Main Droplet Research Articles

Elimination of satellite droplets in droplet streams by superposing harmonic perturbations

In tin-droplet laser-produced plasma sources, uniform droplet streams with large droplet spacing are desired to minimize the interference of explosion on neighboring droplets. Such droplet streams can be generated in low wavenumber regimes. However, satellite droplets easily appear among main droplets in those regimes, resulting in plenty of undesirable debris. Herein, a novel odd harmonic superposition perturbation method is proposed to eliminate satellite droplets and enhance droplet spacing of uniform droplet streams. The superposition number (N) and the phase difference (θ) of odd harmonic perturbations are adjusted to facilitate the coalescence of satellite droplets with main droplets. First, the superposed odd-order harmonic components could induce additional disturbance growth in jet surfaces, and finally lead to the asymmetric necking on filaments formed between two adjacent main droplets, featured as various carrot-shaped configurations. This asymmetric necking will cause unbalanced surface tension forces at the two sides of filaments, resulting in a velocity difference between satellite and main droplets. Based on this principle, by setting N and k to 3 and 0.2, respectively, satellite droplets positioned above main droplets accelerate, while those below decelerate, achieving complete coalescence between main and satellite droplets. Furthermore, the phase difference is found to determine the jet breakup location and satellite droplet merging characteristics. As θ varies from 0° to 90°, the droplet size significantly decreases while the droplet spacing remains constant since the perturbation energy increases. The merge direction of satellite droplets reverses from upward to downward due to enhanced unbalanced surface tension forces and velocity differences. As θ continuously increases to 270°, the droplet size further decreases along with a slight decrease in droplet spacing. Finally, by setting N = 3 and θ = 0°, mono-disperse tin droplet streams with a mean diameter of 31.5 μm and a maximum droplet spacing-to-diameter ratio of 17.7 are successfully formed. This work presents a novel approach for eliminating satellite droplets to achieve uniform tin droplet streams with large droplet spacing without increasing the droplet diameter.

Formation of sodium-alginate droplets in an X-microdevice: Characterization of the pinching efficiency

Experiments and simulations are used jointly to gain a comprehensive insight into the pinching mechanism that generates alginate droplets in an X-microdevice operating in a hydrodynamic flow-focusing configuration. The X-microdevice is fed with an aqueous alginate solution into one inlet channel, while sunflower oil and Span80 are fed into the other two inlet channels. The use of the adaptive mesh refinement and volume of fluid method allows accurate tracking of the interface in numerical simulations. The sensitivities of numerical predictions to the contact angle and the surface tension are estimated through dedicated sets of simulations. Subsequently, numerical simulations and experiments are compared for different flow rates with a satisfactory agreement. We observe that the pinch-off mechanism may lead to the formation of several satellite drops in addition to the main droplet. A pinching performance indicator is suggested based on the amount of alginate that is encapsulated in the main droplet. The effect of operating conditions on the pinching efficiency, frequency, and droplet diameter is discussed to provide valuable information to optimize the droplets production. The pinching efficiency is closely related to the length and diameter of the liquid thread. At low flow rates, a short liquid thread is observed. This leads to the formation of few satellites and, thus, to high pinching efficiency but low droplet production. Increasing the dispersed-phase flow rate slightly reduces the efficiency but significantly increases the production.

An effective droplet sieving method by a trapezoidal stepped microchannel

The droplet sieving process in a trapezoidal stepped microchannel was visually investigated. The sieving mechanism of the small droplet and the moving trajectory of the main droplet were studied. Three flow patterns were found in the experiment: incomplete sieving, complete sieving and main droplet loss regimes. The results show that with the increase of continuous phase superficial velocity Ut, the flow pattern evolves from incomplete sieving to complete sieving and finally to the main droplet loss regimes. The continuous phase flow rate range for the complete sieving regime increases with the growth of main droplet size. Meanwhile, the influences of droplet size and flow rate of continuous phase on the sieving process were investigated. The sieving efficiency decreases with the increase of droplet size of small droplets, whereas it is almost unaffected by the main droplet size. Under the same continuous phase flow rate of regulating channel, the higher continuous phase flow rate of the main channel would lead to lower sieving efficiency.

Upscaled Production of Satellite-Free Droplets: Step Emulsification with Deterministic Lateral Displacement.

Step emulsification is a key technique for achieving scalable production of monodisperse emulsion droplets owing to its resilience to flow fluctuations. However, the persistent issue of satellite droplets, an inherent byproduct of main droplets, poses challenges for achieving truly uniform product sizes. In a previous study, we introduced a module with step-emulsifier nozzles upstream and deterministic lateral displacement (DLD) micropillar arrays downstream to generate satellite-free droplets at a low throughput. In this study, we demonstrate an upscaled parallelized setup with ten modules that were designed to produce satellite-free droplets. Each module integrated 100 step-emulsification nozzles in the upstream region with DLD micropillar arrays downstream. We conducted 3D flow simulations to ensure homogeneous distribution of the input fluids. Uniformly supplying an aqueous polyvinyl alcohol solution and an acrylate monomer as continuous and dispersed phases into the ten modules, the nozzles in each module exhibited a production rate of 539.5 ± 28.6 drop/s (n = 10). We successfully isolated the main droplets with a mean diameter of 66 μm and a coefficient of variation of 3.1% from satellite droplets with a mean diameter of 3 μm. The total throughput was 3.0 mL/h. The high yield and contamination-free features of our approach are promising for diverse industrial applications.

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.

Single droplet formation by controlling the viscoelasticity of polymer solutions during inkjet printing

Inkjet printing has emerged as a potential solution processing method for large-area patterned films. During inkjet printing, a single droplet without satellite droplet is required for high-quality film. Herein, we propose a strategy for obtaining a single droplet by adjusting the reduced concentration (c/c*, where c* is the critical overlap concentration) in the range of 1.0–1.5. Droplet formation can be categorized into three distinct regimes: (1) c/c* < 1.0, satellite droplet; (2) c/c* = 1.0–1.5, single droplet; (3) c/c* > 2.0, no droplet. Furthermore, an inertial-capillary balance led to the 2/3-power scaling of the minimum radius with time for the solutions of c/c* < 1.0. However, for the solutions of c/c* = 1.0–1.5, the ligament radius decreased exponentially with time. Moreover, the Weissenberg number was higher than the critical value of 0.5, indicating that the polymer chains underwent coil-stretch transition. The viscoelastic-capillary balance dominated instead of the inertial-capillary balance. The resulting viscoelastic resistance reduced the length of the ligament and increased the velocity difference between the satellite and main droplets. Consequently, a single droplet was formed. In addition, the law can be successfully generalized to various molecular weights, molecular structures and solvents.

Investigation on the motion of droplets excited by Lamb waves on an inclined non-piezoelectric curved substrate

In this work, the motion of droplets on an inclined non-piezoelectric curved substrate is investigated to study the performance of the Lamb waves (LWs)-driven surface cleaning of the camera lens or other optical components. The droplets do not slide forward on the curved substrate with an inclination less than 5° is verified by experiments. And then, the shape changes of droplets are discussed from experiments and simulation. A two-phase flow simulation model is established using the level set method, which the deformation of gas-liquid interface can be clearly observed when the droplet moves. The observation results that the movement of droplets on the inclined curved glass driven by LW are propelled periodically in a stretching and spreading phases. To investigate the effect of LWs on droplets removal, the movement distance of droplets are measured in four main factors, namely, substrate inclination, input power, droplet volume and surface curvature.

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.

Dynamics of liquid dispersion in a rotating packed bed with single‐layer wire mesh

AbstractThe improvement of liquid dispersion by rotating wire mesh is one of the major causes for the mass transfer and micromixing intensification in rotating packed beds (RPBs). In particular, the initial dispersion region has been proved to have the greatest mass transfer and micromixing efficiency. However, the dispersion mechanism has not been revealed. This study investigated the dynamics of liquid dispersion in an RPB with single‐layer wire mesh. The liquid dispersion behaviors were obtained by high‐speed photography and numerical simulation. The liquid was found to stretch into ligaments and break into the main droplet and several satellite droplets. A new theoretical model was established to reveal the dispersion mechanism of these two stages. The stretching stage depends on the liquid initial momentum and acquired impulse, while the breakup stage was determined by the competition of ligaments recoil and pinch‐off behaviors. The model was validated in good agreement with the experimental and simulation results of the dispersion characteristics.

Microfluidic Coupling of Step Emulsification and Deterministic Lateral Displacement for Producing Satellite-Free Droplets and Particles

Step emulsification, which uses a geometry-dependent mechanism for generating uniformly sized droplets, has recently gained considerable attention because of its robustness against flow fluctuations. However, like shear-based droplet generation, step emulsification is susceptible to impurities caused by satellite droplets. Herein, we demonstrate the integration of deterministic lateral displacement (DLD) to separate the main and satellite droplets produced during step emulsification. Step-emulsification nozzles (16 μm deep) in the upstream region of the proposed device were arrayed on the sidewalls of the main channel (91 μm deep). In the downstream region, the DLD micropillars were arrayed periodically with a critical diameter (cut-off value for size-based separation) of 37 μm. When an acrylate monomer and aqueous polyvinyl alcohol solution were infused as the dispersed and continuous phases, respectively, the nozzles produced monodisperse main droplets in the dripping regime, with an average diameter of ~60 μm, coefficient of variation (CV) value below 3%, and satellite droplets of ~3 μm. Upon entering the DLD region near the sidewall, these main and satellite droplets were gradually separated through the pillars based on their sizes. Finally, off-chip photopolymerization yielded monodisperse polymeric microspheres with an average diameter of 55 μm and a CV value of 2.9% (n = 202).

Droplet separation and sieving mechanism by grooved microchannel

A novel droplet sieving method utilizing grooved microchannel is proposed to achieve the monodispersity of droplets. The sieving performance and mechanism are investigated experimentally. Three different sieving flow regimes are observed in the experiment: incomplete sieving, complete sieving and main droplet rupture. The effects of different operating conditions on sieving efficiency are studied systematically. The results showed that when the total flow rate of the continuous phase in the main channel is lower, the small droplets would accumulate between the main droplets and could not be separated. Complete sieving could be achieved when the main body of the small droplet enters the sieving layer before arriving at the sieving channel. The larger continuous phase flow rate in sieving channel could create thicker sieving layer, which is conducive for small droplets to entering the sieving layer to achieve complete sieving. On the contrary, the higher continuous phase flow rate in the main channel would lead to thinner sieving layer, and the required flow rate in sieving channel would be higher to achieve complete sieving. Under the same sieving channel flow rate, the longer droplet is more apt to rupture. The sieving mechanism of droplets is proposed according to the force analysis in the channel. Whether the main droplet ruptures at the sieving junction depends on the combined action of the suction of the sieving channel, the interfacial tension, and the supporting force of the sieving groove.

Axisymmetric lattice Boltzmann model for three-phase fluids and its application to the Rayleigh-Plateau instability

Based on the multi-component phase field theory, in this paper we propose an axisymmetric lattice Boltzmann model for three-phase fluids. The proposed model takes advantage of two particle distribution functions for capturing phase interface among three different fluids, and another particle distribution function for solving the hydrodynamic equations for flow field. In order to describe the axisymmetric effect arising from the coordinate transformation, we elaborately design the equilibrium distribution function and forcing distribution function in the evolution equation, which ensures that the model can accurately recover the macroscopic governing equation for three-phase fluids. Also, the introduced source terms accounting for the axisymmetric effect contain no additional gradient term, which makes it be simpler than the existing lattice Boltzmann model for axisymmetric three-phase fluids. To validate the proposed model, a series of axisymmetric multiphase benchmark examples are performed, including the static double droplets, the spreading of liquid lens, and the binary-fluid Rayleigh-Plateau instability. It is reported that the present model can accurately capture the phase interface, and the predicted steady shapes of the liquid lens agree well with the analytical profiles. Then, the proposed model is used to study the three-phase Rayleigh-Plateau instability and the effects of the wavenumber and the radius ratio of liquid column on the interfacial dynamic behaviour, the breakup time of liquid threads and the size of daughter droplet are investigated in detail. It can be found that the compound liquid thread at a high wavenumber could break up into one main droplet and one satellite droplet, but the multiple satellite droplets can be produced at a low wavenumber, which leads to that the sizes of main and satellite droplets increase with the wavenumber at first and then decrease with it. Besides, we can observe that the inner fluid undergoes the breakup at earlier time than the middle fluid, and the breakup time for both inner and middle fluids increases with the decrease of the wavenumber. Finally, we can find that increasing the radius ratio of liquid column accelerates the breakup of inner-fluid thread, but prevents the breakup of the middle-fluid thread. In addition, the size of the compound main droplet increases with the radius ratio of liquid column, while the size of the compound satellite droplet doest not change much with it.

Droplet Detection and Sorting System in Microfluidics: A Review.

Since being invented, droplet microfluidic technologies have been proven to be perfect tools for high-throughput chemical and biological functional screening applications, and they have been heavily studied and improved through the past two decades. Each droplet can be used as one single bioreactor to compartmentalize a big material or biological population, so millions of droplets can be individually screened based on demand, while the sorting function could extract the droplets of interest to a separate pool from the main droplet library. In this paper, we reviewed droplet detection and active sorting methods that are currently still being widely used for high-through screening applications in microfluidic systems, including the latest updates regarding each technology. We analyze and summarize the merits and drawbacks of each presented technology and conclude, with our perspectives, on future direction of development.

Primary atomization of liquid jets: Identification and investigation of droplets at the instant of their formation using direct numerical simulation

A detailed investigation of droplet characteristics for the primary atomization of a round liquid jet injected into stagnant gas is performed using direct numerical simulation. The material properties correspond to a Diesel injection, and the numerical framework is based on the volume-of-fluid method. The study is carried out in the statistically steady state, which allows to collect time-averaged droplet formation statistics. A novel algorithm continuously detects droplets at the instant they detach from the liquid core jet, which are referred to as primary droplets. The main droplet characteristics, such as volume, velocity and sphericity, are captured for newly formed primary droplets as well as all other droplets in the domain. This allows a detailed comparison between droplet characteristics during and after their formation. In addition, the droplet Weber, Reynolds and Stokes numbers are computed. These dimensionless numbers govern important physical processes occurring subsequent to the droplet formation, such as potential secondary breakup and droplet motion. One central goal is to provide information relevant for large eddy simulation of sprays in the Eulerian–Lagrangian framework, where the formation of small droplets from the liquid core jet cannot be resolved, and therefore potentially needs to be modeled. Moreover, the relative importance of primary and secondary atomization is estimated for this specific setup. It is found that the distribution of the droplet sizes is very similar for primary droplets and the entire droplet collective. Furthermore, the droplet Weber numbers are significantly below the critical Weber number required for secondary droplet breakup. Together, these two observations indicate that, for the investigated configuration, primary atomization is the dominating process, while secondary atomization only plays a minor role. Moreover, the high droplet volume fraction observed shows that droplet–droplet collisions and coalescence can be expected to influence the spray behavior. To put the obtained results into perspective, empirical correlations for the Sauter Mean Diameter are used to discuss potential trends for higher Reynolds and Weber numbers.

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.

Visualizing water inside an operating proton exchange membrane fuel cell with video‐rate terahertz imaging

AbstractSuccessful water management is critical to achieving high performance in proton exchange membrane fuel cells (PEMFCs). The relatively high sensitivity of terahertz radiation to liquid water is promising as a complementary alternative for flooding detection in PEMFCs. Using a novel, commercially available terahertz source and camera, this paper investigates the feasibility of a compact and low‐cost terahertz imaging system for visualizing water build‐up inside an operating PEMFC, supported by simultaneous high‐resolution optical imaging. Several phenomena of water accumulation and transport, such as membrane hydration, main droplet appearance, water pool formation, growth, and eventual flush out by gases are imaged by terahertz imaging. These results agree with optical imaging and cell voltage readings. The proposed setup is also able to distinguish the effect of different air flow rates.

The optimally chemically striped surface promotes the generation of larger satellite droplets

After impacting the chemically striped surface (CSS), the droplet can split out satellite droplets, greatly increasing the length of the triple-phase contact line (TPCL) to promote droplet evaporation. After the satellite droplets evaporate completely, the main droplet determines the evaporation rate. Therefore, the length of the TPCL and the volume of the main droplet are two critical factors affecting droplet evaporation. Under different droplet diameters and impact velocities, the dimensionless length of the TPCL increases and then decreases with rising stripe width. As the stripe width enlarges, the dimensionless volume of the main droplet firstly decreases and then increases. Therefore, there is an optimized surface to maximize the TPCL length and minimize the main droplet volume. Compared with the non-uniformly striped surface, the surface with a uniform stripe is more conducive to enlarging the length of the TPCL and reducing the volume of the main droplet. This study proposes a theoretical model to forecast the stripe number spanned by the droplet, which determines whether the droplet splits. When the stripe number spanned by the droplet at the maximum spread moment is between 3 and 5, the droplet can split out larger satellite droplets, making the length of the TPCL largest and the volume of the main droplet smallest.

Peculiarities of aluminum particle combustion in steam

This work experimentally addresses aluminum combustion in steam, pure or mixed with diluents, for aluminum particles in size range 40∼80 µm, using an electrodynamic levitator. High-speed videos unveil an unreported and complex mechanism in steam, not observed in other oxidizers. The detached flame is quite faint and very close to the surface. Alumina smoke around the droplet rapidly condenses and coalesces into a large, single orbiting alumina satellite. It eventually collides the main aluminum droplet while generating secondary alumina droplets. A unique feature is the presence of several distinct oxide lobes on the droplet, which merge only at the end of burning and encapsulate the remaining aluminum, possibly promoting an incomplete combustion. The measured burning times in pure water vapor are longer than expected and the efficiency of steam is found to be 30% that of oxygen, lower than the usually accepted value of 60%. A general correlation on burning time, including the major oxidizers, is proposed. Direct numerical simulations are conducted and are in line with experiments, in terms of burning rate or flame stand off ratio. Combustion in steam seems mostly supported by surface reactions, giving a faint flame with low gas temperatures and high hydrogen content. It is speculated that those two specific features could help explain the peculiarity of steam.

Effects of heat transfer on particle suspended Drop-on-Demand inkjet printing using lattice Boltzmann method

Inkjet printing is attracting significant attention as a next-generation process for display production. However, the heat generated during printing and the particles contained in the ink deteriorate the injection accuracy and reliability. Therefore, in this study, an integrated simulation model, including multiphase flow, particle dynamics, and heat transfer, was constructed to analyze the droplet injection process. The effects of particles and heat on asymmetric ejection and satellite droplet formation were analyzed via this numerical model. Even at very low particle concentrations with negligible rheological property changes, the effect of particles on the ejection behavior differed from that of pure ink. The particle-laden droplet was asymmetrically ejected via thread recovery, substrate impact, and capillary processes. The particles in the thread moved the thread breakup point from the main droplet to the end of the thread, thereby accelerating satellite droplet formation. The temperature distribution of the droplets was observed when heat was applied to the print head. The heat transferred to the droplet accelerated the main droplet separation. Recovery of the thread did not occur because of rapid thread breakage, which resulted in poor injection accuracy.

Numerical analysis of ligament instability and breakup in shear flow

In this study, we perform a numerical analysis of the instability of a ligament in a shear flow and investigate the effects of air–liquid shear on the growth rate of the ligament interface, breakup time, and droplet diameter formed by the breakup. The ligament is stretched in the flow direction by the shearing of airflow. Furthermore, as the influence of the shear flow increases, the ligament becomes deformed into a liquid sheet, and a perforation forms at the center of the liquid sheet. The liquid sheet breaks up due to the growth of the perforation and contracts under the influence of surface tension, forming two ligaments with diameters smaller than that of the original ligament. The shearing of the airflow causes the original ligament to elongate, and the cross section of the ligament becomes elliptical, which increases instability. As a result, the growth rate of the ligament exceeds the theoretical value and increases with increasing the wavenumber of the initial disturbance. Therefore, the diameter of the formed droplets in the shear flow decreases due to the increase in the wavenumber that governs the breakup of the ligament, and as the growth rate increases, the breakup time for the ligament decreases. As the velocity difference of the shear flow increases, constrictions of the ligament form earlier and the diameter of the satellite droplet increases. As the diameter of the satellite droplet increases and that of the main droplet decreases, the dispersion of the droplet diameter decreases, making the diameter uniform.