Satellite Droplets Research Articles

Comparative study on the spatial evolution of liquid jet under linear and nonlinear stability theories

In the injecting process of liquid jet, the disturbance wave on jet interface will grow continually, leading to the spatial development and atomization of liquid jet. Studying the spatial evolution of liquid jet will help to deepen the understanding of the mechanism of jet breakup and atomization. In this paper, based on the linear and nonlinear stability theories, the first-order and second-order dispersion equations describing the stability of liquid jet with cavitation bubbles in a coaxial swirling compressible airstream are built, respectively, and the dispersion equation and its solving method are verified by the data in the literature. On this basis, the developments of first-order and second-order disturbance are analyzed, and the spatial evolutions of liquid jet are compared under linear and nonlinear stability theories. The results show that the wavelength and amplitude of the second-order disturbance are much smaller than those of the first-order disturbance. The disturbance development on jet surface is mainly dominated by the development of the first-order disturbance along the axial direction. With the increasing of axial distance, the second-order disturbance gradually begins to play a role in the developing of disturbance. The role of second-order disturbance is mainly reflected in three aspects, i. e., obviously increasing the disturbance amplitude at wave crest, reducing the disturbance amplitude at wave trough (sometimes ups and downs occur), and changing the waveform to a certain degree. The dominant disturbance mode on jet surface will not change under two kinds of theories. By using the nonlinear stability theory, satellite droplets which are found on jet surface in experiments can be reflected, and the shape of main droplet changes obviously from the ellipsoid to sphere. Also, the change of dimensionless radius of liquid jet is greater by nonlinear stability theory than by linear stability theory, which indicates that the oscillation extent of jet surface increases due to considering the second-order disturbance. Therefore, compared with the linear stability theory, the nonlinear stability theory has the advantage that it considers the effects of high-order disturbance on the spatial evolution of liquid jet in addition to the first-order disturbance on jet surface. The nonlinear stability theory can predict the spatial development of liquid jet in more detail than the linear stability theory.

Fluid mechanics of additive manufacturing of metal objects by accretion of droplets – a survey

Paper presents a survey of principles of additive manufacturing of metal objects by accretion of molten metal droplets, focusing on fluid-mechanical problems that deserve being investigated. The main problem is slowness of manufacturing due to necessarily small size of added droplets. Increase of droplet repetition rate calls for basic research of the phenomena that take place inside and around the droplets: ballistics of their flight, internal flowfield with heat and mass transfer, oscillation of surfaces, and the ways to elimination of satellite droplets.

IR laser caused droplet evaporation on the hydrophobic surface

In this work, the characteristics of the water droplet evaporation on the hydrophobic surface was visually studied, which was actuated by the photothermal effect of an infrared laser with the wavelength of 1550nm. The interface temperature was measured by the infrared temperature measurement technique. The variations of the droplet geometrical parameters were captured, with which the evaporation rate was determined by the image process technique. Experimental results indicated that once the IR laser was applied, accompanying with the rapid increase of the interface temperature, the droplet evaporation was instantly induced. Generated vapor was condensed to form satellite droplets near the triple-phase contact line due to such a tiny local heating source that would not significantly change the surrounding temperature. After an increase in the contact radius and corresponding quick decrease of the droplet height, the original droplet gradually shrank. In this process, there existed a period with a relatively stable interface temperature and evaporation rate. In addition, the effects of the laser power and initial droplet volume were also explored. It was shown that both the interface temperature rising and average evaporation rates almost linearly increased with the laser power because more heat was generated by absorbing the light energy. Regarding the initial droplet volume, increasing the droplet volume firstly resulted in an increase in the interface temperature rising and average evaporation rates and then caused both of them to be reduced. The results obtained in this work are helpful for the future applications of droplet-based devices utilizing the photothermal effect.

Visualization of the evolution of charged droplet formation and jet transition in electrostatic atomization

A detailed experimental study on the evolution of charged droplet formation and jet transition from a capillary is reported. By means of high-speed microscopy, special attention has been paid to the dynamics of the liquid thread and satellite droplets in the dripping mode, and a method for calculating the surface charge on the satellite droplet is proposed. Jet transition behavior based on the electric Bond number has been visualized, droplet sizes and velocities are measured to obtain the ejection characteristic of the spray plume, and the charge and hydrodynamic relaxation are linked to give explanations for ejection dynamics with different properties. The results show that the relative length is very sensitive to the hydrodynamic relaxation time. The magnitude of the electric field strength dominates the behavior of coalescence and noncoalescence, with the charge relationship between the satellite droplet and the main droplet being clear for every noncoalescence movement. Ejection mode transitions mainly depend on the magnitude of the electric Bond number, and the meniscus dynamics is determined by the ratio of the charge relaxation time to the hydrodynamic relaxation time.

Dynamic nozzles for drop generators.

In this paper, a novel mechanism allowing greater control over the formation of droplets is presented. This is achieved via the use of a dynamic nozzle of adjustable diameter. It is demonstrated that, by using such a nozzle, it is possible to greatly modify the formation and breakup of the ligament behind the main drop, leading to an overall reduction in the number of satellite droplets. Furthermore, by adjusting the delay between the beginning of the forming of the drop and the start of the nozzle constriction, a greater control over both the number of satellites and the size of the main drop can be achieved. It is also shown that only a minimal reduction of the nozzle's effective diameter is required in order to exploit the positive effects of the technique presented here. This opens the possibility of incorporating the technique into current droplet generator systems, e.g., via the use of piezoelectric driven nozzles or other micro-mechanical actuation technology.

Dispersion and vaporization of a dilute spray of electrified droplets injected in a coflowing hot gas – Application to the vaporization chamber of a minicombustor

A numerical model of a dilute spray of electrically charged liquid droplets vaporizing in a hot gas is formulated based on a Eulerian description of the gas and Lagrangian tracking of the droplets. The model is used to simulate the dispersion and vaporization of a spray in a cylindrical chamber where the droplets are axially injected with a coflow of hot gas. The effects of the initial size of the droplets and of the gas-to-liquid mass flux and inlet temperature ratios are analyzed, and the conditions under which the droplets fully vaporize in the chamber without impacting on its walls are determined. The ranges of operation where these requirements are met widen when the flow rate of liquid is split into a number of sources and injected through different orifices, which also improves the uniformity of the temperature and vapor mass fraction distributions at the outlet of the chamber. The effects of satellite droplets and of an applied electric field that pushes the charged droplets in the direction in which they are injected are considered.

Splash behaviour and oily marine aerosol production by raindrops impacting oil slicks

The high-speed impact of a droplet on a bulk fluid at high Weber number (We) is not well understood but is relevant to the production of marine aerosol by raindrop impact on the sea surface. These splashes produce a subsurface cavity and a crown which closes into a bubble canopy, but a floating layer of immiscible oil, such as a crude oil slick, alters the splash dynamics. The effects of oil layer fluid properties and thickness, droplet size and impact speed are examined by high-speed visualization. Oil layer rupture and crown behaviour are classified by dimensional scaling. The subsurface cavity volume for impact on thick layers is shown to depend on the Reynolds number (Re), although canopy formation at highReintroduces a competingWeeffect since rapid canopy closure is found to retard cavity expansion. Time-resolved kinematic measurements show that thin crude oil slicks similarly alter crown closure and cavity growth. The size and spatial distributions of airborne droplets are examined using high-speed holographic microscopy. The droplets have a bimodal distribution with peaks at 50 and$225~{\rm\mu}\text{m}$and are clustered by size at different elevation angles. Small droplets ($50~{\rm\mu}\text{m}$) are ejected primarily at shallow angles, indicating production by splashing within the first$100~{\rm\mu}\text{s}$and by breakup of microligaments. Larger droplets ($225~{\rm\mu}\text{m}$) are found at steeper elevation angles, indicating later production by capillary instability acting on large ligaments protruding upward from the crown. Intermittent droplet release while the ligaments grow and sweep upward is thought to contribute to the size-dependent spatial ordering. Greater numbers of small droplets are produced at high elevation angles when a crude oil layer is present, indicating satellite droplet formation from ligament breakup. A crude oil layer also increases the target fluid Ohnesorge number, leading to creation of an intact ejecta sheet, which then ruptures to form aerosolized oil droplets.

The Influence of Constitutional Supercooling on the Distribution of Te-Particles in Melt-Grown CZT

A section of a vertical gradient freeze Cd0.9Zn0.1Te boule approximately 2100 mm3 with a planar area of 300 mm2 was prepared and examined using transmitted infrared microscopy at various magnifications to determine the three-dimensional spatial and size distributions of Te-particles over large longitudinal and radial length scales. Te-particle density distributions were determined as a function of longitudinal and radial positions in these strips and exhibited a multi-modal log-normal size density distribution that indicated a slight preference for increasing size with longitudinal growth time, while showing a pronounced cellular network structure. Higher magnification images revealed a typical Rayleigh-instability pearl string morphology with large and small satellite droplets. This study includes solidification experiments in small crucibles of 30:70 mixtures of Cd:Te performed over a wide range of cooling rates which clearly demonstrated a growth instability with Te-particle capture that is suggested to be responsible for one of the peaks in the size distribution using size discrimination visualization. The results are discussed with regard to a manifold Te-particle genesis history as Te-particle direct capture from melt–solid growth instabilities due to constitutional supercooling and as Te-particle formation from the breakup of Te-ribbons via a Rayleigh–Plateau instability.

Numerical and experimental investigation of induced flow and droplet–droplet interactions in a liquid spray

An Euler–Lagrange model is presented that describes the dynamics of liquid droplets emerging from a high-pressure spray nozzle in a relatively large volume (of the order of almost a cubic meter). In the model, the gas phase is treated as continuum, solved on an Eulerian grid, and the liquid phase is treated as a dispersed phase, solved in a Lagrangian fashion, with interphase coupling through state-of-the-art drag relations obtained from direct numerical simulations. The droplets are introduced into the system at high velocities, leading to a turbulent self-induced gas flow which is solved using large eddy simulation. Despite the relatively low liquid volume fraction in the spray, the number density of droplets at the nozzle is still more than 1010m−3, which is why we employ a highly efficient stochastic Direct Simulation Monte Carlo approach to track collisions between droplets. The droplet collision frequency is calculated on the basis of local droplet number density, droplet size and relative velocities of neighbouring droplets within a dynamically adapting searching scope, as described in Pawar et al. (2014. Chem. Eng. Sci. 105, 132–142). We use known correlations from literature to determine the outcome of a binary droplet collision, which depending on characteristic dimensionless numbers can be coalescence, bouncing or, for high velocity impacts, stretching or reflexive separation leading to formation of satellite droplets. Our simulation model is compared with droplet velocities and size distributions obtained from phase Doppler interferometry experiments on an industrial scale hollow-cone pressure swirl nozzle spray. We find semi-quantitative agreement for spray characteristics such as the axial and radial spray velocity, spray jet width, and the dependence of the droplet size distribution on position within the spray. The simulation model enables us to study the relative importance of different droplet collision events occurring in the spray volume.

Effects of gravity on the breakup and instability of a viscous compound jet

Encapsulated droplet formation resulting from the rupture and breakup of a compound liquid thread has numerous applications in industry. Understanding the process through which a compound thread will breakup and form droplets of a desired size is thus of great relevance and may help in developing refined experimental techniques. In this paper, we investigate the breakup and the instability of a viscous compound thread falling under gravity. The governing equations are formulated and a reduced one-dimensional set of equations is obtained using an asymptotic approach. The steady-state solutions, which are dependent on the axial distance along the thread, are determined using a modified Newton’s method. Thereafter, we present a linear temporal instability analysis to study the effects of how key parameters affect the structure and onset of rupture. Finally, we investigate the nonlinear behaviour of waves along the free surface through using a finite difference scheme based on the Lax–Wendroff method and we obtain the breakup times and the sizes of main and satellite droplets.

Generation of inkjet drop of particulate gel

The generation of inkjet drops of colloidal gels is studied experimentally. Particle suspensions are prepared by dispersing spherical polystyrene particles of 620 nm in the 1:1 mixture of deionized water and ethylene glycol. The gels are prepared by adding polyethylene oxide to the suspensions by inducing the depletion interaction between particles. It is demonstrated that inkjet drops can be generated by using the colloidal gels. It is found that the ligament extended from the inkjet nozzle is stabilized so that the drop can be generated without satellite droplets behind the main drop and the velocity of the gel drop is faster than that of the polymer solution at the same concentration. The gel drop generation characteristics are found to be sensitive to input voltage.

Time-resolved mixing and flow-field measurements during droplet formation in a flow-focusing junction

Highly monodispersed emulsions can be produced in microfluidic flow-focusing junctions (Anna et al 2003 Appl. Phys. Lett. 82 364–6, Baroud et al 2010 Lab Chip 10 2032–45). This is the reason why many industrial processes in the medical industry among others are based on droplet manipulation and involve at some point a step of dripping within a junction. However, only a few studies have focused on the flow field inside and outside the droplet, even though it is a necessary step for understanding the physical mechanism involved and for modeling the droplet formation process. Water-in-oil emulsions are produced in flow-focusing junctions of square cross sections. The fluids constituting the emulsion are (i) a 5.0 mPa·s silicon oil for the oil phase and (ii) distilled water containing 2.0 wt% of sodium dodecyl sulfate surfactant for the aqueous phase. Time-resolved shadow particle images are acquired using a microscale particle image velocimetry (µPIV) system and flow fields are calculated using an adaptive PIV algorithm in combination with dynamic masking. Inside the microchannel and in the permanent regime, the droplet has an internal circulation that has been well established by Sarrazin et al (AICHE J. 52 4061–70). But during the formation of a droplet in a flow-focusing junction, the flow field is not so well known, and the circulation in the finger flows forward along the sides and returns along the center. The mechanism can be described in terms of four distinct steps: droplet growth, necking, rupture, and recoil. The liquid expelled from the neck just before rupture is also well observed. The flow field and mixing are measured in detail during a complete cycle of formation of a main droplet and satellite droplets using high-speed imaging. This allows us to develop a better understanding of the different forces that are present and of the physical mechanism of droplet formation.

Plethora of transitions during breakup of liquid filaments

Thinning and breakup of liquid filaments are central to dripping of leaky faucets, inkjet drop formation, and raindrop fragmentation. As the filament radius decreases, curvature and capillary pressure, both inversely proportional to radius, increase and fluid is expelled with increasing velocity from the neck. As the neck radius vanishes, the governing equations become singular and the filament breaks. In slightly viscous liquids, thinning initially occurs in an inertial regime where inertial and capillary forces balance. By contrast, in highly viscous liquids, initial thinning occurs in a viscous regime where viscous and capillary forces balance. As the filament thins, viscous forces in the former case and inertial forces in the latter become important, and theory shows that the filament approaches breakup in the final inertial-viscous regime where all three forces balance. However, previous simulations and experiments reveal that transition from an initial to the final regime either occurs at a value of filament radius well below that predicted by theory or is not observed. Here, we perform new simulations and experiments, and show that a thinning filament unexpectedly passes through a number of intermediate transient regimes, thereby delaying onset of the inertial-viscous regime. The new findings have practical implications regarding formation of undesirable satellite droplets and also raise the question as to whether similar dynamical transitions arise in other free-surface flows such as coalescence that also exhibit singularities.

Measuring droplet size distributions from overlapping interferometric particle images.

Interferometric particle imaging provides a simple way to measure the probability density function (PDF) of droplet sizes from out-focus images. The optical setup is straightforward, but the interpretation of the data is a problem when particle images overlap. We propose a new way to analyze the images. The emphasis is not on a precise identification of droplets, but on obtaining a good estimate of the PDF of droplet sizes in the case of overlapping particle images. The algorithm is tested using synthetic and experimental data. We next use these methods to measure the PDF of droplet sizes produced by spinning disk aerosol generators. The mean primary droplet diameter agrees with predictions from the literature, but we find a broad distribution of satellite droplet sizes.

Selected papers from the 3rd European Conference on Microfluidics: µFlu’12

in microsystems, and microflow visualization. Two special sessions have been devoted to industrial applications of microfluidics and to nanofluidics. This special issue of Microsystem Technologies focuses the attention of the readers on a selection of nine works representative of the research advances in microfluidics presented during the Conference. Carrier et al. experimentally analyzed the mechanism of satellite droplets formation in the wake of the main droplet generated in a flow-focusing junction, with Newtonian or non-Newtonian liquids. By confocal laser scanning microscopy, Ben Hassan et al. experimentally observed the fouling of a filter due to the accumulation of microparticles on a membrane surface, and developed a numerical model able to predict the cake growth during the filtration. The paper of Kong and Nguyen reports a technique for the fabrication of three-dimensional multilayer liquid-metal microcoils by lamination of dry adhesive films; these microcoils can be used for magnetic resonance relaxometry (MRR) measurement in a lab-ona-chip platform. Samouda et al. developed a new setup for the experimental investigation of gaseous microflows by molecular tagging velocimetry—MTV—and discussed its possible use to obtain a direct measurement of velocity slip at the walls in rarefied regimes. Cao et al. designed different tools for microfluidic droplet processing, including an automated “gradient take-up tool” for the generation of segment sequences with gradually changing composition of the individual droplets. Wibel et al. studied a novel microstructured evaporator geometry consisting of curved, instead of straight, microchannels and demonstrated that strong centrifugal forces led to an enhancement of the evaporation efficiency. Calaon et al. evaluated the capability of producing with high volume lab-on-chip devices through injection molding. The Third European Conference on Microfluidics (μFlu’12) was held in Heidelberg, Germany, in December 8–10, 2012, under the sponsorship of the Hydrotechnic Society of France (SHF), the Alma Mater Studiorum Universita di Bologna, the University of Toulouse and the Karlsruhe Institute of Technology. This event has gathered 252 participants from 33 countries. During three days, 174 communications have been presented in 16 thematic sessions including liquid microflows, gas microflows, microsensors and in-situ analytics, fluidic microactuators and micromixing, microfabrication techniques for microfluidic systems, convective micro heat transfer, micro chemical engineering, lab-on-a-chip, electrokinetic microflows, microdroplets management, microflows in biological systems and bioengineering, multi-phase flows

Aerodynamic Effects in Industrial Inkjet Printing

The quality achieved by inkjet printing is limited by various factors, including the nozzle–substrate throw distance, the substrate velocity, and the occurrence of satellite droplets. Under certain conditions, particularly for large throw distances, unacceptable inaccuracies and defects in drop placement occur. In this paper, a new technique based on high-speed imaging and laser optics is presented that allows the visualization of air currents and droplet movement patterns beneath and in the proximity of a printhead and a moving substrate. The images obtained with this technique provide better temporal and spatial resolution than those obtained in previous studies. Tests with two different commercial printheads show that the entrained airflow depends on the interaction with the stream of printed droplets. The formation of unsteady eddies, particularly between nozzle rows, can result in serious errors in drop placement.

Head-on collision of electrically charged droplets

Abstract Interaction between two identical charged droplets is investigated numerically. In the first part, the mechanism of Coulomb attraction between two conducting droplets is investigated. Numerical simulation shows that two conducting droplets carrying charges of the same polarity under some conditions may be electrically attracted. The second part of the study concerns the collision dynamics of two identical dielectric charged droplets. At low Weber numbers, two droplets carrying charges of the same polarity can repel each other. As Weber number increases, the drop collision leads to their coalescence. With Weber number further increased, satellite droplets are formed.

Role of polymer concentration and molecular weight on the rebounding behaviors of polymer solution droplet impacting on hydrophobic surfaces

The impacting and rebounding behaviors of droplets containing polyethylene oxide (PEO) on Teflon-coated hydrophobic surface are investigated using a high-speed imaging system. Maximum spreading of droplets are examined experimentally by varying the concentration of polymer solution. During the spreading of droplets, no significant energy dissipation is found in the PEO solution droplets tested in this study. Energy dissipation during the retraction of contact line increases with the increase in the concentration and molecular weight of the polymer. Molecular weight does not show any noticeable effect when the concentration of the polymer solution is lower than 0.03 wt%. Its effect increases when the concentration is higher than 0.03 wt%, and the energy dissipation increases (threefold) at 0.05 wt% concentration. In addition, the residue composed of small satellite droplets is optically observed. The retraction velocity of contact line is decreased on the area of residue, which adds friction on the surface. A semiempirical model of energy balance equation is derived to estimate the rebounding tendency of a polymer solution droplet as a function of maximum spreading factor, retraction velocity, and reduced concentration. The friction coefficient of the polymer solution shows a linear relationship with reduced concentration.

Nebulization of water/glycerol droplets generated by ZnO/Si surface acoustic wave devices

Efficient nebulization of liquid sessile droplets (water and water/glycerol mixtures) was investigated using standing waves generated using ZnO/Si surface acoustic wave (SAW) devices under different RF powers, frequencies and liquid viscosity (varied glycol concentrations in water). At such high RF powers, there are strong competitions between vertical jetting and nebulization. At lower SAW frequencies of 12.3 and 23.37 MHz, significant capillary waves and large satellite droplets were generated before nebulization could be observed. At frequencies between 23.37 and 37.2 MHz, spreading, displacement or occasionally jetting of the parent sessile droplet was frequently observed before a significant nebulization occurred. When the SAW frequencies were increased from 44.44 to 63.3 MHz, the minimum RF power to initiate droplet nebulization was found to increase significantly, and jetting of the parent droplet before nebulization became significant, although the average size of the nebulized particles and ejected satellite droplets appeared to decrease with an increase in frequency. With the increase of glycerol concentration in the test sessile droplets (or increase in liquid viscosity), nebulization became difficult due to the increased SAW damping rate inside the liquid. Acoustic heating effects were characterized to be insignificant and did not show apparent contributions to the nebulization process due to silicon substrate’s natural effect as an effective heat sink and the employment of a metallic holder beneath the ZnO/Si SAW device substrates.

Electric field-assisted droplet formation using piezoactuation-based drop-on-demand inkjet printing

Droplets with diameters from a few to hundreds of micrometers have found increasing applications in various fields. For inkjet printing, there is always a great need to control and reduce the droplet size for a given nozzle diameter and print viscous fluids by avoiding clogging. This study investigates the electric field-assisted droplet formation process under piezoactuation-based drop-on-demand (DOD) inkjet printing. For better control of droplet monodispersity, the Taylor cone is intentionally suppressed to avoid undesirable satellite droplets. The droplet formation process of deionized water is investigated, and some main conclusions are drawn as follows: (1) with an increase of applied voltage, the droplet velocity increases and the droplet size decreases, (2) the pinch-off location may be different depending on the applied voltage; and (3) the combination effect of the electric field and meniscus oscillation can be utilized to significantly reduce the droplet diameter to less than one-fifth of the orifice diameter. The electric field also demonstrates its capability in facilitating the DOD inkjet printing of high-concentration cell-alginate suspensions.