Coalescence Dynamics Research Articles

Droplet impact on small droplet above hydrophobic microstructure surface

The behavior of an interface is influenced not only by the material and surface pattern but also by the contact conditions. Increasing the Weber number (We) increases the likelihood of droplet splashing, which generates smaller droplets that alter contact conditions. This, in turn, affects the coalescence and morphological evolution of larger impacting droplets. However, the influence of these small droplets on coalescence dynamics under varying Weber numbers and contact sequences remains unclear. To determine the coalescence threshold and deformation characteristics under soft and wettable hard surface conditions, we conducted high-speed imaging experiments of a large droplet colliding with a small droplet resting above a hydrophobic surface. The results indicate that the threshold for droplet coalescence occurs at an eccentricity distance of 1.2 mm, with the effect of the Weber number (1 ≤ We ≤ 9) being limited. Upon contact, the small droplet influences the maximum spreading ratio and contact time by increasing the volume of the impacting droplet, altering its impact direction, hindering spreading, and changing its own morphology. When the impacting droplet contacts the substrate before the small droplet, there is a linear relation between contact time and eccentricity distance. From this, we propose a relationship considering the effects of eccentricity distance and Weber number on contact time. Beyond these effects, the small droplet also influences the transition between symmetric and asymmetric structures of the rebounding droplet, thereby regulating the rebound height.

Acoustic emission inversion for hydraulic fracture geometry with geomechanical constraints

The evaluation of hydraulic fracturing effectiveness in unconventional oil and gas reservoirs is crucial for production enhancement. Traditional assessments have focused on rock properties, overlooking the influence of external factors such as geostress and fracturing fluid characteristics. Acoustic emission methods, which analyze fracture activities and parameters through inversion, have shown potential in evaluating the fracturing effectiveness by indicating complex fracture networks and the dynamics of microcrack coalescence. However, these methods face challenges in accurately determining fracture parameters due to the inversion's inherent uncertainties. This study introduces a novel inversion method that incorporates geomechanical constraints, aiming to improve the precision of fracturing effectiveness evaluation. By comparing high-viscosity gel and supercritical carbon dioxide (SC-CO2) fracturing techniques, the study demonstrates the novel method has capability to distinguish between varied fracture morphologies. The results show that high-viscosity fracturing leads to fractures with more concentrated propagation directions and larger opening angles, while SC-CO2 fracturing produces fractures with more complex propagation paths and smaller opening angles. This approach marks a significant advancement in the field, allowing for a more accurate and quantitative assessment of hydraulic fracturing operation.

Optimizing droplet coalescence dynamics in microchannels: A comprehensive study using response surface methodology and machine learning algorithms.

Droplet coalescence in microchannels is a complex phenomenon influenced by various parameters such as droplet size, velocity, liquid surface tension, and droplet-droplet spacing. In this study, we thoroughly investigate the impact of these control parameters on droplet coalescence dynamics within a sudden expansion microchannel using two distinct numerical methods. Initially, we employ the boundary element method to solve the Brinkman integral equation, providing detailed insights into the underlying physics of droplet coalescence. Furthermore, we integrate Response Surface Methodology (RSM) to effectively optimize droplet coalescence dynamics, harnessing the power of machine learning algorithms. Our results showcase the efficacy of these computational techniques in enhancing experimental efficiency. Through rigorous evaluation utilizing Regression Coefficient and Mean Absolute Error metrics, we ascertain the accuracy of our estimations. Our findings highlight the significant influence of key parameters, specifically the non-dimensional initial distance of the droplets (D), viscosity ratio ( ), Capillary number (Ca), and width (w), as identified by the non-dimensional final droplet-droplet spacing (DD), velocity of the first droplet (VFD), and velocity of the second droplet (VBD), respectively. This comprehensive approach provides valuable insights into droplet coalescence phenomena and offers a robust framework for optimizing microfluidic systems. The most influential parameters on DD are the values of Ad and D, while viscosity has the lowest influence on DD. The most influential parameters on droplet velocity are viscosity and channel width, whereas the initial distance and Ca have the least influence on droplet velocity. The comparison of different machine learning algorithms indicates that the best ones for predicting DD, VFD, and VBD are function, SMOreg, Lazy-IBK, and Meta-Bagging, respectively.

Coalescence Dynamics of Oil Droplets on an Air-Water Interface Driven by Surface Waves

This study reports the unique phenomenon of the coalescence of oil droplets floating over the water surface. For the first time, the coalescence has been initiated through the creation of externally generated low-amplitude surface waves. We used a simple and cost-effective method to manifest the surface waves over the free surface of water to study the merging dynamics. The time-lapse images depict the entire stage of parent droplets merging. The study reveals that the coalescence time required for the complete transformation of parent droplets into the resultant droplet increases as the number of parent droplets over the free surface of water increases. We studied the time-dependent variation in the velocity of two non-identical parent droplets. The experiment reveals that the smaller droplet propagates faster than the larger droplet over a free surface of water. The peak velocities of the two droplets are 2.0 cm/s and 1.07 cm/s, respectively. The point of deposition of droplets does not influence the coalescence phenomenon; whether the droplets are deposited at the center of the petri dish or the wall, they still show coalescence. However, the droplets that are deposited near the center of the petridish propagate faster compared to those deposited near the wall due to the higher intensity of vibration at the center.

Generation, migration, and coalescence of droplets: A state-of-the-art review from the perspectives of wettability, inertia, and electric field

Generation, migration, and coalescence of droplets are some of the fundamental phenomena observed in multiphase microfluidic devices that offer widespread application in interdisciplinary platforms. These phenomena are governed by involved interfacial forces, and tuning these forces through active or passive techniques has emerged as a thriving research domain. Among the available strategies for interfacial force modulation, wettability, electric field, and inertia are some of the key factors that are paid attention as they are largely involved in naturally occurring phenomena and widely applied in technically designed platforms. Motivated by these, this work reviews the studies carried out in the domain of surface wettability and its influence on two-phase flow, to the electrically tuned migration and deformation characteristics of compound drop, and thereafter towards the inertia modulated coalescence dynamics of compound drop, and also explores several unresolved facets that can be addressed by the research community.

Thermal stability and coalescence dynamics of exsolved metal nanoparticles at charged perovskite surfaces

Exsolution reactions enable the synthesis of oxide-supported metal nanoparticles, which are desirable as catalysts in green energy conversion technologies. It is crucial to precisely tailor the nanoparticle characteristics to optimize the catalysts’ functionality, and to maintain the catalytic performance under operation conditions. We use chemical (co)-doping to modify the defect chemistry of exsolution-active perovskite oxides and examine its influence on the mass transfer kinetics of Ni dopants towards the oxide surface and on the subsequent coalescence behavior of the exsolved nanoparticles during a continuous thermal reduction treatment. Nanoparticles that exsolve at the surface of the acceptor-type fast-oxygen-ion-conductor SrTi0.95Ni0.05O3−δ (STNi) show a high surface mobility leading to a very low thermal stability compared to nanoparticles that exsolve at the surface of donor-type SrTi0.9Nb0.05Ni0.05O3−δ (STNNi). Our analysis indicates that the low thermal stability of exsolved nanoparticles at the acceptor-doped perovskite surface is linked to a high oxygen vacancy concentration at the nanoparticle-oxide interface. For catalysts that require fast oxygen exchange kinetics, exsolution synthesis routes in dry hydrogen conditions may hence lead to accelerated degradation, while humid reaction conditions may mitigate this failure mechanism.

Coalescence and Rebound Dynamics in Two Droplets Train Impacting on a Heterogeneous Wettability Surface.

Droplets that can be steered and rebound off surfaces are fundamentally interesting and important due to their promising potential in numerous applications, such as anti-icing and -fogging, spray coating, and self-cleaning. Heterogeneous wettability surfaces have been shown to be an effective means of droplet manipulation. This paper combines numerical simulation with theoretical analysis to investigate the dynamics of two droplets training impacting on and bouncing off a heterogeneous surface (superhydrophobic substrate decorated with a hydrophilic strip). First, the time evolutions of the droplet morphology and velocity vectors are examined to explore the particular dynamic behaviors. At different ratios of the impact velocity, three distinct rebound patterns are observed, and a regime diagram is established. After that, the effects of the impact conditions and surface wettability on the rebound performance of the coalesced droplet are studied systematically. Special attention is paid to the variations of the rebound height and the lateral transportation distance with the Weber number of two droplets and the distance between the impacting point and the hydrophilic stripe. Moreover, a theoretical analysis of two droplets' impact is performed based on the energy conservation. The obtained scaling laws match well with the numerical data in the trend. Our research may strengthen the understanding of the interactions between droplets, which is valuable for the manipulation of multiple droplets in related fields.

In Situ TEM Imaging Reveals the Dynamic Interplay Between Attraction, Repulsion and Sequential Attraction-Repulsion in Gold Nanoparticles.

Recent efforts on manipulating metal nanoparticles (NPs)using an electron beam have offered new insights into nanoparticle behavior, structural transition, and the emergence of new properties. Despite an increasing understanding of the dynamics of electron beam-induced coalescence of NPs, several phenomena are yet to be investigated. Here, we show that repulsion between two NPs is as favorable as coalescence under electron beam irradiation at room temperature. Using small-sized (D ≈ 5.9nm) and large-sized (D ≈ 11.0nm) gold (Au) NPs, and different electron dose rates, a unique sequential attraction-repulsion between NPs is disclosed. The real-time in situ transmission electron microscopy imaging suggest that at a low dose rate, two small-sized AuNPs with 1.0nm particle-particle distance undergo repulsion to 18nm with a diffusion rate of 0.4nmmin-1. For large-sized AuNPs, the repulsion rate is 0.08nmmin-1 at a low dose rate and is comparable to that of small-sized AuNPs at a high dose rate. Surprisingly, large-sized AuNPs at a high electron dose rate displayed attraction in the first 15min, followed by rapid repulsion. This unique sequential attraction-repulsion behavior of NPs offers possibilities to manipulate interparticle distance and properties without inducing dimensional changes for advanced photonic and plasmonic nanodevices.

Impact of polymer molecular weight and dispersity on the coalescence of polypropylene powders suitable for laser powder bed fusion

Understanding and controlling the fundamental processes governing the coalescence of polymers is vital to enable the design of polymeric materials for improved mechanical performance and quality of manufactured structures, including those fabricated via additive manufacturing techniques. Our group has utilized thermally induced phase separation (TIPS) to produce spherical and size controlled polypropylene (PP) powders from 12,000 (12k), 250,000 (250k), and 340,000 (340k) molecular weight (Mw) PP, including 50-50 wt% blends of 12k/250k,12k/340k, and 250k/340k, and a 33-33-33 wt% blend of 12k/250k/340k to investigate the impact of polymer Mw, and thus zero-shear viscosity, on particle coalescence and its implication in laser powder bed fusion. The particles exhibit similar size distributions with an average particle size, Dx(50), in the range of 58 μm–86 μm. The coalescence behavior of the powders, evaluated via hot-stage microscopy, show that adding 12k PP in the blend significantly alters the coalescence dynamics of the 250k and 340k PP, dramatically increasing their coalescence rate. The substantial drop in zero-shear viscosity with addition of 12k PP provides the driving force for the pronounced enhancement in coalescence. Strong agreement between experimental results and the Hopper model of coalescence is observed only if corrected for extensional flow, exemplifying the importance of extensional flow on the coalescence process. The results also indicate that the 12k PP in the blend does not surface segregate in the TIPS process, but is homogeneously distributed in the blend. More broadly, these results provide molecular-level insight into how control of powder molecular weight characteristics and viscosity can offer pathways to optimize the consolidation of particles in manufacturing processes, including laser powder bed fusion.

Three-dimensional mesoscopic investigation of directional coalescence of two droplets impacting on a wall with wettability difference

In this work, a three-dimensional (3D) nonorthogonal pseudopotential lattice Boltzmann method (LBM) was proposed to investigate the coalescence dynamics of two droplets impacting on a wall with wettability difference. The influences of the wettability difference, Weber number, offset distance on the low-wettability side on the coalescence dynamics and the contact-line evolution processes were systematically examined. Both symmetric and asymmetric distributions of the droplet-coalescence behaviors were considered. Our findings reveal that the wettability difference has a significant influence on the asymmetric-retracting and wetting-equilibrium stages, identifying three modes: pin-slip, slip and no-rebound, and slip and rebound. The rebound time is dominated by the high-wettability wall. At a larger Weber number, droplets exhibit a large retracting velocity, which results in increased pumping velocity and earlier rebound time. In addition, a dramatic retraction of the three-phase contact line (TPCL) on the low-wettability wall is observed, leading to the detachment of the liquid bridge from the low-wettability wall, and the formation of a cavity. With increasing offset distance on the low-wettability wall, three different evolution modes are found: coalescence-rebound, coalescence-separation, and non-coalescence. A power function relationship is reported between the Weber number We and the offset distance L* both on the high-wettability wall and low-wettability wall for three modes of coalescence behavior with We∼L*α. The value of the exponent α ranges from 4.6 to 7.4. This study showcases the effectiveness of the 3D nonorthogonal pseudopotential LBM in predicting the complex interface phenomena and characteristics of the multiphase flow structures under investigation.

Formation and coarsening of epitaxially-supported metal nanoclusters

This mini-review describes developments over the last ∼30 years in characterizing the nucleation & growth of epitaxially-supported metal nanoclusters (NCs) or islands during vapor deposition, as well as their post-deposition coarsening. A beyond-mean-field treatment for homogeneous nucleation & growth corrects the deficiencies of traditional treatments in describing, e.g., the island size distribution, but also necessitates consideration of the spatial distribution of islands and their capture zones. We discuss advances in modeling capabilities, including those based upon on an ab-initio level treatment of periphery diffusion kinetics, for description of the non-equilibrium growth shapes of these NCs, focusing on 2D NCs. For post-deposition coarsening of arrays of NCs, there is generally a competition between Ostwald Ripening (OR) and Smoluchowski Ripening (SR). SR is also known as Particle Migration & Coalescence. For 2D NCs in homoepitaxial systems, conventional OR is observed on pristine fcc(111) surfaces, dramatically enhanced OR in the presence of even trace amounts of chalcogens for Cu(111) and Ag(111), and anomalous OR on anisotropic fcc(110) surfaces. The unexpected discovery of SR for fcc(100) homoepitaxial systems prompted extensive analysis of the underlying diffusivities of 2D NCs as a function of size, as well as of NC coalescence dynamics. A comprehensive understanding of these processes is now available. Self-assembly of 3D NCs during deposition, issues related to heterogeneous nucleation, directed assembly, NC growth structure selection, and coarsening are addressed. For SR of 3D epitaxial NCs, recent insights into the size-dependence of diffusivity are described.

Nanoscale particle-droplet coalescence-induced jumping on superhydrophobic surfaces: Insights from molecular dynamics simulations

The removal of solid particles from superhydrophobic surfaces via coalescence-induced droplet jumping has gained increasing attention. However, the underlying mechanisms, especially the nanoscale dynamics of particle-droplet coalescence, remain largely underexplored. In our research, we employ molecular dynamics simulations to investigate the influences of the radius, wettability, and arrangement of solid particles on the particle-droplet jumping velocity and energy conversion efficiency. We observe notable rotational motions during the jumping events. Our findings reveal that the arc length of the wetted area on spherical particles and the spreading time of droplets exhibit a power-law relationship. As the particle-to-droplet radius ratio increases, the jumping velocity and energy conversion efficiency initially increase but subsequently decrease. Moreover, enhanced particle wettability leads to an increase in jumping velocity while a slight decrease in translational energy conversion efficiency. The velocities of coalescence-induced particle-droplet jumping at the nanoscale are consistent with predictions from the momentum model. Significantly, our results show that the rotationally symmetric multi-particle arrangements can effectively enhance the jumping velocity and energy conversion efficiency, thus improving particle removal efficiency. Our study not only deepens the understanding of coalescence-induced particle-droplet jumping behaviors, but also provides a foundation for developing more effective particle removal strategies on superhydrophobic surfaces.

Short-time asymmetric droplet coalescence dynamics on a pre-wetted fiber

This study presents an unprecedented directional transport phenomenon during the coalescence of two droplets on a pre-wetted cylindrical fiber, where the larger droplet is pulled toward the smaller one. The magnitude of this effect often exceeds the gravitational pull, enabling coalescing droplets to climb up a vertical fiber. This occurs primarily because the viscous friction that the droplets experience is negatively correlated with the droplet size. We present a scaling relation and a mass-spring-damper model to explain the phenomenon, which shows good agreement with the experimental results. This research reveals an intriguing aspect of the coalescence dynamics of droplets on a pre-wetted fiber, offering a fresh perspective on the interfacial phenomena in droplet–fiber systems.

Pore-scale investigation of injectivity impairment caused by oil droplets during produced water reinjection using volume of fluid method

Produced water from subsurface may often contain oil droplets, even when not directly extracted from oil wells. Oil droplets can migrate into water-bearing stratigraphic layers, leading to the generation of oily water. This study evaluates the dynamic clogging behavior of oil droplets concerning various injection fluid properties, including injection velocity, interfacial tension, oil droplet size, concentration, viscosity, and medium wettability. The primary objective is to validate common clogging mechanisms associated with oil droplets and quantitatively assess the impact of these parameters on injectivity impairment within porous media. To achieve this, a volume of fluid approach is employed, integrating fluid interfacial properties to account for coalescence and surface adherence. The results are then compared to similar findings in existing literature. Our study reveals that increasing the capillary number enhances injectivity, up to a critical point where the flow regime attains optimal stability, contingent upon relative permeability and phase mobility. Investigation into system wettability demonstrates that while contact angle significantly affects the injectivity index, the impact on injectivity diminishes when altering it beyond 90°. Aligning droplet viscosity with that of the displacing fluid proves to be an effective solution for minimizing injectivity impairment, nearly eliminating damage. This research provides valuable insights into commonly studied emulsion parameters, like Jamin Ratio and oil concentration, and underlines the importance of investigating less-explored factors, such as wettability and oil viscosity, particularly in scenarios involving unstabilized droplets and coalescence dynamics.

Magnetic resonance imaging of a stream of bubbles injected into liquid suspensions

Magnetic resonance imaging (MRI) is a powerful tool for characterizing opaque multiphase flows non-invasively. However, MRI has often (i) had low temporal resolution and thus not captured transient dynamics, (ii) only provided 2D slice images of 3D flows and (iii) been limited to flows in narrow (∼30 mm) tubes with significant wall effects. Here, we apply multi-band echo planar imaging (MB-EPI) with a custom-built radiofrequency coil in a full-body MRI scanner to provide fully 3D images of the dynamics of a stream of bubbles rising through a dense suspension with 151 ms resolution in a 178 mm diameter system. Image processing demonstrates that bubble rise and coalescence dynamics vary significantly with (a) initial spacing between bubbles and (b) particle volume fraction. The ability to image bubble dynamics in dense suspensions as well as in full 3D provides future opportunities to characterize complex, non-axisymmetric, multiphase flows.

Molecular dynamics study of free volume coalescence around nonyl ethoxylate in polyethylene with vinyl acetate‐modified branches

AbstractPolyethylene (PE) is susceptible to environmental stress cracking (ESC). In the presence of an amphiphilic compound and subjected to stress, ESC starts with cavitation followed by slow crack growth and ends with brittle fracture. In this study, we used molecular dynamics simulation to study how branch ends which were chemically modified with vinyl acetate groups affect free volume coalescence around an amphiphilic compound, nonyl ethoxylate (NE), dispersed in branched PE models. Branch ends modified with vinyl acetate significantly impact the free volume coalescence dynamics around NE. Compared with methyl branch ends, vinyl acetate branch ends show a much higher affinity, as quantified by the corresponding radial distribution functions, for the hydrophilic ethylene oxide‐segment of NE. However, this is not the case for the hydrophobic ethylene‐segment. Interestingly, vinyl acetate branch ends tend to reduce the power (amplitude) of the free volume size fluctuations around both the ethylene oxide‐ and ethylene‐segments. Indeed, the powers of the fluctuations with different PE branching characteristics decrease with increasing vinyl acetate concentration. We believe that free volume coalescence leads to cavitation and that vinyl acetate branches could inhibit cavitation, thereby crack propagation in PE. The power results seem to be consistent with the experimental observation that the addition of copolymer ethylene vinyl acetate to low‐density polyethylene improves the ESC resistance of the blend.Highlights Vinyl acetate branches reduce free volume coalescence activities. Vinyl acetate branches are attracted to the hydrophilic segment of NE. Cavitation likely starts from the free volume coalescence around NE.

The role of coalescence and ballistic growth on in-situ electrical conduction of cluster-assembled nanostructured Sn films

The electrical conduction of nanostructured Sn films assembled via Supersonic Cluster Beam Deposition is studied in-situ during film growth. The kinetic energy of Sn nanoparticles, in combination with low melting point of Sn, promotes coalescence phenomena, enabling the investigation of their impact on film morphology and on percolation threshold. A percolation threshold occurring at thicknesses much larger than the dimensions of Sn nanoparticles suggests that coalescence leads to the growth of disconnected, island-like structures. The deposition rate is found to influence coalescence dynamics during the early stages of film growth, allowing for the tuning of film microstructure from a more compact, island-like morphology to a more porous structure. The percolation threshold shifts accordingly from 24 nm to 3 nm film thickness. Upon completion of the percolation phase, film resistivity settles at values 2–3 orders of magnitude larger than that of bulk Sn, attributed to the nanogranular nature of cluster-assembled films. During the “3D conduction” phase, resistivity exhibits an increasing trend with thickness following a power law with an exponent value of 0.76–0.78. This behavior is attributed to the decrease in the density of interconnections between particles in the topmost layer during film growth, consistent with expectations in ballistic growth processes.

The dynamics of vertical coalescence of acoustically levitated droplets

Mobility manipulation of liquid droplets is an important task of digital imicrofluidics. Acoustic levitation has revolutionised the contactless manipulation of liquid droplets for various applications. Acoustic levitation technique can be effectively used to manipulate droplets to obtain their coalescence. This paper reports a unique, versatile, and material-independent approach for the vertical coalescence of the droplets suspended in an acoustic levitator. The acoustic power of the levitator is carefully engineered to obtain vertical coalescence of two liquid droplets. Water, 20% and 40% glycerol–water solutions are used as the working liquids. The results of the experiments revealed three outcomes during the coalescence. The outcomes are analysed and discussed.

Effect of hexyl‐branched backbone size on the size distribution and coalescence of free volume around an amphiphilic molecule

AbstractWe used molecular dynamics simulation to study the size distribution and coalescence of free volume around an amphiphilic molecule (nonyl ethoxylate (NE)) at a concentration of 0.5 wt% in blends of linear and branched polyethylene that contained a small four‐arm alkane (7,12 hexyl octadecane). The branched polyethylene chains had 10 and 82 hexyl branches/1000 backbone carbons. The coalescence dynamics (fluctuation of free volume in time) was quantified by the number of Fourier frequencies and the corresponding power (amplitude). In our previous work, we hypothesized that cavitation, the first step of environmental stress cracking observed experimentally, starts from the free volume coalescence at the interface between NE and polyethylene molecules and showed that hexyl branches in the branched polyethylene molecules suppress such coalescence, suggesting that cavitation, a much longer time scale process, could also be slowed down. The current work showed that the behavior of hexyl branches in branched polyethylene in a blend with linear polyethylene was similar to that in pure branched polyethylene, but that the hexyl branches in the 7,12 hexyl octadecane exhibited the opposite behavior. In particular, they intensified free volume coalescence, especially around the hydrophilic ethylene oxide segments of NE. The addition of 7,12 hexyl octadecane to branched polyethylene alone or blended with linear polyethylene does not seem to slow down free volume coalescence (cavitation), leading us to conclude that the effect of hexyl branches on the free volume coalescence around NE depends on the size of the backbone to which the branches are attached.Highlights Hexyl branches reduce free volume coalescence activities. The longer the backbone is, the stronger the hexyl branch effect. More coalescence activities occur on the hydrophilic segment of NE.

Electrically driven coalescence of charged conical droplet in non-uniform electric field

The dynamic behaviors of charged droplet coalescence in electric field has drawn much attention over the past decades due to its complex underlying physics and potential industrial application. This work experimentally investigated asymmetric coalescence dynamics of conical droplets in non-uniform electric field. With the effect of electric field, the cone apexes of deformed droplets merged with each other to form a liquid bridge that initially expanded but then retracted back gradually. It was found that the bridge length increased fast at initial conical coalescence and shrank slowly at retraction stage in various conditions. In addition, the effect of electric charge distribution and transportation on liquid bridge evolution behaviors was analyzed. The characteristics of cone angle and contact distance during droplet conical coalescence and recoil processes were quantitatively discussed with consideration of different parameters. Besides, the phase diagram for determining droplet coalescence and recoil was illustrated based on contact distance and electric Bond number, where the critical transition boundary was figured out with a linear increasing trend.