Droplet Collision Research Articles

Shear-driven two colliding motions of binary double emulsion droplets

We combine experimental visualization with numerical simulation to explore the hydrodynamic shear-driven binary collision of double emulsion droplets. Two typical colliding motions, passing-over motion and reversing motion, are found and identified by quantitatively characterizing the corresponding detailed motion trajectory and morphology development. Compared with the ordinary single-phase droplets, double emulsion droplets are demonstrated to exhibit similar motion trajectories but different deformation development during the binary collision process, which arise from an additional interaction induced by the inner droplet. Especially, we clarify that two typical colliding motions are determined by the competitions among the drag of passing-flow region and the entrainment from reversing-flow and vortex regions in the matrix fluid, which are significantly affected by the dimensionless shear stress (Ca) and confinement degree of shear flow (Co). With the increasing Co, the colliding motion of binary double emulsion droplets transits from the passing-over to reversing, owing to that the entrainment of the reversing-flow region turns to play a dominant role. The drag of the ambient passing-flow in the matrix fluid is increased by enlarging Ca, resulting in the emergence of passing-over motion of the colliding droplets. Accordingly, a regime diagram is provided to quantitatively recognize the corresponding regime of these two typical colliding motions, as a function of Ca and Co.

Optimisation inspiring from behaviour of raining in nature: droplet optimisation algorithm

In this paper, the droplet optimisation algorithm (DOA) has been proposed. DOA emulates rainfall phenomenon. It employs some special operators to describe the droplet process, including droplet generation, droplet fall, droplet collision, droplet flowing and droplet updating. To compare performance of this algorithm against those of some up-to-date optimisation algorithms, all of the CEC 2005 contest benchmark functions have been employed. The experimental results have proven that DOA is superior to all basic optimisation algorithms and also some up-to-date optimisation algorithms.

Effect of Turbulence on Collisional Growth of Cloud Droplets

We investigate the effect of turbulence on the collisional growth of micrometer-sized droplets through high-resolution numerical simulations with well-resolved Kolmogorov scales, assuming a collision and coalescence efficiency of unity. The droplet dynamics and collisions are approximated using a superparticle approach. In the absence of gravity, we show that the time evolution of the shape of the droplet-size distribution due to turbulence-induced collisions depends strongly on the turbulent energy-dissipation rate [Formula: see text], but only weakly on the Reynolds number. This can be explained through the [Formula: see text] dependence of the mean collision rate described by the Saffman–Turner collision model. Consistent with the Saffman–Turner collision model and its extensions, the collision rate increases as [Formula: see text] even when coalescence is invoked. The size distribution exhibits power-law behavior with a slope of −3.7 from a maximum at approximately 10 up to about 40 μm. When gravity is invoked, turbulence is found to dominate the time evolution of an initially monodisperse droplet distribution at early times. At later times, however, gravity takes over and dominates the collisional growth. We find that the formation of large droplets is very sensitive to the turbulent energy dissipation rate. This is because turbulence enhances the collisional growth between similar-sized droplets at the early stage of raindrop formation. The mean collision rate grows exponentially, which is consistent with the theoretical prediction of the continuous collisional growth even when turbulence-generated collisions are invoked. This consistency only reflects the mean effect of turbulence on collisional growth.

Turbulence Effects of Collision Efficiency and Broadening of Droplet Size Distribution in Cumulus Clouds

This paper aims to investigate and quantify the turbulence effect on droplet collision efficiency and explore the broadening mechanism of the droplet size distribution (DSD) in cumulus clouds. The sophisticated model employed in this study individually traces droplet motions affected by gravity, droplet disturbance flows, and turbulence in a Lagrangian frame. Direct numerical simulation (DNS) techniques are implemented to resolve the small-scale turbulence. Collision statistics for cloud droplets of radii between 5 and 25 μm at five different turbulence dissipation rates (20–500 cm2 s−3) are computed and compared with pure-gravity cases. The results show that the turbulence enhancement of collision efficiency highly depends on the r ratio (defined as the radius ratio of collected and collector droplets r/ R) but is less sensitive to the size of the collector droplet investigated in this study. Particularly, the enhancement is strongest among comparable-sized collisions, indicating that turbulence can significantly broaden the narrow DSD resulting from condensational growth. Finally, DNS experiments of droplet growth by collision–coalescence in turbulence are performed for the first time in the literature to further illustrate this hypothesis and to monitor the appearance of drizzle in the early rain-formation stage. By comparing the resulting DSDs at different turbulence intensities, it is found that broadening is most pronounced when turbulence is strongest and similar-sized collisions account for 21%–24% of total collisions in turbulent cases compared with only 9% in the gravitational case.

Self-Propelled Jump Regime in Nanoscale Droplet Collisions: A Molecular Dynamics Study

Self-propelled jump of droplets is among the most striking phenomena in droplet collisions on substrates. Self-propelled jump phenomena of droplets have been observed in experiments, which have also been reproduced in macro- or mesoscale numerical simulations. However, there have been few previous studies on the phenomena at nanoscales. To unravel the dynamics and mechanisms of nanoscale binary droplet collisions on substrates, head-on collision processes of two identical water droplets with diameters of 10nm on graphite substrates are investigated by molecular dynamics (MD) simulations. By varying the impact Reynolds number of binary droplet collisions on hydrophilic or hydrophobic substrates, we successfully reproduce self-propelled jump of droplets on a super-hydrophobic surface with a contact angle of 143◦ and a relatively high impact Reynolds number of 17.5. Parametric studies indicate that both high impact Reynolds numbers and high hydrophobicity promote self-propelled jump. Moreover, the criterion based on the Ohnesorge number derived from the mesoscopic self-propelled jump regime is insufficient to precisely predict a nanoscale self-propelled jump phenomenon. For this reason, our study includes the impact Reynolds number and the substrate properties like contact angle as additional criteria to refine and extend the current theory for the self-propelled jump behaviours to nanoscales. The study provides insight into the mechanism of self-propelled jump phenomenon at nanoscales.

Micro-reactive Inkjet Printing of Three-Dimensional Hydrogel Structures

AbstractInkjet printing, of the researched techniques for printing of hydrogels, gives perhaps the best potential control over the shape and composition of the final hydrogel. It is, however, fundamentally limited by the low viscosity of the printed ink, which means that crosslinking of the hydrogel must take place after printing. This can be particularly problematic for hydrogels as the slow diffusion of the crosslinking species through the gel results in very slow vertical printing speeds, leading to dehydration of the gel and (if simultaneously deposited) cell death. Previous attempts to overcome this limitation have involved the sequential printing of alternating layers to reduce the diffusion distance of reactive species. In this work we demonstrate an alternative approach where the crosslinker and gelator are printed so that they collide with each other before impinging upon the substrate, thereby facilitating hydrogel synthesis and patterning in a single step. Using a model system based upon sodium alginate and calcium chloride a series of 3D structures are demonstrated, with vertical printing speeds significantly faster than previous work. The droplet collision is shown to increase advective mixing before impact, reducing the time taken for gelation to occur, and improving definition of printed patterns. With the facile addition of more printing inks, this approach also enables spatially varied composition of the hydrogel, and work towards this will be discussed.

Collision-induced jet-like mixing for droplets of unequal-sizes

The internal mixing of droplets upon coalescence is of fundamental importance to a number of applications in microfluidics, micro-scale heat and mass transfer, and rocket engine propulsion. Compared to the well-known surface-tension-induced jet-like mixing in the coalescence of inertialess droplets, collision-induced jet-like mixing was observed recently and remains inadequately understood. In the present study, the collision dynamics and internal mixing of droplets of unequal sizes was numerical simulated by using the lattice Boltzmann phase-field method, with emphasis on unraveling the mechanism of the internal jet formation and therefore on exploring strategies to facilitate such a mixing pattern. The results show that the formation of the internal jet requires two synergetic flow motions favoring low Oh number and high We number: the capillary-pressure-driven radial converging flow induced by the crater restoration to detach the spreading smaller droplet from the surface, and the impact-inertia-driven axial motion along the crater surface to drive the penetration of the detached fluid. The jet-like structure was found to correlate with the evolution of a main vortex ring, which is formed by the vorticity generation on the interface during initial impact, and transported into the droplet during subsequent oscillations. However, due to the absence of the bulge retraction that generates a significant amount of vorticity and to the extended duration for the jet formation, the main vortex is much less intensive compared to that formed by the inertialess droplet coalescence and is therefore less capable of inducing obvious vortex-ring structure in the mixing pattern. Further simulations by manipulating the disparity of the droplet sizes and the disparity of the liquid viscosities show that, the collision of a larger droplet with lower viscosity with a smaller droplet with higher viscosity is effective in facilitating jet-like mixing.

The dynamics of milk droplet\u2013droplet collisions

Spray drying is an important industrial process to produce powdered milk, in which concentrated milk is atomized into small droplets and dried with hot gas. The characteristics of the produced milk powder are largely affected by agglomeration, combination of dry and partially dry particles, which in turn depends on the outcome of a collision between droplets. The high total solids (TS) content and the presence of milk proteins cause a relatively high viscosity of the fed milk concentrates, which is expected to largely influence the collision outcomes of drops inside the spray. It is therefore of paramount importance to predict and control the outcomes of binary droplet collisions. Only a few studies report on droplet collisions of high viscous liquids and no work is available on droplet collisions of milk concentrates. The current study therefore aims to obtain insight into the effect of viscosity on the outcome of binary collisions between droplets of milk concentrates. To cover a wide range of viscosity values, three milk concentrates (20, 30 and 46% TS content) are investigated. An experimental set-up is used to generate two colliding droplet streams with consistent droplet size and spacing. A high-speed camera is used to record the trajectories of the droplets. The recordings are processed by Droplet Image Analysis in MATLAB to determine the relative velocities and the impact geometries for each individual collision. The collision outcomes are presented in a regime map dependent on the dimensionless impact parameter and Weber (We) number. The Ohnesorge (Oh) number is introduced to describe the effect of viscosity from one liquid to another and is maintained constant for each regime map by using a constant droplet diameter (dsim 700 upmu hbox {m}). In this work, a phenomenological model is proposed to describe the boundaries demarcating the coalescence-separation regimes. The collision dynamics and outcome of milk concentrates are compared with aqueous glycerol solutions experiments. While milk concentrates have complex chemical composition and rheology, glycerol solutions are Newtonian fluids and therefore easy to characterize. The collision morphologies of glycerol solutions and milk concentrates are similar, and the regime maps can be described by the same phenomenological model developed in this work. The regime of bouncing, however, was not observed for any of the milk concentrates.

An efficient multi-dimensional implementation of VSIAM3 and its applications to free surface flows

We propose an efficient multidimensional implementation of VSIAM3 (volume/surface integrated average-based multi-moment method). Although VSIAM3 is a highly capable fluid solver based on a multi-moment concept and has been used for a wide variety of fluid problems, VSIAM3 could not simulate some simple benchmark problems well (for instance, lid-driven cavity flows) due to relatively high numerical viscosity. In this paper, we resolve the issue by using the efficient multidimensional approach. The proposed VSIAM3 is shown to capture lid-driven cavity flows of the Reynolds number up to Re = 7500 with a Cartesian grid of 128 × 128, which was not capable for the original VSIAM3. We also tested the proposed framework in free surface flow problems (droplet collision and separation of We = 40 and droplet splashing on a superhydrophobic substrate). The numerical results by the proposed VSIAM3 showed reasonable agreements with these experiments. The proposed VSIAM3 could capture droplet collision and separation of We = 40 with a low numerical resolution (8 meshes for the initial diameter of droplets). We also simulated free surface flows including particles toward non-Newtonian flow applications. These numerical results have showed that the proposed VSIAM3 can robustly simulate interactions among air, particles (solid), and liquid.

Open circuit potential transients associated with single emulsion droplet collisions at an interface between two immiscible electrolyte solutions

Measurements of the open circuit potential (OCP) transients at a sessile aqueous electrolyte drop in contact with a 1,2-dichloroethane (DCE) electrolyte solution were used to detect the collisions of the single DCE-in-water emulsion droplets carrying 0.35M tetradodecylammonium chloride with the interface between two immiscible electrolyte solutions (ITIES). Analysis of the OCP transients yielded the droplet size distribution, which is comparable with distributions obtained from the current transient measurements at a constant applied potential. These results are supported by the dynamic light scattering measurements and the microscope droplet image processing. Observed potential or current spikes appear to be associated with the single collisions of the emulsion droplets with the ITIES followed by the fast droplet ionic charge injection into the electric double layer at the ITIES possibly involving the transfer of Cl− across the droplet/aqueous phase interface, and by the double layer relaxation.

Exploring Chemistry in Microcompartments Using Guided Droplet Collisions in a Branched Quadrupole Trap Coupled to a Single Droplet, Paper Spray Mass Spectrometer.

Recent studies suggest that reactions in aqueous microcompartments can occur at significantly different rates than those in the bulk. Most studies have used electrospray to generate a polydisperse source of highly charged microdroplets, leading to multiple confounding factors potentially influencing reaction rates (e.g., evaporation, charge, and size). Thus, the underlying mechanism for the observed enhancement remains unclear. We present a new type of electrodynamic balance-the branched quadrupole trap (BQT)-which can be used to study reactions in microdroplets in a controlled environment. The BQT allows for condensed phase chemical reactions to be initiated by colliding droplets with different reactants and levitating the merged droplet indefinitely. The performance of the BQT is characterized in several ways. Sub-millisecond mixing times as fast as ∼400 μs are measured for low velocity (∼0.1 m/s) collisions of droplets with <40 μm diameters. The reaction of o-phthalaldehyde (OPA) with alanine in the presence of dithiolthreitol is measured using both fluorescence spectroscopy and single droplet paper spray mass spectrometry. The bimolecular rate constant for reaction of alanine with OPA is found to be 84 ± 10 and 67 ± 6 M-1 s-1 in a 30 μm radius droplet and bulk solution, respectively, which demonstrates that bimolecular reaction rate coefficients can be quantified using merged microdroplets and that merged droplets can be used to study rate enhancements due to compartmentalization. Products of the reaction of OPA with alanine are detected in single droplets using paper spray mass spectrometry. We demonstrate that single droplets with <100 pg of analyte can easily be studied using single droplet mass spectrometry.

Improved models of surface tension and air resistance for multiphysics particle method

ABSTRACT A multiphysics particle method is being developed to simulate the dynamic behaviors of fluid and solid involving their freezing and melting which occur in a severe accident at a nuclear reactor. So far, the conventional particle method code for fluid dynamics has been expanded so that thermodynamics, melting, and freezing can be treated. In this study, new models for the surface tension and air resistance were developed. The developed surface tension model is based on the potential model, where the magnitude of the normal force to the surface is corrected to agree with the theoretical value. A simulation of droplet collisions was conducted to verify the developed model. The simulation results were compared with experimental results and their good agreement was confirmed. The developed air resistance model is based on the assumed pressure distribution around a sphere located in an air stream, hence, the direct simulation of the air phase is not necessary, reducing the computational time. The breakup of a droplet in air was simulated for verification and it was confirmed that reasonable results are obtained using the developed model when the parameters of the analysis object are appropriately chosen.

Study on separation abilities of moisture separators based on droplet collision models

Moisture separators are widely used for eliminating the droplets from the gas–water/steam mixture flows. The volume fraction of droplets is often not small in most separators, so the collision behavior of droplets is crucial in changing their velocity, size and number distributions to affect the separation abilities of these separators. In this paper, the collision models of droplets are established to simulate the droplet-laden flows in the moisture separators. First, a stochastic searching algorithm to find the collision droplet pairs is performed by utilizing the collision kernels and defining the mean free path of a droplet. Second, the criteria to distinguish the different regimes of binary droplet collision are carried out. The regime map drawn by these criteria is highly consistent with that from previous experiments. Third, a set of formulas to predict the velocity, size and number distributions of droplets after bouncing, coalescence, reflexive and stretching separation are proposed based on the conservation law and some empirical relations. Finally, the separation abilities of the cyclone and swirl-vane separators are investigated by simulating the droplet-laden flows coupled with the droplet collision models. As for the cyclone, the simulation separation efficiencies are in good agreement with the experimental data. It is further shown that the separation efficiency curve begins to climb up very quickly in the region with small droplet diameters, and then keep constant as the droplet diameter increasing. As for the swirl-vane separators, the simulated separation efficiencies are little larger than those of the experiment within 5% difference, which is mainly due to the fact that coalescence dominates the collision behaviors from the simulation results. The theoretical and simulation results show that these collision models present a new view to study the flowing behaviors of the droplets in the moisture separators.

Collisions of droplets on spherical particles

Head-on collisions between droplets and spherical particles are examined for water droplets in the diameter range between 170 μm and 280 μm and spherical particles in the diameter range between 500 μm and 2000 μm. The droplet velocities range between 6 m/s and 11 m/s, while the spherical particles are fixed in space. The Weber and Ohnesorge numbers and ratio of droplet to particle diameter were between 92 &amp;lt; We &amp;lt; 1015, 0.0070 &amp;lt; Oh &amp;lt; 0.0089, and 0.09 &amp;lt; Ω &amp;lt; 0.55, respectively. The droplet-particle collisions are first quantified in terms of the outcome. In addition to the conventional deposition and splashing regimes, a regime is observed in the intermediate region, where the droplet forms a stable crown, which does not breakup but propagates along the particle surface and passes around the particle. This regime is prevalent when the droplets collide on small particles. The characteristics of the collision at the onset of rim instability are also described in terms of the location of the film on the particle surface and the orientation and length of the ejected crown. Proper orthogonal decomposition identified that the first 2 modes are enough to capture the overall morphology of the crown at the splashing threshold.

Kinetic energy recovery and interface hysteresis of bouncing droplets after inelastic head-on collision

Binary collision of unequal-size droplets was investigated numerically by using the front tracking method, with particular emphasis in studying the kinetic energy recovery and the interface hysteresis of bouncing droplets. The numerical results were sufficiently validated against the high-quality experimental data in the literature to verify the quantitative predictivity of the numerical methodology in simulating droplet bouncing. Distinct stages of droplet deformation and viscous dissipation during droplet collision were revealed and explained for their dependence on the Weber number and the size ratio. A linear fitting formula that well correlates the kinetic energy recovery factor of bouncing droplets with various collision parameters was proposed and would be practically useful in modeling inelastic droplet bouncing in Lagrangian spray simulation. As an interesting post-collision characteristic of bouncing droplets, the interface hysteresis was found to favor smaller droplet deformation by decreasing the size ratio or decreasing the Weber number or increasing the Ohnesorge number.

Enhanced droplet collision rates and impact velocities in turbulent flows: The effect of poly-dispersity and transient phases

We compare the collision rates and the typical collisional velocities amongst droplets of different sizes in a poly-disperse suspension advected by two- and three-dimensional turbulent flows. We show that the collision rate is enhanced in the transient phase for droplets for which the size-ratios between the colliding pairs is large as well as obtain precise theoretical estimates of the dependence of the impact velocity of particles-pairs on their relative sizes. These analytical results are validated against data from our direct numerical simulations. Our results suggest that an explanation of the rapid growth of droplets, e.g., in warm clouds, may well lie in the dynamics of particles in transient phases where increased collision rates between large and small particles could result in runaway process. Our results are also important to model coalescence or fragmentation (depending on the impact velocities) and will be crucial, for example, in obtaining precise coalescence kernels in such systems.

Control of Drop Impact and Proposal of Pseudo-superhydrophobicity Using Electrostatics

The phenomenon of droplet collision with a charged substrate is investigated numerically by a coupled electro-hydrodynamic model. A charge conservation equation and Poisson equation are solved to obtain the transient electric field. The divergence of Maxwell stress (due to the electric field) is included in the transient momentum equation as a volumetric force to couple the electrostatic force with the hydrodynamics. The interface between the two phases is tracked by volume of fluid method. The motion of the contact line on the solid substrate is controlled by concentric ring shaped charged regions. The electric stress in the vicinity of the contact line restrains its motion in the desired direction, which changes the impact behavior substantially. A hydrophilic surface shows superhydrophobic characteristics when actuated by a sufficient magnitude of electric potential. The phenomenon is analyzed with different parametric variations like electric potential, wetting nature of the substrate, and velocity of...

Particle and Gas Flow Modeling of Wall-impinging Diesel Spray under Ultra-high Fuel Injection Pressures

Advanced models of spray breakup and droplet collision are implemented in OpenFOAM code for comparing the flat-wall impinging and free fuel sprays under ultra-high pressure direct injection diesel engines. The non-evaporating spray and ambient gas flow characteristics are analyzed by a combination of Eulerian and Lagrangian methods for continuous and dispersed phase, respectively. Various injection pressures and two different impinging distances are used. Reynolds Averaged Navier Stokes (RANS) equations are solved using standard k-ε turbulence model. Computational domain and grid size are determined based on a mesh study. Numerical results are validated by published experimental data for free and wall-impinging sprays. The robustness and accuracy of the proposed scheme are confirmed by comparing the main characteristics of spray and surrounding gas against published experimental data. To accomplish this, spray shape, penetration and gas velocity vectors are compared with experimental data and insightful understanding of the spray characteristics are provided. In comparison with free spray, tip penetration has been limited in impinging sprays. Turbulent flow in impinging sprays leads to more induced air motion. Also, impinging spray leads to more pushed-out gas velocity. The obtained results indicate that the numerical findings are generally in good agreement with experimental data in case of ultra-high injection pressures and micro-hole injectors.

Numerical Simulation of Droplets Behavior of Cu-Pb Immiscible Alloys Solidifying under Magnetic Field.

A model has been presented for the coarsening of the dispersed phase of liquid-liquid two-phase mixtures in Cu-Pb alloys under the effect of a high magnetic field (HMF). The numerical results show that the evolution of size distribution is the result of several factors and the diffusional growth, the collision-coagulation of the Cu-rich droplets (gravity sedimentation and Marangoni migration), and melt flow also have obvious effects on the movement of droplets and coarsening process. The effect of the HMF in the coarsening process of Cu-Pb alloy is studied in this work both by simulation and experiment. The analysis shows that the HMF leads to a decrease in the melt flow velocity, and can also lead to a decrease in the moving velocity of Cu-rich droplets. The HMF significantly reduces the coarsening rate of droplets as compared by the distribution evolutions. Finally, it is shown that droplet collision and coagulation can be dramatically retarded by the HMF. The results of the simulation are compared with the experiments performed with immiscible Cu-Pb alloys, and the discrepancy between theory and experiment is discussed.

In situ Confocal Microscopy of Electrochemical Generation and Collision of Emulsion Droplets in Bromide Redox System

For redox flow battery, 1-ethyl-1-methylpyrrolidinium bromide (MEPBr) is a promising bromine-complexing agent that forms insoluble organic phase of MEPBr3. A series of optical images acquired by in-situ confocal microscopy with tens of millisecond interval visualize how MEPBr3 emulsion droplets are electrochemically generated and collide with the electrode surface. Two types of electrodes, i.e. a Pt microdisk of 10μm diameter and a 2.5mm long Pt wire of 25μm diameter, show clear correlation between electrochemical behavior and optical images. The droplets starts growing on the electrode surface at the potential at which oxidative faradaic current starts flowing. As the overpotential increases, the droplets become larger adhered at the electrode surface, from which small droplets start detaching at 0.925V or higher potential. Some of the droplets leave the surface, move back and collide with the electrode surface, thus producing current spikes, which are detected by chronoamperometry simultaneously. In-situ confocal microscopy in this study confirms that the droplets are heterogeneously generated by electrochemical reaction and that individual droplets collide back onto the electrode surface, thus providing a better understanding of the phenomena that happen at redox flow battery electrode surfaces.