Formation Of Satellite Droplets Research Articles

Enhanced control and efficiency in millimeter-scale composite droplets preparation

A microfluidic device utilising the flow focusing method was designed and fabricated for the high-throughput and controllable preparation of millimeter-scale water-in-oil (W1/O/W2) droplets. Two distinct flow focusing modes were employed in order to prepare the composite droplets. In the flow-focused axisymmetric jetting mode, the continuous phase propels the dispersed phase, forming a cone, which subsequently leads to a jet formation downstream of the small hole. When the outer phase is activated, perturbation growth interferes with downstream fragmentation, resulting in composite droplets with excellent monodispersity. In the dripping mode, the dispersed phase fails to form a jet downstream, and the interface disintegrates, resulting in droplet formation at the exit of the small orifice. In the jetting mode, the size and shell-to-core ratio of the generated droplets can be controlled by adjusting the volume of flow of the outer and inner phases, as well as the applied frequency. Furthermore, the applied perturbation allows for precise control of droplet size, which significantly reduces satellite droplet formation and enhances droplet monodispersity. In the dripping mode, the shell-to-core ratio is adjusted by manipulating the ratio of inner to outer flow rates, which is tailored to the specific requirements of the flow-focused dripping mode. The prepared compound droplets exhibit good monodispersity. Finally, the rotational solidification method can be employed to obtain spherical shells with a shell thickness of less than 20 μm. In conclusion, the flow focusing method is an effective, controllable, and stable method for synthesising millimetre-sized composite droplets.

Satellite droplet formation and its inertial separation in integrated microchannels

The breakup of filament is often accompanied by the formation of satellite droplet, which affects the uniformity of droplets, and inertial microfluidic technology is usually used to separate droplets of different sizes. In this study, different filament breakup modes are observed, and the variation of satellite droplet size with operating conditions are analyzed. Based on the experimental results, predictive model for the satellite droplet size is proposed. To better control the separation of particles with different sizes, the focusing and separation process of main and satellite droplets in microdevices are investigated by numerical simulation. It is found that increasing the fluid flow rate, the width of microchannel and rear cavity, and reducing the satellite droplet size are all beneficial for the separation of droplets of different sizes. At last, models for predicting the focusing positions of main and satellite droplets in rear cavity are established, and an integrated microfluidic device is proposed.

Instability and breakup of rayleigh-plateau jets with capillary wave induced by electrowetting-on-dielectric

This paper discusses the lateral disturbances of vertical liquid flow enhancement using electrowetting-on-dielectric (EWOD) technique, which effectively reducing the breakup length of the liquid flow and minimizing the formation of satellite droplets. The EWOD technology is characterized by its minimal space occupation and low energy consumption. The successful implementation of the EWOD phenomenon relies on the formation of a three-phase contact line (TPCL) between the electrodes and the liquid, and the novel EWOD tube structure design provides an extended TPCL, enhancing the amplitude of capillary waves. Through experimental and theoretical analysis, this paper identifies key parameters affecting the liquid breakup process, such as the gap depth, angle of the EWOD tube, EWOD voltage amplitude, and frequency of the AC electrical signal. The research results indicate that the proposed EWOD tube responds rapidly and can consistently and stably manage liquid breakup and reduce the number of satellite droplets.

Rational Design of Liquid-Liquid Microdispersion Droplet Microreactors for the Controllable Synthesis of Highly Uniform and Monodispersed Dextran Microspheres.

Hydrogel microspheres are biocompatible materials widely used in biological and medical fields. Emulsification and stirring are the commonly used methods to prepare hydrogels. However, the size distribution is considerably wide, the monodispersity and the mechanical intensity are poor, and the stable operation conditions are comparatively narrow to meet some sophisticated applications. In this paper, a T-shaped stepwise microchannel combined with a simple side microchannel structure is developed to explore the liquid-liquid dispersion mechanism, interfacial evolution behavior, satellite droplet formation mechanism and separation, and the eventual successful synthesis of dextran hydrogel microspheres. The effect of the operation parameters on droplet and microsphere size is comprehensively studied. The flow pattern and the stable operation condition range are given, and mathematical prediction models are developed under three different flow regimes for droplet size prediction. Based on the stable operating conditions, a microdroplet-based method combined with UV light curing is developed to synthesize the dextran hydrogel microsphere. The highly uniform and monodispersed dextran microspheres with good mechanical intensity are synthesized in the developed microfluidic platform. The size of the microsphere could be tuned from 50 to 300 μm with a capillary number in the range of 0.006-0.742. This work not only provides a facile method for functional polymeric microsphere preparation but also offers important design guidelines for the development of a robust microreactor.

Analysis of drop-on-demand printing characteristics and stability driven by inertial forces

As the core technology in the field of microdroplet related applications, researchers have been striving to develop new driving methods and improve the stability of inkjet printing technology to meet the diverse needs of various materials and applications. In this study, a novel, simple, and cost-effective droplet printing method based on inertial force driving is proposed, and its printing characteristics and stability are investigated through experimental and numerical simulation studies. A numerical model was developed to explore the effects of operating parameters and fluid properties on the printing process. The results showed that for a given fluid, it is easier to form satellite droplets when driven from a smaller nozzle with higher voltage and pulse width. The hydrophilic nature of the nozzle can suppress the formation of satellite droplets, but it is prone to retain liquid, thereby affecting the next printing effect. Under certain operating conditions, fluids with lower density, higher viscosity, and higher surface tension are difficult to be driven but can suppress the formation of satellite droplets and promote printing stability. Finally, a parameter space composed of dimensionless numbers Op representing operating parameters and Z representing fluid properties (reciprocal of the Oh number) was established to investigate the comprehensive influence on the printing. The correctness of this parameter space in guiding the selection of parameters for stable droplet printing was validated through experiments.

Numerical study of head-on collisions between two glass microsphere droplets

The collision of molten glass microsphere droplets represents a fundamental phenomenon in spheronization, yet a comprehensive understanding of this process remains elusive. A numerical simulation is conducted to investigate the head-on collision dynamics of two molten glass microsphere droplets at varying Weber numbers, by integrating the level set and volume of fluid methods. Three distinct collision regimes are identified: merging, separation into satellite-free droplets, and separation leading to the formation of satellite droplets. Furthermore, the critical Weber numbers delineating the different regimes are presented. Examination of axial and radial variations in the droplets reveals the existence of five distinct states spanning the three collision regimes. The distribution of external vortices around the droplets directly influences the outcomes of droplet collisions. High-pressure regions and high-pressure liquid bridges within droplets serve as key factors in determining the merging or separation of the droplets. Region of high pressure at the end of the liquid bridge acts as a critical indicator for distinguishing between collision separations with and without satellite droplet generation. Observations of velocity and pressure distributions in separations that produce satellite droplets are consistent with the end pinch-off mechanism. This study holds significant implications for controlling high sphericity during the spheronization of glass microsphere droplets.

Numerical investigation of nozzle length effects on Rayleigh jet breakup behaviors and droplet formation properties at different modulation amplitudes in liquid droplet radiator

Uniform droplet stream generation is required for a liquid droplet radiator to achieve the efficient heat dissipation of space nuclear power systems. In this study, Rayleigh jets breaking into continuous droplet streams at different modulation amplitudes are numerically simulated to investigate the nozzle length effects on jet breakup behaviors and droplet formation properties. First, simulated results confirm that the growth of secondary instability wave on jet free-surface causes the jet breakup pattern transition from downstream pinching to upstream pinching. As the modulation amplitude is from 0.04 up to 0.16, the nozzle length range where the upstream pinching occurs in the jet breakup is broadened from null to 1–5. The essential reason for the increase of jet breakup length is the reduction of fundamental amplitude and the increase of full velocity relaxation length. Then, a comprehensive prediction model for the velocity-modulated jet breakup length is developed in agreement with the experiments, and the average relative error is below 7.38 %. Finally, two types of satellite droplet formation regimes including rear-merging and forward-merging satellite droplets are identified by the oscillation mode of the jet tip. It is found that the primary droplet generation frequency is equal to the external disturbance frequency and independent of nozzle length and modulation amplitude. Increasing the nozzle length and modulation amplitude can both increase the satellite droplet diameter and primary droplet spacing, while the primary droplet diameter is almost constant at around 1.85.

Cascade Formation of Topological Defects and Satellite Droplets in Liquid Crystals at Dynamic Capillary Instability

The formation of topological defects at the nematic–isotropic liquid interface and near satellite droplets has been detected at the breakup and fragmentation of the bridge of the isotropic phase between nematic domains. This process has been implemented in thin optical cells filled with a liquid crystal. The critical width of the bridge at which a universal time dependence of its width is determined by the capillary velocity (ratio of the surface tension to the viscosity) has been determined.

Pinch-off dynamics in unequal-size droplets head-on collision on a wetting surface: Experiments and direct numerical simulations

There is a growing interest in the optimization of spray systems to minimize reflexive separation and enhance droplet coalescence, which has the potential to greatly benefit industrial and agricultural applications. In this investigation, the pinch-off dynamics in head-on impacts of unequal-size droplets on a hydrophobic surface are explored, employing both experimental and numerical approaches. The study focuses on size ratios ranging from 1.0 to 5.0 and impact Weber numbers up to 208. The captured images from the high-speed camera are meticulously processed and analyzed in a detailed manner. Two distinct scenarios are observed in the experimental findings: (1) reflexive separation occurring without the formation of satellite droplets and (2) reflexive separation characterized by the presence of satellite droplets. Direct numerical simulations are also conducted to probe the underlying dynamics during droplet impact. The direct numerical simulation results closely replicate the experimental results, demonstrating excellent agreement with the dynamics of the pinch-off process. The simulated velocity field demonstrates the liquid's movement away from the neck region, leading to progressive thinning and eventual pinch-off. Furthermore, the study examines the evolution of the neck radius over time (τ), revealing a linear variation in log–log plots. Remarkably, the neck radius scales with τ2/3, even for different size ratios. A regime diagram in We–Δ space is reported.

Instability of cholesteric bridge in isotropic environment with break-up and satellite droplet formation

ABSTRACT We investigate quasi-two-dimensional coalescence of domains of isotropic liquid in chiral liquid crystal in flat optical cells. It is demonstrated that coalescence can be accompanied by instability of the liquid crystal bridge separating the domains. We analyse the transformation of the bridge for materials in a wide range of the pitch of the cholesteric helix and different spatially modulated structures: planar cholesteric, one-dimensional stripe structure, focal conic structure and Blue Phases. The instability is followed by cascade break-up and formation of satellite cholesteric droplets. This picture differs from the standard three-dimensional coalescence scenario, where only a bridge between the droplets forms and grows. Studies of thinning dynamics in the bridge region showed that at the final stage of instability the width of the cholesteric bridge decreased linearly with time. In cholesteric with high chirality and small helical pitch the bridge thinning occurs substantially slower than in cholesteric with large helical pitch.

Experimental investigation of dynamics of primary and satellite droplet formation

Experimental investigation of dynamics of primary and satellite droplet formation

Dynamics of drop formation and characterization of additive manufactured CS/AgNP/PVA composite membranes

AbstractThis study investigated the dynamics of drop formation and the printability of chitosan/silver nanoparticles composite fluid (CS/AgNP) modified with polyvinyl alcohol (PVA) using an inkjet 3D printer. It specifically investigated the relationship between rheological properties and fluid mechanical properties in determining the minimum drop velocity for 3D printing of modified CS ink. Proper matching of modified CS fluid rheological properties to the established physical parameters generated adequate droplets on glass substrates and formed membrane composites. The dynamic viscosity of the CS ink decreased with an increase in the concentration of PVA, which resulted in the disruption of existing molecular forces within the CS/AgNP polymer chains, suggesting that the solvent (PVA) was responsible for reducing the shear stress, surface tension, and viscosity of the composite membranes and subsequently improving the flow rates of the CS matrix at the nozzle orifice. Optimized drop velocity of 1.77 m/s yielded adequate formation of the CS/AgNP/PVA membrane composite with enhanced surface morphology, while an increase in drop velocity to 2.5 m/s brought about the formation of satellite droplets with irregular surface structures in printed CS composites. Therefore, adherence to minimum fluid drop velocity is fundamental to effective inkjet printing of composite membranes.

Liquid thread breakup and the formation of satellite droplets

The breakup of liquid threads into smaller droplets is a fundamental problem in fluid dynamics. In this study, we estimate the characteristic wavelength of the breakup process by means of many-body dissipative particle dynamics. This wavelength shows a power-law dependence on the Ohnesorge number in line with results from stability analysis. We also discover that the number of satellite droplets exhibits a power-law decay with exponent 0.72 ± 0.04 in the product of the Ohnesorge and thermal capillary numbers, while the overall size of main droplets is larger than that based on the characteristic wavelength thanks to the asynchronous breakup of the thread. Finally, we show that the formation of satellite droplets is the result of the advection of pinching points toward the main droplets in a remaining thinning neck, when the velocity gradient of the fluid exhibits two symmetric maxima.

Cascade Formation of Topological Defects and Satellite Droplets in Liquid Crystals at Dynamic Capillary Instability

The formation of topological defects at the nematic–isotropic liquid interface and near satellite droplets has been detected at the breakup and fragmentation of the bridge of the isotropic phase between nematic domains. This process has been implemented in thin optical cells filled with a liquid crystal. The critical width of the bridge at which a universal time dependence of its width is determined by the capillary velocity (ratio of the surface tension to the viscosity) has been determined.

Research on the printing mechanism of electrohydrodynamic satellite-free droplets in pulsed voltage

Electrohydrodynamic (EHD) drop-on-demand (DOD) printing in pulsed voltage is a very promising technology for additive manufacturing at the micro- and nanoscale. However, jet/meniscus retraction during DOD printing creates additional satellite droplets, which can lead to blurred print patterns and thus reduced print resolution. In this paper, the mechanism of satellite droplet formation in EHD DOD printing in pulsed voltage is investigated in detail for the first time. At first, the numerical model for EHD printing is established and the correctness and credibility of the numerical results are verified experimentally. After that, the three key operating parameters peak voltage, voltage duration, and bias voltage are analyzed in detail on the formation mechanism of satellite droplets. The operating phase diagram without satellite droplets is proposed. Finally, the electric Bond number BoE and Ohnesorge number Oh are proposed for the detailed analysis of the physical parameters of the liquid on the generation of satellite droplets, and the prediction model of satellite droplet size is presented. The mechanism of satellite droplet formation in EHD printing is revealed, which provides a theoretical basis for the stable printing of satellite-free droplets and advances its application in high-resolution additive manufacturing.

Effect of drainage device on the transition of dripping and jetting modes

The formation of droplets is a part of many practical engineering problems. Satellite droplets are harmful in the production of traditional Chinese medicines, ink-jet printing, and electronic packaging. It is necessary to investigate the methods to eliminate the satellite droplets. A drainage device was added to the dropper to suppress the formation of satellite droplets. This paper investigated the effects of liquid physical parameters and drainage devices on the fracture length of the neckline and the main-droplet diameter. The effect of the diversion device on the ligament was analyzed using the scaling theories of the Pinch-Off. The effect of the drainage device on the transition of the fluid from the dripping mode to the jetting mode was also investigated. After adding the drainage device, the fracture length of the neckline, the main-droplet diameter, and the number of satellite droplets are significantly reduced. The fracture length of the neckline and the main-droplet diameter decreased with the increase in the length and diameter of the drainage, but the fracture length increased with the increase in liquid depth. With the rise of glycerin mass fraction, the fracture length of the neckline increases, whereas the main-droplet diameter decreases.

Droplet-particle collision dynamics: A molecular dynamics simulation

Molecular dynamics simulations are conducted to investigate the normal collision of the droplet-particle system. A wide range of influencing factors including the initial Weber number (30 ≤ We≤250), equilibrium contact angle (45° ≤ θ ≤ 145°), droplet-particle size ratio (0.5 ≤ Ω ≤ 2), temperature (293 K ≤ t ≤ 573 K) and composition are examined. Based on the atomic trajectories and kinetic energy dissipation during collision, temporal evolutions of evaporation molecules, dimensionless spreading diameter and film thickness are quantified and compared with available formulations. A total of seven collision outcomes are observed, which can be summarized in the regime map. Two types of disintegration, i.e. ligament-structured disintegration and conical-structured disintegration, exhibit distinct energy dissipation modes. An increasing We and a decreasing θ would lead to an increase in the maximum spreading diameter, while the minimum film thickness is less sensitive to θ. Additionally, evaporation during collisions is primarily influenced by the initial Weber number, because of the formation of satellite droplets.

Numerical investigation of the effect of operating parameters on droplet ejection in a double ring electrohydrodynamic printing device

Electrohydrodynamic (EHD) printing is an additive manufacturing technology that has many advantages such as high resolution and a wide range of available materials, etc. In the present work, we proposed a double ring electrode ejection device with two coaxial rings as electrodes that operates at pulsed voltage. The device could overcome some drawbacks existing in traditional EHD printing devices, such as unstable ejection caused by changing electric field. In order to study the ejecting phenomenon and the effects of operating parameters, a numerical model based on the Phase field method was established, which fully considered the electrical force including Coulomb force and polarization force. We found four possible ejection modes caused by various jet lengths and values of surface tension force at the voltage turn-off time, and a droplet can be generated if the parameters are in a suitable range. Any operating parameter that is too high will lead to the formation of satellite droplets, while any operating parameter that is too low will lead to no ejection. Additionally, when the voltage is turned off, if the jet has been generated and the surface tension force at the tip of the jet is excessively large, a droplet will be ejected but return to the nozzle eventually.

Numerical study of continuous liquid tin jet breakup and satellite droplet formation

This study proposed a velocity modulation model in which the main flow and perturbation were defined as velocity inlet boundary conditions to simulate liquid tin jet breakup into droplets with external disturbances. The volume of the fluid method was implemented for interface tracking, and adaptive mesh refinement was adopted to guarantee the accuracy of perturbation evolution at the interface during numerical iterations. When the dimensionless wave number is 0.7, almost no satellite droplets are formed. However, when the dimensionless wave number decreases to 0.51, satellite droplets are generated evidently and exhibit from backward-merging to forward-merging with the primary droplets as the disturbance amplitude increases. From the velocity profile, the jet evolution can be divided into three regions: non-breakup, droplet streams, and breakup-merging regime. The droplet sequence uniformity is poor with a small disturbance amplitude. Compared with the conventional velocity modulation model, the proposed model can describe the transition of satellite droplets from backward-merging to forward-merging with increased disturbance amplitude. If the dimensionless wave number is higher than 0.3, only forward-merging occurs with large disturbance amplitudes. Furthermore, in the condition that the dimensionless wave number decreases to 0.25 and below, satellite droplets merge forward and backward simultaneously. Increasing the disturbance amplitude makes the mergence of satellite droplets with the main droplet significantly faster when the dimensionless wave number is 0.3 or below. On the contrary, if the dimensionless wave number is more significant than 0.38, the mergence of satellite droplets slows down with the increase in the disturbance amplitude.

Optimal Design of Droplet Ejection for PZT Printhead Based on Surrogate Model

Droplet ejection technology is widely used in green and intelligent manufacturing. A stable jetting can be defined as no obvious satellite droplets during the whole ejection process, which is of great importance to ensure the quality and efficiency of the printed products; However, due to the multi-parameter features and the interaction between different physics, using traditional analytical-based approaches to analyze and/or optimize is usually difficult and even unfeasible. Experimental tests using a PZT printhead design-optimization method based on surrogate modeling are proposed in this paper to overcome this challenge, which can synthesize the advantages of numerical simulation. The basic data for surrogate model construction was obtained by the Computational Fluid Dynamics (CFD) numerical-based model, which was developed to predict the flow characteristic under different parameter settings of the printhead. The accuracy of the developed numerical model was validated by performing experimental tests; thereby, the predictive ability of the numerical model in droplet ejection was verified. With the validated numerical model, the Design of Experiments (DoE) was performed to generate the necessary training and validation sample dataset required by the surrogate modeling. Thereafter, four surrogate modeling methods were adopted to construct the relationship between the design parameters and flow features, where the Kriging (KRG) was identified as the optimal modeling method. Based on the developed KRG model, global sensitivity analysis (GSA) of the parameters was carried out with Sobol’s method; thereby, the influence of different parameters can be quantified. Finally, a genetic algorithm (GA) was used to optimize the structure of the droplet printhead. Through validation, the optimized design model increases the droplet ejection speed by 20.84% while keeping no satellite droplet formation, confirming the efficient and stable printhead ejection, and verifying the feasibility and effectiveness of the analysis/optimization method proposed in this paper.