Drop Coalescence Research Articles

Surfactant monolayers at oil–water interfaces. Behavior upon compression and relation to emulsion stability

AbstractSurfactant monolayers modify the surface tension of fluid surfaces, and they confer to the surfaces a resistance to mechanical perturbances, such as compression or dilatation. The resistance can be characterized by elastic and viscous moduli, that affect the phenomena involving the motion of liquid surfaces such as wetting, two‐phase flow, foaming and emulsification, rheology and stability of foams and emulsions. Some of these phenomena, for instance coalescence of bubbles or drops, are extremely rapid, and although coalescence seems correlated with the elastic compression modulus, no quantitative comparison has been made. Indeed, this modulus is frequency dependent, and cannot be measured by most conventional devices at the short timescales during which coalescence events occur. In this paper, we first review the current understanding on foam and emulsion stability, highlighting the role of surface rheology in the stability of these systems, important for their formulation. We present tension measurements for various surfactant systems, nonionic and cationic, at oil–water interfaces. We show calculations of the high frequency elastic modulus using the Gibbs adsorption equation and compare the results to previous measurements at air–water interfaces. The moduli measured imposing a rapid expansion of the monolayers are consistently smaller, in particular at oil–water interfaces. We discuss the possible origin of the differences between the two types of interfaces.

The Coalescence of Charged and Uncharged Drops Under Electric Field

The Coalescence of Charged and Uncharged Drops Under Electric Field

Machine learning and physics-driven modelling and simulation of multiphase systems

We highlight the work of a multi-university collaborative programme, PREMIERE (PREdictive Modelling with QuantIfication of UncERtainty for MultiphasE Systems), which is at the intersection of multi-physics and machine learning, aiming to enhance predictive capabilities in complex multiphase flow systems across diverse length and time scales. Our contributions encompass a variety of approaches, including the Design of Experiments for nanoparticle synthesis optimisation, Generalised Latent Assimilation models for drop coalescence prediction, Bayesian regularised artificial neural networks, eXtreme Gradient Boosting for microdroplet formation prediction, and a sub-sampling based adversarial neural network for predicting slug flow behaviour in two-phase pipe flows. Additionally, we introduce a generalised latent assimilation technique, Long Short-Term Memory networks for sequence forecasting mixing performance in stirred and static mixers, active learning via Bayesian optimisation to recover coalescence model parameters for high current density electrolysers, Gaussian process regression for drop size distribution predictions for sprays, and acoustic emission signal inversion using gradient boosting machines to characterise particle size distribution in fluidised beds. We also offer perspectives on the development of a shape optimisation framework that leverages the use of a multi-fidelity multiphase emulator. The results presented have applications in chemical synthesis, microfluidics, product manufacturing, and green hydrogen generation.

Are turbulence effects on droplet collision–coalescence a key to understanding observed rain formation in clouds?

Rain formation is a critical factor governing the lifecycle and radiative forcing of clouds and therefore it is a key element of weather and climate. Cloud microphysics-turbulence interactions occur across a wide range of scales and are challenging to represent in atmospheric models with limited resolution. Based on past experiments and idealized numerical simulations, it has been postulated that cloud turbulence accelerates rain formation by enhancing drop collision-coalescence. We provide substantial evidence for significant impacts of turbulence on the evolution of cloud droplet size distributions and rain formation by comparing high-resolution observations of cumulus congestus clouds with state-of-the-art large-eddy simulations coupled with a Lagrangian particle-based microphysics scheme. Turbulent coalescence must be included in the model to accurately represent the observed drop size distributions, especially for drizzle drop sizes at lower heights in the cloud. Turbulence causes earlier rain formation and greater rain accumulation compared to simulations with gravitational coalescence only. The observed rain size distribution tail just above cloud base follows a power law scaling that deviates from theoretical scalings considering either a purely gravitation collision kernel or a turbulent kernel neglecting droplet inertial effects, providing additional evidence for turbulent coalescence in clouds. In contrast, large aerosols acting as cloud condensation nuclei ("giant CCN") do not significantly impact rain formation owing to their long timescale to reach equilibrium wet size relative to the lifetime of rising cumulus thermals. Overall, turbulent drop coalescence exerts a dominant influence on rain initiation in warm cumulus clouds, with limited impacts of giant CCN.

Inkjet Printing on Hydrophobic Surface: Practical Implementation of Stacked Coin Strategy

While inkjet printing on many hydrophilic surfaces is achieved through control of drop spacing and droplet deposition delay, the same for hydrophobic substrates proves challenging. Low surface energies of hydrophobic surfaces prevents intact and uniform lines of low‐viscosity ink to form. In this article, the stacked coin printing strategy used for hydrophilic surfaces, is adapted for hydrophobic surfaces. Stacked coin morphology is seen when droplet deposition time between two sequentially deposited droplets is longer than the evaporation time of the first droplet. On hydrophobic surfaces, the parameter window for successful printing is smaller than on hydrophilic surfaces, thus an investigation is needed to implement this methodology. Experiments were conducted using an inkjet printer with variable stage speed and stage temperature. Silver nanoparticle ink was used to print on Teflon–AF substrates. We identified the following regimes: isolated droplets, isolated multi‐droplets, broken line, true stacked coin, and delamination. The relationship between substrate temperature, drop spacing, and droplet deposition delay controls the occurence of each regime. In this study, 180 °C was identified as the critical temperature for instantaneous drying of the studied ink, and a maximum drop spacing of 20 μm to print continuous lines.

Inertial coalescence of drops with some viscosity

When two fluid drops touch, they coalesce due to surface tension. At early times, there is only a relatively small fluid bridge joining the drops. An asymptotic solution is presented for an inertial regime of early-time coalescence, in which inertial forces balance surface tension at leading order. It is demonstrated that viscosity nevertheless has a leading-order effect. Radial momentum is created at the tightly curved edge of the fluid bridge by the net force $2\gamma$ (per unit length) due to surface tension. This momentum is left behind the radially expanding bridge edge in a thin viscous wake. The divergent volume flux in the wake entrains fluid from above and below the bridge, and drives an inviscid irrotational flow in the drops on the scale of the bridge radius. This flow widens the gap between the drops ahead of the bridge, and the larger gap width results in a lower rate of coalescence. Including viscosity in this way improves the agreement between theory and the available experimental and numerical data.

Coalescence of non-spherical drops with a liquid surface

We employ three-dimensional numerical simulations to explore the impact dynamics of non-spherical drops in a deep liquid pool by varying the aspect ratios (Ar) and Weber numbers (We). We observe that when a non-spherical drop is gently placed on a liquid pool, it exhibits a partial coalescence phenomenon and the emergence of a daughter droplet for Ar>0.67. In contrast to the prolate (Ar<1) and spherical drops (Ar=1), an oblate (Ar>1) drop with a high aspect ratio encapsulates air in a ring-like bubble within the pool and emerges a liquid column that undergoes Rayleigh–Plateau capillary instability, leading to the formation of two daughter droplets with complex shapes. When the parent drop is impacted with finite velocity, our observations indicate that increasing the Weber number leads to elevated crater heights on the free surface for all aspect ratios. A prolate drop produces a less pronounced wave swell and exhibits a prolonged impact duration owing to its negligible impact area. Conversely, an oblate drop generates a much wider wave swell than spherical and prolate drops. We analyze the relationship between rim formation dynamics and the kinetic and surface energies of the system. Finally, we establish an analogy by comparing the dynamics of a freely falling non-spherical drop, undergoing topological oscillations during its descent from a height, with the impact dynamics of parent drops of various shapes striking the liquid surface with an equivalent velocity. Our investigation involving non-spherical drops contrasts the extensive studies conducted by various researchers on the impact of a parent spherical drop just above the free surface of a liquid pool.

Head-on impact-driven coalescence and mixing of drops of different polymeric materials

Head-on impact-driven coalescence and mixing of drops of different polymeric materials

Heat transfer in drop-laden turbulence

Heat transfer by large deformable drops in a turbulent flow is a complex and rich-in-physics system, in which drop deformation, breakage and coalescence influence the transport of heat. We study this problem by coupling direct numerical simulation (DNS) of turbulence with a phase-field method for the interface description. Simulations are run at fixed-shear Reynolds and Weber numbers. To evaluate the influence of microscopic flow properties, like momentum/thermal diffusivity, on macroscopic flow properties, like mean temperature or heat transfer rates, we consider four different values of the Prandtl number, which is the momentum to thermal diffusivity ratio: $Pr=1$ , $Pr=2$ , $Pr=4$ and $Pr=8$ . The drop volume fraction is $\varPhi \simeq 5.4\,\%$ for all cases. Drops are initially warmer than the turbulent carrier fluid and release heat at different rates depending on the value of $Pr$ , but also on their size and on their own dynamics (topology, breakage, drop–drop interaction). Computing the time behaviour of the drops and carrier fluid average temperatures, we clearly show that an increase of $Pr$ slows down the heat transfer process. We explain our results by a simplified phenomenological model: we show that the time behaviour of the drop average temperature is self-similar, and a universal behaviour can be found upon rescaling by $t/Pr^{2/3}$ . Accordingly, the heat transfer coefficient $\mathcal {H}$ (respectively its dimensionless counterpart, the Nusselt number $Nu$ ) scales as $\mathcal {H}\sim Pr^{-2/3}$ (respectively $Nu\sim Pr^{1/3}$ ) at the beginning of the simulation, and tends to $\mathcal {H}\sim Pr^{-1/2}$ (respectively $Nu\sim Pr^{1/2}$ ) at later times. These different scalings can be explained via the boundary layer theory and are consistent with previous theoretical/numerical predictions.

Explainable AI models for predicting drop coalescence in microfluidics device

In the field of chemical engineering, understanding the dynamics and probability of drop coalescence is not just an academic pursuit, but a critical requirement for advancing process design by applying energy only where it is needed to build necessary interfacial structures, increasing efficiency towards Net Zero manufacture. This research applies machine learning predictive models to unravel the sophisticated relationships embedded in the experimental data on drop coalescence in a microfluidics device. Through the deployment of SHapley Additive exPlanations values, critical features relevant to coalescence processes are consistently identified. Comprehensive feature ablation tests further delineate the robustness and susceptibility of each model. Furthermore, the incorporation of Local Interpretable Model-agnostic Explanations for local interpretability offers an elucidative perspective, clarifying the intricate decision-making mechanisms inherent to each model’s predictions. As a result, this research provides the relative importance of the features for the outcome of drop interactions. It also underscores the pivotal role of model interpretability in reinforcing confidence in machine learning predictions of complex physical phenomena that are central to chemical engineering applications.

Modeling binary collision of evaporating drops

We investigate the interactions between two drops in a heated environment and analyze the effect of evaporation on bouncing, coalescence and reflexive separation phenomena. A reliable mass transfer model is incorporated in a coupled level-set and volume-of-fluid framework to accurately model the evaporation process and the evolution of drop interfaces during the interactions. The numerical technique is extensively validated against the benchmark problems involving the evaporation of a single drop. We analyze the contour plots of temperature and vapor mass fraction fields for each collision outcome. Our numerical simulations reveal that vapor entrapment during the separation process, with high-velocity vapor manages to escape. Increasing evaporation rates result in slower post-collision drop separation. Furthermore, the differences in kinetic energy and surface energy are analyzed for different Stefan numbers. The coalescence of drops exhibits energy oscillations until dissipation, while the bouncing and reflexive separations lack such oscillations. In the reflexive separation regime, the kinetic energy of the drops becomes zero after detachment.

A new experimental set-up for aerosol stability investigations in microgravity conditions

The temporal and spatial evolution of dispersed media is a fundamental problem in a wide range of physicochemical systems, such as emulsions, suspensions and aerosols. These systems are multiphasic and involve compounds of different densities. They are therefore subject to the influence of gravity which determines the sedimentation rate of their dispersed phase. This effect can be dominant and prevent a detailed study of the phenomena occurring between the constituents themselves, such as the coalescence of drops in emulsions, the evaporation of droplets or the flocculation in suspensions. In this context, the Centre National d’Etudes Spatiales (CNES) has recently supported the development of a new instrument to produce populations of droplets, a few micrometers in radius, under controlled conditions with the objective of allowing a detailed study of their properties in microgravity conditions. The principle of this instrument is to generate, by a fast compression/expansion of air, populations of water droplets and to track their evolution by optical scanning tomography in transmission mode within a volume of approximately 2 mm 3 . Parabolic flight experiments have shown the possibility to generate and accurately follow the evolution of populations of several hundred droplets for more than 20 s. The first experimental results show that it is possible to study their evaporation kinetics or their motion when imposing von Karman swirling flows. This work is part of the AEROSOL project of DECLIC-EVO supported by CNES and aims to help the understanding of cloud microphysics which remains a critical open problem in the context of global warming.

Hybrid modeling of drop breakage in pulsed sieve tray extraction columns

Accurate models for pulsed sieve tray extraction columns (PSEs) depend on the correct prediction of the drop diameter to estimate extractive mass transfer across the phase boundary. Phenomenologically, the drop diameter is determined by a balance of drop breakage and coalescence. While for most industrial solvent systems, coalescence plays a minor role; breakage is mostly the dominant phenomenon determining the drop diameter. However, most modeling approaches for drop breakage in PSEs are characterized by a trade-off between a broad validity range and good prediction accuracy. To overcome this limitation, we developed a hybrid breakage model for drop breakage in PSEs in which a physical-empirical model basis is enhanced by data-driven parameter estimator models (PEMs). The hybrid model is based on a revised form of Garthe’s breakage model, for which we developed a linear PEM for the model parameters and two data-driven PEMs for dstab and d100, respectively. The hybrid breakage model was validated on 743 experimental data sets and evaluated based on the pull metric. In a sensitivity analysis, the model correctly predicted the breakage probability over a wide range of solvent properties, operating conditions, and sieve tray geometries. In future studies, the hybrid breakage model can be incorporated into extraction column models without an initial parametrization.

A Review on the Coalescence of Confined Drops with a Focus on Scaling Laws for the Growth of the Liquid Bridge.

The surface-tension-driven coalescence of drops has been extensively studied because of the omnipresence of the phenomenon and its significance in various natural and engineering systems. When two drops come into contact, a liquid bridge is formed between them and then grows in its lateral dimensions. As a result, the two drops merge to become a bigger drop. The growth dynamics of the bridge are governed by a balance between the driving force and the viscous and inertial resistances of involved liquids, and it is usually represented by power-law scaling relations on the temporal evolution of the bridge dimension. Such scaling laws have been well-characterized for the coalescence of unconfined or freely suspended drops. However, drops are often confined by solid or liquid surfaces and thus are a different shape from spheres, which affects their coalescence dynamics. As such, the coalescence of confined drops poses more complicated interfacial fluid dynamics challenges compared to that of unconfined drops. Although there have been several studies on the coalescence of confined drops, they have not been systematically reviewed in terms of the properties and geometry of the confining surface. Thus, we aim to review the current literature on the coalescence of confined drops in three categories: drop coalescence on a solid surface, drop coalescence on a deformable surface, and drop coalescence between two parallel surfaces with a small gap (i.e., Hele-Shaw cell), with a focus on power-law scaling relations, and to suggest challenges and outlooks for future research on the phenomena.

Fine Flow Structure at the Miscible Fluids Contact Domain Boundary in the Impact Mode of Free-Falling Drop Coalescence

Registration of the flow pattern and the matter distribution of a free falling liquid drop in a target fluid at rest in the impact mode of coalescence when the kinetic energy (KEn) of the drop exceeds its available surface potential energy (ASPe) was carried out by photo and video recording. We studied the evolution of the fine flow structure at the initial stage of the cavity formation. To carry out color registration, the observation field was illuminated by several matrix LED and fiber-optic sources of constant light. The planning of experiments and interpretation of the results were based on the properties of the complete solutions of the fundamental equations of a fluid mechanics system, including the transfer and conversion of energy processes. Complete solutions of the system of equations describe large-scale flow components that are waves or vortices as well as thin jets (ligaments, filaments, fibers, trickles). In experiments, the jets are accelerated by the converted available surface potential energy (ASPe) when the free surfaces of merging fluids were eliminated. The experiments were performed with the coalescence of water, solutions of alizarin ink, potassium permanganate, and copper sulfate or iron sulfate drops in deep water. In all cases, at the initial contact, the drop begins to lose its continuity and breaks up into a thin veil and jets, the velocity of which exceeds the drop contact velocity. Small droplets, the size of which grows with time, are thrown into the air from spikes at the jet tops. On the surface of the liquid, the fine jets leave colored traces that form linear and reticular structures. Part of the jets penetrating through the bottom and wall of the cavity forms an intermediate covering layer. The jets forming the inside layer are separated by interfaces of the target fluid. The processes of molecular diffusion equalize the density differences and form an intermediate layer with sharp boundaries in the target fluid. All noted structural features of the flow are also visualized when a fresh water drop isothermally spreads in the same tap water. Molecular diffusion processes gradually smooth out the fast-changing boundary of merging fluids, which at the initial stage has a complex and irregular shape. Similar flow patterns were observed in all performed experiments; however, the geometric features of the flow depend on the individual thermodynamic and kinetic parameters of the contacting fluids.

Drop rise and interfacial coalescence initiation in Bingham materials

Drop coalescence in viscoplastic materials is present in various industrial applications and the environment. The plasticity of the surrounding material affects drop rise, collision, and film drainage dynamics, and knowledge about these is essential for designing and operating industrial mixer and separator units. Despite its importance, the coalescence of drops in yield stress materials is not entirely understood. In this work, we investigate the effects of the surrounding material plasticity on the rise and interfacial coalescence initiation of Newtonian drops using direct numerical simulations. Plastic effects contribute to the formation of smaller and spherical films, which facilitate the film drainage process on the one hand, but also to an increase in the resistance of the film to flow, which makes the drainage process more difficult on the other hand. The fluids’ interfaces are less deformable for high surface tension regimes, and the flow resistance effects become more significant than the film shape change effects. As a result, the drainage time tends to increase with the level of plasticity. For low surface tension regimes, the fluid interface is more deformable, and film drainage time tends to decrease with an increase in the level of plasticity.

An investigation on the impact of two vertically aligned drops on a liquid surface

The dynamics of two vertically coalescing drops and a pool of the same liquid have been investigated using a Coupled Level Set and Volume of Fluid (CLSVOF) method. Such a configuration enables us to study the dynamic interaction of an arbitrary-shaped liquid conglomerate, formed owing to drop–drop coalescence, with a pool. Similar to drop–pool and drop–drop interactions, partial coalescence is observed when a conglomerate interacts with a pool. The presence of the pool below the father drop is found to influence the coalescence characteristic of the two drops. At the same time, the movement of the capillary waves resulting from the interaction of two drops governs the coalescence dynamics of the conglomerate with the pool. As liquid interfaces interact and generate capillary waves at multiple locations, complex trajectories of capillary waves are observed, which play a crucial role in determining the pinch-off characteristics of the satellite during conglomerate–pool interaction. We examine the effect of the ratio of the diameters of the lower/father drop to the upper/mother drop (Dr) on the coalescence dynamics while maintaining the size of the mother drop constant. The variation in the coalescence dynamics due to change in Dr is quantified in terms of the residence time (τr), pinch-off time (τp) and the satellite diameter to conglomerate diameter ratio (Ds/Dc). The coalescence dynamics of the conglomerate is then compared with that of an equivalent spherical drop of the same volume and also with that of a drop initialized with the same shape as that of the conglomerate. Finally, the regions of complete and partial coalescence for the conglomerate–pool interactions are demarcated on the Weber number–diameter ratio (We−Dr) space.

High-efficient and robust fog collection through topography modulation

Janus wettable material is considered one of the most promising candidates for fog collection. However, the applications of fog collectors are confined by many weaknesses nowadays, such as tedious fabrication methods, low mechanical stability and durability, and poor collecting efficiency. Among them, improving fog harvesting efficiency is a big challenge to be overcome. Herein, a series of hydrophobic-superhydrophilic Janus system has been successfully fabricated by a facile and eco-friendly method including etching and interface modification. Importantly, under the inspiration of natural creatures, the topography of hydrophobic surface in Janus system can be modulated by modifying substances with different low surface energy, effectively improving the fog collecting performance, and obtaining an excellent fog harvesting efficiency of 3718 mg·cm−2·h−1 in unenclosed fog environment. The underlying mechanism is designed to discuss the enhancement of fog collection in terms of fog capture, drop coalescence and drop transportation. Meanwhile, it is recyclable and durable even maintained for at least 5 months. Moreover, it exhibits good stability during mechanical, thermal and ultraviolet (UV) resistance testing. Overall, the findings open up a new avenue to design Janus materials for efficient fog harvesting by regulating micromorphology and promote a promising candidate for addressing water scarcity.

Synthesis of gold nanoparticles in emulsion–emulsion precipitation route: Experiment, mechanism and simulation

Soft templates like water-in-oil emulsion drops (of 1-100μm diameter), have been used for synthesis of nanoparticles; with specific mean particle diameter and narrow particle size distribution. In this context, two separate emulsions have been reacted by an emulsion–emulsion precipitation route. Consequently, two different kinds of interacting populations coexist — emulsion drops evolving through drop coalescence and breakage, with multiple nanoparticle populations growing inside each emulsion drop. However, no model framework currently exists to simulate these two highly interacting populations, for predicting evolution of nanoparticle size. To this end, presently gold nanoparticles (GNPs) have been used as a model system, to explore the nanoparticle formation mechanism. The metal salt precursor and reducing agent (NaBH4 or N2H4) are prepared in two separate water-in-oil emulsions and are reacted upon mixing to form GNPs. A kinetic Monte Carlo (kMC) scheme accounting for drop coalescence, drop breakage, nucleation, particle growth and particle–particle coagulation was developed to handle simultaneous size and number evolution of aqueous emulsion drops and GNP populations. We find that, the mean GNP diameter decreases (from 6.9 to 3.5 nm) with increasing molar ratio (M) of reducing agent to precursor concentration. Further, increasing the precursor concentration at a fixed M, does not affect the final particle size. Our kMC simulation results not only agree well with experimental mean particle diameter and coefficient of variation (COV) of particle diameter, but was also validated with full particle size distribution of GNPs. So, M can be used as a tunable parameter for controlling GNP diameter experimentally.

Batch-Operated Condensed Droplet Polymerization to Understand the Effect of Temperature on the Size Distribution of Polymer Nanodomes

Size-controlled polymer nanodomes (PNDs) benefit a broad cross-section of existing and emerging technologies. Condensed droplet polymerization (CDP) is a vacuum-based synthesis technology that produces PNDs from monomer precursors in a single step. However, the effect of synthesis and processing conditions on the PND size distribution remains elusive. Towards size distribution control, we report the effect of substrate temperature, on which monomer droplets condense, on the size distribution of PNDs. We take a reductionist approach and operate the CDP under batch mode to match the conditions commonly used in condensation research. Notably, despite the rich knowledge base in dropwise condensation, the behavior of nonpolar liquids like a common monomer, i.e., 2-hydroxyethyl methacrylate (HEMA), is not well understood. We bridge that gap by demonstrating that dropwise condensation of HEMA follows a two-stage growth process. Early-stage growth is dominated by drop nucleation and growth, giving rise to relatively uniform sizes with a lognormal distribution, whereas late-stage growth is dominated by the combined effect of drop coalescence and renucleation, leading to a bimodal size distribution. This new framework for understanding the PND size distribution enables an unprecedented population of PNDs. Their controlled size distribution has the potential to enable programmable properties for emergent materials.