Satellite Droplets Research Articles

Simulation & modelling of dilute solutions in drop-on-demand inkjet printing: a review

This review is about the most important matters for advancing inkjet printing with a focus on piezoelectric droplet on demand (DOD) inkjet thin-film devices. The Nano material compounds can be incorporated into a polymeric matrix and deposited by piezoelectric inkjet printing. Current problems in advanced printers are discussed as embodied in liquid filament breakup along with satellite droplet formation and reduction in droplet sizes. Various model that predicts the printability of dilute, mono disperse polymer solutions in drop-on-demand “DOD” inkjet printing have been discussed. For satellite droplets, it is exhibited which liquid filament break-up treatment can be predicted via using a combination of two pi-numbers, including the Weber number. The layer was printed over other printed layers including electrodes composed of the conductive polymers and also several polymers. It has been discussed, some polymer materials are suitable for deposition and curing at low to moderate temperatures and atmospheric pressure, allowing for the use of polymers or paper as supportive substrates for the devices, and greatly facilitating the fabrication process. Furthermore, through this review, it has been discussed scaling analyses for designing and operating of inkjet heads. Because of droplet sizes from inkjet nozzles are typically on the order of nozzle dimensions, a numerical simulation is shown for explaining how to reduce droplet sizes through employing a novel input waveform impressed on the inkjet-head liquid inflow without changing the nozzle geometries. Regardless of their any less performance, inkjet printer head as a technique for the mentioned devices presents many advantages, the most notable of which are quickly fabricating and patterning, substrate flexibilities, avoidance of material wastage via applying “DoD” technologies.

Simulation and Experiment on Droplet Volume for the Needle-Type Piezoelectric Jetting Dispenser.

The needle-type piezoelectric jetting dispenser is widely applied in the microelectronics packaging field, and it is important to control the droplet size to ensure that the droplet jetting process is successful. In this study, we analyzed the influences of system parameters, such as air pressure, nozzle size, needle strokes, and liquid properties, on droplet size and morphology by considering the droplet formation and separation process through a numerical simulation. An experimental platform was also designed to verify the reliability of the simulations and further analyze strategies for controlling the droplet size. We found that the droplet volume can be increased with an increase in air pressure, needle strokes, and nozzle size until the flow-stream or satellite droplets appear. On the other hand, very small values of these parameters will lead to adhesion or micro-dots. A large nozzle and needle displacement should be chosen for the high-viscosity liquid in order to produce normal droplets. The results also show the recommended ranges of parameter values and suitable droplet volumes for liquids with different viscosities, and these findings can be used to guide the droplet volume control process for needle-type jetting dispensers.

Characteristics of drop-on-demand droplet jetting with effect of altered geometry of printhead nozzle

As a precision micro-electromechanical actuator, the geometry of drop-on-demand (DoD) printhead nozzle could be altered resulting from the accumulated manufacturing tolerances (AMT) and partial nozzle clogging (PNC) which largely influences the droplet jetting dynamics. To explore the effect of altered nozzle geometry on the DoD droplet formation characteristics, a three-dimensional (3D) multi-relaxation-time (MRT) lattice Boltzmann (LB) model coupled with nonideal nozzle plate wettability is presented to handle the complex droplet jetting process. For typical Z=11.57, with the hydrophobic nozzle plate, the velocities of final droplet are increased with the nozzle volume decreasing θN=49° and PNC. The non-ideal hydrophilic nozzle plate could eliminate the effect of altered nozzle geometry which exhibits the identical trajectories of droplet jetting. As Z number increasing to Z=19.8, the overall velocities of liquid filaments and resulting droplets are increased considerably. However, the effect of AMT decreases the velocity of filament tail and the recombination of satellite and main droplets could not occur for θN=49° which is undesirable for DoD inkjet printing. For case of PNC, the leftward deviation of recombined droplet is increased for the non-ideal hydrophilic nozzle plate and large Z number which greatly deteriorates the droplet jetting directionality.

Jetting performance of two lactam compounds in reactive dye solution

Digital inkjet printing technology has great significance in textiles. In this paper, influences of two additives on the dye aggregation and jetting performance of reactive dye solutions are investigated, and the mechanism is analyzed. We explored the physical properties and jetting performance of reactive dye solutions with 2-pyrrolidone (PY) or N-methyl pyrrolidone (NMP) by testing UV–visible absorption spectrum, rheological properties, surface tension, and observing the droplet formation. The results showed that PY and NMP could inhibit the dye aggregation. Moreover, two lactam compounds decreased the surface tension and increased the viscosity of dye solutions by the interaction between lactam compounds and reactive dye. PY and NMP could reduce the generation of satellite droplets of dye solutions. In addition, 5% PY/Red 218 and 5% NMP/Red 218 solutions produced better color images on cotton fabrics.

Experimental study of the Ohnesorge number effect on the size of droplets formed as a result of the jet capillary breakup

The theoretically calculated dependence of the sizes of the main and satellite droplets on the dimensionless wave number of the perturbation of the surface of the Newtonian fluid jet is proved experimentally. It is also shown that an increase in the fluid viscosity significantly changes the dynamics of development of capillary waves in the jet and the mechanism of formation of satellite droplets.

Technology for Production of Monodisperse Spherical Granules

The conducted study shows the possibility of improving the technology for producing monodisperse spherical granules. By modifying the surface of a die, it becomes possible to utilize the technology when granulating ErNi alloy. A potential for using the regime of forced capillary jet breakup with satellite droplets to expand the size-based operating range of the granulators in the finely-dispersed region has been demonstrated. To improve the granular quality, the forced capillary breakup regime with an excitation wavelength of about λ = 4.5d should be used.

Jet dynamics during vaporization of water drops in hot oil films

We experimentally investigate the vaporization of water droplets immersed in a hot oil film, with moderate temperaturedifferentials of 30–50 °C. In this regime, only a fraction of the water droplet vaporizes, but results in a symmetric vertical jet of oil. We provide detailed high-speed imaging of the physical process and quantitatively describe the vapor bubble growth, jet formation, jet speed and satellite droplets resulting from the jet break-up. The principal findings are that the jet speeds (vjet∼O(1) m/s) are inversely correlated to the oil film thickness (δ∼O(1) mm), whilst the surface tension-driven break-up results in primary satellite droplets whose normalized diameters also scale inversely with film thickness. Lastly, we provide observations of a water ‘peeling’ mechanism which occurs inside the vapor bubble, leading to a re-entrant jet that ultimately causes a secondary vaporization event.

Effect of finite conductivity on the nonlinear behaviour of an electrically charged viscoelastic liquid jet

In this paper a one-dimensional numerical study on the nonlinear behaviour of an electrically charged jet of Oldroyd-B viscoelastic, Taylor–Melcher leaky dielectric liquid is carried out. The effect of surface charge level, axial wavenumber and finite conductivity on the nonlinear evolution of the jet is investigated. Different structures including beads-on-a-string with/without satellite droplets, quasi-spikes and spikes are detected, and their domains in the plane of the non-dimensional axial wavenumber and the electrical Bond number are illustrated. The underlying mechanisms in the formation of the structures are examined. It is found that tangential electrostatic force plays a key role in the formation of a quasi-spike structure. Decreasing liquid conductivity may lead to a decrease in the size of satellite droplets or even the complete removal of them from a beads-on-a-string structure, induce the transition from a beads-on-a-string to a quasi-spike structure or postpone the appearance of a spike. On the other hand, finite conductivity has little influence on filament thinning in a beads-on-a-string structure, owing to the fact that the electrostatic forces are of secondary importance compared with the capillary force. The difference between the finite conductivity, large conductivity and other cases is elucidated. An experiment is carried out to observe spike structures.

Study on the breakup of liquid jet in a coaxial swirling compressible gas flow

The breakup length and position of liquid jet are the important parameters to determine the atomization quality. The nonlinear dispersion equation is used to study the breakup length and position of liquid jet with cavitation bubbles in a coaxial swirling compressible gas flow. First, the comparison of the jet breakup characteristics under linear and nonlinear stability theories is made, and then the effects of swirling gas, fluid compressibility and cavitation bubbles on jet breakup length are analyzed. The results show that the second-order perturbation may accelerate the breakup of liquid jet and may also inhibit the jet breakup when nonlinear stability theory is taken. In addition, the breakup position of liquid jet may appear after the main droplet and also appear after the satellite droplet. With the increase in gas rotational strengths, fluid compressibility and bubble volume fractions, the breakup length decreases, which indicates that swirling gas, fluid compressibility and cavitation bubbles can accelerate the jet breakup to a certain extent. In general, the effect of fluid compressibility on jet breakup length is the most obvious.

Effects of drive amplitude on continuous jet break-up

We develop a one-dimensional model of jet breakup in continuous inkjet printing to explore the nonlinear behavior caused by finite-amplitude modulations in the driving velocity, where jet stability deviates from classic (linear) “Rayleigh” behavior. At low driving amplitudes and high Weber numbers, the spatial instability produces drops that pinch-off downstream of the connecting filament, leading to the production of small satellite droplets between the main drops. On the other hand, we identify a range of driving amplitudes where pinching becomes “inverted,” occurring upstream of the filament connecting the main drops, rather than downstream. This inverted breakup is preferable in printing, as it increases the likelihood of satellite drops merging with the main drops. We find that this behavior can be controlled by the addition of a second harmonic to the driving signal. This model is in quantitative agreement with a full axisymmetric simulation, which incorporates nozzle geometry.

Shedding from chemically-treated oil droplets rising in seawater

The degree to which droplet shedding (tip-streaming) can modify the size of rising oil droplets has been a topic of growing interest in relation to subsea dispersant injection. We present an experimental and numerical approach predicting oil droplet shedding, covering a wide range of viscosities and interfacial tensions.Shedding was observed within a specific range of droplet sizes when the oil viscosity is sufficiently high and the IFT is sufficiently low. The affected droplets are observed to reduce in size, as smaller satellite droplets are shed, until the parent droplet reaches a stable size.Shedding of smaller droplets is related to the viscosity-dominated modified capillary number (Ca′), especially for low dispersant dosages recommended for subsea dispersant injection. This, in combination with the IFT-dominated Weber number (We), characterise droplets into three possible states: 1) stable (Ca′ < 0.21 &We<12); 2) tip-streaming (Ca′ > 0.21 &We<12); 3) unstable and subject to total breakup (We>12).

Signatures of slip in dewetting polymer films.

Thin polymer films on hydrophobic substrates are susceptible to rupture and hole formation. This, in turn, initiates a complex dewetting process, which ultimately leads to characteristic droplet patterns. Experimental and theoretical studies suggest that the type of droplet pattern depends on the specific interfacial condition between the polymer and the substrate. Predicting the morphological evolution over long timescales and on the different length scales involved is a major computational challenge. In this study, a highly adaptive numerical scheme is presented, which allows for following the dewetting process deep into the nonlinear regime of the model equations and captures the complex dynamics, including the shedding of droplets. In addition, our numerical results predict the previously unknown shedding of satellite droplets during the destabilization of liquid ridges that form during the late stages of the dewetting process. While the formation of satellite droplets is well known in the context of elongating fluid filaments and jets, we show here that, for dewetting liquid ridges, this property can be dramatically altered by the interfacial condition between polymer and substrate, namely slip. This work shows how dissipative processes can be used to systematically tune the formation of patterns.

Numerical and experimental evaluation of droplet breakage of O/W emulsions in rotor-stator mixers

Emulsification of a high viscosity oil in water mixture was studied in a rotor-stator mixer. Experimental characterization of drop sizes and high-speed visualizations of drop breakup phenomena were performed, combined with computational fluid dynamics analysis of the flow field and population balance modeling. Single-phase flow simulations were carried out with a sliding mesh CFD model and combined with analysis of streamlines, turbulent eddy dissipation fields and high-speed visualizations of drop breakage. From frames taken over few seconds, with the oil-water system initially fully segregated, three drop breakage mechanisms were identified, supported by the CFD analysis: (i) a combination of the large scale circular motion in the tank and the fluid jet emanating from the stator holes; (ii) droplets that are pulled into the rotor – stator system from the bottom and flow through the gap between the stator and rotor, undergoing extremely high shear stresses, being expelled through the stator slots in several fragments, and iii) droplets that remain caught at the recirculation zones in the stator holes, increasing exposure time to high shear during the rotor blade passage. Finally, an optimization algorithm was coupled to a population balance model and the measured drop size distributions were reproduced in good agreement with experimental data, including the bimodal behavior attributed to the generation of satellite droplets.

Continuous Particle Trapping, Switching, and Sorting Utilizing a Combination of Dielectrophoresis and Alternating Current Electrothermal Flow.

We propose a simplified multifunctional traffic control approach that effectively combines dielectrophoresis (DEP) and alternating current electrothermal (ACET) flow to realize continuous particle trapping, switching, and sorting. In the designed microsystem, the combined DEP and ACET effects, which are symmetrically generated above a bipolar electrode surface, contribute to focus the incoming colloidal particles into a thin beam. Once the bipolar electrode is energized with an electric gate signal completely in phase with the driving alternating current (AC) signal, the spatial symmetry of the electric field can be artificially reordered by adjusting the gate voltage through field-effect traffic control. This results in a reshapable field stagnant region for precise switching of particles into the region of interest. Moreover, the integrated particle switching prior to the scaled particle trapping experiment is successfully conducted to demonstrate the feasibility of the combined strategy. Furthermore, a mixture of two types of particle sorting (i.e., density, size) with quick response performance is achieved by increasing the driving voltage with a maximum gate voltage offset, thus, extending the versatility of the designed device. Finally, droplet switching and filtration of the satellite droplets from the parent droplets is performed to successfully permit control of the droplet traffic. The proposed traffic control approach provides a promising technique for flexible manipulation of particulate samples and can be conveniently integrated with other micro/nanofluidic components into a complete functional on-chip platform owing to its simple geometric structure, easy operation, and multifunctionality.

Study of a nanodroplet breakup through many-body dissipative particle dynamics

Breakup of a nanodroplet is a common phenomenon of great importance in the nanoprinting and the electrohydrodynamic jet printing, which affects the accuracy and efficiency of droplet delivery. When the diameter of a decaying jet reduces to nanometers, the breakup mechanism remains unclear because the traditional continuum theory fails. In this work, a mesoscale method, many-body dissipative particle dynamics, has been developed to investigate the breakup process of water, glycerol, and ethanol nanodroplets. Generally, a falling nanodroplet deforms and breaks up with the following stages, symmetrical deformation, thin-neck appearance, and drop-tip motion. The breakup time, the neck length, the minimum diameter of the neck before breakup, and the tip velocity of the formed tail after breakup have been examined. It is found that the neck length shows an exponential relationship with the time. Compared to the similarity solution near the separation point, the exponent relation between the minimum diameter of the neck and the reduced time has been verified. Moreover, the exponent (n) for different fluids can be roughly estimated by the Ohnesorge (Oh) number as n = 0.1015 log(Oh) + 0.6776. The tip velocity varies as the inverse square root of the reduced time when the tip shrinks slowly. When the tip shrinks rapidly, the exponential relationship between the tip velocity and the reduced time is predicted, which is also valid for shrinking a satellite droplet. This study provides a fundamental understanding of the nanodroplet breakup for improvement of their dynamical behaviors in a real application.

Modeling condensation on structured surfaces using lattice Boltzmann method

A single component, two-phase lattice Boltzmann model based on the Shan-Chen pseudopotential model is coupled to a continuum-based thermal energy solver. The model is verified using the Stefan problem and Nusselt’s falling film. We then use the model to simulate 2D drop-wise condensation of a saturated vapor on hydrophobic structured surfaces. We report the normalized condensed mass and condensation rate as we vary the spacing between structures, numerical interface thickness, and structure topology. For a non-dimensional spacing of s=6.4, a primary droplet engulfs each post after a non-dimensional thermal diffusion time of t∗≈1.1 (square), t∗≈0.59 (semi-circular), and t∗≈2.38 (equilateral). The growth of this thermally resistant primary droplet is fed by coalescing satellite droplets characterized by low heat transfer resistance. These small satellite droplets continuously nucleate, grow and merge into the primary droplet resulting in condensation rates four to seven times greater than the film-wise condensation rate. These small droplets only appear to form when the ratio of numerical interface thickness w to structure length L is sufficiently small (w/L<0.1).

Real time observation of binder jetting printing process using high-speed X-ray imaging

A high-speed synchrotron X-ray imaging technique was used to investigate the binder jetting additive manufacturing (AM) process. A commercial binder jetting printer with droplet-on-demand ink-jet print-head was used to print single lines on powder beds. The printing process was recorded in real time using high-speed X-ray imaging. The ink-jet droplets showed distinct elongated shape with spherical head, long tail, and three to five trailing satellite droplets. Significant drift was observed between the impact points of main droplet and satellite droplets. The impact of the droplet on the powder bed caused movement and ejection of the powder particles. The depth of disturbance in the powder bed from movement and ejection was defined as interaction depth, which is found to be dependent on the size, shape, and material of the powder particles. For smaller powder particles (diameter less than 10 μm), three consecutive binder droplets were observed to coalesce to form large agglomerates. The observations reported here will facilitate the understanding of underlying physics that govern the binder jetting processes, which will then help in improving the quality of parts manufactured using this AM process.

Experimental Study of the Solder Paste Jet Printing Process Using High Speed Photography and Rheological Methods

The jet printing process of Sn-58Bi lead-free solder paste involving expansion, necking, pinch-off and satellite droplet formation was observed and analyzed with the aid of high-speed photography. The viscosity and phase angle of the solder paste at three temperatures were measured using a rheometer. Spattering behavior of the solder paste was observed at 55°C. The spatter on the substrate came from a second satellite droplet which was produced in the second pinch-off of the solder paste and collided with the nozzle. Satellite droplets were produced at three temperatures when droplets break off, and the number of satellite droplets was determined at each temperature. The appropriate temperature could reduce the viscosity of the solder paste and improve the liquid-like behavior, which is conducive to realizing the jet printing process with an ideal ratio of height to diameter of the solder joints. According to the demand for jet solder paste, high-speed photography and rheological methods can help establish the relationship between jet printing performance and materials design.

A comprehensive understanding of enhanced condensation heat transfer using phase separation concept

A comprehensive analysis of enhanced condensation with phase separation concept is presented, for which mesh-membrane-tube (MMT) is suspended in a tube. A twill Dutch weaved mesh screen and two plain Dutch weaved mesh screens are used to fabricate MMT. Our study reveals that liquid leakage across MMT not only keeps better condensation on condenser wall, but also decreases pressure drop rise penalty. To modulate stratified-flow, the #1 MMT with smallest dp has the largest capillary force to pump liquid towards core region to expose more condenser surface with vapor, where dp is pore diameter. To modulate annular-flow, finest mesh wires of #1 MMT ensure the best wetting to liquid to prevent condenser wall from being impacted by satellite droplets. These mechanisms explain the best performance of #1 MMT, reaching a maximum heat transfer enhancement ratio of 1.82. The three MMTs share a single curve of nozzle discharge coefficient versus Reynolds number. The similar performance of #2 and #3 MMTs is due to identical dp/φ, where φ is mesh open porosity. Fine mesh wires and small mesh pores are suggested to enhance condensation heat transfer. MMT are recommended to be used in condenser tube upstream when vapor mass qualities larger than 0.1.

On the breakup of spiralling liquid jets

The generation of drops from a jet spiralling out of a spinning device, under the action of centrifugal force, is considered for the case of small perturbations introduced at the inlet. Close to the inlet, where the disturbances can be regarded as small, their propagation is found to be qualitatively similar to that of a wave propagating down a straight jet stretched by an external body force (e.g. gravity). The dispersion equation has the same parametric dependence on the base flow, but the base flow is, of course, different. Further down the jet, where the amplitude of the disturbances becomes finite and eventually resulting in drop formation, the flow appears to be quite complex. As shown, for the regular/periodic process of drop generation, the wavelength corresponding to the frequency at the inlet, increasing as the wave propagates down the stretching jet, determines, in general, not the volume of the resulting drop but the sum of volumes of the main drop and the satellite droplet that follows the main one. The proportion of the total volume forming the main drop depends on how far down the jet the drops are produced, i.e. on the magnitude of the inlet disturbance. The volume of the main drop is found to be a linear function of the radius of the unperturbed jet evaluated at the point where the drop breaks away from the jet. This radius, and the corresponding velocity of the base flow, have to be found simultaneously with the jet’s trajectory by using a jet-specific non-orthogonal coordinate system described in detail in Shikhmurzaev &amp; Sisoev (J. Fluid Mech., vol. 819, 2017, pp. 352–400). Some characteristic features of the nonlinear dynamics of the drop formation are discussed.