Satellite Droplets Research Articles

Electrohydrodynamic coalescence of droplets using an embedded potential flow model.

The coalescence, and subsequent satellite formation, of two inviscid droplets is studied numerically. The initial drops are taken to be of equal and different sizes, and simulations have been carried out with and without the presence of an electrical field. The main computational challenge is the tracking of a free surface that changes topology. Coupling level set and boundary integral methods with an embedded potential flow model, we seamlessly compute through these singular events. As a consequence, the various coalescence modes that appear depending upon the relative ratio of the parent droplets can be studied. Computations of first stage pinch-off, second stage pinch-off, and complete engulfment are analyzed and compared to recent numerical studies and laboratory experiments. Specifically, we study the evolution of bridge radii and the related scaling laws, the minimum drop radii evolution from coalescence to satellite pinch-off, satellite sizes, and the upward stretching of the near cylindrical protrusion at the droplet top. Clear evidence of partial coalescence self-similarity is presented for parent droplet ratios between 1.66 and 4. This has been possible due to the fact that computational initial conditions only depend upon the mother droplet size, in contrast with laboratory experiments where the difficulty in establishing the same initial physical configuration is well known. The presence of electric forces changes the coalescence patterns, and it is possible to control the satellite droplet size by tuning the electrical field intensity. All of the numerical results are in very good agreement with recent laboratory experiments for water droplet coalescence.

Phase-field simulation of Rayleigh instability on a fibre

In this paper, we present a phase-field method for Rayleigh instability on a fibre. Unlike a liquid column, the evolutionary dynamics of a liquid layer on a fibre depends on the boundary condition at the solid-liquid interface. We use a Navier–Stokes–Cahn–Hilliard system to model axisymmetric immiscible and incompressible two-phase flow with surface tension on a fibre. We solve the Navier–Stokes equation using a projection method and the Cahn–Hilliard equation using a nonlinearly stable splitting method. We present computational experiments with various thicknesses of liquid thread and fibre. The numerical results indicate that the size of the satellite droplet decreases as the thicknesses of the thread and fibre increase.

The role of wettability of nonideal nozzle plate: From drop‐on‐demand droplet jetting to impact on solid substrate

The dynamics of drop‐on‐demand (DoD) droplet formation and subsequently impact on the solid substrate are investigated using a three‐dimensional (3‐D) multirelaxation‐time (MRT) pseudopotential lattice Boltzmann (LB) model. The wettability of nonideal nozzle plate and solid substrate is modeled by a geometric scheme within the LB framework. The dynamics of droplet formation are explored in a range of the inverse of Ohnesorge number , , and , and the Reynolds number , , and . For , no satellite droplet is observed and the wettability of nozzle plate greatly influences the velocity and length of jetting fluids. For , the filament breakup and recombination are observed. The moment of filament breakup is delayed with advancing contact angle increasing. For with , the primary and satellite droplets could not be recombined with and which agree with the literature. Whereas with , the recombination occurs. The dynamics of subsequent oscillating droplet impact on the substrate are similar to that of equilibrium droplet which could obtain high‐resolution printed features. Consequently, considering with large and numbers, the printable range could be extended which could help increase the printing frequency and boost the production outputs of inkjet printing. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2837–2850, 2018

Effect of soluble surfactant on regime transitions at drop formation

Formation of surfactant-laden aqueous drops by liquid flow through a capillary is studied and compared with two reference pure liquids, water and low viscosity poly(dimethylsiloxane). Attention is paid to two transitions: (i) between regimes with and without satellite droplet formation and (ii) from dripping to jetting. It is shown that transition from dripping to jetting occurs at critical Weber number WeJ = 1.2 ± 0.1 based on dynamic surface tension on the flow timescale. Critical Weber number for transition to the regime without satellite droplets depends noticeably on the liquid surface tension and therefore cannot be used as a single parameter characterising this transition. Flow rate at transition decreases with decrease of surface tension for pure liquids and solutions of surfactants with critical micelle concentration, CMC > 10 mM. For solutions of surfactants with CMC < 1 mM transition to the regime without satellite droplets occurs at flow rates either larger or smaller than that of pure solvent depending on concentration. Anomalously high transition flow rates are related to surfactant redistribution during the time between the primary and secondary pinch-off.

Liquid jet trajectory and droplet path influenced by combined cross flow and electric fields

This study investigates an ethanol liquid jet subjected to combination of an air crossflow and a normal electric field. The results on the liquid jet trajectory and subsequent droplets flight paths are presented. The liquid jet trajectory was found as a function of two non-dimensional quantities; the liquid jet to the crossflow momentum ratio and the electroinertial number. The electroinertial number is defined as the ratio between the liquid jet specific momentum and the electric force. A correlation is introduced for the jet trajectory in low crossflow speeds and electric field intensities. The same two quantities control the detached droplets flight paths. Satellite droplets flight angles are also reported with a correlation for their separation angle, which can be useful in applications where uniform droplet production is important.

Controlling the polymer ink's rheological properties and viscoelasticity to suppress satellite droplets

Stable and single droplet generation is essential in drop-on-demand (DOD) inkjet printing process to deposit homogeneous and flat film. However, polymer's rheological properties and viscoelasticity can influence filament break up and droplet formation, which may lead to the formation of satellite droplets. Controlling the Z constant (related to fluid viscosity, and surface tension) and Weissenberg (Wi) number can suppress the satellite droplets and get stable and single droplet. Here, mixed solvents (chloride benzene (CB) and high viscosity cyclohexylbenzene (ChB)), different molecular weight and concentration were employed to tune the polyfluorene (PFO) viscosity, surface tension and viscoelasticity. According to the droplet ink-jetting behavior of different CB/ChB ratio, PFO molecular weight and concentration, it's found that only when the speed of the secondary droplet is faster than that of the primary droplet, a single droplet could be formed. At last, we concluded that for PFO inks 9 ≤ Z ≤ 55, Re ≥ 3 and Wi = 0.5 were adequate judgement for a stable and single droplet formation and the two factors should be controlled simultaneously to ensure a stable and single droplet.

High-throughput production of satellite-free droplets through a parallelized microfluidic deterministic lateral displacement device

We present a parallel numbering-up device for microfluidic production of satellite droplet-free emulsions. The device consists of two stacked layers made of polydimethylsiloxane (PDMS). The bottom layer combines eight parallel sets of a microfluidic droplet generator (MFDG) and deterministic lateral displacement (DLD) array for size-based separation of main and satellite droplets. The top layer has input reservoirs to supply both the disperse and continuous phases evenly to the eight channels of the bottom layer. We employed 3D flow simulations to find the reservoirs most suitable for equal inflow distribution. Water-in-oil (W/O) droplets comprised of main droplets (∼67 μm in diameter) and satellite droplets (1–20 μm) were generated in the parallelized MFDGs, and they were then completely separated through the DLD arrays having a critical diameter of Dc = 37.1 μm. Thus, we confirmed production of satellite droplet-free emulsion droplets at 0.2 ml/h, eight times the processing throughput of single device (= 0.025 ml/h) without decrease in performance.

Effect of soluble surfactants on pinch-off of moderately viscous drops and satellite size

HypothesisSurfactant redistribution in a liquid bridge close to drop detachment depends on competition between the bridge deformation rate and surfactant equilibration rate. Surfactant effect can be different in situations when diffusion coefficient changes independently of thinning kinetics or in line with it. Using moderately viscous liquids should allow both situations to be explored experimentally. ExperimentsFormation of liquid drops at the tip of capillary is studied experimentally for silicone oils and for surfactant-laden and surfactant-free water/glycerol mixtures of moderate viscosity with particular attention to the kinetics of liquid bridge close to pinch-off and formation of satellite droplets. FindingsEffect of surfactant depends on the dynamic regime of the bridge thinning. In the presence of surfactant, inertial kinetics slows down close to pinch-off demonstrating effective surface tension smaller than dynamic surface tension. An acceleration of thinning kinetics caused by depletion of surfactant from the liquid bridge was observed in viscous and visco-inertial regimes. The size of satellite droplets has a maximum versus viscosity; increasing with surfactant concentration at smaller viscosities and decreasing with an increase of surfactant concentration at largest studied viscosity, where inversion of the pinch-off point was observed for surfactant solutions.

Mechanism for regulation and control of emulsion droplet generation in co-flow microfluidic device via electric field

Applying the active control of electric field to the preparation of micro-droplets via the traditional microfluidic technology has attracted great attention because it can effectively improve the controllability of the preparing process. Therefore, a full understanding of mechanism for the regulation and control of microdroplets's generation by the microfluidic technology and electric field will provide interesting possibilities for the active control of producing required microdroplets in the practical applications. A transient theoretical model is developed via the coupling of phase-field method and electrostatic model to numerically investigate the generation of the single-phase droplets in a co-flow microfluidic device under the control of a uniform direct-current electric field. Via the numerical simulations based on the transient model, the control mechanisms of the electric field on dynamic behaviors of the droplets generation are revealed, and the influences of flow and electric parameters on the droplets generation characteristics are elucidated. The results indicate that the electrostatic field is able to generate an electric field force toward the inner phase fluid in the normal direction of the interface between two-phase fluids with different electric parameters. The electric field force enhances the necking and breaking of the inner fluid interface, which accelerates the droplets' generation, increases droplet deformation degree, and reduces droplet size. As the electric capillary number increases under the same hydrodynamic capillary number, the droplet formation pattern is transformed from dripping regime with only a single droplet formed per cycle to another dripping regime with one main droplet formed together with the following satellite droplets per cycle. In addition, according to the numerical results in this work, we organize a regime diagram to quantitatively represent the respective regime of these two flow patterns as a function of hydrodynamic capillary number and electric capillary number. The regime diagram indicates that with the increase in hydrodynamic capillary number and electric capillary number, the viscous drag force and electric field force are strengthened, which induces the formation of a slender liquid thread of inner fluid at the later stage of the necking process. This contributes to triggering the Rayleigh-Plateau instability on the liquid thread of inner fluid, and thus facilitating the generation of satellite droplets via the breakup of the liquid thread.

Immiscible impact dynamics of droplets onto millimetric films

The impact of liquid droplets onto a film of an immiscible liquid is studied experimentally across a broad range of parameters [ $$Re = O(10^{1}-10^{3})$$ , $$We = O(10^{2}-10^{3})$$ ] with the aid of high-speed photography and image analysis. Above a critical impact parameter, $$Re^{1/2}We^{1/4} \approx 100$$ , the droplet fragments into multiple satellite droplets, which typically occurs as the result of a fingering instability. Statistical analysis indicates that the satellite droplets are approximately log-normally distributed, in agreement with some previous studies and the theoretical predictions of Wu (Prob Eng Mech 18:241–249, 2003). However, in contrast to a recent study by Lhuissier et al. (Phys Rev Lett 110:264503, 2013), we find that it is the modal satellite diameter, not the mean diameter, that scales inversely with the impact speed (or Weber number) and that the dependence is $$d_\mathrm{{mod}} \sim We^{-1/4}$$ .

Rayleigh Instability-Assisted Satellite Droplets Elimination in Inkjet Printing.

Elimination of satellite droplets in inkjet printing has long been desired for high-resolution and precision printing of functional materials and tissues. Generally, the strategy to suppress satellite droplets is to control ink properties, such as viscosity or surface tension, to assist ink filaments in retracting into one drop. However, this strategy brings new restrictions to the ink, such as ink viscosity, surface tension, and concentration. Here, we report an alternative strategy that the satellite droplets are eliminated by enhancing Rayleigh instability of filament at the break point to accelerate pinch-off of the droplet from the nozzle. A superhydrophobic and ultralow adhesive nozzle with cone morphology exhibits the capability to eliminate satellite droplets by cutting the ink filament at breakup point effectively. As a result, the nozzles with different sizes (10-80 μm) are able to print more inks (1 < Z < 38), for which the nozzles are super-ink-phobic and ultralow adhesive, without satellite droplets. The finding presents a new way to remove satellite droplets via designing nozzles with super-ink-phobicity and ultralow adhesion rather than restricting the ink, which has promising applications in printing electronics and biotechnologies.

Droplet splitting on chemically striped surface

After a hydrophilic surface is partially coated with a superhydrophobic material, the resulting chemically patterned surface has a strong ability to split droplets. For example, a 2.54-mm-diameter water droplet impinging on a chemically striped surface at 0.58m/s can split off a satellite droplet. In this article, the droplet splitting behavior is investigated by the coupled level set/volume-of-fluid method. It is found that as the impact velocity increases, the number of satellite droplets tends to rise. When the impact velocity reaches 1.69m/s, a large number of satellite droplets are produced, increasing the length of the triple-phase contact line. Compared with that on an uncoated hydrophilic surface, the triple-phase contact line length of a droplet impinging on the chemically striped surface improves by 81.93% at the same impact velocity, and the longer triple-phase contact line can greatly enhance droplet evaporation on a hot surface. Furthermore, the impact position of the droplet significantly affects the length of the triple-phase contact line. When the droplet strikes a hydrophilic stripe, the triple-phase contact line length can be greatly enlarged (by 169.66%). Moreover, the mechanism of droplet splitting can be explained as follows: a pressure difference caused by the hysteretic movement of the liquid on the superhydrophobic stripes forces the liquid to move away from the superhydrophobic area to the hydrophilic area.

Inkjet printing of viscoelastic polymer inks

Inkjet printing is a new fabricating method that can realize the precise film deposition. For polymer inks, the coil-stretch transition of polymer chains always impacts the ink droplet formation and a beads-on-a string structure filament is formed, thus generating unwanted satellite droplets. This review provides a short introduction of the dynamic process of the droplet formation. Then fluid rheological requirements for a printable polymer ink are summarized. Finally the strain hardening phenomenon of polymer chains in the filament formation and its impact on polymer ink-jetting are discussed. The research of viscoelastic polymer inks shows that rheological parameters and viscoelasticity are two key factors that determine the printability of polymer inks.

Two‐stage stabilizer addition protocol as a means to reduce the size and improve the uniformity of polymer beads in suspension polymerization

ABSTRACTA two‐stage stabilizer addition protocol is suggested for reducing the size and improving the uniformity of polymer beads resulting from conventional suspension polymerization. The stabilizer load was divided into an initial charge and a secondary addition. The use of a low concentration of stabilizer in the initial charge served to assist drop rupture while avoiding significant reduction in drop size and production of too many satellite droplets. The secondary addition time of stabilizer occurred just before the onset of the growth stage when drops were vulnerable to coalescence but robust against break up due to their high viscosity. The secondary addition of stabilizer served to provide stability to monomer drops during the growth stage and as a result the drops underwent limited coalescence. This resulted in the formation of smaller and more uniform polymer beads in comparison to beads obtained by conventional suspension polymerization at the same overall concentration of stabilizer. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018, 135, 45671.

Dynamics of spreading of impinged droplets on the curved-grooved surface

Impact of droplets on rough surfaces has many industrial applications. Various types of splashing and spreading of liquid droplets result due to impingement of the droplets on the different surfaces incorporating formation of satellite droplets. Dynamics of splashing and spreading is different with respect to the point of impact—groove or hill—on the grooved surface. Physics of spreading of impacted droplets on the curved-grooved surfaces is not known so far. Impact of droplets on curved-grooved surface has been studied for a narrow range of Weber number to know the abrupt change in projected area of splashed droplets. Such abrupt change in the geometry of splashed droplets due to exaggerated elongation in the direction of groove was observed for narrow range of Weber numbers from 42 to 45. The present findings explore new direction for further fundamental research work to comprehend the physics of dynamics of impacted droplets for development of new theory helpful for spray painting, printing, and designing of shielding structures.

Instability of gas-surrounded Rayleigh viscous jets: Weakly nonlinear analysis and numerical simulation

The instability of gas-surrounded Rayleigh viscous jets is investigated analytically and numerically in this paper. Theoretical analysis is based on a second-order perturbation expansion for capillary jets with surface disturbances, while the axisymmetric two-dimensional, two-phase simulation is conducted by applying the Gerris code for jets subjected to velocity disturbances. The relation between the initial surface and velocity disturbance amplitude was obtained according to the derivation of Moallemi et al. [“Breakup of capillary jets with different disturbances,” Phys. Fluids 28, 012101 (2016)], and the breakup lengths resulting from these two disturbances agree well. Analytical and numerical breakup profiles also coincide satisfactorily, except in the vicinity of the breakup point, which shrinks forcefully. The effects of various parameters (i.e., oscillation frequency, Reynolds number, Weber number, and gas-to-liquid density ratio) have also been examined by comparing spatial growth rate, second-order disturbance amplitude, breakup length, and the breakup profiles at low frequency, where obvious satellite droplets form, versus different parameters. In addition, the competition between Rayleigh instability and Kelvin-Helmholtz instability has been examined using an energy approach.

Oscillation of satellite droplets in an Oldroyd-B viscoelastic liquid jet

The oscillation characteristics of satellite droplets in the beads-on-a-string structure of an Oldroyd-B viscoelastic liquid jet are studied numerically using a one-dimensional model.

Influence of the Surface Viscosity on the Breakup of a Surfactant-Laden Drop.

We examine both theoretically and experimentally the breakup of a pendant drop loaded with an insoluble surfactant. The experiments show that a significant amount of surfactant is trapped in the resulting satellite droplet. This result contradicts previous theoretical predictions, where the effects of surface tension variation were limited to solutocapillarity and Marangoni stresses. We solve numerically the hydrodynamic equations, including not only those effects but also those of surface shear and dilatational viscosities. We show that surface viscosities play a critical role to explain the accumulation of surfactant in the satellite droplet.

Separation of main and satellite droplets in a deterministic lateral displacement microfluidic device

We present a novel DLD microfluidic device for preparing satellite-free main droplets and monodispersed satellite droplets.

Features of Capillary Breakup of a Liquid Jet at Ohnesorge Numbers Larger Than Unity

A theoretical study has been made of the forced capillary breakup of a jet of viscous liquid at a value of the Ohnesorge number larger than unity. The regions of breakup of the jet without the formation of satellites have been determined. The dependences of the dimensions of main and satellite droplets on the wave number have been obtained for different Ohnesorge numbers.