet impacting on a static hemispherical liquid film

Experiment study of a droplet impacting on a static hemispherical liquid film was conducted. The static hemispherical liquid film was formed by a first droplet impacting on a dry solid surface, and the diameter, impact velocity, and liquid properties of the second droplet were the same with the first one. A high-speed camera was used to capture the deformation process of the impacting droplet at a shooting speed of 4000 frames per second. The effects of droplet Weber number and Reynolds number on the spread factor and flatness factor were analyzed quantitatively. The result shows that as increasing of droplet Weber number, the phenomena of spread, formation of liquid crown, and splashing occurred subsequently after the droplet impacted on the liquid film. The maximum spread factor of the liquid film after droplet impacting on the static hemispherical liquid film is higher comparing to the case of droplet impacting on the dry solid surface under the same impacting condition. Further, with the increase of droplet Weber number, the maximum spread factor of the liquid film increases. With the decrease of droplet Reynolds number, the maximum spread factor of the liquid film d ecreases and formation of the liquid crown is inhabited.

Characteristics of a free-falling single-droplet of water-in-oil emulsion broken up by a pulse laser

Water-emulsified oils have been used in a variety of combustion systems, and their atomization characteristics have been studied to control combustion. In particular, many studies have been conducted on micro-explosions, in which an emulsion droplet is broken up into a number of smaller fragments mainly due to phase change of dispersed micro-scale water droplets. In this study, the breakup phenomena of a free-falling single droplet of water-emulsified liquid-fuels (n-decane, n-dodecane, and n-hexadecane) were investigated experimentally. The external energy of a pulse laser was introduced into the emulsion droplet, after which the dynamic response of the emulsion droplet were examined. It was found that the breakup trends were different depending on parameters such as oil type, oil concentration, and laser energy. The dynamic behaviors were categorized into four regimes, and their criteria were related to the effective Weber number of the emulsion droplets. Their physical characteristics are discussed and some empirical relationships are suggested regarding configurational characteristics such as the swelling scale of a liquid membrane, the number of secondary droplets, and the droplet diameter.

Two jets during the impact of viscous droplets onto a less-viscous liquid pool.

It is generally accepted that a Worthington jet occurs when a droplet impacts onto a liquid pool. However, in this experimental study of the impact of viscous droplets onto a less-viscous liquid pool, we identify another jet besides the Worthington jet, forming a two-jet phenomenon. The two jets, a surface-climbing jet and the Worthington jet, may appear successively during one impact event. By carefully tuning the impact conditions, we find that the two-jet phenomenon is jointly controlled by the droplet-pool viscosity ratio, the droplet Weber number, and the droplet-pool miscibility. The mechanism of the surface-climbing jet is completely different from that of the Worthington jet: the liquid in the pool climbs along the surface of the droplet and forms a liquid layer which converges at the droplet apex and produces the surface-climbing jet. This surface-climbing jet has a very high speed, i.e., an order of magnitude higher than the droplet impact speed. The effects of the impact speed, droplet viscosity, droplet size, and surface tension on the surface-climbing jet are also analyzed. This study not only provides physical insights into the mechanism of droplet and jet dynamics but also will be helpful in the optimization of the droplet impact process in many relevant applications.

Droplet oscillation mechanism and its free surface behavior on impacting a heated hydrophobic surface at low Weber numbers

Oscillation mechanism and free surface behavior of micro-droplets (300, 400, and 500 µm in diameter), impinging on a dry, hydrophobic heated surface was investigated using the volume of fluid (VOF) method. It was observed that the droplets exhibit unique oscillation characteristics at low Weber numbers for different contact angles and surface temperatures. At higher contact angles, droplet deformation was retarded, and it tends to retain its shape. This increased its chances of bouncing away from the surface. With increasing surface temperature, the tendency of the droplet to bounce away from the surface also increased. The oscillation behavior was significantly influenced by droplet size, contact angle with the surface and by surface temperature. Larger sized droplets had lower oscillation frequency. An increase in contact angle or surface temperature led to the lowering of the oscillation frequency of droplets. However, droplet Weber number was found to have no significant effect on oscillation frequency. At these low value of Weber numbers, all droplet sizes investigated showed slightly under-damped harmonic motion with amplitude exponentially decaying toward zero.

Deformation characteristics and energy conversion during droplet impact on a water surface

The present work studies experimentally and numerically the impact of water droplets with different Weber numbers (We) on a water surface. Correlations between Weber number and geometric sizes of central jet, secondary droplet, and secondary central jet are analyzed using linear regression. The experimental and numerical results are compared qualitatively and quantitatively and show good agreement. In addition, the energy conversion during the impact process is calculated using a numerical integration method. It is concluded that the ratio of the secondary droplet to the initial droplet diameters is approximately within 1.2–2, and this diameter ratio correlates linearly with the Weber number within the experimental ranges tested. When 360 &amp;lt; We &amp;lt; 713, the secondary central jet is generated. Moreover, the target liquid adsorbs around 70% of the initial total energy. The total energy remains around 64% when the cavity reaches its maximum depth, whereas it remains around 39% when the kinetic energy of the central jet reaches its minimum.

A droplet/wall impact model and simulation of a bipropellant rocket engine

Droplet impact on a solid wall contributes to droplet vaporization and cooling on the inner wall. A new droplet/wall impact model is developed and fitted from the experimental data, which takes both kinematic parameters of the impinging droplets and thermal parameters of the solid wall into consideration. The model describes the behavior of droplets after impact and identifies five representative regimes, i.e., stick/spread, suspend, rebound, boiling including breakup, and splash, through the critical Weber number of droplets and wall temperature. To assess the new model, numerical simulations were performed of propellant droplets impacting the wall of a bipropellant rocket engine chamber. A comparison with experimental data shows better predictions of the wall temperature of the chamber than obtained from previous models. A larger number of large-sized monomethylhydrazine and nitrogen tetroxide droplets in the boiling induced breakup and splash regimes break into smaller droplets when using the new model. There are also temperature peaks near the impact points and near the throat. Especially in the throat of the combustion chamber, the new model predicts the wall temperature distribution accurately, offering improved prediction of the combustion chamber and assessing thermal protection of the throat.

A parametric study on the droplet detachment process from the ceiling under the effect of gravity

Purpose The purpose of this paper is to numerically investigate the effect of various parameters such as density ratio, surface wettabilities and Weber number on the droplet dripping and detachment process. Design/methodology/approach By using algebraic volume of fluid method, the governing equations are solved using a collocated finite volume approach in two-dimensions. Findings The results indicate that, for small densities of droplet, it adheres to the surface except when the surface is hydrophobic, while an increase in Weber number or presence of an additional droplet in the vicinity led to detachment. Originality/value The paper explores various characteristics of a droplet when two competing forces, namely, gravity and surface tension, act simultaneously. The detachment is observed for a given initial droplet size, as it becomes denser in an uniform gravitational field. The effect of droplet affinity for two droplets is also presented using the simulations.

Mapping electrospray modes and droplet size distributions for chitosan solutions in unentangled and entangled concentration regimes

Chitosan is a natural polymer that exists as a polyelectrolyte in acidic aqueous solutions. The solution viscosity strongly depends on the polymer’s molecular weight and concentration in the solution, and the solution pH. Microparticle production by electrospraying is of significant interest in the drug delivery applications of this biocompatible polymer. We report herein a study aimed at empirical understanding of the influence of electrospray process parameters on the size distribution of microdroplets of chitosan solutions with different molecular weights and concentrations. How the nature of interchain interactions in the solution affects the electrospray mode, was studied for different applied voltages, V, over a wide range of solution flow rates, Q. Stable cone-jets were observed only for solutions in the unentangled regime. Unlike solutions of non-polymeric electrolytes of comparable viscosities, the chitosan droplet size distribution generally showed a strong dependence not only on Q but also on V and the solution viscosity. Carrying out the electrospraying process at a higher voltage in the stable cone-jet mode resulted in smaller and more narrowly dispersed droplets. For the droplets produced in this mode, We∼Re1.79, where We and Re are the droplet Weber and Reynolds numbers, respectively. The order of dependence of the Sauter mean droplet diameter on Q was found to be 0.26. Diameters of droplets produced in (or close to) the precession mode exhibited a significantly weaker dependence on Q. For a given wt% concentration in solution, a polymer of lower molecular weight resulted in a lower droplet size polydispersity index.

Dynamics of a single droplet with different viscosity impact onto a stainless-steel surface

The phenomena of droplet-surface interaction have important applications in many industrial fields. In different scenarios, the viscosity of the liquid droplet that impacts on the solid surface is usually different, and the viscosity of the droplet has a great impact on the results of the droplet impingement. In this paper, the phenomena of single droplets with different viscosity (deionized water, 50% glycerol/water solution, 99% glycerol/water solution) and different Weber number (We) in the range of 147.6-939.4 impacting on a flat stainless-steel plate were recorded by a high-speed camera at 4,000 fps, and the spreading behaviour of droplets with different properties were observed. The effect of droplet viscosity and Weber number on the droplet spread on the solid surface is quantitatively analysed, and the results demonstrate that the increase in Weber number has a promoting effect on the maximum spreading diameter, whereas the increase in viscosity has the opposite effect. For high viscosity drops (99% glycerol/water solution), retraction hardly occurs after the maximum spread diameter is reached. Finally, empirical correlations of the normalized maximum spread diameter as a function of the Weber number for droplet of different fluids were derived based on the present experimental data.

Observation of a mixed regime for an impinging droplet on a sessile droplet

This article reports experimental results of the presence of a mixed regime where rebound or coalescence occurs when a liquid droplet with low impact velocity impinges on a static sessile droplet, deposited on a flat aluminum surface. In particular, the present study suggests possible reasons why this mixed occurs with nearly the same probabilities with the use of the sequential images captured by two high-speed cameras from the 767 experimental cases. It is also demonstrated that the mixed regime is substantially affected by static droplet volumes, Weber numbers, and offset distances between impinging and static droplets. In the mixed regime, rebound may occur because a relatively large air-film maintains to prevent film drainage for coalescence. The lubrication theory is utilized to estimate film thickness between two droplets and is compared to the critical film thickness. The upper limit of the Weber numbers in the mixed regime decreases with an increase in the offset distance, owing to a rotational droplet motion causing air-film elongation. The contact time during rebound slightly increases with the static sessile droplet volume. It is observed that the measured contact times increases with a decrease in impact velocity, showing cushioning effect by air-film. On the other hand, a coalescence is observed to intermittently in the mixed regime because the air-film layer existing at the interface has an irregular shape by oscillation of an impinging droplet.

Experimental and Numerical Visualization of Heat Transfer and Hydrodynamics Induced by Double Droplet Train Impingement

The objective of this study was to visualize and simulate the thermal physical process during double droplet train impingement for three different horizontal impact spacings (S = 0.65 mm, 1.2 mm and 2 mm). Two identical HFE-7100 droplet trains were produced using a piezoelectric droplet generator at a frequency of 6000 Hz with a corresponding droplet Weber number of 312. A translucent sapphire substrate with a thin film ITO coating was used as heater in the experiments. The heat transfer and hydrodynamics of double droplet train impingement have been visualized using IR thermal imaging and high speed optical imaging techniques, respectively. The double droplet train impingement process was also simulated numerically using the Coupled Level Set-Volume of Fluid (CLS-VOF) approach with dynamic mesh adaption (DMA). Humps were observed both numerically and experimentally between two adjacent impact craters due to the interactions caused by the impinging droplet trains. It was found that the hump height decreased when impact spacing increased. IR images show that higher impact spacing leads to better heat transfer performance, which could be due to the lower hump height at greater impact spacing conditions. It was also observed that higher impact spacing leads to better thermo-hydrodynamics within and outside the impingement zone. In summary, results show that horizontal impact spacing plays a significant role in double droplet train impingement cooling. This work was supported by the National Priority Research Program of the Qatar National Research Fund, Grant No.: NPRP 6-1304-2-525.

Experimental investigation on the characteristic of jet break-up for butanol droplet impacting onto a heated surface in the film boiling regime

In view of the importance of atomization, droplet breakup induced by high Weber number and vapor bubble during droplet impacting onto a solid and heated surface has been studied extensively, but the understand on jet break-up phenomenon in the film boiling regime is still lacking. Thus, the work is trying to study the dynamic of jet break-up of n-butanol, a potential alternative biofuel for internal combustion engine, under the influence of Weber number. During experiment, a high-speed camera, set at 512 × 512 pixels, 10,000 fps, and 20 μs exposure time was used to visualize the droplet impacting behavior. The droplet falling height was set from 1 cm to 9 cm with interval of 0.5 cm, with corresponded Weber number around from 6.94 to 102.12. The heated surface temperature was set at 250 °C, to ensure the impact locates at the film-boiling regime. The results show that the jet break-up is dominated by Rayleigh-Plateau instability, the secondary droplet is formed through contraction of symmetric unstable surface waves since the waves are clearly observed on the jet column. Under tested wall conditions, the jet break-up only takes place when the Weber number of butanol droplet is around from 14.34 to 89.13. Within the jet break-up regime, the number of separated droplets first increases then decreases with Weber number increasing, and reaches the maximum at We = 65. The length of jet break-up first increases slowly then decreases rapidly and then increases with Weber number. While, the time of jet break-up first decrease then increase with Weber number and also reaches the minimum at We = 65.20. In addition, the timing of jet break-up is fitting well with the theory of Rayleigh instability.

Initiation of the Worthington jet on the droplet impact

The deformation of liquid droplets upon impact induces Worthington jets for a certain range of impact velocities. Although the growth of such a jet and its tip velocity are predicted from cases similar to droplet impact, the mechanism behind jet formation is yet to be understood. The present study uses high-speed visualization of droplet impact on a superhydrophobic surface to understand jet initiation in terms of the collapse of an air cavity. Water droplets with diameters of 2.0 and 3.0 mm are generated with the droplet Weber number varying from 2 to 20. The jet velocity is measured from the captured images, from which the maximum velocity is found to be We ∼ 7. The jet velocity at We ∼ 7 is approximately 15 times greater than the impact velocity. Moreover, surface waves are generated upon impact with the solid surface, and they induce an oscillation of the droplet cap as they propagate from the solid–liquid contact line to the top portion of the droplet. Furthermore, we find that the phase of the oscillation is related to the Weber number and greatly influences the jet velocity because it determines the initial conditions for jet generation.

Collision dynamics of a single water droplet impinging on a high-temperature pool of oil

The article presents the dynamic process of a single water droplet impinging on a hot oil surface with various temperatures ranging from 205 to 260 $$^\circ \hbox {C}$$ . Distilled water is used to produce water droplets with different diameters. The impact behavior is recorded by using a high-speed digital camera with the speed of 2000 fps. The result shows that two typical phenomena, including crater–jet–bubble and vapor explosion, can be observed. The vapor explosion occurs when the oil temperature is higher than 210 $$^\circ \hbox {C}$$ . The oil temperature, the droplet size, and the Weber number are found to have significant influence on the vapor explosion time. The higher the oil pool temperature is, the earlier the vapor explosion occurs. Vapor explosion time increases with the droplet size, while decreases as the droplet Weber number increases. Moreover, the maximum heat absorption for a single water droplet immersing into the hot oil is calculated considering the changes of the droplet size. Both dimensionless maximum crater depth and maximum jet height increase with the pool temperature due to the surface tension, viscous force and decreasing density of the hot oil.

Impact of Droplets on Liquid Films in the Presence of Surfactant

The impact of droplets on liquid films is ubiquitous in natural and industrial processes, and surfactants can significantly alter the impact process by changing the local surface tension. Here we study the impact of droplets on liquid films in the presence of surfactant using high-speed photography, and reveal the flow pattern by dye-tracing. The effects of the droplet size and speed, and the initial film thickness on the impact process are elucidated. The results show that the flow is significantly affected by adding surfactant to the droplet, the liquid film, or to both phases. In particular, the film dye patterns form concentric circles and flower-shaped structures at low and high droplet Weber numbers, respectively. We also show how surfactant-induced Marangoni stresses modify these flow patterns, and alter the characteristics of the phenomena associated with the impact process, such as the propagation of capillary waves, the evolution of the crown, and the formation of secondary droplets. During the impact of surfactant droplets on thin water films, the Marangoni stresses can be sufficiently strong so as to drive film dewetting.

Droplet deformation and heat transfer in isotropic turbulence

The heat and mass transfer of deformable droplets in turbulent flows is crucial to a wide range of applications, such as cloud dynamics and internal combustion engines. This study investigates a single droplet undergoing phase change in isotropic turbulence using numerical simulations with a hybrid lattice Boltzmann scheme. Phase separation is controlled by a non-ideal equation of state and density contrast is taken into consideration. Droplet deformation is caused by pressure and shear stress at the droplet interface. The statistics of thermodynamic variables are quantified and averaged over both the liquid and vapour phases. The occurrence of evaporation and condensation is correlated to temperature fluctuations, surface tension variation and turbulence intensity. The temporal spectra of droplet deformations are analysed and related to the droplet surface area. Different modes of oscillation are clearly identified from the deformation power spectrum for low Taylor Reynolds number $Re_{\unicode[STIX]{x1D706}}$, whereas nonlinearities are produced with the increase of $Re_{\unicode[STIX]{x1D706}}$, as intermediate frequencies are seen to overlap. As an outcome, a continuous spectrum is observed, which shows a decrease in the power spectrum that scales as ${\sim}f^{-3}$. Correlations between the droplet Weber number, deformation parameter, fluctuations of the droplet volume and thermodynamic variables are also developed.