Satellite Droplets Research Articles

Liquid transfer between two separating plates for micro-gravure-offset printing

Experimental investigations of the liquid transfer between two separating plates have been carried out, with the aim of increasing the ink transfer ratio in micro-gravure-offset printing. A sessile droplet is divided into two by moving one plate vertically with respect to a fixed plate. The surface contact angles of the sessile droplet on the two plates were of particular interest in this study because the volume ratio of the two droplets varies with the contact angles. Various methods for controlling the surface contact angle, including chemical treatment, plasma surface modification and electrowetting-on-dielectric were assessed. Image analysis of the droplets was carried out to estimate the surface contact angles and to measure the volumes of the droplets. The liquid transfer process and related phenomena, such as satellite droplet generation and the variation in the contact areas between the droplets and the plates, were observed. The experimental results help us to determine the optimal surface contact angles of the plate cylinder, blanket cylinder and substrate for micro-gravure-offset printing.

A numerical investigation of central binary collision of droplets

The paper presents a numerical investigation of the central collision of two equal-sized droplets in a gaseous phase. The investigation is based on the numerical solution of the Navier–Stokes equations in their axi-symmetric form using the finite volume technique. The Volume of Fluid Method (V.O.F) is employed for tracking the liquid–gas interface. An adaptive local grid refinement technique developed recently is used in order to increase the resolution around the interface. By using two V.O.F indicator functions the identity of each droplet is preserved and can be detected after droplet contact until coalescence. The results are compared with available experimental data and provide a very detailed picture of the collision process, the ligament formation and dimensions, the pinch off mechanism and the creation of the satellite droplet. The conversion of the droplet’s kinetic energy to the surface energy and vise versa, the energy viscous dissipation as well as the maximum deformation of the droplets are also evaluated.

Superhydrophobicity of Biological and Technical Surfaces under Moisture Condensation: Stability in Relation to Surface Structure

The stability of superhydrophobic properties of eight plants and four technical surfaces in respect to water condensation has been compared. Contact and sliding angles were measured after application of water drops of ambient temperature (20 degrees C) onto cooled surfaces. Water evaporating from the drops condensed, due to the temperature difference between the drops and the surface, on the cooled samples, forming "satellite droplets" in the vicinity of the drops. Surface cooling to 15, 10, and 5 degrees C showed a gradual decrease of superhydrophobicity. The decrease was dependent on the specific surface architecture of the sample. The least decrease was found on hierarchically structured surfaces with a combination of a coarse microstructure and submicrometer-sized structures, similar to that of the Lotus leaf. Control experiments with glycerol droplets, which show no evaporation, and thus no condensation, were carried out to verify that the effects with water were caused by condensation from the drop (secondary condensation). Furthermore, the superhydrophobic properties after condensation on cooled surfaces from a humid environment for 10 min were examined. After this period, the surfaces were covered with spherical water droplets, but most samples retained their superhydrophobicity. Again, the best stability of the water-repellent properties was found on hierarchically structured surfaces similar to that of the Lotus leaf.

Numerical Simulation of Unsteady Flows and Shape Oscillations in Liquid Droplets Induced by Deployment Needle Retraction

Retractable opposed needles are often used in reduced-gravity droplet combustion experiments to deploy droplets prior to ignition. Needle retraction induces droplet shape oscillations and internal flows that can have important effects on subsequent droplet behaviors. In the present paper, the unsteady flows and droplet shape oscillations associated with deployment needle retraction are investigated using the commercial CFD software package Fluent. A volume-of-fluid method with a second-order upwind scheme and a dual time stepping solver is employed to solve the conservation equations in 2-d and 3-d simulations of droplets prior to ignition. A moving-mesh method is employed to model needle movements. Calculations indicate that rapid needle retraction causes ligament formation between a droplet and a needle, with ligament breakage sometimes resulting in the formation of satellite droplets. Needle retraction also induces droplet shape oscillations that rapidly decay, though significant internal flows are predicted to remain within droplets even after droplet shape oscillations have damped to low levels. The calculations indicate that the initial needle spacing can have important effects on droplet shape oscillations and internal flow characteristics. Comparison of model predictions and experimental data is favorable.

A collapsing bubble-induced microinjector: an experimental study

In this study, a new drop-on-demand actuation mechanism, which uses an oscillating bubble as actuator is proposed and its feasibility is investigated via the consideration of two important design parameters, namely, bubble distance to free surface and nozzle dimension. The droplet ejection process captured using high-speed photography technique shows that such an actuation mechanism has interesting features and perhaps some advantages over the conventional ones (thermal bubble, piezoelectric, etc.) employed in inkjet printers such as the ejection of a droplet free of satellite droplets and others.

Fabrication of LCD color filter using laser-induced thermal spray printing

The color filter of the LCD panel is fabricated using the laser induced thermal spray printing (LITSP) method, which ejects the ink droplets from the blind-holes of the donor plate to the substrate by the bubble pressure due to rapid laser heating. The compositions of the dye and pigment inks are determined experimentally, which consists of 5% colorant, 24% epoxy, 6% hardener, 5% xylene, 30% n-butanol, and 30% BCA. The effects of the laser power and travel speed on the quality of the print pattern are analyzed experimentally. The phenomena of ink ejection are investigated numerically through thermal and fluid dynamic analysis. The ink droplet is transferred successfully when the top surface of the hole in the donor plate is heated above 122 °C for longer than 10 ms. The quality of the print pattern is enhanced by employing the laser- and fume-masks, which provide the localized heating on the top surface of the hole and remove the satellite droplets and fume.

Simulation of liquid transfer between separating walls for modeling micro-gravure-offset printing

A numerical study of the liquid transfer processes that occur during micro-gravure-offset printing is carried out. Specifically, liquid transfer between two parallel separating plates and between a trapezoidal cavity and an upward moving plate are simulated, as models of the printing of ink from the offset pad onto the substrate and the picking up of ink from the gravure plate by the offset pad, respectively. During the liquid transfer between two parallel plates, the stretching, breaking and recoil of the liquid are illustrated, and the generation of a satellite droplet is observed. The influences of the separation velocity, liquid viscosity, surface tension, gravity force, and contact angles on the liquid transfer are estimated. For the transfer of liquid from the cavity to the upward moving plate, the findings indicate that the process can be divided into three stages: (1) a whole stretching stage; (2) a central stretching, breakup and recoil stage; and (3) an equilibrium stage. The final width of transferred liquid is closely related to the contact angle at the upper plate, while the cut height is mainly affected by the contact angle at the cavity side wall. The effects of the initial distance and cavity shape are also discussed.

Non-linear waves along a rotating non-Newtonian liquid jet

A liquid jet may be curved due to the influence of wind or gravity but more commonly, as is the case in industrial prilling, due to the rotation of the container from which it emerges. In prilling, pellets are manufactured by utilising the breakup of a curved liquid jet, and liquids commonly used in prilling are non-Newtonian. In this paper we investigate the influence of rotation, surface tension and viscosity on the breakup of a spiralling slender power-law liquid jet with applications to industrial prilling. The non-linear evolution equations for the jet radius and axial velocity are solved numerically using the method of finite differences. Numerical simulations allow us to explore the effects of changing the amplitude (or alternatively the frequency) of initial disturbances on breakup lengths and the size of main and satellite droplets.

The effect of surfactants on the instability of a rotating liquid jet

It has long been known that the presence of surfactants on the free surface of a liquid jet can create surface tension gradients along the interface. The resulting formation of tangential stresses along the surface lead to Marangoni type flows and greatly affect the resulting dynamics of rupture. In this way surfactants can be used to manipulate the breakup of a liquid jet and control the size of droplets produced. In this paper we investigate the effects of insoluble surfactants on the breakup of rotating liquid jets with applications to industrial prilling. Using a long wavelength approximation we reduce the governing equations into a set of one-dimensional equations. We use an asymptotic theory to find steady solutions and then carry out a linear instability analysis on these solutions. We show that steady state centreline solutions are independent of viscosity to leading order and that the most unstable wavenumber and growth rate of disturbances decrease as the effectiveness of surfactants is increased. We also numerically solve these equations using a finite difference scheme to investigate the effects of changing the initial surfactant concentration and other fluid parameters. Our results show that differences in breakup lengths between rotating surfactant-laden jets and surfactant-free jets increase with the rate of rotation. Moreover, we find that satellite droplet sizes decrease as the rate of rotation is decreased with the effect of surfactants amplifying the reduction in sizes. Furthermore, the presence of surfactants at fixed rotation rates is shown to produce larger main droplets at low disturbance wavenumbers whilst satellite droplets are smaller for moderate disturbance wavenumbers κ ≈ 0.7 .

Numerical modelling of sequential droplet impingements

During the process of thermal spray coating, molten powders are sprayed and deposited on substrates to generate protective coatings. It is essential to have a clear understanding of the physics of droplet impingement on the surface of substrates for better control of the generation of splats and the structure of coating. A numerical model is developed in this paper to simulate the dynamics of transient flow during the impingement process, including spreading, break-up, air entrapment and solidification. The computation is achieved using the technique of volume of fluid surface tracking within a fixed Eulerian structured mesh. The three-dimensional simulation is able to accurately give a demonstration of dynamic flow patterns such as the generation of fingers, satellite droplets and pores during impingement. The numerical model is validated with experimental data from the tin droplet measurement and excellent agreement is found between the simulation and the experiment.

A Level-Set Method for Simulation of a Thermal Inkjet Process

A numerical approach is presented for computing a thermal inkjet process, in which bubble growth and collapse acts as a driving mechanism for ink droplet ejection. The liquid–vapor and liquid–air interfaces are tracked by a level-set method which is modified to include the effect of phase change at the liquid–vapor interface and is extended to treat the contact angle condition at an immersed solid surface. The compressibility effect of a bubble is also included in the analysis to account for the high vapor pressure caused by instantaneous bubble nucleation. The whole process of the thermal inkjet, including jet breaking, satellite droplet formation, and ink refill, as well as bubble growth and collapse, is simulated without employing a simplified bubble growth model.

Droplet generation from pulsed micro-jets

This paper presents an experimental study on the fluid dynamics of pulsed micro-jets (orifice diameter 20 μm), including jet breakup and droplet formation. The pulsed micro-jets were generated using a piezoelectric inkjet printhead with varied working voltages and ejection frequencies. For low ejection frequencies, meniscus had time to relax before the next pulse was applied. For every single pulse, fluid was ejected in the form of free liquid ligaments, which eventually contracted into droplets. The maximum length of ligaments increased with the working voltage. Satellite droplets were observed when high working voltage was applied. For high ejection frequencies, a periodically perturbed jet was formed, and droplets were generated from the jet through pinch-off. After pinch-off, liquid threads between droplets contracted into satellite droplets, which coalesced with main droplets. The jet length was longer than the maximum ligament length of the low-frequency ejection. The jetting process with high ejection frequency was found to consist of an undesired startup stage followed by a repeatable stage. Droplets with larger size and higher velocity were generated in the startup stage, and the startup stage lasted longer for a higher working voltage.

Generation of Monodisperse Micron‐Sized Droplets using Free Adjustable Signals

AbstractThis paper describes the generation of small water droplets in the size range down to a few microns. Commercially available inkjet printing devices are not suitable for producing such droplets since they produce satellite droplets. Furthermore, standard drop‐on‐demand devices are normally restricted to the generation of droplets with the same size as the orifice diameter. Using a new and more sophisticated computer‐based signal generation system, smaller‐sized droplets can be generated from the same orifice. A key feature of the design is the generation of freely definable pulses. This enables the generation of acoustic modes within the fluid of the droplet generator, which leads to the generation of droplets without satellites. Only very few pulse forms enable the generation of suitable acoustic modes. Therefore, it is necessary to look for the specific pulse corresponding to the chosen droplet generator. Flexible pulse form generation appears to be more suitable than simple pulse forms for the generation of such droplets.

Droplet formation from a pulsed vibrating micro-nozzle

Micro-droplet formation from a passive vibrating micro-nozzle driven by a pulsed pressure wave is numerically simulated. The micro-nozzle is formed from an orifice in a thin walled plate that is allowed to freely vibrate due to the pressure loading on the plate. The analysis couples the fluid flow from the nozzle and the resultant droplet formation with the nozzle vibration calculated using large deflection theory. The problem is made nondimensional based on the capillary parameters of time, velocity and pressure. The applied pressure and nozzle material properties are varied to alter the vibration characteristics of the orifice plate used to form the nozzle. The initiation of drop formation is found to coincide with a threshold impulse input, defined as the product of the pressure magnitude and the pulse duration. Increasing the impulse can result in multiple satellite droplet formation, but the effect on the primary droplet size is minor. The vibration of the nozzle only weakly influences the droplet break-off time, but is shown to significantly affect the droplet volume, shape, and satellite droplet formation.

Effects of Pulse Voltage on the Droplet Formation of Alcohol and Ethylene Glycol in a Piezoelectric Inkjet Printing Process with Bipolar Pulse

The dynamics of droplet formation of liquid in a piezoelectric inkjet printing process with bipolar pulse and drop-on-demand (DOD) mode is investigated in this study. Two liquids with different viscosities and surface tension coefficients; alcohol and ethylene glycol, are studied. The effects of pulse voltage on the droplet formation are also examined. A piezoelectric actuated inkjet printhead with a nozzle orifice of 30 mm in diameter is employed to conduct the investigations at room temperature (25 � C). The complex morphologies of the droplets during their formation, which include ejection and stretching of liquid, contraction of liquid column, pinch-off of liquid column from nozzle exit, breakup of liquid column into primary droplet and possible satellites, and combination of primary drop and satellites, are demonstrated. The droplet size is in the range of 23–37 mm. The investigations also show a workable pulse voltage range; between 28 and 40 volts, exists for the droplets to be smoothly generated and ejected for alcohol where viscosity and surface tension coefficient are smaller. The range is between 30 and 50 volts for ethylene glycol. Within this workable voltage range, one single droplet for each pulse can be achieved with lower voltage. For the intermediate voltage, two droplets are generated initially and collide into one during the flying stage. For the higher voltage, multiple droplets are formed without recombination. It is also found that the velocities of the main droplet and satellite droplet in the different voltage ranges are responsible for whether the multiple initial droplets can be recombined. [doi:10.2320/matertrans.MRA2007217]

Octopus‐shaped instabilities of evaporating drops

AbstractWe report on instabilities during spreading of volatile liquids, with emphasis on the novel instability observed when isopropyl alcohol (IPA) is deposited on a monocrystaline Si wafer. This instability is characterized by emission of drops ahead of the expanding front, with each drop followed by smaller, satellite droplets, forming the structures which we nickname ‘octopi’ due to their appearance. A less volatile liquid, or a substrate of larger heat conductivity, suppress this instability. We have formulated a theoretical model that reproduces the main features of the experiment. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Ultra-high-resolution monolithic thermal bubble inkjet print head

A monolithic inkjet print head, fabricated with silicon micromachining technology and capable of generating microscale liquid droplets, is developed and shown to function successfully. The print head uses a dense array of thermal bubble inkjet devices, made on a single silicon wafer. Each device is made of a Pt heater stack, a small, shallow fluid chamber, and a refilling channel formed by a Ge-sacrificial etching process, a deep-etched through-wafer feeding hole, and a micron-scale nozzle opened in a thin nitride membrane by plasma etching. Experimental results with a high resolution video imaging system show that this print head is capable of generating water droplets as small as 3 µm in diameter (0.014 pL), about 1/70th the volume of the droplets produced by existing inkjet systems. The printing process is also found to be stable, uniform in droplet size and velocity, and free of satellite droplets at optimum operation conditions. At small distances between the print head and substrate, droplet spreading is also small. This print head is then a capable tool for ultra-high-resolution inkjet printing and can be used in research areas where delivery of micron-scale fluid droplets is desired.

Influence of space charge on the scale-up of multiplexed electrosprays

The effect of the space charge of the homopolarly charged droplets in a system of multiplexed electrosprays is investigated. The system consists of a microfabricated liquid distributor with multiple electrospray sources held at a high voltage, a nearby extractor electrode plate held at an intermediate voltage, and a grounded electrode further downstream. The system is very compact, with a spatial density as large as 250 sources / cm 2 . Experimentally, we observed that the system performance was limited by the occurrence of path reversal of the satellite droplets, accumulating on the extractor electrode, flooding it and ultimately causing the electrospray to cease operation. To prevent this phenomenon, hereafter referred to as satellite trapping, and “sweep” the satellites downstream, the driving field between the extractor electrode and the ground must be increased. The system behavior was modeled by a simple line-of-charge approximation, which was validated by a more detailed Lagrangian model and by experiments on an individual electrospray. Subsequently, the line-of-charge model was extended to the multiplexed system yielding a satisfactory comparison between the computed minimum driving field that is necessary to prevent satellite path reversal and experimental values. Additional analytical approximations of the multilines-of-charge model yielded a scaling law showing the dependence of the space charge on: (i) the primary droplet residence time, (ii) the current emitted per unit area, and (iii) a dimensionless parameter, α , that is the ratio of the distance between the extractor electrode and the ground electrode to the distance between neighboring nozzles. As a result, guidelines for the design of multiplexed electrosprays are established on a fundamental basis, without the need for costly and empirical microfabrication prototyping.

Role of Dimensionality and Axisymmetry in Fluid Pinch-Off and Coalescence

We present data on the pinch-off and coalescence of thin liquid alkane lenses floating on water. Pinch-off in quasi-2D lenses is distinctly different from pinch-off in axisymmetric 3D drops and involves a cascade of satellite droplets which extends to micron length scales. In contrast, coalescence of lenses is qualitatively similar to coalescence of 3D drops. Coalescence is predicted to involve entrainment of the exterior fluid as the droplets merge. This reentrant folding is obscured in 3D droplets but is clearly visible in coalescence of thin lenses.

Numerical study on bouncing and separation collision between two droplets considering the collision-induced breakup

The main purpose of the present study is to perform numerical study on bouncing and separation collision between two droplets considering the collision-induced breakup. In this study, the collision model proposed in our previous study is used for simulation of collision-induced breakup, and we modify this model to consider the effect of liquid property on the behavior of droplet-droplet collision. This collision model is based on the conservation laws for mass, momentum, and energy between before and after collision and provides several formulae for post-collision characteristics of colliding droplets and satellite droplets. Improving the accuracy of the model, in this study, appreciate criterion for bouncing collision is added and dissipation energy during collision process is newly modeled. To validate the new model, numerical calculations are performed and their results are compared with experimental data published earlier for binary collisions of water, propanol, and tetradecane droplets. It is found from the results that the new model shows good agreement with experimental data for the number of satellite droplets. It can be also shown that the predicted mean diameter by the new model decrease with increasing the Weber number because of the collisioninduced breakup, whereas the O’Rourke model fails to predict the size reduction via the binary droplet collision.