Drop Coalescence Research Articles

Numerical analysis of drop coalescence in cavity flow using CESE method

On the basis of the space-time conservation element and solution element method and by applying the hybrid particle level-set function, the drop coalescence in a dual-layer vertical channel has been numerically studied. Interactions between the flow field and the drop migration are observed. Main eddies and secondary vortexes induced by the drop coalescence are examined. Deformation and migration of the drop are mainly controlled through interfacial tension and the shear stress gradient. Drop coalescence is related to a viscous dissipation of energy.

Coalescence of drops on the free-surface of a liquid pool at elevated temperatures

The coalescence dynamics of ethanol drops injected from a needle on the free-surface of an ethanol pool maintained at a higher temperature than the drop is experimentally studied using a high-speed imaging system. The drop is always kept at 25 °C, and the temperature of the ethanol pool is varied using a heater. The coalescence behavior depends on the size of the drop, the height of the needle tip from the free-surface, and the temperature of the ethanol pool. A parametric study is carried out by varying these parameters. The drop exhibits a residence period at low impact velocity, when it floats on the free-surface before the coalescence begins. Subsequently, the complete coalescence and partial coalescence dynamics are observed for different sets of parameters considered. It is found that increasing the temperature of the ethanol pool reduces the residence time of the drop. This phenomenon is explained by analyzing the forces acting on the drop and the capillary waves generated due to the temperature gradient between the drop and the ethanol pool. During partial coalescence, we also observed that the diameter of the daughter droplet decreases as the size of the primary drop and pool temperature are increased. As expected, due to the gravity effect, increasing the size of the drop also decreases the residence time. A regime map designating the complete coalescence and partial coalescence dynamics is plotted in the pool temperature and drop impact height space.

Closed-form theoretical model of the secondary drop size in partial coalescence—Capturing pertinent timescales and viscous forces

One of the most important outcomes of partial drop coalescence is the ratio of the secondary drop radius to the primary drop radius, known as the drop ratio, ri. This ratio is thought to be approximately constant and independent of physical parameters of the fluids involved. However, this study reveals that ambient fluid viscosity can alter the size of the secondary drop and the drop ratio consequently. Using scaling analysis, we derive a model that predicts the behavior of the drop ratio as a function of the Ohnesorge number, a dimensionless ratio of viscous to inertial forces. In addition, we present our experimental results of coalescing drops on a planar interface under the influence of surface tension gradients. A high-speed digital camera is used to observe the evolution of drops as they coalesce with a bulk liquid. We show that this process is influenced by the surface tension gradient between the drop and the bulk liquid. The ratio of the secondary drop to the primary drop in partial coalescence is smaller than the reported values for coalescence without a surface tension gradient. The analytical model derived through this study is based on a new modified Ohnesorge number that includes surface tension gradients. Our analytical model is compared against other models and the results illustrate good agreement with our experimental findings and experimental data in the literature.

Experimental investigation of hydrodynamics and heat transport during vertical coalescence of multiple successive drops impacting a hot wall under saturated vapor atmosphere

In this study, hydrodynamics and heat transport during the vertical coalescence of multiple successive drops impacting a hot wall are analyzed experimentally. This study addresses the influence of wall superheat and the frequency of drop generation on the hydrodynamics and heat transport. The experiments are conducted under a pure vapor atmosphere with the refrigerant FC-72 at a saturation temperature of 54.5°C, corresponding to a system pressure of 0.94 bar. The drops are generated with a constant diameter of 1.14 mm and a constant impact velocity of 0.54 m s−1. An infrared camera with a high spatial and temporal resolution is used to capture the temperature field on the surface of the heater. The local heat flux distribution is derived from the temperature field by solving the transient three-dimensional heat conduction equation within the substrate. The total heat flow is evaluated by integrating the local heat flux over the footprint of the drop. The impact parameters (drop size and impact velocity) are evaluated through post-processing of the black/white images captured using a high-speed camera. The maximum spreading radius and maximum heat flow observed after the impact of each successive drop are higher than those observed after the impact of the previous drop. For instance, in the case of a wall superheat of 12.4 K and an impact frequency of 10 Hz, the maximum spreading radius and maximum heat flow observed after the impact of the fourth drop increased by approximately 35% compared with those observed after the impact of the first drop on a dry wall. The distribution of wall heat flux during the spreading phase of the second impacting drop is characterized by the appearance of two thin ring-shaped zones of high heat flux. The time evolutions of the drop shape and heat flow depend on the wall superheat and are independent of the frequency of drop generation within the studied range of parameters.

Surfing of drops on moving liquid–liquid interfaces

The delayed coalescence of drops with the interface between a moving aqueous layer and an oil phase is investigated in a novel flow channel. Drops are released onto oil–aqueous interfaces moving at velocities from 0 cm s−1 up to 3.4 cm s−1 . The evolution of the drop shape, the film thickness between the drop and the bulk liquid, and the velocities of the drop surface and the bulk interface were measured with planar laser-induced fluorescence. As the interface speed increases, the drop coalescence is delayed. This is attributed to the lubrication pressure that develops in the draining film. This pressure was calculated by using the drop shape and the tangential velocities of the drop surface and the bulk interface, and was shown to increase with the interface velocity. The film forming between the drop and the bulk liquid has a dimple shape, symmetric about the centreline. With increasing interface velocity, the dimple shifts to the front part of the drop, resulting locally in a low pressure, which leads to film rupture. As the film breaks, ‘oil drops on a string’ formations are entrained into the water phase, which is rarely seen when a drop coalesces with a stationary liquid–liquid interface. The velocity fields in the drop were investigated with particle image velocimetry. It is found immediately after reaching the interface that the drops accelerate to reach the interface speed. Initially there is a strong internal circulation in the drops, which decays quickly as the drops approach the speed of the interface.

Initial regime of drop coalescence

What is the initial regime of coalescence when two drops just touch at a point? This long-standing problem has proven formidable because of the smallness of the bridge that is required to connect the drops at the initial instant in any continuum simulation. Here, initial bridge radii, heights, and radii of curvature as small as 10${}^{\ensuremath{-}6}$, 10${}^{\ensuremath{-}12}$, and 10${}^{\ensuremath{-}18}$ are achieved, showing that coalescence always begins in a Stokes regime. The inertially limited viscous regime is shown to be a Taylor-Culick-like regime seen only when drops are initially separated by a finite distance.

Optimal placement of droplets for UV nanoimprint lithography

Optimizing the locations and sizes of droplets are key to reduce defects and increase throughput of ultraviolet nanoimprint lithography (UVNIL). Previously, simulation models describing the flow and coalescence of multiple fluid drops were developed and used to predict the fluid flow during spreading and feature filling. However, the effect of small channels on the resulting capillary pressure is neglected even though the flow along small channels or grooves is encountered in UVNIL. In this study, an accurate method to estimate capillary pressure boundary conditions at the fluid-air interface is developed along with fluid simulation. A method to estimate and compute the anisotropic capillary pressure for templates with line and space patterns is presented. It is found that the droplets flow faster in the direction of the pattern not only because of anisotropic permeability but also the nanostructure of the template, which further propels anisotropic spreading of the droplets by exerting larger capillary pressure. Using the new capillary pressure boundary condition, the simulation of multidrop spreading in UVNIL is performed to study the effects of anisotropic capillary pressures caused by the template structure. A simulation approach to determine optimal droplet placement was developed. From the simulation, a general rule of thumb is developed: delaying droplet merging as much as possible and reducing the number of merging events.

Molecular Dynamics Study of the Temperature-Dependent Coalescence of Liquid Nanodrops: Implications for Microfluidics

Drop coalescence is central to diverse processes involving microfluidics in industrial, engineering, and scientific realms and has attracted much attention in recent years. Here, the effect of temp...

STUDY OF PARAMETERS AFFECTING THE COALESCENCE OF DIMETHYL DISULFIDE DROPS IN A MEROX UNIT

Abstract This study focuses on the coalescence of dimethyl disulfide drops with the mother phase at a flat aqueous-organic interface between dimethyl disulfide and different sodium hydroxide solutions. Drop coalescence is an important part of the Merox process for regenerating the solvent. A digital high-frame rate camera was used for recording drops coalescence and duration time. Drops of dimethyl disulfide were directed in different sodium hydroxide solutions as the continuous phase. Applying the experimental design method, the influences of independent variables of drop size and physical properties on coalescence time were investigated. Computational fluid dynamics (CFD) was employed to simulate the drops released from a nozzle, moving toward the interface, and the CFD results were validated by experimental data. The maximum deviation between the predicted and experimental coalescence times was 18.7%. It was found that, among the physical properties, interfacial tension plays the most important role on the coalescence time. Based on the results, a correlation for coalescence time was proposed.

Comprehensive characterization of TiO2 inks and their application for inkjet printing of microstructures

This work having an experimental character aims to study the drop coalescence process during the inkjet printing. Exemplified by titania-based inks, the influence ofn substrate wettability, desired structure design, and printing parameters, such as ink rheology, drop spacing, and drying temperature, on printing results is comprehensively investigated. The strategies of avoidance of printing defects, such as thickening, coffee-ring effect, undesired drop spreading, and coalescence, are discussed based on extensive experimental data. The obtained experimental data is compared with existing theoretical models and allows a deeper understanding and prediction of possible defects in inkjet printed structures, as well as setting parameters leading to better printing results.

Numerical simulation of a novel non-uniform electric field design to enhance the electrocoalescence of droplets

Abstract The behavior of binary droplet collision, exposed to an external electric field is studied numerically. Based on a fundamental understanding of the role of the electric field in the coalescence of aqueous drops in an immiscible oil phase, it is possible to optimize the design and operation of these external stimulators. In this research, numerical modeling of electrocoalescence is implemented, using Computational Fluid Dynamics (CFD) methods. Level set method is used to evaluate water droplet evolution in an oil phase under a novel concentric semi-elliptic non-uniform electric field configuration. The observations show that the shape of applied non-uniform fields can remarkably alter the electrocoalescence performance in a nontrivial way, which is sensitive to the drop-medium system. In addition to the shape of the medium, some other parameters such as droplets initial distance, initial skew angle of the droplets, applied voltage amplitude and oil viscosity are analyzed in the present paper. Our results can be useful in designing an optimum electrode configuration, achieving an efficient electrocoalescence.

An experimental study on the effect of conductivity, frequency and droplets separation on the coalescence of two aqueous drops under an electric field

The coalescence of water drops, dispersed in oil, is critical to the destabilization of a water-in-oil emulsion under an electric field. In this work, we determine the conditions for coalescence or non-coalescence of two aqueous water drops that are suspended in an insulating oil and subjected to a uniform electric field. Specifically, we investigate the effect of the conductivity of the droplet phase (σ), the type of oils (silicone oil and castor oil), the effect of waveform AC and DC and frequency, and the separation between the droplets on the electrocoalescence/non-coalescence of two suspended aqueous drops. The main highlights are, (i) we provide expressions for critical electrocapillary number (Cac) vs. σ for silicone oil (Cac=0.010×σ−0.20) that shows cone-cone and castor oil (Cac=0.022×σ−0.15) that shows cone-dimple mode of contact. (ii) Two closely spaced drops can coalesce at electrocapillary numbers much higher than the critical electrocapillary number for widely spaced drops due to a smaller cone angle at the point of contact. These results should be important in the design of industrial electrocoalescers.

A level-set immersed interface method for simulating the electrohydrodynamics

A method is proposed for simulating the electrohydrodynamics (EHD). The level-set method is used to capture the interface to take its advantage in handling topological change. In order to accurately solve the Poisson equation with interface jump conditions for the electric potential, a simple version of the level-set based immersed interface method (IIM) is developed. This version avoids the local coordinate transform in the original IIM in literature, reducing the complexity of the algorithm significantly. The IIM achieves second-order accuracy for both the electric potential and its gradient. A level-set extrapolation procedure is presented to calculate the electric surface force. Numerical simulations on drop deformation, breakup and coalescence in both 2D and 3D are presented.

Influence of Different Silica Nanoparticles on Drop Size Distributions in Agitated Liquid‐Liquid Systems

AbstractThe impact of different silica nanoparticles on rheology, interfacial tension and drop size distributions in liquid‐liquid systems is determined experimentally. The particles vary in wettability and specific surface area. In contrast to commonly used high‐energy devices for Pickering emulsion preparation, low energy input by stirring allows to quantify drop breakage and coalescence in steady state and dynamic conditions. The experiments can provide essential information for drop size model development in nanoparticle‐stabilized emulsions.

Coalescence of Water Drops at an Oil–Water Interface Loaded with Microparticles and Surfactants

This work investigates the coalescence of water droplets settled on a water–oil interface in the presence of microparticles and surfactant. The successive stages of the coalescence process, including interstitial film formation, drainage, rupture, and retraction, are analyzed in detail. This leads us to distinguish between contrasted situations depending on the nature of the surfactant and its affinity with the microparticles. Hydrophilic particles have been previously shown to promote coalescence by means of a bridging mechanism. In that case, coalescence is a deterministic process that lasts the time required for the drainage to make the film thickness equal to the size of the particles. However, the present study shows how surfactants can totally change the effect of the particles upon coalescence. When surfactant both stabilizes the water–oil interface and adsorbs onto the particles, the bridging mechanism is inhibited and the coalescence becomes a random process. Since molecular forces between facing film interfaces are not attractive, thermal fluctuations are required to initiate the formation of a hole in the adsorbed surfactant layer. Provided the surfactant concentration in the bulk is large enough to ensure that the interfaces are close to saturation, the coalescence is delayed by a stochastic time interval and the drop coalescence becomes a Poisson process. These results shed a new light on the mechanisms of droplet coalescence in complex industrial applications where surfactant and particles are present, either purposely added or present as uncontrolled contaminants.

Effect of polymer-coated gold nanoparticle stabilizers on drop coalescence

Polymer-coated gold nanoparticles (PGNPs) can be used as stabilizers in immiscible polymer blends, similar to block-copolymers (BCs). However, the PGNP gold cores increase the magnitude of the disjoining pressure (Π), i.e., the van der Waals interaction for unit area, in the film between the drops, favoring coalescence. This might explain the counterintuitive 70% drainage time (td) reduction for polymeric drops stabilized by PGNPs compared to those stabilized by BCs, as reported in recent flow-induced head-on collision experiments in extensional flow, despite PGNPs being more surface active. Knowledge of the mechanisms determining td is fundamental for designing effective PGNP compatibilizers. Here, we performed a parametric study of those experiments via boundary integral simulations, treating PGNPs as surfactants and utilizing for the first time a disjoining pressure expression which includes the effect of interfacial PGNPs (ΠPGNP). In particular, we varied the PGNP concentration and core size in ΠPGNP, the surface diffusivity (Ds) via the surface Peclet number, and the surface elasticity via the Marangoni number. Flow-induced coalescence was very sensitive to all three parameters. td was reduced up to 60% for touching 3 nm core diameter PGNPs, increasing significantly the coalescence probability for drop sizes <5 µm, but the soft coronas diminished this effect considerably. Thus, other causes, besides the enhanced Π, had to be simultaneously present to explain the dramatic experimental td reduction; the most likely is a Ds higher than its Stokes-Einstein relation estimate and the PGNP ligands being in a dry-brush regime, leading to entropic attraction between the drop interfaces.

Conservative mathematical model and numerical simulation of batch gravity settling with coalescence of liquid-liquid dispersions

Population balance equations (PBE) provide a suitable a framework for dealing with drop breakage and coalescence. In addition, modeling of the solid particle sedimentation process based on Kynch’s theory has been successfully used and validated in mineral processing and wastewater treatment. In this work, we present a model that merges the coalescence process with hindered polydisperse sedimentation. The PBE model is projected onto a partial differential equation (PDE) system by discretizing the droplet volume. Because there is loss of mass in the system when the daughter droplets are greater than the larger species considered for the numerical solution, two terms that produce the conservation of the mass or total volume of the dispersed phase are incorporated into the PDE system. The resulting PDE system is split into two systems: homogeneous PDEs and ordinary differential equations (ODEs). The homogeneous PDEs and the ODEs are discretized using a first-order central differencing scheme and the second-order, two-stage Runge-Kutta method, respectively. The model predicts the vertical variation of the composition of the dispersed phase layer that forms at the top or bottom of the gravity settler. The proposed model was calibrated and validated through an experiment with an oil and water system. In particular, simulations illustrate the effects of: the continuity of the dispersion (oil-in-water and water-in-oil) and the standard deviation of the initial droplet volumes on phase separation quality, as well as the influence of the coalescence frequency on the average droplet volume.

Effect of Boundary Layer Dynamics on the Profiles of Rain Drop Size Distribution During Convective Rain

The profiles of rain microstructures have been investigated for different types of precipitation using microrain radar observations at a tropical location Kolkata (22.57° N, 88.37° E). A prominent dip in radar reflectivity ( $Z$ ) profile has been observed near the boundary layer at high rain rates. This phenomenon is due to the break-up of raindrops into smaller sizes at around 2 km height during intense convective events. The boundary layer dynamics decides the dominance of one of the two processes, namely, coalescence and break-up of rain drops, and determines the drop size distribution profile near the boundary layer. A sharp gradient of vertical velocity at 1–2 km heights is responsible for enhanced drop break-up resulting in an increase in the small drop number density.

Mass Transfer Accompanying Coalescence of Surfactant-Laden and Surfactant-Free Drop in a Microfluidic Channel.

The coalescence of two different drops, one surfactant-laden and the other surfactant-free, was studied under the condition of confined flow in a microchannel. The coalescence was accompanied by penetration of the surfactant-free drop into the surfactant-laden drop because of the difference in the capillary pressure and Marangoni flows causing a film of surfactant-laden liquid to spread over the surfactant-free drop. The penetration rate was dependent on the drop order, with considerably better penetration observed for the case when the surfactant-laden drop goes first. The penetration rate was found to increase with an increase of interfacial tension difference between the two drops, an increase of flow rate and drop confinement in the channel (for the case of the surfactant-laden drop going first), an increase of viscosity of the continuous phase, and a decrease of viscosity of the dispersed phase. Analysis of flow patterns inside the coalescing drops has shown that, unlike coalescence of identical drops, only two vortices are formed by asymmetrical coalescence, centered inside the surfactant-free drop. The vortices were accelerated by the flow of the continuous phase if the surfactant-laden drop preceded the surfactant-free one, increasing the rate of penetration; the opposite was observed if the drop order was reversed. The mixing patterns on a longer time scale were also dependent on the drop order, with better mixing being observed for the case when the surfactant-laden drop goes first.

Inkjet Printing in Liquid Media: Intra-Volumetric Drop Coalescence in Polymers

The tendency to develop flexible and transparent materials has been growing in the last decade. As inkjet printing technology has become a widespread method for the fabrication of functional materials, the investigation of the inkjet printing process seems to be essential with regard to polymers, which are a viscous and flexible media. In this study, we evaluated the dependence of ink drop coalescence on process parameters such as polymer viscosity (controlled by polymerization time), drop spacing and drop speed. The results showed that drop coalescence was mostly influenced by drop speed, while drop spacing and substrate polymer viscosity did not significantly affect the printing results. The presented data are crucial for understanding the processes involved in the fabrication of flexible materials by inkjet printing.