Droplet-droplet Interactions Research Articles

Research on water droplet interception mechanism of sheet-type drift eliminator based on three-dimensional transient numerical simulation

A three-dimensional transient numerical study was conducted on the sheet-type drift eliminator single-channel to reveal the droplet interception mechanism, using a mechanical draft wet cooling tower (MDWCT) as a typical operating environment. The droplet-air, droplet-droplet, droplet-film, and film-air interactions were considered comprehensively from the aerodynamics and heat transfer. The results indicate the existence of two distinct types of droplet escape: primary escape and secondary escape. The Stokes number (St) ≤ 1 for the vast majority of primary escaped droplets, whereas the secondary escaped droplets exhibit a considerable range of St. The correlation curves between the escape rate and the Stokes number (Stin) is similar under different inlet velocities (vin). The escape rate first decreases and then increases as Stin increases. There is a safety zone (Stin from 0.83 to 18.62) where the escape rate is near zero. For the studied eliminator, the specific safety zone is 65∼190 μm. The mass flow rate of escaped droplets first decreases and then increases as vin increases. The secondary escape dominates instead of primary escape when vin ≥ 7 m/s. This paper provides theoretical support for improving interception efficiency of eliminator while extending the methods for drift reduction and water savings.

Enhancing the Thermal Stability of Zein Particle-Stabilized Aeratable Emulsions Through Genipin-Protein Cross-Linking and Its Possible Mechanism of Action.

Protein particle-stabilized emulsions often lack thermal stability, impacting their industrial use. This study investigated the effects of genipin (GP)-zein cross-linked particles with varying GP-to-protein weight ratios (0/0.02/0.1:1) on emulsion thermal stability. Enhanced stability was observed at the GP level of 0.1. Heat treatment increased the covalent cross-linking in raw particles and emulsions. Isolated particles from heated emulsions grew in size (micrometer scale) with higher GP levels, unlike heated raw particles (nanoscale). GP-protein cross-linking reduced the droplet-droplet and particle-emulsifier interactions in the heated emulsion. Spectroscopic analysis and electrophoresis revealed that GP-zein cross-linking increased protein structural stability and inhibited nondisulfide and non-GP cross-linking reactions in heated emulsions. The GP-zein bridges between particles at the oil-water interface create strong connections in the particle layer (shell), referred to as "particle-shell locking", enhancing the thermal stability of emulsion significantly. This insight aids the future design of protein-particle-based emulsions, preserving properties like aeratability during thermal processing.

Droplet tilings in precessive fields: hysteresis, elastic defects, and annealing.

Two-component Marangoni contracted droplets can be arranged into arbitrary two-dimensional tiling patterns where they display rich dynamics due to vapor-mediated long-range interactions. Recent work has characterized the centered hexagonal honeycomb lattice, showing it to be a highly frustrated system with many metastable states and relaxation occurring over multiple timescales [Molina et al., Proc. Natl. Acad. Sci. U. S. A., 2021, 118, e2020014118]. Here, we study this system under the influence of a rotating gravitational field. High amplitudes are able to completely disrupt droplet-droplet interactions, making it possible to identify a transition between field-dominated and interaction-dominated regimes. The system displays complex hysteresis behavior, the details of which are connected to the emergence of linear mesoscale structures. These mesoscale features display an elasticity that is governed by the balance between gravity and long-range vapor-mediated attractions. We find that disorder plays an important role in determining the dynamics of these features. Finally, we demonstrate annealing the system by progressively reducing the field amplitude, a process that reduces configurational energy compared to a rapid quench. The ability to manipulate vapor-mediated interactions in deliberately designed droplet tilings provides a novel platform for table-top explorations of multi-body interactions.

Numerical simulation of binary droplet collisions using a Front Tracking interface technique

Droplet-droplet interactions of highly viscous liquids or suspensions are relevant in a broad range of industrial applications, such as spray drying, fuel injection or, coating and granulation. The efficiency of these processes is heavily determined by the surface area and volume of the droplets. To operate these processes efficiently, it is critical to accurately describe the physical mechanisms dominating the collision. Nonetheless, a complete description of the forces governing the collision is still missing, particularly when the liquids have a high viscosity. Front tracking techniques represent a promising alternative for studying droplet-droplet interactions as they ensure a sharper representation of the liquid-gas interface. In this work, the Local Front Reconstruction Method (LFRM) is the front tracking technique chosen as it allows merging and break-up. The validation of this method is extended for different Weber numbers, impact parameters, and liquid properties by determining the capabilities of LFRM to reproduce the collision of glycerol solution droplets. The simulation results are validated with dedicated experiments performed at the same Weber and impact parameter conditions. In the majority of the studied collisions, LFRM shows a good correspondence with experiments and literature, which proves the ability of LFRM to capture droplet collisions under the studied conditions.

Ejected microcrystals probe jammed states of droplets in cyclodextrin-based emulsions

The cyclodextrin (CD)-based emulsions exhibit complex instability behaviors such as rapid flocculation and creaming, and how to capture droplet dispersion states of the emulsions remains a great challenge. Here we prepare the CD-based emulsions with different oil-water volume ratios and CD concentrations by using high-pressure homogenization, and characterize the emulsion droplets by using optical microscopy and confocal laser scanning microscopy. We evaluate the effects of homogenization pressure on the stability of the emulsions, identify armored droplets with different surface features, measure interfacial concentrations of adsorbed ICs microcrystals, and observe ejection of the oil/CD inclusion complexes (ICs) microcrystals from the droplet surface. The droplet dispersion states are sensitive to the dynamic buildup and evolving morphologies of the interfacial microcrystals, and there are clear correlations between the properties of the ejected microcrystals and the characteristics of the emulsions. We ascribe the subsequent ejection of ICs microcrystals from the droplet surface to consolidation and deformation of the films formed between neighboring droplets. The ejection of the ICs microcrystals affords a simple method to detect the droplet-droplet interactions and phase transitions in the CD-based emulsions, which might be a generic feature in the broader context of the creaming processes of emulsions.

Visual analysis of interface deformation in multiphase flow

In multiphase flows, the evolution of fluid-fluid interfaces is of interest in many applications. In addition to fluid dynamic forces governing the flow in the entire volume, surface tension determines droplet interfaces. Here, the analysis of interface kinematics can help in the investigation of interface deformation and the identification of potential breakups. To this end, we developed a visualization technique using metric and shape tensors to analyze interface stretching and bending. For interface stretching, we employ the eigenpairs of the metric tensor defined for the deformation rate of the fluid surface. For interface bending, we present a technique that locally captures the interface curvature change in terms of a shape tensor, extracting its principal directions and curvatures. We then visualize interface deformation by combining both representations into a novel glyph design. We apply our method to study multiphase flow simulations with particular emphasis on interface effects. These include the interplay between fluid dynamics and surface tension forces leading to breakup processes following droplet collisions, as well as droplet-droplet interactions of different fluids where Marangoni convection along the surface is explicitly taken into account.Graphical abstract

Investigation of Nanostructure and Interactions in Water-in-Xylene Microemulsions Using Small-Angle X-ray and Neutron Scattering.

The ability to modulate the size, the nanostructure, and the macroscopic properties of water-in-oil microemulsions is useful for a variety of technological scenarios. To date, diverse structures of water-in-alkane microemulsions stabilized by sodium bis(2-ethylhexyl) sulfosuccinate (AOT) have been extensively studied. Even though the decisive parameter which dictates the phase behavior of micremulsions is the nature of the continuous phase, relatively very few reports are available on the structure and interactions in the microemulsions of aromatic oil. Here, we present a fundamental investigation on water-in-xylene microemulsions using small-angle neutron scattering (SANS) at a fixed molar ratio (ω) of water to AOT. We elucidate the microstructural changes in the water-AOT-xylene ternary system at dilute volume fractions (Φ = 0.005, 0.01, 0.03), where the droplet-droplet interactions are absent, to moderately concentrated systems (Φ = 0.05, 0.10, 0.15, and 0.20), where colloidal interactions become important. We also characterize the reverse microemulsions (RMs) for thermally induced microstructural changes at six different temperatures from 20 to 50 °C. Depending on the magnitude of Φ, the scattering data is found to be well described by considering the RMs as a dispersion of droplets (with a Schulz polydispersity) which interact as sticky hard spheres. We show that while the droplet diameter remains almost constant with increase in the volume fraction, the attractive interactions become prominent, much like the trends observed for water-in-alkane microemulsions. With increase in temperature, the RMs showed a marginal decrease in the droplet size but no pronounced dependence on the interactions was observed with the overall structure remaining intact. The fundamental study on a model system presented in this work is key to understanding the phase behavior of multiple component microemulsions as well as their design for applications at higher temperatures, where the structure of most RMs breaks down.

BINARY HARD-SPHERE COLLOID-DROPLET MIXTURES WITH THE PYRITE-TYPE STRUCTURE

We investigate the assembly of a binary mixture of patchy colloids and droplets into crystal structures by use of the space-filling principle and Metropolis Monte Carlo simulations. Here, colloids with six patches in an octahedral symmetry attract droplets, whereas the colloid-colloid and droplet-droplet pairwise interactions are purely hard-core repulsions. Within parameter space regions that allow for stable binary crystals, we find the formation of different structure types, which are colloidal analogs of the NaCl phase and pyrite (FeS2) phase, as a function of the droplet-to-colloid sphere diameter ratio. This finding is consistent with theoretical predictions. Notably, while the NaCl structure type is a commonly known structure of hard-sphere colloids and nanoparticles, the formation of the FeS2 structure type from colloidal dispersion has not been explored. Our approach suggests a potential route to obtain colloidal crystals with more complex structures.

Non-simultaneous droplet impingement cooling of a solid heated surface

High generation of heat in the electronics industry presents a roadblock for further innovations in higher processing power due to complications associated with overheating. Commonly used air-based systems cannot cool high-performance electronics, mainly due to the relatively poor thermo-physical properties of air. Spray cooling is a technique capable of cooling or quenching objects at very high temperatures and heat fluxes. While there has been considerable research on single droplet impact to study the fundamentals of spray cooling, multiple droplet impingement offers more realistic realisations of the dynamics of spray phenomena. In this paper, we examined the fluid dynamics and heat transfer of multiple droplet impingement using high-speed imaging and fast heat flux measurements to capture droplet-droplet and droplet-surface interactions at constant droplet Weber number. We investigated an individual droplet and two non-simultaneous droplets of water at a constant horizontal droplet spacing and different time separations to analyse the heat transfer at different initial surface temperatures. Although not affected significantly by the surface temperature, the maximum diameter of the combined droplets decreased for increasing time separation due to the kinematic discontinuity from the interaction between droplets moving in opposite direction. For small time separation, the spreading droplet contact line of the first droplet collided with the moving contact line of the second droplet. The receding and the quasi-static contact lines of the first droplet was strongly and mildly impacted by the second spreading droplet diameter, respectively. However, all quasi-static droplet diameters increased for non-simultaneous droplet scenario, following by a small reduction in the droplet diameter when the surface temperature increased due to evaporation. Depending on the surface temperature and time separation between droplets, it was found that the peak heat transfer rates for non-simultaneous droplet impingement scenarios can be increased by 68% to 100% when compared to a single droplet case due to higher combined droplet diameter and fluid volume in contact with the heated solid surface. However, the overall droplet cooling efficiency was higher for the single droplet case, showing that the droplet-droplet interaction can decrease the potential cooling performance of droplets. The present study provides knowledge combining droplet-droplet interaction and heat transfer performance for future spray cooling system design and optimisation.

Tunable crystal structures of binary mixtures of various patchy colloids and droplets

In this work, a series of binary mixtures of patchy colloids with desired symmetries, including quadrangle, pentagon, hexagon, is studied by means of Metropolis Monte Carlo simulations. The patches on the colloid surface attract the droplets via the Pickering effect, while both the colloid-colloid and the droplet-droplet interactions are pure hard-core. We find a rich phase diagram by tuning the size ratio, particle packing fraction, angle parameter. The four-patch and six-patch colloids can easily assemble into the different crystal structures, while the five-patch colloids can form a local ordered state that is similar to a quasicrystal with a five-fold symmetry. In the self-assembled structures of six-patch colloids, both droplets and colloids form hexagonal orders, however, they arrange in themselves on different sublattices. Considering the four patches in a quadrilateral geometry, we show that the simulated systems undergoes a structural transition from a rectangle lattice to square lattice and then to rhombohedral lattice upon changing the characteristic angle. In addition, the absence of crystal structures in the trapezoidal patches suggests that the geometrical constraint in order to form the crystal states is that the patchy pattern needs to have the inversion center located at the diameter of the colloidal sphere.

CFD simulation of agglomeration and coalescence in spray dryer

Particle size distribution is of utmost importance in spray dryers. Controlling the degree of agglomeration and coalescence is vital for manufacturing products that conform to the requirements. To predict the particle size accurately, this study presents a CFD model of particle agglomeration and droplet coalescence in a counter-current spray dryer. The stochastic agglomeration model was modified to incorporate more realistic droplet-droplet, droplet-particle and particle-particle interactions. Binary droplet collisions in the atomization zone of a spray dryer can result in either coalescence or separation. The boundaries between collision regimes were experimentally determined, and existing binary collision models were validated for water and milk concentrate to include the effect of viscous forces on collision outcomes. A high-speed camera was used to record the kinematic and physical properties of the droplets to identify various collision regimes. A suitable model was then incorporated in CFD simulations of spray drying. Using existing experimental data from a counter-current spray dryer with strong agglomeration, it is shown that the model can accurately predict product particle properties under different process conditions.

High-viscosity Pickering emulsion stabilized by amphiphilic alginate/SiO2 via multiscale methodology for crude oil-spill remediation

The separation of crude oil from oily water and collection of the emulsion constituents has attracted significant attention. We demonstrate that the relationships between inherent dynamic factors and the performance of a Pickering emulsion stabilized by SiO2 particles with adsorbed hydrophobically modified sodium alginate derivatives (HMSA), a natural pH-sensitive polysaccharide, can be clarified via a multi-scale methodology. Functionalization of the silica surface with HMSA controls particle dispersibility, as verified by turbidity and stability analyses, the zeta potential, and transmission electron microscopy measurements. The interaction mechanism between HMSA and SiO2 nanoparticles was elucidated by both experimental adsorption measurements and computer simulations, which showed qualitative consistency. The aggregation/disaggregation of HMSA/SiO2 particles achieved by tuning the pH of the solution facilitated reversible dispersibility/collectability behavior. Overall, a high-viscosity Pickering emulsion system based on particle-particle and droplet-droplet interactions, which can be filtered for the recovery of spilled crude oil, was demonstrated.

A CFD study of the transport and fate of airborne droplets in a ventilated office: The role of droplet-droplet interactions.

Previous studies reported that specially designed ventilation systems provide good air quality and safe environment by removing airborne droplets that contain viruses expelled by infected people. These water droplets can be stable in the environment and remain suspended in air for prolonged periods. Encounters between droplets may occur and droplet interactions should be considered. However, the previous studies focused on other physical phenomena (air flow, drag force, evaporation) for droplet transport and neglected droplet interactions. In this work, we used computational fluid dynamics (CFD) to simulate the transport and fate of airborne droplets expelled by an asymptomatic person and considered droplet interactions. Droplet drag with turbulence for prediction of transport and fate of droplets indicated that the turbulence increased the transport of 1 µm droplets, whereas it decreased the transport of 50 µm droplets. In contrast to only considering drag and turbulence, consideration of droplet interactions tended to increase both the transport and fate. Although the length scale of the office is much larger than the droplet sizes, the droplet interactions, which occurred at the initial stages of release when droplet separation distances were shorter, had a significant effect in droplet fate by considerably manipulating the final locations on surfaces where droplets adhered. Therefore, it is proposed that when an exact prediction of transport and fate is required, especially for high droplet concentrations, the effects of droplet interactions should not be ignored.Electronic Supplementary MaterialSupplementary material is available in the online version of this article at 10.1007/s11783-021-1465-8 and is accessible for authorized users.

Droplet shape relaxation in a four-channel microfluidic hydrodynamic trap

Here, we trap and control the position of droplets to study their dynamics using hydrodynamic forces alone without an external field. The hydrodynamic trap is adapted from a previously implemented Stokes trap by incorporating a drop-on-demand system to generate droplets at a T-junction geometry on the same microfluidic chip. We then study confined droplet dynamics in response to perturbation by applying a millisecond-pressure pulse to deform trapped droplets. Droplet shape relaxation after cessation of the pressure pulse follows an exponential decay. The characteristic droplet shape relaxation time is obtained from the shape decay curves for aqueous glycerol droplets of varying viscosities in the dispersed phase with light and heavy mineral oils in the continuous phase. Systems were chosen to provide similar equilibrium interfacial tensions (5-10 mN/m) with wide variations of viscosity ratios. It is found that the droplet shape relaxation shows a strong dependence on droplet radius, and a weak dependence on the ratio of dispersed to continuous phase viscosity. The relaxation time is smaller for the highest viscosity ratios, potentially indicating that the dominant viscosity controls the droplet shape relaxation time in addition to the interfacial tension and droplet size. Droplet shape relaxation time can be used inform the response of droplets in an emulsion when subjected to transient flows in various processing conditions. Finally, an application of this platform for directly visualizing individual droplet coalescence in a planar extensional flow is presented. The microfluidic four-channel hydrodynamic trap can thus be applied for studying fundamental physics of droplet deformation and droplet-droplet interactions on the micro-scale to provide an enhanced understanding of emulsion behavior on an individual droplet level.

Crystal structures in binary hard-sphere colloid-droplet mixtures with patchy cross interactions.

A binary mixture of droplets and patchy colloids, where patches are arranged in tetrahedral symmetry, is studied with Metropolis Monte Carlo simulations. The colloidal patches attract droplets, while both the colloid-colloid and the droplet-droplet interactions are hard sphere like. We find stable crystal structures with atomic analogs ZnS,CaF_{2}, and fcc or hcp (face centered cubic or hexagonal close packed) of the droplets coexisting with a dispersed fluid of the colloids. The simulated crystal structures agree well with those predicted by close-packing calculations for an intermediate range of droplet-colloid size ratios. A discrepancy between the simulations and theoretical predictions occurs at low and high size ratios. The results of the simulations for mixtures with anisotropic colloid-droplet interactions reveal a richer phase diagram, with ZnS-gas and ZnS-fluid coexistence, as compared to the isotropic case. For the example of a square planar patch arrangement, we find a particular crystal structure, consisting of two interpenetrating fcc or hcp lattices with right bond angles. Such a structure has no known atomic analog. Our study of generic models of anisotropic colloid-droplet mixtures could provide a promising way towards the fabrication of novel and complex colloidal structures.

Crystallization at droplet interfaces for the fabrication of geometrically programmed synthetic magnetosomes.

Biological systems demonstrate exquisite three dimensional (3D) control over crystal nucleation and growth using soft micro/nanoenvironments, such as vesicles, for reagent transport and confinement. It remains challenging to mimic such biomineralization processes using synthetic systems. A synthetic mineralization strategy applicable to the synthesis of artificial magnetosomes with programmable magnetic domains is described. This strategy relies on the compartmentalization of precursors in surfactant-stabilized liquid microdroplets which, when contacted, spontaneously form lipid bilayers that support reagent transport and interface-confined magnetite nucleation and growth. The resulting magnetic domains are polarized and thus readily manipulated using magnetic fields or assembled using droplet-droplet interactions. This strategy presents a new, liquid phase procedure for the synthesis of vesicles with geometrically controlled inorganic features that would be difficult to produce otherwise. The artificial magnetosomes demonstrated could find use in, for example, drug/cargo delivery, droplet microfluidics, and formulation science.

Modeling wall film formation and vaporization of a gasoline surrogate fuel

To simulate the wall film formation and vaporization processes in gasoline direct-injection spark-ignition engines including considerations of the physical properties and vapor-liquid equilibrium of multi-component fuels, spray-wall interaction sub-models were implemented with the 3D-CFD software HINOCA which has been developed for automotive engine cylinder simulations. The models used were the Senda model for spray-wall impingement including splash, deposition, droplet-droplet interactions, and droplet-film interactions; the O'Rourke model for heat transfer and film vaporization; a simple film flow model considering momentum conservation; and Raoult's law for vapor-liquid equilibrium. First, the model validated the calculated results for a single-component fuel (iso-octane) through comparisons with experimental data in terms of wall film area and heat flux between the wall and film. Second, numerical simulations were conducted with a 5-component gasoline surrogate fuel which was designed taking into account the average octane number, aromatic content, and distillation characteristic. The results showed clear differences in the contributions of the 5 components to the wall film, and the possibility that the aromatic content with higher carbon atoms could be a source of soot formation.

Effect of volume fraction on droplet break-up in an emulsion flowing through a microfluidic constriction

This paper reports the effect of the droplet volume fraction on the breakup of droplets within an emulsion flowing as a two-dimensional monolayer through a tapered microchannel into a constriction. To obtain emulsions with different volume fractions, a concentrated emulsion with droplet volume fraction φ = 0.85 is injected into the channel and diluted on-chip by introducing an additional continuous phase at different flow rates. At a fixed flow rate, the breakup fraction decreases significantly when the droplet volume fraction φ decreases below 0.50. This result is consistent with our previous report showing that droplet breakup in the emulsion arises primarily from droplet-droplet interactions, which are expected to decrease significantly in dilute emulsions. Furthermore, an optimal location for the introduction of the additional continuous phase is identified to be approximately one to two droplet diameters upstream of the constriction. Away from this optimal location, the dilution of the emulsion is ineffective. Finally, we find that while a higher emulsion volume fraction packs more drops per unit volume, the propensity of the drops to undergo breakup limits droplet throughput if droplet integrity and assay accuracy are to be maintained. At a droplet breakup fraction of 0.10, diluting the emulsion 2.1 times from φ = 0.85 to φ = 0.40 increases the droplet throughput by ∼1.5 times.

Droplet collisions of water and milk in a spray with Langevin turbulence dispersion

In this work we investigate droplet-droplet collision interactions in a spray system using an Eulerian-Lagrangian model with subgrid turbulence dispersion. The effect of different droplet viscosities on the type and frequency of droplet collision is investigated, knowledge of which is essential for industrial processes such as spray drying for production of milk powder. The dispersed phase is treated with Lagrangian transport of droplets and the turbulent self-induced gas flow using large eddy simulation (LES). A stochastic Direct Simulation Monte Carlo (DSMC) method is used to detect collisions between droplets. The outcome of a binary collision is described by a collision boundary models for water and milk concentrates. A turbulence dispersion model, based on the Langevin equation, accounts for the stochastic subgrid fluid velocity fluctuations along the droplet trajectory. We compare the spray dynamics with and without droplet interactions and turbulence dispersion. For a spray with typical droplet size of 50 µm, we find that the turbulence dispersion model enhances the total collision frequencies by approximately 25%. The performance of the turbulent dispersion model is tested by investigating the rate of collisions for different milk concentrates. The evolution of size distributions inside the spray is strongly influenced by the complementary effects of collision boundary models and turbulence dispersion.

Droplet Jumping: Effects of Droplet Size, Surface Structure, Pinning, and Liquid Properties.

Coalescence-induced droplet jumping has the potential to enhance the efficiency of a plethora of applications. Although binary droplet jumping is quantitatively understood from energy and hydrodynamic perspectives, multiple aspects that affect jumping behavior, including droplet size mismatch, droplet-surface interaction, and condensate thermophysical properties, remain poorly understood. Here, we develop a visualization technique utilizing microdroplet dispensing to study droplet jumping dynamics on nanostructured superhydrophobic, hierarchical superhydrophobic, and hierarchical biphilic surfaces. We show that on the nanostructured superhydrophobic surface the jumping velocity follows inertial-capillary scaling with a dimensionless velocity of 0.26 and a jumping direction perpendicular to the substrate. A droplet mismatch phase diagram was developed showing that jumping is possible for droplet size mismatch up to 70%. On the hierarchical superhydrophobic surface, jumping behavior was dependent on the ratio between the droplet radius Ri and surface structure length scale L. For small droplets ( Ri ≤ 5 L), the jumping velocity was highly scattered, with a deviation of the jumping direction from the substrate normal as high as 80°. Surface structure length scale effects were shown to vanish for large droplets ( Ri > 5 L). On the hierarchical biphilic surface, similar but more significant scattering of the jumping velocity and direction was observed. Droplet-size-dependent surface adhesion and pinning-mediated droplet rotation were responsible for the reduced jumping velocity and scattered jumping direction. Furthermore, droplet jumping studies of liquids with surface tensions as low as 38 mN/m were performed, further confirming the validity of inertial-capillary scaling for varying condensate fluids. Our work not only demonstrates a powerful platform to study droplet-droplet and droplet-surface interactions but provides insights into the role of fluid-substrate coupling as well as condensate properties during droplet jumping.