Liquid Sheet Research Articles

Breakup of thin liquid films with viscous interfaces

Thin liquid films are ubiquitous in nature and have many practical applications. From biological films to the curtain coating process, thin films are present in both large and small scales. Despite their importance, understanding the stability of these films remains a significant challenge due to the fluid–fluid interface that is free to deform, affected by interfacial tension and complex rheological behavior. Instabilities in thin films are often caused by van der Waals attractions, which can lead to the rupture of the layer. To investigate the rupture dynamics, numerical methods are commonly used, such as asymptotic derivations of the lubrication theory or interface tracking methods. In this paper, we present a computational study of the breakup dynamics of a stationary thin liquid sheet bounded by a passive gas with a viscous interface, using the arbitrary Lagrangian–Eulerian method and the Boussinesq–Scriven constitutive law to model the rheological behavior. Our results demonstrate that the stability of thin liquid films is influenced by both surface rheology and disjoining effects and that the viscous character of the interface can delay sheet breakup, leading to more stable films.

Liquid jet dispersion after impact on a highly curved surface

A liquid jet impacting on a wire mesh is a phenomenon that occurs in such industrial applications as rotating packed beds or agricultural spraying. To derive a fundamental understanding of the behaviour of a dispersion generated by the whole mesh, a simple geometric case needs to be studied. This paper focuses on the dispersion of a liquid jet impacting on a single stainless steel rod studied with a high-speed visualisation. It is found that two liquid sheets are formed with sheet characteristics described by a dispersion angle αe, a sheet velocity vs, and a breakup length Lb. Three stages of the angular development of the dispersion are observed based on the liquid flow rate and the exit orifice diameter. A correlation for the dispersion angle growth is proposed based on the experimental results. Perforated, segmented and wave-assisted sheet breakup regimes are found in the recorded images with their presence dependent on the impact velocity. A correlation for the breakup length is proposed for the sheets based on similarities with flat fan nozzle theory.

Engraving of stainless-steel wires to improve optical quality of closed-loop wire-guided flow jet systems for optical and X-ray spectroscopy.

This paper describes performance enhancement developments to a closed-loop pump-driven wire-guided flow jet (WGJ) for ultrafast X-ray spectroscopy of liquid samples. Achievements include dramatically improved sample surface quality and reduced equipment footprint from 7 × 20cm2 to 6 × 6cm2, cost, and manufacturing time. Qualitative and quantitative measurements show that micro-scale wire surface modification yields significant improvements to the topography of the sample liquid surface. By manipulating their wettability, it is possible to better control the liquid sheet thickness and to obtain a smooth liquid sample surface, as demonstrated in this work.

Impingement of unlike-doublet liquid jets with different surface tensions

The effect of surface tension asymmetry on the atomization of unlike-doublet impinging jets was experimentally studied. Three typical features were identified, including wrinkled sheet edge, inner-sheet patch, and serrated bottom rim. The wrinkled sheet edge represents the propagation front of the Marangoni flow subsequent to rim encapsulation. The inner-sheet patch is caused by the through-plane mixing across the liquid sheet with uneven thickness and results in the occurrence of the serrated bottom rim. In the presence of these Marangoni-driven flow structures, the liquid sheet tends to be more unstable, and atomization is improved for unlike-doublet impinging jets, as the breakup length is reduced and smaller droplets are generated compared to like-doublet impinging jets.

Large-eddy simulation, convective instability, and modal causality of coaxial supersonic air–water jets considering a swirl effect

An annular liquid sheet sheared by a coaxial supersonic gas stream with a swirling effect is investigated using Large Eddy Simulation. Despite its wide applications in aerospace and medical devices, the instability and spatial characters have been barely investigated due to the high complexity under supersonic condition. Unlike the conventional use of the temporal dynamic mode decomposition (DMD), DMD is applied in the axial direction to evaluate the transient convective instability. The high-velocity cases show significantly stronger instability in the nozzle near-field. However, swirling has only marginal effects on the convective instability. In addition, proper orthogonal decomposition (POD) extracts the essential spatial topology of velocity, momentum, and pressure fields. Pulsatile and flapping instabilities are observed in the gas flow, where liquid flow demonstrates the schrink/expansion as well as the flapping instabilities. In addition, all POD modes of the pressure field take the form of coherent wavepacket structures, and their wavelength and spatial forms of the wavepackets are dependent on the gas flow speed rather than the swirling. Time coefficients of the leading POD modes of momentum and pressure fields show an interesting correlation. Hence, the causal–effect relationship between these leading modes of momentum and pressure field is quantified via transfer entropy from the information theory. The transfer entropy from the pressure field to the momentum field is generally higher than vice versa, and this trend is enhanced by the swirling in the low-velocity condition.

Computational fluid dynamics analysis of an agricultural spray in a crossflow

Spraying is the most widely used method for pesticide application and the resulting spray drift has become a major concern. Reliable spray simulations can help to better understand this phenomenon and evaluate methods to prevent it. This paper proposes a methodology to set up a computational fluid dynamics simulation of sprays. A number of benchmark flows were studied to assess the accuracy of the proposed method. The simulation of a jet in a crossflow was able to capture counter-rotating vortex pairs and the predicted trajectory agreed with experimental data. A multiple-injector technique is then used to replicate the velocity distribution of sprays without modelling the liquid sheet breakup. Spray simulations were able to capture air entrainment and predicted a realistic droplet distribution pattern. The volume of droplets deposited on the collector lines in drift simulations was in good agreement with experimental data in the near field. As the droplets moved further downstream, however, a deviation between the simulation results and experimental data was observed. The drift simulation results indicated that in a wind speed of 2ms−1, droplets of diameter <75μm are prone to drift.

Primary spray breakup from a nasal spray atomizer using volume of fluid to discrete phase model

Spray atomization process involves complex multi-phase phenomena. Abundant literature and validation of spray modeling for industrial applications like fuel injection in internal combustion and turbine jet engines are available. However, only a handful of studies, primarily limited to discrete phase modeling, of low-pressure applications, such as nasal spray exists. This study aims to provide insight into the external and near-nozzle spray characterization of a continuous spray and establishes good validation against the experiment. A three-dimensional (3D) x-ray scanner was used to extract the internal nasal spray nozzle geometry which was reconstructed to build a 3D computational model. A novel volume-of-fluid to discrete phase transition model was used to track the liquid phase and its transition to droplets, which was based on the shape and size of the liquid lumps. In this study, an early pre-stable and stable phase of spray plume development was investigated. Qualitative and quantitative analyses were carried out to validate the computational model. A liquid column exited a nozzle which distorted at its base with advancement in time and eventually formed a hollow-cone liquid sheet. It then disintegrated due to instability that produced fluctuations to form ligaments resulting in secondary breakup. This study provides in-depth understanding of liquid jet disintegration and droplet formation, which adds value to future nasal spray device designs and techniques to facilitate more effective targeted nasal drug delivery.

Weakly nonlinear instability analysis of viscous planar liquid sheet under varicose mode of initial disturbance with co-flowing gas streams and prediction of resulting spray characteristics

A theoretical investigation of the effects of viscosity is presented for breakup of a planar viscous liquid sheet subjected to a fundamental varicose mode of disturbance in the presence of moving gas medium. A classic perturbation technique up to second order has been employed to derive the linear and nonlinear interface disturbances. The breakup model is coupled with Maximum Entropy Formalism to predict the final spray characteristics. Findings reveal that within an initial range of Re, imposition of first harmonic on the fundamental disturbance produces a faster breakup as compared to the fundamental disturbance alone. As a result, first harmonic produces a destabilizing effect in the first regime, whose range is identified as 1 <Re < 20.3, 1<Re < 13.35 and 1<Re < 10.53 for gas velocity ratio 2.25, 2.50 and 2.75, respectively. Above this initial range of Re, first harmonic exhibits a stabilizing effect as it produces a delayed breakup when compared with the fundamental mode alone. However, a larger increase in dominating linear growth rate with Re negates the reduction of first harmonic in the destabilizing regime as well its damping effect in the stabilizing regime, resulting in an overall reduction in breakup time with the increase in Reynolds number. Analysis of spray characteristic suggests formation of finer droplets at higher gas velocity ratios. Moreover, reduction in liquid viscosity decreases the range of droplet diameter for gas velocity ratios 2.25 and 2.50.

Simultaneous impact of droplet pairs on solid surfaces

This study investigates the dynamics of the simultaneous impact of two droplets on a dry substrate. We develop a new micro-controlled droplet generator that releases two equally sized water droplets simultaneously on-demand, with no trailing droplets. The impact Weber number, based on impact droplet size and velocity, and the inter-droplet spacing relative to the impact droplet size are varied in the ranges of 54 to 155 and 1.32 to 2.25, respectively, leading to the strong interaction of the spreading lamellae that form a central uprising sheet, which eventually deposits or breaks into tiny droplets. We analyse the impact processes for both deposition and splashing of the uprising sheets. Simultaneous high-speed imaging from two orthogonal views of the droplet impacts quantifies the three-dimensional structure of the sheet morphology, including the temporal evolution of the rim-bounded ‘semilunar’ shape, surface waves, rim corrugations and finger formation, and deposition or splashing of the liquid sheet. The characteristics of the sheet surface waves and the rim instabilities are quantified. Novel scaling is developed for the maximum sheet height, sheet width and thickness, which considers the geometrical constraints and mass balance of the interacting lamellae to describe the temporal evolution of a ‘semilunar’ uprising sheet and is in good agreement with the measurements. The uprising sheet splashing generates larger droplets than those from splashing of single-droplet impacts, and it occurs due to the end-pinching of sheet fingers and at conditions that single-droplet impacts lead only to liquid deposition.

Spray impact onto a hot solid substrate: Film boiling suppression by lubricant addition

Spray cooling of solid substrates is one of the methods used in various industrial processes such as forging, quenching or other metallurgical applications, electronics, pharmaceutical industry, medicine, or for cooling of powerful electrical devices. Spray cooling is governed by various hydrodynamic and thermodynamic processes, like drop impact, heat conduction in the substrate and convection in the spreading drops, and different regimes of boiling. The problem of modeling spray cooling becomes even more challenging if the liquid is multicomponent. The presence of components with various physicochemical properties (surfactants, binders, dispersed particles, etc.) can significantly affect the entire process of spray impact, as well as the outcome of the known cooling regimes and could lead to a formation of a thin deposited layer on the substrate. In this experimental study, spray impact onto a substrate, initially heated to temperatures significantly exceeding the liquid saturation point, is visualized using a high-speed video system. The heat transfer associated with spray impact is characterized using an array of thermocouples installed in a thick metal target. As a working fluid, a mixture of a distilled water and industrial white lubricant was used. It is observed that the presence of very small concentrations of lubricant augments the heat flux dramatically, particularly at high wall temperatures, at which usually film boiling is observed for spray cooling by using distilled water. Three main mechanisms lead to the increase of heat flux and shift of the Leidenfrost point. They are caused by the significant viscosity increase of the evaporating lubricant solutions, by an increase of the substrate wettability and by the emergence of stable liquid sheets between bubbles, preventing their coalescence and percolation of the vapor channels.

A plasma self-confinement method induced by mutual extrusion of shock waves for liquid analysis of LIBS

To overcome the problems of poor plasma stability and low measurement repeatability caused by fluctuation and sputtering of liquid, a method called plasma self-confinement is proposed for liquid measurement by laser-induced breakdown spectroscopy (LIBS) in this work. With the help of shadow images, it was found that the liquid target could be returned to a calm state in a very short time, and the plasma back shock wave could be suppressed effectively. A quantitative analysis of the sodium chromate solution showed that the self-absorption could be reduced and the repeatability and sensitivity could be improved by plasma self-confinement mode LIBS when compared with liquid sheet mode LIBS.

Effects of physical property changes of expelled respiratory liquid on atomization morphology

A better understanding of the fluid dynamics of disease transmission by disintegrated respiratory droplets has been the focus of great attention since the recent outbreak of COVID-19. In particular, human respiratory activities such as coughing, sneezing and even talking and eating expel a large amount of pathogen-laden droplets. Particularly, during eating or drinking, the physical properties of saliva can be changed. In this study, we investigate the atomization morphology of expelled artificial saliva mixtures from the perspective of varying fluid physical properties, specifically surface tension and dynamic viscosity. Using high-speed shadowgraph experiments on artificial saliva, we visualize and analyse the disintegration of saliva liquid sheets into ligaments and droplets. We find that the viscosity and surface tension affect the droplet size formed from expelled saliva and follow scaling laws that have been previously observed and predicted for constant shear viscosity. We conclude that the changes in physical properties of saliva induced by eating and drinking tend to favour the formation of smaller droplets during sneezing or coughing, which could drive the airborne transmission pathway of pathogens. Furthermore, we derive a theoretical model based on scaling arguments that shows the breakup time of ligaments produced from the artificial saliva mixtures is dependent on the capillary number.

Vibration and jitter of free-flowing thin liquid sheets as target for high-repetition-rate laser-ion acceleration

Very thin free-flowing liquid sheets are promising targets for high-repetition-rate laser-ion acceleration. In this work, we report the generation of micrometer-thin free-flowing liquid sheets from the collision of two liquid jets, and study the vibration and jitter in their surface normal direction. The dependence of their motion amplitudes on the generation parameters is studied in detail. The origins of the vibration and jitter are discussed. Our results indicate that when the generation parameters are optimized, the motion amplitudes in the stable region can be stabilized below 3.7 μm to meet the stringent requirement of sheet position stability for a tight-focusing setup in laser-ion acceleration experiments.

Experimental study on the oscillatory Kelvin–Helmholtz instability of a planar liquid sheet in the presence of axial oscillating gas flow

The oscillatory Kelvin–Helmholtz (K–H) instability of a planar liquid sheet was experimentally investigated in the presence of an axial oscillating gas flow. An experimental system was initiated to study the oscillatory K–H instability. The surface wave growth rates were measured and compared with theoretical results obtained using the authors’ early linear method. Furthermore, in a larger parameter range experimentally studied, it is interesting that there are four different unstable modes: first disordered mode (FDM), second disordered mode (SDM), K–H harmonic unstable mode (KHH) and K–H subharmonic unstable mode (KHS). These unstable modes are determined by the oscillating amplitude, oscillating frequency and liquid inertia force. The frequencies of KHH are equal to the oscillating frequency; the frequency of KHS equals half the oscillating frequency, while the frequencies of FDM and SDM are irregular. By considering the mechanism of instability, the instability regime maps on the relative Weber number versus liquid Weber number (Werel–Wel) and the Weber number ratio versus the oscillating frequency (Werel/Wel– $\varOmega$ s2) were plotted. Among these four modes, KHS is the most unexpected: the frequency of this mode is not equal to the oscillating frequency, but the surface wave can also couple with the oscillating gas flow. Linear instability theory was applied to divide the parameter range between the different unstable modes. According to linear instability theory, K–H and parametric unstable regions both exist. However, note that all four modes (KHH, KHS, FDM and SDM) corresponded primarily to the K–H unstable region obtained from the theoretical analysis. Nevertheless, the parametric unstable mode was also observed when the oscillating frequency and amplitude were relatively low, and the liquid inertia force was relatively high. The surface wave amplitude was small but regular, and the evolution of this wave was similar to that of Faraday waves. The wave oscillating frequency was half that of the surface wave.

Experimental Study on Breakup Characteristics of Hollow Cone Spray in Gas Crossflow

Hollow cone spray with a medium spray half-cone angle (in the range of 36°–45°) exposed to a gaseous crossflow is a situation that has been extensively investigated experimentally. In this experiment, flow visualization techniques are employed to examine the initial liquid sheet thickness at the nozzle orifice exit and the sheet breakup process. The dynamics of the primary breakup of the sheet is analyzed based on the observations of the sheet breakup in the near-nozzle region. The experimental results show that the breakup mechanism of the liquid sheet varies greatly depending on liquid centrifugal momentum and aerodynamic force. Four distinct breakup modes are observed, and the breakup regimes are mapped in the parametric space based on the liquid Weber number (84–2175) and the liquid-to-air momentum ratio (22–8455). It is observed that the leeward side of the sheet is dominated by shear oscillation breakup within the range of the liquid-to-air momentum ratio less than 600. The influences of the aerodynamic Weber number on breakup frequency and the number of surface waves observed on the leeward side sheet are discussed by analyzing the spray images. The breakup-regime transition criteria for hollow cone spray in crossflow and the trajectory of spray in crossflow are proposed by employing a multivariable regression method.

Experimental Study on the Dynamic Characteristics of Gas-Centered Swirl Coaxial Injector under Varying Ambient Pressure

To determine the dynamic characteristics of a gas-centered swirl coaxial injector under backpressure, an experimental system of dynamic injection in a backpressure chamber was constructed. Filtered water and nitrogen were used as simulant media for rocket propellants, which are typically used with this kind of injector. An inertial flow pulsator was manufactured to generate the pulsation of the flows that feed to the liquid injector. The electric conductance method was adopted to measure liquid film thickness. After the pulsation of incoming flow in the feedline was tested, and the operating conditions for the injector to start pulsating were validated, the effects of the chamber backpressure and the recess length of the injector on the dynamic characteristics of spray, such as liquid film thickness, breakup length, and amplitude of pulsation, have been investigated in detail. Experimental results demonstrated that the increase in chamber backpressure prompts the liquid sheet to rupture earlier with a shorter breakup length, which results from the increased density of the ambient gas. Chamber backpressure suppresses the pulsation of the outlet flow, especially for a longer recess length. Moreover, a decrease in the recess length results in a reduction in breakup length due to an intense gas–liquid shearing in a narrower recess section. For a lower backpressure, the amplitude of outlet flow generally increases when the recess length increases. However, this phenomenon is not obvious for the conditions of higher backpressure and lower pulsation frequency.

Impingement and breakup characteristics of free opposed impinging jets with unequal nozzle diameter

The free opposed impinging jets with unequal nozzle diameter is developed to improve mixing efficiency at unequal flowrates for liquid–liquid reactions. The liquid sheet breakup characteristics and droplet behavior are investigated using particle image velocimetry. Water, 40w% glycerol-water (40G), and 50% glycerol-water (50G) under different jet velocities and nozzle diameters are studied for comparison, the correlation equations are obtained and the errors are analyzed. When the jet velocity increases, the liquid sheet breakup mode exhibited a closed-rim mode, open-rim mode, rimless mode, wave or ligament mode, and fully developed mode for water and 40G under a nozzle diameter of 1.5–2 mm, and the first four modes were observed with the high viscosity liquid (50G) or under a large nozzle diameter (2–3 mm). As the jet velocity increases, the dimensionless breakup length increases sharply at the closed-rim and open-rim modes, and then decreases at the rimless mode. The sheet thickness, Sauter mean diameter, average droplet diameter, and droplet velocity decrease, and the droplet size becomes more uniform with increasing jet velocity. However, the opposite variation trend is observed with increasing viscosity and nozzle diameter, and the effect is more significant at u < 4.25 m/s. The droplet average diameter increases at u = 2.12 m/s and 3.18 m/s and decreases at u ≥ 4.25 m/s downwards along y-axis due to the coalescence and secondary breakup of droplets. The droplet velocity becomes lower as droplets move downwards along y-axis from −40 mm to −50 mm due to the dissipation of momentum. The results reveal that the increase of viscosity and nozzle diameter has a negative effect on liquid sheet and droplet behavior at low jet velocities. The rimless mode is the key mode affecting the transition of the sheet breakup mechanism, and after this mode, the negative effects of viscosity and nozzle diameter weaken due to the high momentum, which promotes the breakup of the liquid sheet and droplets. It will provide theoretical support for the mixing mechanism with unequal flowrates, and is helpful to expand the application of free opposed impinging jets.

Modeling the impingement deformation and solidification of a hollow zirconia droplet onto a dry substrate and solidified layer

Despite the numerous research studies involving the solidification of continuous molten metal droplet impingement on dry substrates during the process of plasma spraying, the impingement between a hollow molten metal droplet and a solidified layer has, to date, not yet been thoroughly explored. A liquid shell enclosing the air cavity forms a hollow droplet. The coupled level set and volume of fluid method is used to track the air–liquid interface, and the enthalpy–porosity method is used to track the liquid–solid interface. A two-dimensional axis symmetric model is adopted to describe the impingement and solidification process. This study includes a detailed investigation of transient impact deformation and solidification. The heat transfer characteristics of the solidification of a continuous dense and hollow molten droplet impacting on a dry substrate and solidified layer are studied and compared. A thin solidified layer appears and develops between the droplet and the substrate, and the impacting droplet finally pins to the surface with mainly the liquid solidified. For a hollow droplet impact on the solidified layer, a splashed crown liquid sheet forms from the drop-solidified layer neck area. Various temperatures of the solidified layer induce a different development of the crown, spreading, and rebound counter-jet. The deterioration of local heat transfer is attributed to a strong fluctuation of the rebound counter-jet and the existence of an annular cavity (formed by the crown sheet falling back). Attention should be paid to this phenomenon in industrial applications involving droplet impact.

Conical liquid sheet morphology and 3D droplet distribution of aviation kerosene pressure-swirl spray with digital off-axis holography

In this study, the test performance of high-resolution digital off-axis holography for the non-spherical droplet characteristics and spatial distribution in the primary breakup region of a pressure-swirl nozzle were experimentally investigated, with spatial resolution of 4.5μm and 3.0μm. The field of interest (FOI) was restricted within 9 mm downstream of the nozzle outlet, where the primary and some secondary breakup processes take place. The liquid investigated here is RP-3 kerosene, and the injection pressure and liquid temperature were controlled in the range of 0.5 ∼ 1.0 MPa and 250 ∼ 291 K separately. Clear spray morphology and deformed droplet image were obtained through the holographic reconstruction process. Droplet extraction criteria were proposed to distinguish deformed droplets from ligaments. The overall drop size and ellipticity distribution were quantified and discussed. The results show that the overall drop size distributions near the nozzle are also typical single-peaked curves. The proportions of non-spherical droplet increase as the fuel pressure and temperature increase. The spatial Sauter mean diameter (SMD) distributions of spray at different positions downstream of the nozzle were calculated, with the grid size of 1 × 1 × 1 mm3, showing the doughnut-like annular SMD and droplet number distribution profiles of the hollow conical spray. As the temperature and fuel pressure decrease, SMD distribution becomes uneven and larger. Fine droplets exist in the region where the perforation and primary breakup process occur, and the SMD increases over the axial distance due to the breakup process of ligaments near the nozzle. Results also prove that digital off-axis holography presented here is expected to realize the 3D viewing of the conical liquid sheet and statistical quantification of the droplet where primary and secondary breakup processes mainly occurred.

Unrelaxed tensile stress impacts on the instability of viscoelastic sheets with the gas velocity oscillation

A temporal instability analysis of a viscoelastic liquid sheet with unrelaxed tensile stresses in the oscillation gaseous flow field has been studied with the Floquet method in the present research. Effects of the oscillated amplitude and frequency of incoming gaseous flow on the instability features in the different instability regions are analyzed systematically. Results reveal that the unrelaxed tensile stress has a positive effect on stabilizing the liquid sheet, while the higher oscillation amplitude would promote the sheet breakup. Besides, it is indicated that when the stress tensor would be controlled by the viscoelastic effects, elastic impacts would suppress the breakup, while it shows an opposite impact when the stress tensor is dominated by the tensile stress. The existence of parametric instability regions is influenced by the oscillated and elastic parameters as well.