Satellite Droplets Research Articles

Interfacial instability of thin ferrofluid films under a magnetic field

AbstractWe study magnetically induced interfacial instability of a thin ferrofluid film subjected to an applied uniform magnetic field and covered by a non-magnetizable passive gas. Governing equations are derived using the long-wave approximation of the coupled static Maxwell and Stokes equations. The contact angle is imposed via a disjoining/conjoining pressure model. Numerical simulations show the patterning resulting from unstable perturbations and dewetting of the ferrofluid film. We find that the subtle competition between the applied field and the van der Waals induced dewetting determines the appearance of satellite droplets. The results suggest a new route for generating self-assembled ferrofluid droplets from a thin film using an external magnetic field. An axisymmetric droplet on a surface is also studied, and we demonstrate the deformation of the droplet into a spiked cone, in agreement with experimental findings.

Effect of process parameters on copper droplet ejecting by pneumatic drop-on-demand technology

Stable generation of copper droplets is a key issue in fabricating copper parts by drop-on-demand (DOD) technology. The process parameters such as supply pressure and electronic pulse width have significant effect on pressure variation and droplet formation. In the present work, a pressure acquisition system was first set up to measure the pressure variation in crucible. Then the measured pressure data were applied on a 2D axisymmetric model as inlet conditions to study the influence of process parameters on copper droplet formation. The results indicated that the peak pressure in crucible increased linearly with the increase of supply pressure. As supply pressure increased, the jet velocity and the limiting length increased to critical value and droplet could be generated. The peak width increased with the rise of electronic pulse width. By increasing the electronic pulse width, the time of pressure above threshold value increased and the jet limiting length grew to critical value for breakup. However, if supply pressure and electronic pulse width were too large, satellite droplets would be formed. Pure copper droplet generating experiments were conducted to obtain appropriate parameters. Single droplet was generated while supply pressure was between 60kPa and 100kPa and pulse width was between 550μs and 1550μs. Also the range of pulse width varied as the supply pressure increased for generating single droplet. The statistics of droplet diameter suggested that droplet diameter increased with the increase of supply pressure. Electronic pulse width had influence on the droplets size and the standard deviation increased with the increase of electronic pulse width. So small supply pressure and electronic pulse width should be used for generating uniform droplets.

Study of Droplet Formation Process during Drop-on-Demand Inkjetting of Living Cell-Laden Bioink

Biofabrication offers a great potential for the fabrication of three-dimensional living tissues and organs by precisely layer-by-layer placing various tissue spheroids as anatomically designed. Inkjet printing of living cell-laden bioink is one of the most promising technologies enabling biofabrication, and the bioink printability must be carefully examined for it to be a viable biofabrication technology. In this study, the cell-laden bioink droplet formation process has been studied in terms of the breakup time, droplet size and velocity, and satellite formation using a time-resolved imaging approach. The bioink has been prepared using fibroblasts and sodium alginate with four different cell concentrations: without cells, 1 × 10(6), 5 × 10(6), and 1 × 10(7) cells/mL to appreciate the effect of cell concentration on the droplet formation process. Furthermore, the bioink droplet formation process is compared with that during the inkjetting of a comparable polystyrene microbead-laden suspension under the identical operating conditions to understand the effect of particle physical properties on the droplet formation process. It is found that (1) as the cell concentration of bioink increases, the droplet size and velocity decrease, the formation of satellite droplets is suppressed, and the breakup time increases, and (2) compared to the hard bead-laden suspension, the bioink tends to have a less ejected fluid volume, lower droplet velocity, and longer breakup time.

Rupture of an evaporating liquid bridge between two grains

The study examines rupture of evaporating liquid bridges between two glass spheres. Evolution of the bridge profile has been recorded with the use of high-speed camera. Geometrical characteristics of the bridge were then used to calculate evolution of the variables during the process: Laplace pressure, capillary force, and surface tension force. For the purpose of reference, the bridge evolution is followed also during kinematic extension. During both processes the diameter of the neck decreases, with an acceleration of about 1–2 ms before the rupture. Two distinct rupture modes are observed, depending on the bridge aspect ratio. After the rupture, the mass of liquid splits, forming two separate oscillating drops attached to the spheres, and a suspended satellite droplet. Just before the rupture, an increasing repulsive Laplace pressure, and decreasing negative surface tension force develop. Capillary force follows the trend of the surface tension force, with an accelerating decline. Duration of the whole process and liquid mass stabilization is from 10 to 60 ms.

Breakup behavior of a molten metal jet

The breakup behavior of a molten metal jet into a still gas was studied numerically. Droplet formation was modeled by imposing a sinusoidal waveform perturbation or an amplitude-modulated waveform perturbation. The effect of the temperature on the jet breakup behavior was examined by modeling the liquid metal properties, including density, viscosity, and surface tension, as a function of the temperature. The process by which a molten metal jet was ejected from an orifice exit was modeled to include the wetting of the molten metal on the orifice surface at the gas interface using a dynamic contact angle (θD). The effects of the oscillation amplitude (A=0.10–0.30), the Strouhal number (St=0.20–0.50) and the Weber number (We=11.63–129.19) were studied. The imposition of a periodic perturbation yielded linear or nonlinear breakup behavior in the molten metal jet. The conditions found to be optimal for the continuous generation of uniform droplets were identified by optimizing the uniformity of the main droplet, the regular distance between main droplets, the presence of satellite droplets, and the coalescence of the droplets due to surface instabilities and hydrodynamic interactions. The effects of the modulated amplitude (B) and the frequency ratio (N) on the coalescence and separation of neighboring droplets were examined.

Electric field-assisted manipulation of liquid jet and emanated droplets

Controlling and manipulating liquid jets are of great interest in practical and scientific aspects. In the present work effects of transverse uniform electric field on behaviour of liquid jet, streaming downward due to the gravity, is experimentally investigated in details by performing a precise image processing of the extracted high speed video frames. In the experiments, by altering liquid flow rate and applied electric field strength, authors have tried to study the interplay of electrical and hydrodynamic forces which are indeed the main factors acting on the jet behaviour e.g. deflection, rhythmic motion, breakup mechanism and satellite droplets formation. Major aim of this study is to manipulate liquid jet so as to attain uniformly sized droplets by removing satellite droplets which has potential applications in various industrial and laboratorial units. This procedure was performed by applying dielectrophoretic force to the water jet as a polar liquid. Furthermore the droplets and also satellites behaviour, influenced by transverse electric field, have been investigated thoroughly.

The formation and breakup of molten oxide jets under periodic excitation

The experiments on the capillary breakup of slag jets at high temperatures are presented in this article. The impact of external excitations on the disintegration process was investigated in a furnace with optical access filmed at frame rates up to 10,000 fps. A synthetic calcia‐alumina slag was used to form jets at different temperatures (1570–1660°C) and jet velocities (0.6–1.4 ms−1). The impact of external vibration on the breakup was evident: for low jet velocities, the jet length decreased, the droplet size increased, satellite droplet formation was hindered, and a distinct “pumping mechanism” was observed. For jets with higher velocity, the jet length decreased by 30%, the droplet generation frequency increased from 20 to 250 droplets per second, the drop sizes were uniform, and satellite formation was also suppressed. In this case, the ideal case in which the volume of one wave instability forms one droplet was achieved. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3350–3361, 2014

Effect of flow rates of the continuous phase on droplet size in dripping and jetting regimes in a simple fluidic device for coaxial flow

We studied the water-in-oil (W/O) emulsion droplet formation in a simple coaxial microfluidic device with varying the flow rate of continuous phase and investigated the effect of the flow rate on the size and coefficient of variance of the emulsion droplets. The emulsion droplets prepared in the dripping regime at a low flow rate of the continuous phase exhibited a uniform size distribution. The increase in the flow rate of the continuous phase resulted in a transition from the dripping regime to the jetting regime. The emulsion droplets produced in the jetting regime exhibited multimodal size distributions, which is mainly attributed to the formation of satellite droplets. Based on the calculated Capillary number (Ca) and the Weber number (We), we suggest that the flow rate of the continuous phase and the viscosity of the discontinuous phase are the key factors for determining the regime of droplet formation. We believe that these results can serve as a guideline for the determination of flow rates for the production of uniform emulsion droplets in coaxial fluidic devices.

Experimental investigation on falling ferrofluid droplets in vertical magnetic fields

The dynamic behaviors of a water-based ferrofluid droplet falling in silicone oils subjected to vertical gradient magnetic fields were studied experimentally. The effects of magnetic field, droplet diameter and oil viscosity are investigated. It is found that the droplet undergoes significant deformation with its shape transforming from an initial oblate ellipsoid to a sphere, then to a prolate ellipsoid and finally to a teardrop. We observe more obvious deformation for a bigger droplet in a lower viscosity of the oil and a higher field gradient. Even the satellite droplet appears accompanying with the breakup of the droplet tail, which can be explained by the non-uniform field distribution. To predict the transient velocity of the droplet, a theoretical velocity model is presented. Both the experimental and theoretical results show that the velocity increases with either the field gradient or the droplet size, but decreases as the oil viscosity increases. The behaviors of two falling droplets with different initial diameters in the current magnetic fields were also studied. If the initial separation distance between them does not exceed a threshold, the droplets eventually come into contact to form a dimer moving along the field direction. When the field is suddenly applied in the middle of the journey of the droplet pair, they would be rearranged and aggregated aligning with the field due to the magnetophoretic effects.

Effect of the fluid injection configuration on droplet size in a microfluidic T junction

The effect of confinement on the droplet formation in T junctions was studied for three configurations of fluid injection. The sizes of the main droplets and the satellite droplets were measured in the squeezing and dripping regimes. The evolution of droplet sizes with capillary number in the continuous phase is similar to that in flow-focusing junctions, i.e., the size of the main droplets decreases with an increase of this capillary number, while the size of the satellite droplets increases with an increase of this capillary number. While in the range of flow rates investigated the injection configuration does not exhibit a significant effect on the main droplet sizes, it does have an effect on the size of the satellite droplets. The latter ones are smaller when the neck rupture of the droplet occurs on an angle of the microsystem.

A novel approach for drop-on-demand and particle encapsulation based on liquid bridge breakup

A simple and robust way is devised to generate picoliter droplets out of a single microliter drop for the use of generating monodisperse droplets in droplet-based microfluidics. A single aqueous drop is placed between two hydrophilic substrates and then immersed in silicone oil, to form a liquid bridge. Then one substrate is moved away with a predefined velocity. As the distance between two glass plates increases, the liquid bridge breaks up and smaller droplets or satellites are formed. A picoliter-droplet was successfully dispensed on demand repeatedly for 100times within 2% relative standard deviation in size under velocity-controlled system. It is found that, for the case of fixed inner and outer fluids, the droplets of nearly the same size are generated over several orders of the moving velocity. Also, the size of the maximum satellite droplet increases with the increase of the mother drop size and inner fluid viscosity, and it decreases with the increase of the outer fluid viscosity. Its feasibility of cell and particle encapsulation has been confirmed by capturing a single Arabidopsis thaliana protoplast as well as polystyrene microparticles successfully using this method without complex control. Based on these results, a simple forcep was designed to dispense ultrasmall droplets and its functionality was confirmed to be similar with the velocity controlled case without external devices. This simple method is expected be used to divide a small amount of bio sample on-demand into several smaller droplets for further analyses.

J0440304 液体架橋の破断過程を利用したピコリットル液滴の生成([J044-03]ソフトマター・イノベーション(3),機械材料・材料加工部門)

In the process of breakup of stretching a liquid bridge, sometimes a daughter droplet is generated. We use this phenomenon for picoliter droplet formation. When the liquid bridge between micrometer heads is stretched, its waist becomes narrower with increasing the distance between heads. Above a certain distance, the waist spontaneously becomes narrower. And then, it breaks up. In this process, very small amount of droplet is left between two mother droplets. It is called daughter droplet or satellite droplet. To use this process for liquid droplet formation, we carried out experiments with some reagents. Effects of volume of mother liquid bridge and surface tension, kinematic viscosity on the volume of daughter droplet are investigated. 3.0picoliter droplet can be generated with this method.

An approach to design and fabrication of a piezo-actuated microdroplet generator

In this research, a piezo-actuated microdroplet printing device for drop on demand (DOD) is studied. Microdroplet devices are used in applications such as inkjet printing, rapid prototyping, and production of metal powder. An experimental device is designed and manufactured, in which the fluctuation of a flexible diaphragm–by a piezoelectric element–pushes the liquid out of the nozzle and produces droplets. The deflection of diaphragm due to different voltages is investigated by analytical and experimental study. In experiments, beside deflection voltage, the effect of suction and compression time and nozzle diameter on droplet size, droplet velocity, satellite droplets, and cutoff length is also investigated. High-speed camera is used to take photo of the formation of droplets. In order to calculate droplet diameter and velocity, outputs of high-speed camera are processed by MATLAB R2008a. Results obtained by analytical and experimental are in good agreement with each other and could be used to control droplet properties. It is shown that the device is able to produce droplet of diameter from 450 to 1,000 μm. Velocity of droplet can be also controlled in a range of about 0.2 to 1.4 m/s. The repeatability is investigated by ink printing on a paper attached to a rotary table.

Multifluid Eulerian model of an electrospray in a host gas

AbstractAn Eulerian multifluid model is used to describe the evolution of an electrospray plume and the flow induced in the surrounding gas by the drag of the electrically charged spray droplets in the space between an injection electrode containing the electrospray source and a collector electrode. The spray is driven by the voltage applied between the two electrodes. Numerical computations and order-of-magnitude estimates for a quiescent gas show that the droplets begin to fly back toward the injection electrode at a certain critical value of the flux of droplets in the spray, which depends very much on the electrical conditions at the injection electrode. As the flux is increased toward its critical value, the electric field induced by the charge of the droplets partially balances the field due to the applied voltage in the vicinity of the injection electrode, leading to a spray that rapidly broadens at a distance from its origin of the order of the stopping distance at which the droplets lose their initial momentum and the effect of their inertia becomes negligible. The axial component of the electric field first changes sign in this region, causing the fly back. The flow induced in the gas significantly changes this picture in the conditions of typical experiments. A gas plume is induced by the drag of the droplets whose entrainment makes the radius of the spray away from the injection electrode smaller than in a quiescent gas, and convects the droplets across the region of negative axial electric field that appears around the origin of the spray when the flux of droplets is increased. This suppresses fly back and allows much higher fluxes to be reached than are possible in a quiescent gas. The limit of large droplet-to-gas mass ratio is discussed. Migration of satellite droplets to the shroud of the spray is reproduced by the Eulerian model, but this process is also affected by the motion of the gas. The gas flow preferentially pushes satellite droplets from the shroud to the core of the spray when the effect of the inertia of the droplets becomes negligible, and thus opposes the well-established electrostatic/inertial mechanism of segregation and may end up concentrating satellite droplets in an intermediate radial region of the spray.

Formation of satellite droplets in flow-focusing junctions: volume and neck rupture

This work focuses on the rupture of the neck of a main droplet, leading to the formation of satellite droplets in a flow-focusing junction. The size of these satellites is determined by image analysis. Emphasis is given to the influence of viscosity and rheological behaviour of the fluids, using both Newtonian and non-Newtonian fluids as continuous phases. The scaling of the size of the satellite droplet with the capillary number of the continuous phase shows two different areas separated by a critical capillary number of 10Â?2. Below this critical capillary number, the size of satellites hardly changes. Above this critical value, the size of the droplet increases almost linearly with the capillary number. This critical value appears also as a difference in shape of the rupture of the neck of the droplet for Newtonian continuous fluids: symmetrical for low capillary numbers and asymmetrical rupture of the neck of the droplet for higher capillary numbers. The higher the viscosity ratio (viscosity of dispersed phase/viscosity of continuous phase), the bigger is the main satellite droplet. For more viscous dispersed phases, numerous satellite droplets can be formed. When the continuous phase is non-Newtonian (polyacrylamide solutions) the number of satellites droplets is even higher and their sizes are found interdependent according to a cascade scenario.

Laser-induced forward transfer of silver nanoparticle ink: time-resolved imaging of the jetting dynamics and correlation with the printing quality

In this work, we used time-resolved imaging to study the dynamics of the laser-induced forward transfer (LIFT) process of a silver nanoparticle (NP) ink (NP size: 30–50 nm). LIFT is a versatile direct write technique in which a variety of functional materials can be transferred from a donor substrate to a receiving substrate with high spatial resolution. Two different LIFT configurations were employed: (a) dynamic release layer (DRL)-assisted LIFT, in which direct expose of the silver NP ink to laser irradiation is prevented, and (b) DRL-free LIFT, in which the silver NP ink is exposed to laser irradiation. Jetting dynamic behavior, initiated by a cavitation bubble generation and expansion, was observed in both LIFT configurations. However, jetting dynamics were significantly milder in the case of DRL-assisted LIFT, resulting in a wide laser fluence processing window (100–230 mJ/cm2) for high uniformity and reproducibility printing of silver NP ink droplets. On the contrary, DRL-free LIFT resulted in smooth jetting dynamics only for a narrow laser fluence window (30–40 mJ/cm2). The explanation of the different dynamics is based on the different mechanisms that govern the conversion of the laser pulse energy to a dynamic cavitation bubble for each LIFT configuration, i.e., (a) heat diffusion, mediated by the DRL layer, in DRL-assisted LIFT and (b) microcavitation around the silver NPs due to near field enhancement when no DRL is used. In addition, the mechanism of formation of undesirable satellite droplets around the main deposited droplets was studied by using a flexible polymeric receiving substrate. The importance of the smooth jetting behavior, achieved by DRL-assisted LIFT, was highlighted for high-resolution printing of silver NP ink as well as for ensuring enhanced LIFT processing stability.

Two-way coupled numerical simulation of electrospray with induced gas flow

The gas flow induced by droplet motion has been included in the numerical simulation of electrosprays. Steady state solutions were sought iteratively in a computational scheme that fully couples a 3D Lagrangian model for the droplet dynamics with a steady state 2D axisymmetric Eulerian model for the induced gas flow. To resolve the reactive drag force on the gas by the droplets we employ Gaussian filters with variable kernel widths that depend on the droplet number density. We have applied this scheme to an experimentally characterized spray from the literature comprised of non-evaporating primary and satellite droplets in air. The predicted characteristics of the droplet plume (droplet number density, droplet velocity, droplet size distribution) better match the experimental values when the induced airflow is accounted for than when it is not (assuming still air). It is shown that the induced airflow contributes to faster moving droplets, shrinkage of plume, and a prominent flux about the spray axis (centerline), as compared with the simulations assuming still air. Induced airflow results in an increase of 80% in axial droplets velocity at the centerline at the collection counterplate. The ratio of mass flux at the centerline between the cases of moving and still air equals 2.6 at the counterplate. We have also observed that the radial segregation by size of the satellite droplets is sensitive to the functional relationship between their charge-to-mass ratio and diameter. Induced gas flow is expected to have important implications in the simulation of droplet evaporation and vapor concentration in electrosprays.

Deflection of continuous droplet streams using high-voltage dielectrophoresis

We report a novel scheme for steering a high-velocity continuous droplet stream using the dielectrophoretic force. The droplet stream is created using the continuous ink jet method. A liquid jet is ejected from a nozzle at high pressure and is controllably broken up into uniform droplets 30–90 μm in diameter with velocities up to 20 m/s. Voltages up to 2 kV are used to energize a high-voltage probe located downstream from the nozzle to induce the formation of a nonuniform electric field in the vicinity of the probe tip. The stream is passed through the electric field, subjecting the droplets to the dielectrophoretic force in the direction of the electric field maxima. Our scheme provides precise displacement of the droplet stream and requires less hardware than traditional steering methods. Less hardware means the distance between the printing nozzle and receiving substrate is minimized, enabling more accurate droplet positioning and higher print resolution. Other applications of high-voltage dielectrophoresis for droplet steering includes on/off control and manipulation (or removal) of satellite droplets. A simple linear relationship predicts the deflection of the droplet stream in the vicinity of a high-voltage probe as a function of the governing parameters. This relationship holds true for a large range of droplet sizes, stream velocities, geometries, and electric field strengths.

Effects of droplet collision phenomena on the development of pressure swirl sprays

In this work, the sprays generated by a pressure swirl atomizer were examined for different liquid injection pressures and particularly, the effects of the droplet collision phenomena on the axial evolution of the droplet size distribution were carefully studied. Sizes and droplet velocities were measured by means a phase Doppler particle analyzer and number concentrations and liquid volume fluxes for different droplet classes, were evaluated using a full data post-processing based on the droplet transit time inside the probe volume. The collision rates between droplet classes were calculated and some collision outcomes as coalescence and separation were investigated.In all the sprays studied, the highest collision rates were obtained in the region where both high number concentration and elevated relative velocity between droplets were measured. A progressive increase of the droplet mean diameter was produced along the sprays due to the coalescing collisions. As injection pressure increased, higher droplet collision rates and higher inertia collisions were found. The separation with formation of satellite droplets was a more frequent collision outcome. In addition, bigger axial mean free paths were calculated and hence, a more moderated axial increase of the droplet mean diameter was obtained.

Dilute nanoemulsions via separation of satellite droplets

A facile method is suggested for fabrication of dilute nanoemulsions. In a typical emulsification process, drops are usually accompanied by off-grade satellite droplets. The size of these satellite droplets ranges from hundreds of nanometers to above microns. Experiments were carried out to assess the possibility of separation of nanodrops from macroemulsions made via a conventional method in order to produce nanoemulsions. A low-power homogenizer was used to produce parent emulsions which were then injected from the bottom to a glass column containing water and allowed to cream. By monitoring drops remaining in the bottom of the column, it is clearly shown how progressively smaller they become with time yielding eventually dilute nanoemulsions. The average diameter of drops reduced to 100nm when oil with high viscosity was used. The concentration of resulting nanoemulsions increased with increasing viscosity and ratio of the disperse phase of parent emulsions.