Droplet Swarms Research Articles

A CFD‐PBM‐ANN framework to simulate the liquid–liquid two‐phase flow in a pulsed column

AbstractCFD‐PBM numerical simulation is a powerful tool in the research of droplet swarm behavior. In this work, an artificial neural network (ANN) based droplet breakage frequency function is established based on the directly measured data from our previous studies. Then, the weights and biases of ANN are embedded into the CFD‐PBM code in the form of matrices and vectors. For the first time, a CFD‐PBM‐ANN simulation framework is established. Simulation results are in good agreement with the experimental data under different operation conditions. The cumulative droplet size distribution decreases with the increase of interfacial tension and pulse intensity. It is also found by the simulation that the droplet breakage frequency is relatively high at the edge of disc and doughnut plate, which is accordant with the distribution of turbulent energy dissipation and velocity gradient.

Arrangement and feedback effects of droplet swarms in a parallel microchannel device

Droplet swarms are the dominant form of highly dispersed microdroplets in cavities. During the self-assembly of droplet swarms, the continuous phase is inclined to flow along the path of the minimum resistance, while the arrangement of the droplet swarms seeks to minimize the potential energy, and the two mechanisms compromise in competition. In this paper, the ability of droplet swarms to timely adjust the morphology is measured by the ratio of the average flow rate of the two-phase flow to that of the droplet swarms, thereby clarifying the dominant mechanism of the arrangement of droplet swarms. The arrangement of droplet swarms dominated by different mechanisms and their distribution are introduced, and the prediction method for the arrangement of droplet swarms is proposed. The mechanism underlying the breakup of the microdroplets in the cavity is elucidated, and three modes of the breakup in the cavity are introduced. Furthermore, a resistance model for the microdevice is established to quantify the fluctuations of pressure difference and flow rate resulting from the formation of droplet swarms. The feedback effects of droplet swarms on the uniformity of droplet formation and flow patterns are analyzed, revealing the ideal flow range for the formation of highly dispersed droplets in microchannels. This paper elucidates the arrangement and the feedback effects of droplet swarms, which will guide the application of microdevices in reaction and mass transfer processes.

Quorum Sensing in Emulsion Droplet Swarms Driven by a Surfactant Competition System.

Quorum sensing enables unicellular organisms to probe their population density and perform behavior that exclusively occurs above a critical density. Quorum sensing is established in emulsion droplet swarms that float at a water surface and cluster above a critical density. The design involves competition between 1) a surface tension gradient that is generated upon release of a surfactant from the oil droplets, and thereby drives their mutual repulsion, and 2) the release of a surfactant precursor from the droplets, that forms a strong imine surfactant which suppresses the surface tension gradient and thereby causes droplet clustering upon capillary (Cheerios) attraction. The production of the imine-surfactant depends on the population density of the droplets releasing the precursor so that the clustering only occurs above a critical population density. The pH-dependence of the imine-surfactant formation is exploited to trigger quorum sensing upon a base stimulus: dynamic droplet swarms are generated that cluster and spread upon spatiotemporally varying acid and base conditions. Next, the clustering of two droplet subpopulations is coupled to a chemical reaction that generates a fluorescent signal. It is foreseen that quorum sensing enables control mechanisms in droplet-based systems that display collective responses in contexts of, e.g., sensing, optics, or dynamically controlled droplet-reactors.

Numerical Evaluation of Sodium Droplet Swarm Combustion and Its Modeling Optimization

Because of its superior thermal-hydraulic qualities, liquid sodium has been applied to a variety of industries, including energy storage, solar energy, sodium-cooled fast reactors, and aerospace. However, fires brought on by sodium leaks at high pressure can have major thermodynamic repercussions and put employees and equipment in use at risk directly or indirectly. As a result, a realistic and accurate forecast of the combustion behavior of sodium droplet swarm can offer technical backing for the use of liquid sodium in engineering as well as a way of sodium fire prevention and control. Spray dynamics (droplet settling, droplet particle size distribution, etc.), combustion kinetics (premixed combustion, gas phase combustion, etc.), sodium aerosol diffusion, and other specialized phenomena all contribute to the complex process of sodium droplet swarm combustion. The NACOM code created by Brookhaven National Laboratory for sodium droplet swarm combustion is utilized in this paper as a framework. The code is first validated using the benchmark of the sodium droplet swarm combustion tests carried out by prestigious institutions. The validation results demonstrate that the code’s drag model, droplet combustion model, and heat transfer model are to blame for the significantly overestimated thermodynamic effects of sodium droplet swarm combustion. NACOM is subsequently developed twice for the authors’ previously developed vapor-liquid two-layer-structure drag model, chemical kinetic combustion model, and suitable heat transfer coefficient. It is then thoroughly assessed for the separate-effects tests and integral-effects test. The evaluation results demonstrate that the optimized drag model accelerates the settling of sodium droplets due to the consideration of the sodium-vapor drag reduction effect, reducing the thermodynamic effects of liquid sodium combustion; the optimized premixed combustion model can accurately predict the low-temperature sodium droplet swarm combustion conditions, resolving the issue of serious misvaluation of the original version of NACOM. The associated research findings can serve as valuable resources and tools for deeper comprehension of the combustion effects and mechanisms of sodium droplet swarm under various operating settings (such as leakage rate and oxygen concentration).

Unstable spray pattern and cooling performance of cryogen spray coupled with cold air jet: An experimental study

This study focuses on the interactions between cryogen spray cooling (CSC) and cold air jet (CAJ), as well as the heat transfer performance upon CAJ-CSC impingement assisted for laser dermatology. CAJ is found to collapse downstream spray on the windward side, enhancing fluctuations of R1234yf spray width. Standard deviation (SD) distribution identifies that fluctuations at nozzle exit are attributed to ambient-to-spray interactions, which is also confirmed by the proper orthogonal decomposition (POD) analysis. The third POD mode highlights jet-to-spray interactions on the windward side of spray, yielding an enhanced instability by 1.72 times when CAJ flow rate (Q) increases from 4 to 8 m3/h. The closer location to the spray center on the same radial side corresponds to a faster thermal response and a lower temperature drop (ΔT). ΔT on the windward side decreases due to the considerable CAJ-induced droplet swarm drift. The heat transfer degrades on the leeward side due to the thermal gas boundary layer originating from the inclined CAJ sweep. Nevertheless, the CAJ with a small flow rate (4 m3/h) enhances the heat transfer at spray center, yielding a minimum surface temperature of −32.3 °C. Comparative investigation indicates R134a has superior cooling performance but more significant instabilities inside spray plume. R1234yf serves a relatively stable sub-cooling region within a radial distance of ±1 mm from spray center characterized by low spray fluctuations and high temperature drops at Q = 4 m3/h. Substitution of R1234yf for R134a still needs heat transfer enhancement for clinical considerations.

Two-way Eulerian-Lagrangian coupling approach in GASFLOW code for containment spray modelling

Spray droplets are considered to have significant effects on the gas mixing and depressurization in the containment of nuclear power plants during hypothetical accident scenarios. The Eulerian-Lagrangian approach, which enables the two-way mass, momentum, and energy coupling of the continuous gas and the dispersed spray droplets, is promising to model the behaviours of spray droplets in 3D simulations of the full-scale containment. Two-way heat and mass transfer models have been developed in the 3D CFD code GASFLOW. The particle group method is applied in the Lagrangian approach to track the droplets. The ordinary differential equations which couple the local heat and mass exchanges between each droplet group and the surrounding gas mixtures have been solved using the Runge-Kutta method. The GASFLOW coupling this new approach is validated by TOSQAN water spray experiments, which demonstrate the good feasibility of implementing the approach. The analysis of the impact of the spray on containment atmosphere indicates that: 1) the droplet swarm entrains and mixes the surrounding gas, breaking up the gas stratification, with turbulent diffusion dominating momentum mixing in dead zones; 2) the thermal and mass exchanges between the spray droplet swarm and gas jointly determine the atmosphere depressurization, with the evaporation of the spray-formed film/sump on heat structures of great importance for the containment pressure development; and 3) these spray thermodynamic and dynamic effects highly depend on the droplet size distribution and the spray shape.

Horizontal and Vertical Coalescent Microrobotic Collectives Using Ferrofluid Droplets.

Many artificial miniature robotic collectives have been developed to overcome the inherent limitations of inadequate individual capabilities. However, the basic building blocks of the reported collectives are mainly in the solid state, where the morphological boundaries of internal individuals are clear and cannot genuinely merge. Miniature robotic collectives based on liquid units still need to be explored; such on-demand mergeable swarm systems are advantageous for adapting to the changing external environment. Here, a strategy to achieve a coalescent collective system wepresented that exploits the ferrofluid droplets' splitting and coalescence properties to trigger the formation of horizontal multimodal and vertical gravity-resistant collectives and unveil pattern-enabled robotic functionalities. When subjected to a time-varying magnetic field, the droplet swarm exhibits a variety of morphologies ranging from horizontal collectives, including vortex-like, chain-like, and crystal-like patterns to vertical layer-upon-layer patterns. Using experiments and simulations, the formation and transformation of different morphological collectives are shown and their robust environmental adaptability are demonstrated. Potential applications of the multimodal droplet collectives are presented, including exploring an unknown environment, targeted object delivery, and fluid flow filtration in a lab-on-a-chip. This work may facilitate the design of microrobotic swarm systems and expand the range of materials for miniature robots.

Mesoscale effect on droplet formation in a step-emulsification microdevice with parallel microchannels

The monodispersity of droplet generation in parallel microchannels is critical for particle synthesis, chemical reactions, and separations. The mesoscale concept of compromise in competition is critical to reveal complex changes in the dominant mechanisms during droplet formation. In this paper, the uniformity and fluid distribution mechanism of droplet generation in a step-emulsification microdevice with 10 parallel microchannels are investigated by a high-speed camera. It is found that the spontaneous breakup of droplets dominated by interface tension is conducive to the uniform generation of droplets, and the feedback effect of droplet swarms in the cavity reduce the monodispersity of droplets. The pressure drop model in parallel microchannels is constructed. Compromise in competition between microchannels in energy storage phenomenon is analyzed, and the influence of hydrodynamic feedback effect of droplet swarms and the compromise in competition on fluid distribution is explained. The dripping region are improved through the strategy of expelling the droplet swarms by gravity, and droplets with coefficients of variation below 2% are prepared. Finally, a semi-empirical prediction model of droplet size is established.

Coalescence law of microdroplet swarms in microchannels

Droplet microfluidic technology refers to the technique of preparing and controlling microscale monodisperse droplets by shear force and interfacial tension of two immiscible phases accurately, which has a wide range of applications in biomedicine, chemical reaction enhancement, nanoparticle preparation, and other fields due to its efficient mass and heat transfer, easy manipulation, rapid response, and high throughput. In the application of droplet microfluidic technology, coalescence often occurs due to the structural complexity of microchannels, which limits the practical application performance. The mechanism of droplet coalescence has been widely studied in conventional reactors, among which the liquid film drainage theory is the most widely accepted. To achieve accurate control of the droplet coalescence process, there have been many studies on droplet coalescence in microchannels. A variety of microchannel structures have been proposed and the mechanism and influencing factors of double droplets coalescence have been explored. However, most of the existing studies on coalescence are based on cross structures, mainly studying the coalescence of double droplets in confined systems. There is still a lack of research on the coalescence process of droplet swarms, which is more widespread in practical applications. Therefore, this work used the rectangular expansion structure to realize the droplet coalescence and explored the effects of two-phase flow rate, continuous phase viscosity, surfactant concentration, and the size of expanding channel on the droplet coalescence behavior. The coalescence types, probabilities, and size distributions of microdroplet swarms under different factors were summarized. The time distribution of liquid film drainage in the droplet coalescence process and the influence of various factors on it were further analyzed based on the liquid film drainage theory.

Self-assembly of droplet swarms and its feedback on droplet generation in a step-emulsification microdevice with parallel microchannels

• Three-dimensional and two-dimensional arrays of droplet swarms in step-emulsification microdevices are revealed. • The dependence of the self-assembly of droplet swarms on the droplet size and the volume fraction of the dispersed phase is explored. • The control mechanisms of the self-assembly behavior of the droplet swarms are analyzed. • Feedback effect of the self-assembly of droplet swarms on the droplet generation is focused. Self-assembly of droplets in microfluidics is an emerging technology for high-throughput analysis and material synthesis. However, in step-emulsification microdevices, the self-assembly behavior of droplet swarms remains unclear. In this article, droplet swarms are formed due to sequential droplet generation and collected in the cavity. The self-assembly of droplet swarms and its feedback effect on the droplet generation in a step-emulsification microdevice with 10 parallel microchannels are studied by a high-speed camera. Droplets self-assemble into three-dimensional and two-dimensional arrays with specific geometric features in the confined space. The dependence of the self-assembly of droplet swarms on the droplet size and the volume fraction Φ of the dispersed phase is explored. It is found that the self-assembly of droplet swarms is controlled by the depletion force, confinement effect, and interaction between droplets. Finally, from the perspective of mesoscale principle, the weakening of the feedback is beneficial to improve the monodispersity of droplets.

Distribution of liquid-liquid two-phase flow and droplet dynamics in asymmetric parallel microchannels

The numbering-up of microchannels in parallel is usually engineered to achieve high-throughput production of droplets, and the flow distribution of fluids and uniformity of droplets in parallel microchannels are core issues for droplet formation. In this work, the distribution of liquid–liquid two-phase flow and droplet dynamics in asymmetric parallel microchannels are investigated by using a high speed camera, and the factors affecting the stability and uniformity of droplets are explored. The dynamic behavior of droplet swarm in the rear cavity and its feedback effect on droplet generation at T-junctions are revealed. The microfluidic devices with various configurations are designed to investigate its effects on flow distribution. In addition, based on the principle of hydrodynamic resistance for the liquid-liquid two-phase flow in microchannels, the prediction for the distribution of liquid-liquid two-phase flow under slug flow is proposed.

Predictability and benefits of coupled Eulerian-Lagrangian approach over Eulerian characterization of droplet annular flow

Wavy annular flow and subsequent droplet dispersion in air-water two-phase flow has been studied numerically using conventional Eulerian volume of fluid (VOF) solver and coupled Eulerian-Lagrangian approach. The VOF based investigation has been reported to highlights the formation of droplet swarm and its population dynamics. Coupled Eulerian-Lagrangian method has also been shown to replicate similar features with lesser computational effort. Entrainment, deposition, fragmentation and unification are traced from the numerical simulation, which ultimately predicts the volume filling behavior of the droplets inside the tube. Flow kinematics around droplet is critically assessed numerically for finding out reasons behind deposition, fragmentation and unification. A comparative behavior between different velocity ratios of gas and liquid flow rates are presented which clearly shows higher entrainment rate as shear between annular liquid and gaseous core increases. An assessment of the droplet population in coupled Eulerian-Lagrangian method shows the generation of the smaller sized spherical droplet by entrainment and fragmentation route.

The Kinetics of Phase Separation in Liquid‐Liquid Extraction: Modeling of Droplet Swarm Coalescence

AbstractThe kinetics of droplet‐bulk coalescence in liquid‐liquid phase separation was investigated. A modified 1st order rate model was applied to fit the data of three series of experiments with different physical properties. This rate model can characterize the coalescence curve with two kinetic parameters, which are basically just fit parameters. The fit parameters were compared with the physical properties of the investigated systems. They compare well with the density, viscosity, and interfacial tension. The outcome of this study offers a simple and easy to apply tool for kinetic modeling of the coalescence process.

Mass transfer process intensification for SO2 absorption in a commercial-scale wet flue gas desulfurization scrubber

To intensify SO2 absorption process in wet flue gas desulfurization (WFGD) spray scrubber, a comprehensive CFD model coupled transfer process with chemical reactions is established by Eulerian‒Lagrangian method and verified in a commercial-scale device of 330 MW coal-fired power unit. The desulfurization performance is significantly affected by both the property of each droplet and the dispersion of droplet swarm, which are determined by the spray behaviors. Three dominant factors, including droplet diameter, injection direction and spray morphology, are explored to optimize the spray conditions for intensifying SO2 absorption process. Differing from the ideal plug flow, the optimal diameter of droplet in non-ideal flow is obtained by considering the synergistic effect of the uniformity of gas–slurry distribution and the dynamics of SO2 mass transfer. Compared with the single-direction spray with downward or upward injection, the dual-direction spray reaches a great balance between the competitive effects of the uniformity of gas‒slurry flow and the interfacial area for mass transfer. The influence of spray morphology on mass transfer process is essentially the difference of dispersion characteristics of droplets in the middle part of scrubber. A design scheme combining full-cone and hollow-cone nozzles is suggested for improving the overall SO2 removal efficiency.

Whole-cell biocatalytic synthesis of S-(4-chlorophenyl)-(pyridin-2-yl) methanol in a liquid–liquid biphasic microreaction system

This work aims to synthesize S-(4-chlorophenyl)-(pyridin-2-yl) methanol (S-CPMA) in a green, economic, and efficient way. In the water–cyclohexane liquid–liquid system, recombinant Escherichia coli (E. coli) was used as a whole-cell catalyst and retained > 60% of its catalytic activity after five reuse cycles. In situ accumulation of the substrate/product in the organic phase effectively improves substrate tolerance and reduces product inhibition and toxicity. Meanwhile, a microreaction system consisting of membrane dispersion and three-dimensional (3D) bending-microchannel was developed to successfully generate droplet swarms with an average diameter of 30 μm. Large specific surface area provided high mass transfer efficiency between phases. While the analogous reaction in a traditional stirred tank required > 270 min to achieve a yield of > 99%, in this biphasic microreaction system, the yield reached 99.6% with a high enantiomeric excess (ee) of > 99% in only 80 min. Efficient synthesis was achieved by reducing the time by 70%.

Combining level-set method and population balance model to simulate liquid–liquid two-phase flows in pulsed columns

The level-set method and population balance model (PBM) were combined to develop a numerical framework for the simulation of liquid–liquid two-phase flows in a pulsed disc and doughnut column (PDDC). First, breakup behavior in droplet swarms in a local area of the PDDC was elucidated under a low holdup condition using a modified level-set method with multi-levels. The droplet breakup frequency function and the daughter droplet size distribution function were determined via statistical analysis on the breakup behavior in droplet swarms. The determined droplet breakup kernel functions were then plugged into the PBM to simulate liquid–liquid two-phase flows in the full-scale PDDC. The calculated droplet size distribution agreed well with the experimental results. The developed numerical framework provides a strategy to simulate two-phase flows avoiding the use of adjustable parameters which are dependent on experiments.

Model‐based equipment design for the biphasic production of 5‐hydroxymethylfurfural in a tubular reactor

AbstractHerein, a novel concept for the acid catalyzed dehydration of fructose (FRC) to 5‐hydroxymethylfurfural (5‐HMF) in a biphasic tubular reactor is presented. Reaction kinetic models were developed based on experiments performed in a newly developed lab‐scale autoclave that enables a decoupled investigation of single‐phase reaction and 5‐HMF mass transfer. Our reaction kinetic models allow an accurate description of the biphasic reaction. Subsequently, we integrate the reaction kinetic models in the model‐based design of a tailored reactor unit. This reactor unit employs the concept of in‐situ extraction in a countercurrent flow of a monodisperse droplet swarm within a continuous aqueous phase. From reactor calculations, we obtain a maximum 5‐HMF yield of 76% at full FRC conversion. Countercurrent in‐situ extraction enables over 99% 5‐HMF recovery in the organic phase.

Modeling of Sedimentation and Creaming in Suspensions and Pickering Emulsions

Suspensions and emulsions are prone to kinetic instabilities of sedimentation and creaming, wherein the suspended particles and droplets fall or rise through a matrix fluid. It is important to understand and quantify sedimentation and creaming in such dispersed systems as they affect the shelf-life of products manufactured in the form of suspensions and emulsions. In this article, the unhindered and hindered settling/creaming behaviors of conventional emulsions and suspensions are first reviewed briefly. The available experimental data on settling/creaming of concentrated emulsions and suspensions are interpreted in terms of the drift flux theory. Modeling and simulation of nanoparticle-stabilized Pickering emulsions are carried out next. The presence of nanoparticles at the oil/water interface has a strong influence on the creaming/sedimentation behaviors of single droplets and swarm of droplets. Simulation results clearly demonstrate the strong influence of three-phase contact angle of nanoparticles present at the oil/water interface. This is the first definitive study dealing with modeling and simulation of unhindered and hindered creaming and sedimentation behaviors of nanoparticle-stabilized Pickering emulsions.

Numerically simulating droplet breakup in droplet swarm using modified level set method with multi-levels

A modified level set method with multi-levels was developed to simulate the breakup behavior of multi-droplets in the turbulent flow of a pulsed disc and doughnut column. This free interface capturing method uncovered the mechanisms of three droplet breakup patterns that were observed in experiments: (1) breakup owing to shearing effect, (2) breakup because of collision with plate surfaces, and (3) breakup due to interface instability. The simulation results also indicated that the breakup frequency of 2-mm droplets increased from 0.1 to 0.6 s−1 and the breakup duration decreased from 0.025 to 0.015 s when the pulsation intensity increased from 8 to 14 mm/s. Multiple breakage occurred when the droplet size increased to 3 mm. The simulation results agreed well with our previous experimental results.

Fault-tolerant Covariance Intersection for localizing robot swarms

This paper examines the important problem of cooperative localization in robot swarms, in the presence of unmodeled errors experienced by real sensors in hardware platforms. Many existing methods for cooperative swarm localization rely on approximate distance metric heuristics based on properties of the communication graph. We present a new cooperative localization method that is based on a rigorous and scalable treatment of estimation errors generated by peer-to-peer sharing of relative robot pose information. Our approach blends Covariance Intersection and Covariance Union techniques from distributed sensor fusion theory in a novel way, in order to maintain statistical estimation consistency for cooperative localization errors. Experimental validation results show that this approach provides both reliable and accurate state estimation results for Droplet swarms in scenarios where other existing swarm localization methods cannot.