Coalescence Regime Research Articles

Effect of electrowetting induced capillary oscillations on coalescence of compound droplets

HypothesisCoalescence time depends on the drainage rate of the fluid-bridge separating the droplets. Drainage rate is determined by external forcing and properties of the surrounding fluid. Modulating external forcing using electrowetting induced interface motion should allow control of the drainage rate, thereby affecting the coalescence time. Hence, quick coalescence or prolonged non-coalescence can be obtained for compound droplets on the microfluidic lab-on-chip systems. ExperimentsUsing high-speed imaging, we have investigated the effect of electrowetting induced capillary oscillations on the coalescence of compound droplets consisting of water core encapsulated in an oil shell. A systematic study was performed by varying the shell viscosity and actuation parameters (i.e. amplitude, frequency and waveform). FindingsFor actuated interface, we observed specific regimes of coalescence or non-coalescence, whereas in absence of actuation, coalescence was observed in finite time. Non-coalescence was attributed to the continuous modulation of the oil-bridge width, which was caused by the interface motion. Oil-bridge width modulation was seen to be dependent on the amplitude and shape of the excited capillary modes (axisymmetric and non-axisymmetric). These modes were tuned by the actuation parameters. This is the first report of controlling coalescence dynamics by using electrowetting induced interface motion.

Coalescence of two initially spherical bubbles: Dual effect of liquid viscosity

The coalescence and interaction of two inline bubbles in viscous ambient liquids are explored using axisymmetric computations. The incompressible Navier–Stokes equations for gas-liquid flow are solved numerically through a tree-based finite volume method. Starting from spherical shape, the deformation and evolution of bubbles are simulated by a volume-of-fluid (VOF) method that combines a balanced surface tension force calculation and a height function curvature estimation. High mesh resolution is achieved by dynamic, adaptive mesh refinement to finely resolve the local topological evolutions during coalescence. The influence of liquid viscosity, for which Galilei number Ga ranges from 1 to 150, is studied under different Eötvös numbers Eo. It is discovered that the outcome of coalescence is determined by the competition between the two liquid circulations (vortex rings) around bubbles. We find that the inter-bubble interaction is always enhanced by reducing liquid viscosity. However, the effect of liquid viscosity on bubble coalescence is dual and the minimum coalescence time is obtained at a moderate Ga with other parameters fixed. A comprehensive map of coalescence regime is provided, where four distinct coalescence regimes are identified and three critical Galilei numbers are defined. The motion of bubbles in different coalescence regimes are also analyzed and compared. Our work contributes to a further understanding of the coalescence and interaction of bubbles.

How Do Different Liquid Metal Films Coalesce on Carbon Substrates?

Droplet coalescence plays an indispensable role in diverse natural and industrial processes. However, it is still unclear that how the wettability and microstructure of the substrates influence the coalescence. Molecular dynamics simulations were used to investigate the coalescence behaviors of liquid metal films on carbon substrates. Two different coalescence regimes climbing-coalescence and coating-coalescence were, respectively, observed in Cu–Al and Cu–Ag systems on graphene. The balance of metal–substrate and metal–metal interactions was regarded as the key factor to determine the coalescence regimes. Additionally, the effects of surface roughness and atomic arrangement of substrates on the movements of droplets were also analyzed on other carbon materials. Our findings offer a thorough understanding of the relationship between coalescence and wettability and could have important implications in self-assembly, three-dimensional printing, and microfluidic devices.

Coalescence of Cluster Beam Generated Sub‐2 nm Bare Au Nanoparticles and Analysis of Au Film Growth Parameters

AbstractIn this work is presented the growth model for Au films grown on a carbon substrate at room temperature by using as building blocks Au nanoparticles (NPs) with 1.4 nm mean size generated via remote cluster beam synthesis and soft landing on the substrate. The key results highlighted in this work are that 1) the deposited nanoparticles coalesce at substrate level in such a way that the film growth is 3D, 2) newly formed nanoparticles at substrate level are predominantly magic number clusters and 3) coalescensce takes place as soon as two neighboring nanopartciles come closer than a critical distance. The film growth was investigated by TEM as a function of Au load, in the range 0–1.2 μg/cm2. Two distinct regimes are identified: the “landing regime” and the “coalescence regime”. During the latter the film growth is 3D with a dynamic scaling exponent z of 2.13. Particular attention was devoted to the study of the evolution of the NP population from the moment they are generated with the cluster beam generator to the moment they land on the substrate and coalesce with other NPs. Our results show that 1) the NPs generated by the cluster beam are heterogeneous in size and are made by more than 95% by Au Magic numbers, mainly Au20 and Au55 and 2) kinetic processes (coalescence) at substrate level is capable of producing NPs populations made of larger Au magic numbers containing up to several thousands of Au atoms. Experimental and simulation results provide insight into the coalescence mechanism and provide strong evidence that the NPs coalesce when the nearest neighbor distance is below a critical mark. The critical distance is at its minimum 0.4‐0.5 nm and it is still unclear whether it is constant or not although the best matching simulation results seem to point to a superlinear dependence from the NP size difference between two neighboring candidate coalescing NPs. The coalescence phenomenon investigated in this work pinpoints the unique self‐organization properties of these small Au NPs in creating films with a stable edge‐to‐edge mean nearest neighbor distance of the order of 1.4 nm.

Drop breakup and drop pair coalescence using front-tracking method in three dimensions

In this paper, the deformation, breakup of a drop in shear flow and drop pair coalescence are studied using a finite difference/front tracking method. The drop deformation in shear flow was first studied in a Stokes regime and was compared with experimental and numerical results. A new algorithm that changes the topology of the interface dynamically and globally was developed to study drop break-up in shear flow after reaching a critical limit. Break-up simulation was first carried out in a Stokes regime. To validate the method performance and topology changing algorithm, results were compared with other numerical methods. Moreover, by obtaining a critical capillary number at finite Reynolds numbers and comparing the results with available data in this area, good agreement was observed that shows the ability of the method and the present topology changing algorithm. Different coalescence regimes for drop pair collision were also captured using the present topology changing algorithm. The present method is capable to simulate other multiphase flow problems that to some extent include collision and breakup of drops.

Hydrodynamic Study of a Gas–liquid–solid Bubble Column Employing CFD–BPBM Method

AbstractThe computational fluid dynamics – bubble population balance model (CFD–BPBM) was employed to predict the hydrodynamic characteristics of a gas–liquid–solid bubble column. A 3D time dependent numerical study was performed and the bubble size distributions at the conditions of different superficial gas velocity (0.089 m/s–0.22 m/s), solid volume fraction (0.03–0.30) and particle density (2500 kg/m3–4800 kg/m3) in the three–phase system were investigated, and the simulation results were compared with the experimental results. The bubble diameters ranging from 1 mm to 64 mm were divided into ten classes. The predicted pressure changing with the bed height had a good agreemeet with the experimental result. The bubble number density predicted decreased when the bubble size increased at each superficial gas velocity, and the bubble coalescence rate became greater than the breakup rate when Ugshifted from 0.089 m/s to 0.16 m/s. The bubble interaction was similar at 0.16 m/s and 0.22 m/s both at particle size dp= 75 μm and 150 μm. The bubble size corresponding to the maximum of the bubble volume fraction increased as Ugincreased. The particles can make the bubble break up and coalesce simultaneously when the solid volume fraction was larger than 0.20, and therefore the particles had a contribution to both of the bubble coalescence and breakup in the bubble coalescence regime (Ug= 0.16 m/s). The effect of the particle density was similar with that of the solid volume fraction. Increasing the particle density can enhance the breakup rate of the large bubbles.

Anisotropic coalescence criterion for nanoporous materials

Ductile fracture through void growth and coalescence depends significantly on the plastic anisotropy of the material and on void size, as shown by experiments and/or numerical simulations through several studies. Macroscopic (homogenized) yield criteria aiming at modeling nanoporous materials have been proposed only for the growth regime, i.e. non-interacting voids. The aim of this study is thus to provide a yield criterion for nanoporous materials relevant for the coalescence regime, i.e. when plastic flow is localized between voids. Through homogenization and limit analysis, and accounting for interface stresses at the void-matrix interface, analytical coalescence criterion is derived under the following conditions: axisymmetric loading, orthotropic material obeying Hill’s plasticity, cylindrical voids in cylindrical unit-cell. Incidentally, an orthotropic extension of the existing isotropic modeling of interface stresses through limit analysis is described and used. The proposed coalescence criterion is then extended to account for combined tension and shear loading conditions. Numerical limit analyses have been performed under specific conditions / materials parameters to get supposedly exact (up to numerical errors) results of coalescence stress. A good agreement between the analytical coalescence criteria derived in this study and numerical results is found for elongated spheroidal voids, making them usable to predict the onset of void coalescence in ductile fracture modeling of nanoporous materials.

The X-Ray Micro-Tomography Backed by Molecular Dynamics Simulations in the Analysis of Shock-Induced Damage in Ductile Materials

We have studied spallation in single crystal of metals under shock at very high strain rate. Our work has been devoted to understanding, and predicting the dynamic ductile damage processes of nucleation, growth and coalescence of voids in these extreme conditions of impact. Recovered sample only indicates final state of damage. Molecular Dynamics calculations are predicting the phenomenon over time. However we need experimental results to validate and improve simulations and models. X-ray tomography analyses are appropriate to extract pore volume distributions. Our study on ductile materials allowed us to conclude that experimental analyses exhibit two power laws attributed to growth and coalescence regimes. Moreover power law is scale invariance so it is possible to compare experiment (macroscopic) to calculation (microscopic). We show that there are good correlations between experimental and Molecular Dynamics pore volume distribution. Thanks X-ray microtomographies findings we progress in understanding the phenomenon of dynamic damage.

Bed expansion and multi-bubble behavior of gas-liquid-solid micro-fluidized beds in sub-millimeter capillary

Hydrodynamic study was performed on the gas-liquid-solid micro-fluidized beds with 0.8mm bed diameter and multi-bubbles through high speed camera recording system. Flow regimes including dispersed bubble flow, coalesced bubble flow and slug flow were identified from the multi-bubble flow. Wall effect at the small bed-to-particle diameter ratio led to the occurrence of bubble coalescence and flow regime transition at lower solid holdups. Obvious bed contraction appeared only at lower liquid velocities or higher gas velocities. The diameter range of the spherical micro-bubbles in the micro-fluidized beds was 200–500μm. The bubble size in dispersed bubble flow was normally distributed and slightly increased with the solid holdup. And in coalesced bubble flow, the bubble size was decided by the overall coalescence probability and presented a special step distribution. The larger coalesced bubbles concentrated the distribution of bubble terminal velocity. And the bubble terminal velocity decreased with the solid holdup and inversely with the bubble size. In dispersed bubble flow regime, there was positive linear relationship between the apparent viscosity and the solid holdup. Three-phase micro-fluidized beds meet the further development of micro-reactors, and this study on the hydrodynamic characteristics contributes to their wider application.

LMB simulation of head-on collision of evaporating and burning droplets in coalescence regime

In this paper, collision of two identical evaporating or burning droplets is simulated in coalescence regime. To do this, based on Lee’s two phase flow framework a lattice Boltzmann scheme is proposed for evaporation and combustion simulation of liquid fuel droplet. The effect of evaporation rate on collision outcome is investigated by changing Stefan number for various Weber numbers. Variation of droplet kinetic energy and viscous energy loss as well as changes in droplet oscillations after coalescence is studied for different evaporation rates. Comparing collision of evaporating and non-evaporating droplets with the same surface tension, revealed that the evaporation process reduces the surface tension effect. An effective surface tension is introduced to measure the effect of evaporation rate on collision process. The effective surface tension is a function of Stefan number, Weber number and time. It decreases by increasing Stefan or Weber number but increases with time. For collision of burning droplets, it was revealed that the combustion increases the kinetic energy of droplets before collision. Intensified velocity vortexes, which is made by the high temperature flame zone, is most likely the cause of droplet energy increment before collision.

Dendrite fragmentation in alloy solidification due to sidearm pinch-off.

Dendrite sidebranch detachment is an important fragmentation mechanism during the solidification of alloys. The detachment occurs at the junction between a sidearm and its parent stem. While this pinching process is driven by capillarity, the presence of solidification opposes the instability. Using a simple numerical model of a single sidearm, we are able to capture the essential dynamics of dendrite sidebranch development and the resulting morphological transitions. While shortly before pinch-off the neck itself obeys well-known universal scaling relations, the overall evolution of the sidearm shape sensitively depends on its initial geometry and the rate of solidification. It is found that pinch-off only occurs over limited ranges of geometrical parameters and cooling rates and is generally bounded by sidearm retraction and coalescence regimes. Simple scaling relations are identified that provide the bounds for the pinch-off regime. Pinching at the branching point is shown to be faster than the Rayleigh-Plateau instability of an infinitely long cylinder.

Bubble coalescence and breakup in turbulent bubbly wake of a ventilated hydrofoil

Auto-venting turbines have been proposed as a promising solution to the problem of low oxygen content in the discharged downstream water of an electric power plant. The current design of these turbines relies primarily on computational simulation. The experimental studies that focus on the physical processes occurring in turbulent bubbly wake are urgently needed to improve the performance of these simulations in predicting the bubble size distribution behind auto-venting turbines. Therefore, in the current study, we conducted detailed experimental investigations into the bubble size distributions in the wake of a ventilated hydrofoil. The mean bubble statistics is measured at different liquid velocities and air entrainment rates, and then the variation in mean bubble statistics is studied at different downstream locations in the wake. The bubble size distributions at different downstream locations have revealed the presence of distinct coalescence-dominant and breakup-dominant regimes. Analytical expressions are derived for the prediction of maximum stable diameter and Sauter mean diameter of bubbles, in the breakup and coalescence regimes, respectively. The observations from high speed imaging provide support for the measurements of bubble statistics, and physical insights into different mechanisms of bubble breakup and coalescence in turbulent wake. It is hoped that these insights will aid in developing generic model of bubble size distribution, and will help researchers improve bubbly flow simulations for auto-venting turbines.

CFD simulation of hydrodynamics of gas–liquid–solid three-phase bubble column

A 3D time dependent numerical study was performed to study the gas–liquid–solid three-phase flow dynamics in bubble columns by employing the Eulerian–Eulerian–Eulerian three-fluid approach. The three-phase bubble column of Gandhi et al. (Powder Technol. 1999, 103 (2), 80–94), Rampure et al. (Can. J. Chem. Eng. 2003, 81 (3–4), 692–706) and our previous study (Powder Technol. 2014, 260, 27–35) were studied. A mathematical model of a gas–liquid–solid three-phase flow was built. The effect of numerical schemes (wall boundary conditions, momentum discretization schemes and time steps) was discussed. CFD simulations were performed to study the sensitivity of the interphase drag models (different liquid–solid, gas–solid and gas–liquid drag models), and the predictions were compared with the experiments. The results showed that no-slip conditions for the wall boundary conditions, 0.001s for the calculation time step and second-order Upwind for momentum discretization, had better prediction results. The appropriate interphase drag forces to describe the three phase flow found in this study were the Zhang–Vanderheyden model, which was used as a gas–liquid drag model, Schiller–Naumann model, used as a liquid–solid drag model, and gas–solid drag force, which was not considered. The appropriate numerical schemes and interphase drag models were utilized to simulate the hydrodynamic parameters (time-averaged gas holdup, solid holdup, liquid axial velocity) in a gas–liquid–solid bubble column. The effects of superficial gas velocity, particle volume fraction, particle size and density were analysed and discussed. Four flow regimes of a gas–liquid–solid bubble column were simulated; the CFD results were compared with the experimental flow structures, and it was found that the bubble coalescence regime was better depicted. Superficial gas velocity had a large effect on the gas holdup of the bed, and the effect of solid volume fraction (Vs=0.03–0.30) and particle size (dp=75μm–270μm) on the distributions of time-averaged solid holdup and liquid axial velocity was greater than that of particle density (ρp=2500kg/m3–4800kg/m3). When particle size dp≥150μm and solid volume fraction Vs≥0.09, the hydrodynamic parameters had a strong dependency on dp and Vs. The larger the values of the Vs, dp and ρp were, the larger the axial solid concentration gradient was.

Regimes during liquid drop impact on a liquid pool

Water drops falling on a deep pool can either coalesce to form a vortex ring or splash, depending on the impact conditions. The transition between coalescence and splashing proceeds via a number of intermediate steps, such as thick and thin jet formation and gas-bubble entrapment. We perform simulations to determine the conditions under which bubble entrapment and jet formation occur. A regime map is established for Weber numbers ranging from 50 to 300 and Froude numbers from 25 to 600. Vortex ring formation is seen for all of the regimes; it is greater for the coalescence regime and less in the case of the thin jet regime.

In situ seriate droplet coalescence under an optical force

We demonstrated the induced coalescence of droplets under a highly accurate optical force control. Optical scattering and gradient forces were used to push and trap the droplets prior to coalescence within a microfluidic channel. The behavior of the droplets under the influence of an optical force was predicted using an analytical model that agreed well with the experimental data. The optical gradient force accelerated and decelerated the droplet within the laser beam region, and the drag force acting on the droplet was thoroughly characterized. A description of the optical trap was presented in terms of the momentum transfer from the photons to the droplet, effectively restricting droplet motion inside the microfluidic channel prior to coalescence. A phase diagram was plotted to distinguish between the three regimes of droplet coalescence, including the absence of coalescence, coalescence, and multiple coalescence events. The phase diagram permitted the laser power input and the net flow rate in the microfluidic channel to be estimated. This technique was applied to the synthesis of biodegradable gel microparticles.

Kinetic Monte Carlo simulation of the initial growth of Ag thin films

A Monte Carlo model for simulation of the 3-Dimension growth of Ag thin film on the amorphous Si substrate is presented. Three principal dynamic processes for each atom are considered in the description of thin film growth: deposition, diffusion and re-evaporation. The diffusion activation energy calculated by many-body semiempirical potential is related to the positions of the atoms. It is equal to the energy difference between the total energy of the system before and after the diffusion. The influences of the substrate temperature and the deposition rate on the transitions of island morphologies in thin film growth at the initial stage have been studied in detailed. The results show that with the increase of the substrate temperature or the decrease of the deposition rate, the size of the island increases, and the number of islands decreases. There are two distinct stages captured by the model in island coalescence regime, which consistent with that of the experiment.

Coalescence and noncoalescence of sessile drops: impact of surface forces.

Due to capillarity, sessile droplets of identical liquids will instantaneously fuse when they come in contact at their three-phase lines. However, with drops of different, completely miscible liquids, instantaneous coalescence can be suppressed. Instead, the drops remain in a state of noncoalescence for some time, with the two drop bodies connected only by a thin neck. The reason for this noncoalescence is the surface tension difference, Δγ, between the liquids. If Δγ is sufficiently large, then it induces a sufficiently strong Marangoni flow, which keeps the main drop bodies temporarily separated. Studies with spreading drops have revealed that the boundary between instantaneous coalescence and noncoalescence is sharp (Karpitschka, S.; Riegler, H. J. Fluid. Mech. 2014, 743, R1). The boundary is a function of two parameters only: Δγ and Θ(a), the arithmetic mean of the contact angles in the moment of drop-drop contact. It appears plausible that surface forces (the disjoining pressure) could also influence the coalescence behavior. However, in experiments with spreading drops, surface forces always promote coalescence and their influence might be obscured. Therefore, we present here coalescence experiments with partially wetting liquids and compare the results to the spreading case. We adjust different equilibrium contact angles (i.e., different surface forces) with different substrate surface coatings. As for spreading drops, we observe a sharp boundary between regimes of coalescence and noncoalescence. The boundary follows the same power law relation for both partially and completely wetting cases. Therefore, we conclude that surface forces have no significant, explicit influence on the coalescence behavior of sessile drops from different miscible liquids.

Coalescence of dry foam under water injection.

When a small volume of pure water - typically a drop - is injected within an aqueous foam, it locally triggers the rupture of foam films, thus opening an empty cavity in the foam's bulk. We consider the final shape of this cavity and we quantify its volume as a function of the volume of injected water, the diameter of the bubbles and the liquid fraction of the foam. We provide quantitative understanding to explain how and when this cavity appears. We epitomize the dilution of surfactants at the water-air interfaces as the main cause lying behind the coalescence process. We identify a new coalescence regime for which a critical surfactant concentration rules the stability of the foam.

Flow patterns and transitions in a rectangular three-phase bubble column

The flow patterns and transitions in a rectangular gas–liquid–solid three-phase bubble column were studied. The influence of solid volume fraction, particle size and particle density on the flow regime transitions of the three-phase bubble column was investigated experimentally. Experiments were carried out for solid volume fraction Vs=0.03–0.3, average particle size dp=48μm–270μm, particle density ρp=2500kg/m3–4800kg/m3, and superficial gas velocity Ug=0.007m/s–0.7m/s in a rectangular bubble column measured 0.8m tall, 0.1m long and 0.01m wide. Four distinct flow patterns and three transition points were observed in this experimental system, and the four flow regimes were discrete bubble regime, transition regime, bubble coalescence regime and strong turbulent regime, which were determined on the basis of criteria as well as schematic diagrams and typical flow pattern images obtained from a high-resolution digital charge couple device (CCD) camera. Typical flow patterns maps were plotted for illustrating flow regime transitions under different particle conditions. It was found out that particle volume fraction and particle density had an effect on the flow pattern transitions; when increasing the values of particle volume fraction and the particle density respectively, the values of the flow regime transition points all decreased. Particle size had a little effect on flow regime transition points when the particle size shifted in the range of 48μm to 150μm; when particle size was larger than 150μm and increased to 270μm, the operation ranges of the transition regime and the bubble coalescence regime decreased.

Model-Free Unraveling of Supported Nanoparticles Plasmon Resonance Modes

Plasmonics of Ag, Au, and Zn nanoparticles supported on Al2O3(0001), TiO2(110), and ZnO(0001) substrates has been probed by surface differential reflectivity spectroscopy (SDRS) during vapor deposition growth. Parallel and perpendicular interfacial susceptibilities (ISs), or “optical thicknesses”, which characterize only the dielectric response of the film, are derived from experimental spectra in p- and s-polarization using an inversion procedure based on Kramers–Kronig transform. The consistency of the approach is checked against sum rules. Plasmonic contributions are unraveled by decomposing ISs into damped oscillators and identified with the help of dielectric simulations of truncated supported spheres or spheroids. Beyond the common Drude behavior of Ag, Au, and Zn, the comparison between the three metals demonstrates the paramount role of interband transitions in the ISs profiles. While gold and silver show free electron plasmon modes, zinc exhibits polarization modes of bound electrons. However, despite those differences, the resonant modes that are identified herein are universal for supported particles. Particle shape, equilibrium aspect ratio, image field, polydispersity, and interface-induced damping are discussed by analyzing changes in frequencies, oscillator strengths, and broadenings. Deposit-induced band gap absorption for semiconductor substrate and switches from growth to coalescence regimes are evidenced. Static and dynamic coalescence are characterized by power law exponents as a function of particle size. Therefore, the unique framework that is proposed opens strong prospects in the optical characterization of growth, metal/semiconductor interfaces, and gas adsorption.