Thin Liquid Film Research Articles

Free surface water waves generated by instability of an exponential shear flow in arbitrary depth

The stability of an exponential current in water to infinitesimal perturbations in the presence of gravity and capillarity is revisited and reformulated using the Weber and Froude numbers. Some new results on the generation of gravity-capillary waves are presented, which supplement the previous works of Morland et al. [“Waves generated by shear layer instabilities,” Proc. Math. Phys. Sci. 433, 441–450 (1991)] and Young and Wolfe [“Generation of surface waves by shear-flow instability,” J. Fluid Mech. 739, 276–307 (2014)] on finite depth. To consider perturbations at much larger scales, special attention is given to the stability of exponential currents only in the presence of gravity. More precisely, the present investigation reveals significant insights into the stability of exponential shear currents under different environmental conditions. Notably, we have identified that the dimensionless growth rate increases with the Froude number, providing a deeper understanding of the interplay between shear layer thickness and surface velocity. Furthermore, our analysis elucidates the dimensional wavelength of the most unstable mode, emphasizing its relevance to the characteristic shear layer thickness. Additionally, within the realm of gravity-capillary instabilities, we have established a sufficient condition for the stability of exponential currents based on the Weber number. Our findings are supported by stability diagrams at finite depth, showing how the size of stable domains correlates with the characteristic thickness of the shear layer. Moreover, we have explored the stability of a thin film of liquid in an exponential shearing flow, further enriching our understanding of the complex dynamics involved in such systems.

Hydrodynamic characteristics of the microlayer under vapour bubbles on solid surfaces

This study investigates the hydrodynamic behaviour of the microlayer, a thin liquid film of a few micrometres thickness that forms beneath vapour bubbles during boiling under specific conditions. This microlayer serves as a rapid heat transfer medium through evaporation due to its low thermal resistance, making it a compelling subject for enhanced heat transfer research. We employ the geometric Volume-Of-Fluid (VOF) method for numerical simulations, allowing us to accurately replicate the growth of a vapour bubble on solid surfaces. The computational approach offers a level of detail and resolution that can compensate for certain aspects of microlayer behaviour absent in experimental methods. Our simulations reveal the complete spatial distribution of the microlayer and the profiles of the bubble interface near the meniscus front (the part of the interface near the solid). We compare the results with experimental data and conduct simulations with various bubble growth laws to explore how the microlayer responds to different growth scenarios. These findings lay the foundation for incorporating the microlayer’s contribution to overall boiling heat transfer in future models, potentially unlocking new avenues for enhanced heat transfer applications.

Numerical investigation of bubble dynamics and flow boiling heat transfer in cylindrical micro-pin-fin heat exchangers

Micro-pin-fin evaporators are a promising alternative to multi-microchannel heat sinks for two-phase cooling of high power-density devices. Within pin-fin evaporators, the refrigerant flows through arrays of obstacles in cross-flow and is not restricted by the walls of a channel. The dynamics of bubbles generated upon flow boiling and the associated heat transfer mechanisms are expected to be substantially different from those pertinent to microchannels; however, the fundamental aspects of two-phase flows evolving through micro-pin-fin arrays are still little understood. This article presents a systematic analysis of flow boiling within a micro-pin-fin evaporator, encompassing bubble, thin-film dynamics and heat transfer. The flow is studied by means of numerical simulations, performed using a customised boiling solver in OpenFOAM v2106, which adopts the built-in geometric Volume of Fluid method to capture the liquid–vapour interface dynamics. The numerical model of the evaporator includes in-line arrays of pin-fins of diameter of 50μm and height of 100μm, streamwise pitch of 91.7μm and cross-stream pitch of 150μm. The fluid utilised is refrigerant R236fa at a saturation temperature of 30 °C. The range of operating conditions simulated includes values of mass flux G=500–2000kg/(m2s), heat flux q=200kW/m2, and inlet subcooling ΔTsub=0–5K. This study shows that bubbles nucleated in a pin-fin evaporator tend to travel along the channels formed in between the pin-fin lines. Bubbles grow due to liquid evaporation and elongate in the direction of the flow, leaving thin liquid films that partially cover the pin-fins surface. The main contributions to heat transfer arise from the evaporation of this thin liquid film and from a cross-stream convective motion induced by the bubbles in the gap between the cylinders, which displace the hot fluid otherwise stagnant in the cylinders wakes. When the mass flow rate is increased, bubbles depart earlier from the nucleation sites and grow more slowly, which results in a reduction of the two-phase heat transfer. Higher inlet subcooling yields lower two-phase heat transfer coefficients because condensation becomes important when bubbles depart from the hot pin-fin surfaces and reach highly subcooled regions, thus reducing the two-phase heat transfer.

Periodic Precipitation in a Confined Liquid Layer.

Pattern formation is a ubiquitous phenomenon in animate and inanimate systems generated by mass transport and reaction of chemical species. The Liesegang phenomenon is a self-organized periodic precipitation pattern always studied in porous media such as hydrogels and aerogels for over a century. The primary consideration of applying the porous media is to prevent the disintegration of the precipitation structures due to the sedimentation of the precipitate and induced fluid flow. Here, we show that the periodic precipitation patterns can be engineered using a Hele-Shaw cell in a confined liquid phase, restricting hydrodynamic instability. The patterns generated in several precipitation reaction systems exhibit spatiotemporal properties consistent with patterns obtained in solid hydrogels. Furthermore, analysis considering the Rayleigh-Darcy number emphasizes the crucial role of fluidity in generating periodic precipitation structures in a thin liquid film. This exploration promises breakthroughs at the intersection of fundamental understanding and practical applications.

Impact of roasted oat flour on the gas cell structure of steamed oat cake and its underlying mechanism

Roasting (or called stir-frying) can modify the properties of oat flour and improve the poor quality of steamed oat cake, especially uneven gas cell and high hardness, but the underlying mechanism remains unclear. The properties of protein-starch network matrix of oat dough (made by roasted oat flours with gelatinization degrees of 30%, 50% 70% and 90%) before and after steaming were investigated, as well as the air/water interfacial characteristics of oat dough liquor. Results revealed that adding roasted oat flour with moderate gelatinization degree to the raw oat flour (ROF) could significantly improve the quality of steamed oat cakes, and their average pore size and specific volume reached the corresponded maximum values when roasted oat flour with gelatinization degree of 50% (G50) was added, which were 1.97 mm and 2.56 mL/g, respectively. Roasted oat flour with moderately gelatinization could not only facilitate the formation of protein polymers by promoting disulfide cross-linking of larger monomer proteins in both raw and steamed oat dough, but also induce the conversion of random coil to α-helix and β-sheets structure, resulting in an ordered protein secondary structure. Meanwhile, the improvement of short-range molecular order structure of starch in oat dough was observed for ROF/G50（w/w = 1:1）sample (RG50). Additionally, compared to ROF, RG50 sample possessed the strongest foaming stability, which increased from 32.70% to 61.43%. In conclusion, the quality enhancement of steamed oat cake can be attributed to the combined effects of changes in the protein-starch matrix and the thin liquid film induced by moderately roasted oat flour.

Dynamic wire-pull rubber diaphragm for rapid formation and spatio-temporal investigation of multi-shape free-standing liquid films

Quantitative manufacturing and characterization of thin films are relevant in different scientific and industrial fields. Especially, for the studies of fluid dynamics, the experimental verification of theoretical models creates the need of a free-standing liquid film formation. Driven by the lack of fast and accurate liquid film forming technology, we present a novel device able to fabricate thin free-standing liquid films, which is based on a dynamic and adjustable diaphragm, the opening of which allows for the rapid formation of a self-supported liquid film confined in a wire-pull rubber band. The quantitative thickness mapping of the film formation and its time-resolved evolution are performed by digital holography in real-time. This builds up a strategy that allows for the accurate liquid film formation with controllable size and volume. As the results, multi-shape and multi-material thin films under controllable and stable conditions are successfully formed, including free-standing water, soapy water and glycerol films. A label-free spatio-temporal analysis method for flow dynamics is proposed: The full-field time series of film thickness is reassembled in a new coordinate system composed of radius, time, and thickness. Such spatio-temporal analysis reveals details of leveling and drainage processes. To the best of our knowledge, this is the first full-field quantitative thickness analysis of multi-shape and multi-material thin films. The proposed Dynamic Wire-pull Rubber Diaphragm (DWRD) together with the digital holography add-on offer characterization abilities with an unprecedented level of details allowing for a deeper understanding of the underlying thin film dynamics that can be useful in several different scientific and technological fields as biotechnology, life science, and nanotechnology.

Effects of Non-Uniform Heat Source-Sink and Nonlinear Thermal Radiation on MHD Heat and Mass Transfer in a Thin Liquid Film

Effects of Non-Uniform Heat Source-Sink and Nonlinear Thermal Radiation on MHD Heat and Mass Transfer in a Thin Liquid Film

Thin film flow of chemically reactive nonlinear thermally radiative magnetized variable viscosity fluid over a stretchable surface with non-uniform heat source/sink and Fick’s mass flux theory

The study of thin film flow over a stretching sheet holds significant importance from an industrial perspective due to its relevance in various manufacturing and engineering processes. In the present investigation, we delved into the combined influence of non-uniform heat source/sink on the governing heat and mass transfer equations in a thin liquid film on a permeable stretching surface. We have considered the nonlinear thermal radiation and implemented convective-type boundary conditions. Our analysis examined the effects of crucial physical parameters, including non-uniform heat source/sink, thermal radiation, chemical reaction, magnetic parameter , Prandtl number, Schmidt number, and unsteadiness parameter in the range [−3.5, 2.0], [−2, 5], [0, 1], [0.3, 4.0], [1, 7], [0.8, 1.7], [0.7, 2.0], respectively. It is found that a non-uniform heat source/sink mitigated the temperature gradient, while an elevation in the Schmidt number intensified the mass transfer rate. The validation process enhanced the robustness and reliability of our numerical simulations.

Self-Organization via Dewetting in Polymeric Assemblies.

Dewetting is a spontaneous process involving a thin liquid film that minimizes interfacial energy by reducing the surface area via the generation of defects on the film. In industry, dewetting is regarded as a problem that results in defects or a heterogeneous surface; however, in this study, dewetting is intentionally induced to create various patterns at intended positions spontaneously with polymeric materials and nanoparticles. The dewetting-induced patterning process is conducted by controlling the capillary force and evaporation ratio through an evaporative self-assembly system. The linear-polymeric arrays on the substrate played an important role in modifying the surface geometry and treatment for a heterogeneous surface, and an additional patterning process is performed on patterned arrays to create dewetting-induced self-organizing patterns. Here, this method is used to introduce material arrays with specific shapes such as dots, dumbbells, potbellies, Vs, and trapezoids.

Influence of typical liquid fuels on foam properties of critical components of environmentally friendly aqueous film-forming foams

In this study, the influence mechanism of typical fuels (oils) on the foam properties of mixture of hydrocarbon and fluorocarbon surfactants was investigated. A mixed solution was prepared based on a nonionic hydrocarbon surfactant (APG-0810) and a zwitterionic C6 fluorocarbon surfactant (short-chain). The effect of different oils (heptane, kerosene, diesel, and transformer oil) on the physical property parameters, foamability, oil resistivity of foam and single vertical liquid film of the mixture are systematically investigated. Results indicate that the viscosity of mixture increases, but the conductivity, surface activity, and initial foam height decreases with addition of the four oils. The drainage and volume decay of the foam are accelerated by the presence of oils. In addition, the presence of oils accelerates liquid film thinning through affecting drainage, especially for the oil with higher density, water solubility, and volatility. The four oils showed different effect on foam properties due to the difference in nature and emulsification of them. Among them, the foam properties under the action of heptane is the best, and the oil resistivity of foams is the best. This study can provide theoretical guidance for oil resistivity of hydrocarbon and fluorocarbon surfactant stabilized foams.

A Lagrangian meshfree model for solidification of liquid thin-films

In this paper, a new method to model solidification of thin liquid films is proposed. This method is targeted at applications like aircraft icing and tablet coating where the formation of liquid films from impinging droplets on a surface form a critical part of the physics of the process. The proposed model takes into account the (i) unsteadiness in temperature distribution, (ii) heat transfer at the interface between the solid and the surface, (iii) volumetric expansion/contraction and (iv) the liquid thin-film behaviour, each of which are either partly or fully ignored in existing models. The liquid thin-film, modelled using the Discrete Droplet Method (DDM), is represented as a collection of discrete droplets that are tracked in a Lagrangian sense. The height of the liquid film is estimated as a summation of Gaussian kernel functions associated with each droplet. At each droplet location, a solid height is also computed. The evolution of the solid height is governed by the Stefan problem. The flow of the liquid thin-film is solved just as in the case of DDM, while also taking into consideration the shape of the solidified region lying beneath the droplet. The results presented in this work show the reliability of the proposed model in simulating solidification of thin-films and its applicability to complex problems such as ice-formation on aircraft wings. The model has been verified for canonical problems that have analytical solutions. For the more complex problems of icing, the results of the model are compared with data from literature, without considering a background air flow. The comparison can be improved by coupling this model with suitable air flow solvers, as shown in the final test case.

Study on the film thickness and surface wave velocity of the thin liquid film formed by a round jet obliquely impinging on a horizontal plate

For a thin liquid film (in a supercritical flow) prior to the formation of a non-circular hydraulic jump formed by a round jet obliquely impinging on a horizontal plate, the time-averaged film thickness and the surface wave velocity are extracted based on the measured transient film thickness. On the one hand, the effect of many factors, including the jet velocity, impingement angle, azimuthal angle, liquid viscosity, and surface tension, on the time-averaged film thickness and surface wave velocity are discussed. When the jet Reynolds number increases to about 1.4×104, the film thickness profile suddenly increases, and the transition of liquid flow from laminar to turbulent occurs. Meanwhile, a rapid increase is observed downstream of the turbulent film thickness profile. The influence of surface tension on the time-averaged film thickness and surface wave velocity is negligible for thin liquid films before non-circular hydraulic jumps. Nonetheless, the surface tension has a significant influence on the interface profile of non-circular hydraulic jumps. Furthermore, a “crescent” kink region upstream of the jump can be identified when the surface tension is lower than 40.6 mN/m. On the other hand, experimental results are used to verify the prediction accuracy of existing approximate solutions. The laminar approximate solution with a quadratic boundary layer velocity profile can accurately predict the film thickness distribution of most laminar thin liquid films, except downstream of the thin liquid films with a dynamic viscosity higher than 9.71 mPa s. The surface wave velocities are found to be close to the predicted surface velocities of the approximate solutions.

Experimental study of single droplet impingement on a thin liquid film under a non-uniform electric field

Droplet impingement on a thin liquid film has been extensively applied in the field of spray cooling due to its powerful heat and mass transfer properties. In this study, the impact dynamics of a single droplet impacting on a thin liquid film under a non-uniform electric field was experimentally investigated. Ethanol was employed as the working fluid, and the impact behaviors were captured by high-speed photography technology. The results showed that the impact process sequentially exhibits the phenomena of the liquid crown and liquid column. Five typical crown patterns were identified, and the unique “jet crown” mode was first reported. The crown dimension analysis indicated that the maximum crown height increased with the increase in electric Bond number (0 ≤ BoE ≤ 583.48), while the crown width was likely independent of BoE. Furthermore, this study provided the splashing threshold of the crown under a non-uniform electric field by coupling the BoE with an empirical formula determining the splashing threshold. In addition, a unique phenomenon of jetting liquid columns was obtained. During the ascent phase of the liquid column, the vertical downward acceleration of the liquid column was significantly greater than the gravitational acceleration. The presence of an electric field introduced fluctuations in the liquid column's acceleration, causing the direction of acceleration to alternate between upward and downward. This study contributes to a deeper understanding of the physical mechanisms underlying the electric field modulation of droplet impingement behavior.

Enhanced contact flexibility from nanoparticles in capillary suspensions

Hypothesis: Sample-spanning particle networks are used to induce structure and a yield stress, necessary for 3D printing of porous ceramics and paints. In capillary suspensions, a small quantity of immiscible secondary fluid is incorporated into a suspension. By further adding nanoparticles with a range of hydrophobicities, the structure of the bridges and microparticle-microparticle contacts is expected to be modified, resulting in a tunable yield stress and shear moduli. Moreover, the compressibility of these samples, important in many processing and application steps, is expected to be sensitive to these changes.Experiment: The nanoparticle hydrophobicity was altered and their position relative to the microparticles and the bridges was examined using confocal microscopy where the correlation between bridge size and network structure was observed. A step-wise uniaxial compression test on the confocal was conducted to monitor the microparticle movement and structural changes between capillary suspension networks with and without nanoparticles.Findings: Our observation suggests that nanoparticles induce the formation of thin liquid films on the surface of the microparticles, mitigating contact line pinning and promoting internal liquid exchange. Additionally, nanoparticles at microparticle contact regions further diminish Hertzian contact, enhancing the capacity for rearrangement. These effects enhance microparticle movement, narrowing the bridge size distribution.

Parametric study of water spray cooling on enhanced relatively large surfaces

Spray cooling as an effective cooling technique is widely used in practice. Compared to small heating surfaces, the significantly increase of surface would pose a great challenge to the significant enhancement of spray cooling. Specially, single nozzle spray cooling suffers from non-uniform liquid thin film on a relatively large heating surface, severely inhibiting the formation of efficient thin film evaporation. In this study, two enhanced surfaces such as straight fin surface and cubic fin surface with a relatively large heating surface of 4 cm2 were designed for single nozzle spray cooling. A parametric study was conducted with aims to evaluate the effects of flow rate, spray distance and enhanced surfaces on the formation of thin liquid film and then the performance of spray cooling. Visualization was presented to observe the development of liquid film to elucidate the enhanced mechanism of spray cooling. In this work, spraying height is varying from 20 to 40 mm. Coolant flow rate is ranging from 70 to 100 ml/min. The experimental results show the distribution of liquid film plays an important role in spray cooling, especiallyin the single-phase regime. In two-phase regime, nucleate boiling is significantly boosted on the engineered surfaced. For instance, the cubic fin surface leads to an enhancement of HTC of nearly 24 % compared to that of flat surface.

Numerical study of Two-Phase flow behavior during dryout in a Two-Phase closed thermosyphon under thermal boundary conditions

This paper presents a two-dimensional axisymmetric two-phase closed thermosyphon (TPCT) model filled with R-134a refrigerant using the Volume of Fluid (VOF) method, Lee model, and Continuum Surface Force (CSF) method within Computational Fluid Dynamics (CFD) and simulates the flow characteristics inside the TPCT during the occurrence of dry out. Specifically, it discusses the two-phase flow in the condensation and evaporation sections when dry out occurs. The results indicate that the condensation section exhibits varying forms of vapor–liquid interface waves at different times. Phenomena such as liquid carryover and entrainment become increasingly prominent over time, contributing significantly to refrigerant blockages and dryout in the evaporation section. The mechanism behind dryout in the evaporation section is revealed to be the result of the initially continuous falling film being disrupted by fluctuations in the liquid–vapor interface, leading to the premature drying of thin liquid films in the troughs of these waves.

Actuating droplets with electrowetting: Force and dynamics

AbstractElectrowetting on dielectric (EWOD) allows rapid movement of liquid droplets on a smooth surface, with applications ranging from lab‐on‐chip devices to micro‐actuators. The in‐plane force on a droplet is a key indicator of EWOD performance. This force has been extensively modeled but few direct experimental measurements are reported. We study the EWOD force on a droplet using two setups that allow, for the first time, the simultaneous measurement of force and contact angle, while imaging the droplet shape at 6000 frames/s. For several liquids and surfaces, we observe that the force saturates at a voltage of approximately 150 V. Application of voltages of up 2 kV, that is, 10 times higher than is typical, does not significantly increase forces beyond the saturation point. However, we observe that the transient dynamics, localized at the front contact line, do not show saturation with voltage. At the higher voltages, the initial front contact line speed continues to increase, the front contact angle temporarily becomes near zero, creating a thin liquid film, and capillary waves form at the liquid–air interface. When the localized EWOD forces at the contact line exceed the capillary forces, projectile droplets form. Increasing surface tension allows for higher droplet forces, which we demonstrate with mercury.

Probing time-resolved plasma-driven solution electrochemistry in a falling liquid film plasma reactor: Identification of HO2- as a plasma-derived reducing agent.

Many applications involving plasma-liquid interactions depend on the reactive processes occurring at the plasma-liquid interface. We report on a falling liquid film plasma reactor allowing for in situ optical absorption measurements of the time-dependence of the ferricyanide/ferrocyanide redox reactivity, complemented with ex situ measurement of the decomposition of formate. We found excellent agreement between the measured decomposition percentages and the diffusion-limited decomposition of formate by interfacial plasma-enabled reactions, except at high pH in thin liquid films, indicating the involvement of previously unexplored plasma-induced liquid phase chemistry enabled by long-lived reactive species. We also determined that high pH facilitates a reduction-favoring environment in ferricyanide/ferrocyanide redox solutions. In situ conversion measurements of a 1:1 ferricyanide/ferrocyanide redox mixture exceed the measured ex situ conversion and show that conversion of a 1:1 ferricyanide/ferrocyanide mixture is strongly dependent on film thickness. We identified three dominant processes: reduction faster than ms time scales for film thicknesses >100 µm, •OH-driven oxidation on time scales of <10ms, and reduction on 15ms time scales for film thickness <100 µm. We attribute the slow reduction and larger formate decomposition at high pH to HO2- formed from plasma-produced H2O2 enabled by the high pH at the plasma-liquid interface as confirmed experimentally and by computed reaction rates of HO2- with ferricyanide. Overall, this work demonstrates the utility of liquid film reactors in enabling the discovery of new plasma-interfacial chemistry and the utility of atmospheric plasmas for electrodeless electrochemistry.

Modeling the stability of thin liquid film flows on a uniformly heated slippery inclined substrate: A realistic approach

We investigate the stability of gravity-driven, Newtonian, thin liquid film falling down a uniformly heated slippery rigid inclined wall. The authors of previous research works considered specified temperature (ST) boundary condition to study the effects of slip length. However, the ST boundary condition does not include the effects of heat fluxes at wall–air and wall–liquid interfaces and so fails to incorporate the real situation. Consequently, we consider heat flux/mixed-type boundary condition as the thermal boundary condition on the rigid plate. This boundary condition involves the heat flux from the rigid plate to the surrounding liquid and the heat losses from the wall to the ambient air. Using long-wave expansion method, we construct a highly nonlinear evolution equation in terms of the film thickness at any instant. Using normal mode approach, the linear study reveals the stabilizing (destabilizing) behavior of the wall film Biot number (dimensionless slip length). It is found that the destabilizing tendency of the slip length is more in the absence of thermocapillary stress. The linear study reveals that the destabilizing role of MB may be controlled to some extent by increasing the wall film Biot number Bw. Using asymptotic expansions of the flow variables in terms of the small wave number k, the Orr–Sommerfeld boundary value problem gives an onset of instability in terms of critical Reynolds number. It slightly differs from that of the same as obtained by Benney's long-wave expansion method, due to the consideration of small free surface Biot number [B=O(ϵ)]. For arbitrary wave numbers, using Chebyshev spectral collocation method, the effect of Marangoni number (Ma), slip length (δ), and wall film Biot number (Bw) on the H, S, P, and shear modes of instability are discussed in detail. Near the threshold, both Ma and δ show the destabilizing effect on H mode of instability, whereas Bw gives the stabilizing effect. Interestingly, their roles on H mode of instability becomes diametrically opposite far from the onset of instability. For S mode, both Ma and Bw display the destabilizing effect, whereas δ plays the dual role. For P mode, both Ma and δ show the destabilizing effect, whereas Bw plays the stabilizing role. The slip length (δ) plays the stabilizing role, in the case of shear mode. In the absence of thermocapillary effect, the vorticity balance at the liquid–air interface explains that the amplitude of the vorticity perturbation amplifies the surface deformation due to the presence of inertia and the slip length. In the absence of the slip length, a weakly nonlinear study transforms the evolution equation to the famous Kuramoto–Sivashinsky (KS) equation.

Impact dynamics of non-spherical droplets on a thin water film

A droplet impinging on a liquid film finds numerous applications in diverse scientific fields. Although studies have primarily focused on spherical droplets, a droplet can present both spherical shape and non-spherical shape at the moment of impact. In the present study, the impact dynamics of a non-spherical droplet on a thin liquid film is investigated experimentally. The results show that, under the same film thickness and Weber number conditions, the splashing and deposition regimes are different for different droplet shapes such as prolate, sphere, and oblate. It is found that the splashing threshold (Ksp) is changed according to the shape of the droplet. Under the same condition when a spherical droplet is in the deposition mode, an oblate droplet is more likely to splash and form secondary droplets, while a prolate droplet is more splash-resistant even at higher Weber numbers. A modified theoretical model for crown radius evolution is developed. The predictions of theoretical model are found to agree well with the experimental results for spherical and non-spherical droplets. Moreover, at the same Weber number, a prolate droplet has a relatively higher maximum crown height than those of an oblate droplet and a spherical droplet.