Binary Droplet Research Articles

Molecular-Level Investigation of Binary Fluid Droplets Impacting Surfaces

Droplets impacting with surfaces are commonly encountered processes in the field of protective coatings. The behavior of a colliding binary liquid droplet is sensitive to the impact velocity, surface wetting properties, and the droplet composition. Modeling molecular dynamics and classical density functional theory studies of impacting droplets as well as interfacial-surface free energies was reported on. The presence of two components in the liquid drop makes the surface collision a complicated problem. During the collision the kinetic energy of the drop is converted into heat. Thus, the temperature varies during the collision and throughout the droplet. Two extreme situations were captured by performing both adiabatic and isothermal simulations. Molecular dynamics and classical density functional theory were used to explore the effects of the mixing parameter on the phase diagram of the binary AB mixed droplets. The location of liquid–vapor and liquid–liquid phase separation was determined. In addition, the value of the interfacial tensions of all interfaces was computed. These can be used to predict when an A-rich and B-rich droplet will stay attached and when it will detach.

Bouncing dynamics of binary equal-sized high-viscosity molten glass droplets in head-on collisions

Despite extensive research on head-on droplet collisions over the past decades, detailed investigations into the bouncing behavior of high-viscosity droplets, such as molten glass droplets, are still scarce. In this study, a volume-of-fluid method coupled with dual marker functions is employed to simulate the collision dynamics of molten glass droplets. The results show good agreement with experimental observations in both spatial and temporal dimensions. Theoretical analysis reveals a critical Weber number of 22 for bouncing and coalescence of molten glass droplets with a diameter of 100 μm. Below this threshold, we examine the bouncing behavior across various Weber numbers, categorizing the process into four distinct stages: mutual proximity, radial expansion, suction separation, and reverse separation, and providing a detailed analysis of velocity, pressure, and energy at each stage. As the Weber number increases, vortices sequentially emerge at 4, 8, 12, and 16, suggesting a strong correlation between droplet deformation and vortex generation. At lower Weber numbers, the air film pressure between droplets transitions smoothly between radial expansion and suction separation. However, between Weber numbers 9 and 22, a distinct concave pressure phenomenon is observed during suction separation. Pressure chattering occurs at the beginning of radial expansion and the end of suction separation. Furthermore, the results indicate that the cumulative viscous dissipation energy consistently approaches half of the initial kinetic energy, irrespective of the Weber and Ohnesorge numbers.

Direct numerical simulation of coalescence and separation of binary droplet collision with lamella stabilization

Binary droplet collision is a fundamental aspect of various natural phenomena and industrial applications. In this work, direct numerical simulation of coalescence and separation of binary droplet collision is performed over a wide range of Weber numbers and impact factors. The incompressible Navier–Stokes equations are solved by the finite volume approach, coupled with the volume of fluid method. To address the inaccurate prediction of thin lamella in simulation, a lamella stabilization method is introduced to resolve the lamella by adjusting the grid resolution. Compared with experimental data, it is validated that the lamella can be accurately and fully captured with this lamella stabilization method. Moreover, the analysis of shape and energy during the collision is conducted, and the variation of lamella is described in detail, particularly the evolution of the thickness of lamella. The results suggest that for obtaining the full variation of lamella, the maximum refinement size of the grid can reach D/4096. It is also found that without lamella stabilization, excessive dissipation can lead to the failure of predicting coalescence and separation, especially for the cases in the transition between coalescence and separation. Furthermore, even if the same collision outcome can be obtained without lamella stabilization, the number and size of droplets have obvious differences.

Binary imidazolium based aqueous ionic liquid droplet on a rough surface: a molecular dynamics study

Ionic liquids (ILs) have garnered immense attention due to their tunable physicochemical properties. In this study, we delve into the wetting behaviour and interfacial properties of aqueous binary IL mixtures containing [EMIM] [BF4] and [HMIM] [BF4] on both smooth and rough graphite surfaces. Employing classical molecular dynamics simulations, we systematically explored the effects of IL concentration and surface morphology on wetting phenomena. To ensure the equilibrium of the systems, we began by calculating the interaction energies between the components. Subsequently, contact angles were computed, shedding light on the wetting characteristics of the aqueous binary IL mixtures. We meticulously examined the density profiles of the IL systems from the substrate to unravel the dominance of one IL over the other, exploiting the hydrophilic nature of [EMIM] [BF4] and the hydrophobic nature of [HMIM] [BF4]. A comprehensive analysis of hydrogen bond distribution allowed us to discern the intricate nature of these aqueous binary IL droplets. We probed the changes in intermolecular forces within the aqueous IL solution by investigating surface tensions. The tunability of these ILs emerges as a significant aspect of our study, paving the way for their tailored application in engineering and scientific domains. Schematic diagram showing the density distribution of hydrophilic and hydrophobic ILs ([EMIM] [BF4] and [HMIM] [BF4]) in water and also the hydrogen bond (HB) distribution of anion ([BF4]−) water inside the droplet on a pillared surface with a surface fraction ( f ) of 0.4 and pillar height of H = 4 .

Self‐organized Patterns in Non‐reciprocal Active Droplet Systems

Non‐equilibrium patterns are widespread in nature and often arise from the self‐organization of constituents through nonreciprocal chemotactic interactions. In this study, we demonstrate how active oil‐in‐water droplet mixtures with predator‐prey interactions can result in a variety of self‐organized patterns. By manipulating physical parameters, the droplet diameter ratio and number ratio, we identify distinct classes of patterns within a binary droplet system, rationalize the pattern formation, and quantify motilities. Experimental results are recapitulated in numerical simulations using a minimal computational model that solely incorporates chemotactic interactions and steric repulsion among the constituents. The time evolution of the patterns is investigated and chemically explained. We also investigate how patterns vary with differing interaction strength by altering surfactant composition. Leveraging insights from the binary droplet system, the framework is extended to a ternary droplet mixture composed of multiple chasing droplet pairs to create chemically directed hierarchical organization. Our findings demonstrate how rationalizable, self‐organized patterns can be programmed in a chemically minimal system and provide the basis for exploration of emergent organization and higher order complexity in active colloids.

Self-Organized Patterns in Non-Reciprocal Active Droplet Systems.

Non-equilibrium patterns are widespread in nature and often arise from the self-organization of constituents through nonreciprocal chemotactic interactions. In this study, we demonstrate how active oil-in-water droplet mixtures with predator-prey interactions can result in a variety of self-organized patterns. By manipulating physical parameters, the droplet diameter ratio and number ratio, we identify distinct classes of patterns within a binary droplet system, rationalize the pattern formation, and quantify motilities. Experimental results are recapitulated in numerical simulations using a minimal computational model that solely incorporates chemotactic interactions and steric repulsion among the constituents. The time evolution of the patterns is investigated and chemically explained. We also investigate how patterns vary with differing interaction strength by altering surfactant composition. Leveraging insights from the binary droplet system, the framework is extended to a ternary droplet mixture composed of multiple chasing droplet pairs to create chemically directed hierarchical organization. Our findings demonstrate how rationalizable, self-organized patterns can be programmed in a chemically minimal system and provide the basis for exploration of emergent organization and higher order complexity in active colloids.

Collision dynamics of binary equal-size droplets at high pressures: a focus on stretching separation and reflexive separation

ABSTRACT Stretching separation and reflexive separation are two collision regimes that give rise to satellite droplets, significantly impacting the droplet size distribution. However, the influence of high pressure on these regimes remains unclear. This paper investigates the collision dynamics of binary equal-size droplets under varying ambient pressures using the volume of fluid method and adaptive mesh refinement. The results show that vortices, generated during droplet motion changes or ligament ruptures, facilitate mass transport within the droplet–droplet deformation. Additionally, this paper summarizes four phases of droplet deformation in the separation regimes, which are delayed in stretching separation and advanced in reflexive separation with increasing ambient pressure. Elevated ambient pressure restricts droplet movement, resulting in tougher ligament fractures, smaller satellite droplets, and an expanded coalescence regime boundary. Unlike previous works, this paper incorporates gas kinetic and dissipation energies during droplet collisions at high pressures, revealing that at 7 MPa, the gas dissipation energy is comparable to the liquid dissipation energy and cannot be neglected. To account for these effects, a pressure-dependent formula is integrated into the composite collision model under the Lagrangian framework, offering enhanced predictions of droplet size within the stretching separation regime.

Dynamic Partitioning of Surfactants into Nonequilibrium Emulsion Droplets.

Characterizing the propensity of molecules to distribute between fluid phases is key to describing chemical concentrations in heterogeneous mixtures and the corresponding physiochemical properties of a system. Typically, partitioning is studied under equilibrium conditions. However, some mixtures form a single phase at equilibrium but exist in multiple phases when out-of-equilibrium, such as oil-in-water emulsion droplets stabilized by surfactants. Such droplets persist for extended times but ultimately disappear due to droplet dissolution and micellar solubilization. Consequently, equilibrium properties like oil-water partition coefficients may not accurately describe out-of-equilibrium droplets. This study investigates the partitioning of nonionic surfactants between shrinking microscale oil droplets and water under nonequilibrium conditions. Quantitative mass spectrometry is used to analyze the composition of individual microdroplets over time under conditions of varying surfactant composition, concentrations, and oil molecular structures. Within minutes, nonionic surfactants partition into oil droplets, reaching a nonequilibrium steady-state concentration that can be over an order of magnitude higher than that in the aqueous phase. As the droplets solubilize over hours, the surfactants are released back into water, leading to transiently high surfactant concentrations near the droplet-water interface and the formation of a microemulsion phase with a low interfacial tension. Introducing ionic surfactants that form mixed micelles with nonionic surfactants reduces partitioning. Based on this observation, stimuli-responsive ionic surfactants are used to modulate the nonionic surfactant partitioning and trigger reversible phase separation and mixing inside binary oil droplets. This study reveals generalizable nonequilibrium states and conditions experienced by solubilizing oil droplets that influence emulsion properties.

Impingement of binary nanodroplets on rough surfaces: a molecular dynamics study

Roughness or texture endow the solid surface with the ability of some particular property of water repellency that has been employed in a variety of practical applications, including self-cleaning, icing-resistant, and so forth. However, the understanding of the dynamic evolution of impacting binary droplets on rough surfaces is not satisfactory, especially at the nanoscale. In this work, we investigate the impact process of the binary droplet system, a suspending droplet impacts a sessile one deposited on hydrophobic textured surfaces, via molecular dynamics (MD) simulations. Dynamic evolutions from MD simulations under various impact conditions are discussed, including coalescence, spreading, retraction and vibration, and bouncing. The free energy variation during the impacting process is calculated to reveal the mechanisms behind the impact dynamics. The effect of the surface texture on the spreading and retraction is investigated, and the corresponding maximum spreading diameter is also discussed. Finally, we investigate the effect of the surface texture on bouncing behavior, which is found to promote the droplet bouncing at low We range but suppress the bouncing behavior at high We range.

Numerical investigation of non-Newtonian droplet collisions: Comparison of volume of fluid and the local front reconstruction method with experimental data

Droplet-droplet collisions of non-Newtonian fluids are often encountered in industrial applications such as spray drying, fluid catalytic cracking, coating and granulation. However, there has been limited focus on a comprehensive analysis of the dynamics of these non-Newtonian binary droplet collisions. In this work, the non-Newtonian binary droplet collisions of 500 ppm xanthan gum solutions are simulated using the Volume of Fluid method and the Local Front Reconstruction Method to determine the applicability of these methods for the simulations of binary non-Newtonian droplet collisions. After verification, the simulations are compared to experimental data from literature. The outcomes for off-center collisions in the simulations resemble the experimental observations, including the oscillation of the ligament. For head-on collisions, the initial interactions and collision dynamics can be predicted with both methods at low Weber numbers, while LFRM shows improved performance at higher Weber numbers. Further, the use of an effective viscosity for the simplified representation of the droplet collision has been proven unsuccessful due to the absence of a universal effective viscosity for all situations.

Simulation of group of droplets evaporation

Droplet evaporation occurs in many natural phenomena and industrial processes; hence, several studies have been conducted on droplet evaporation. In many applications, a group of droplets evaporate and the interaction between them affects the evaporation process. In this paper, the front-tracking method is used to simulate the droplets groups evaporation. Since the front-tracking method uses a Lagrangian grid for each droplet, this method offers good accuracy in predicting the shape, the displacement and the evaporation rate of droplets. The numerical method has been developed to simulate the evaporation of binary droplets. The fluid surrounding the droplets is modeled as a gas mixture, so the numerical method can be used to simulate multiphase-multicomponent problems. The front-tracking method requires very fine grid resolution to simulate flows at high-density ratios; therefore, the method is rarely used at high-density ratios. In this paper, a two-step method is used to move the front at high-density ratios without requiring a very fine grid resolution. First, a static droplet evaporation is simulated, and the results are compared with the analytical solutions; evaporation of a Decane droplet is then simulated, and the results are compared with the experimental data. Subsequently, the evaporation of a binary droplet is modeled. The evaporation of a group of static droplets is also simulated, and the effect of droplets interaction is investigated. Next, the evaporation of three injected droplets is simulated, and the effect of some parameters on droplets interaction is probed. The evaporation rate and displacement of each droplet are calculated and compared with the single droplet. Finally, the evaporation of the groups of droplets is simulated, and the effect of different arrangements of droplets on the evaporation rate is studied. Understanding the droplets interactions is helpful in predicting droplet spray behavior and developing numerical methods. Thus, the presented results are useful to achieve a better understanding of the droplets interaction phenomenon, its outcomes, and the parameters affecting evaporation rate.

Component Effects in Binary Droplet Impact Behaviors on the Heated Plate: Comparison Study of Ethanol/Propanol and Ethanol/Water Droplets and Observation of Novel Bubble Shrinkage Phenomenon

This work aims to investigate the effect of liquid physical properties on the behavior of binary droplets impact on the heated smooth aluminum alloy plate with a high-speed imaging system. Two groups of mixed solutions with similar boiling point differences are selected as the working liquid, in which the low-boiling-point components are both ethanol and the high-boiling point components are propanol and water, respectively. Compared to the ethanol/propanol binary droplets, the experimental results show that the ethanol/water binary droplets have diverse impact phenomena and significantly broad transition boiling regimes, as well as the reduced droplet residence time and increased Leidenfrost temperature point. With the decreasing ethanol content in ethanol/water binary droplets, these effects become more prominent. For secondary atomization, the ethanol/water binary droplet undergoes parent droplet breakup into fragment droplets with larger diameters (Ds > 0.3 mm). Both binary droplets produce satellite droplets with small diameters (Ds < 0.3 mm) by puffing and ejection. In terms of the ethanol/propanol binary droplet impact, the probability of puffing is higher and the satellite droplet diameters are small. In the ethanol/water binary droplet impact, the probability of ejection is higher and the satellite droplet diameter distribution is wider. When an ethanol/water binary droplet of 25 vol.% ethanol content impacts the heated wall at Ts = 120 °C, a novel large bubble shrinkage phenomenon occurs at the late stage of droplet evaporation. This phenomenon is proposed to be relevant to the increasing surface tension and saturation temperature with decreasing ethanol content, as well as the decreasing ambient temperature above the top surface of the bubble.

Oblique impingement of binary droplets at the nanoscale on superhydrophobic surfaces: A molecular dynamics study.

The impacting phenomenon of nanodroplets has received much attention due to their importance in various industrial applications. The oblique impingement of single droplets is well understood; however, the effect of oblique angle on impacting the dynamics of multiple droplets at the nanoscale is very limited. To address this gap, we perform molecular dynamics (MD) simulations to study the impacting dynamics of binary nanodroplets with various oblique angles (αob) and Weber numbers (We). Using MD simulations, we directly capture the detailed morphological evolution of the impacting binary droplets with various given conditions. Compared to the oblique impingement of a single droplet, the evolution of impacting binary droplets involves two novel dynamic characteristics: the asymmetric dynamics with droplet preferential spreading in the y direction and the rotating of the coalescing droplet. The mechanisms underlying are well studied. The asymmetric dynamics is a result of the velocity gradient of the outer edge of the spreading droplet, and the rotating effect is due to the change in angular momentum induced by surface force. The analysis and study of these phenomena have never been mentioned in previous studies of single droplet. Finally, we investigate the effect of αob and We on normalized moving distance (L/Dsin) and contact time (tc). This work paves the way for offering a comprehensive understanding of the oblique impingement of binary nanodroplets.

Characterizing boiling behaviors in water/ethanol binary droplet impact on a heated plate

This work experimentally investigates the transition boiling behaviors of water/ethanol binary droplets impact on a heated smooth aluminum alloy plate with a high-speed imaging system, forming a more finely defined impact behavior regime map. The dynamic Leidenfrost point temperature exhibits a non-monotonic variation trend with ethanol fraction. Binary droplets exhibit two characteristic boiling behaviors at specific temperatures (Ts) and droplet compositions (Φe), including corona boiling and prompt boiling, distinguished by the elevation of a crown-shaped thick liquid lamella and the prompt generation of numerous secondary droplets from the contact line, respectively. Both boiling behaviors are featured with the violent breakup of parent droplet into about 10 or more fragment droplets (secondary droplets with D ≥ 0.3 mm) and the short residence times on the wall, while exhibiting different splash angle distributions of satellite droplets (secondary droplets with D < 0.3 mm). Characteristic parameter analysis of the two boiling behaviors is conducted to provide qualitative mechanistic explanations. Corona boiling occurs at Φe = 25% & 50% with a lower temperature range (Ts ≤ 200 ℃), the liftoff of the liquid layer is attributed to the combined effect of decelerated wetting speed caused by evaporation and the vapor-induced lift. Prompt boiling occurs at Φe = 25% & 50% with Ts ≥ 220 °C and Φe = 75% with Ts < 200 °C, the intensity of the bubble cloud determines whether the central part of the droplet forms a jet or a liquid bulk filled with microbubbles. This work will provide some new insights into the boiling behaviors and the regulation of secondary atomization of binary solution droplets impact studies.

Droplet collision of hypergolic propellants

AbstractIn the present mini‐review, droplet impacting on a liquid pool, jet impingement, and binary droplet collision of nonreacting liquids are first summarized in terms of basic phenomena and the corresponding nondimensional parameters. Then, two representative hypergolic bipropellant systems, a hypergolic fuel of N,N,N′,N′‐tetramethylethylenediamine (TMEDA) and an oxidizer of white fuming nitric acid (WFNA) and a monoethanolamine‐based fuel (MEA‐NaBH4) and a high‐density hydrogen peroxide (H2O2), are discussed in detail to unveil the rich underlying physics such as liquid‐phase reaction, heat transfer, phase change, and gas‐phase reaction. This review focuses on quantifying and interpreting the parametric dependence of the gas‐phase ignition induced by droplet collision of liquid hypergolic propellants. The advances in droplet collision of hypergolic propellants are important for modeling the real hypergolic impinging‐jet (spray) combustion and for the design optimization of orbit‐maneuver rocket engines.

Numerical Simulation of Rotational Separation in Binary Droplet Collisions by the Improved Two-Phase Lattice Boltzmann Method

Numerical Simulation of Rotational Separation in Binary Droplet Collisions by the Improved Two-Phase Lattice Boltzmann Method

Solutal and Gravitational Effects during Binary Mixture Droplets Evaporation

Solutal and Gravitational Effects during Binary Mixture Droplets Evaporation

Droplet–jet collision following the monodispersedly dripping of coaxial binary droplets above a pool surface

In the present study, the collision between a falling droplet and a rising Worthington jet was experimentally studied. The event is followed by the monodispersedly dripping of coaxial binary droplets into a quiescent pool of glycerol solution. Different concentrations of the solution are considered. Unique droplet–jet collision characteristics are observed when the dripping flow rate is manipulated to release binary droplets. When the first droplet impacts the pool, a significant disturbance is imposed onto the pool, forming a deep crater followed by a Worthington jet. The second droplet is timed to collide with the rising jet to create a unique mushroom-shaped droplet–jet collision. Two jet pinch-off modes (tip pinch-off and no pinch-off) and four distinct collision regimes (partial rebounding, end-pinching, elongated, and clotted central jet collision) are recognized. Liquid viscosity and jetting mode significantly influence the collision dynamics and splattering characteristics. To achieve partial rebounding collision at low Weber number, a high-impact coefficient incorporating characteristic dimensions of the droplets and the Worthington jet is required, whereas a low-impact coefficient is required at high Weber number to attain clotted jet collision. The overall end-pinching phenomenon occurs due to the interaction between liquid flow toward the jet tip and the retraction of the tip, which causes the jet neck diameter to decrease on a capillary timescale. As the impact parameter decreases, the Worthington jet is inhibited, and the mushroom-shaped collision splash spreading is suppressed.

Evaporation dynamics of a binary mixture droplet subjected to forced convection

Evaporation of binary mixture droplets (BMDs) is a ubiquitous natural phenomenon with numerous industrial applications. In this study, a theoretical model of BMD evaporation under forced convection is established by considering the influence of evaporative cooling, thermal and Marangoni effects, convection, and a Stefan flow. The dynamic evaporation of a binary ethanol–water droplet on a heated substrate is simulated, and the internal and external flow structures of the droplets and their interactions are investigated. The influence of temperature-dependent physical properties on the evaporation dynamics is analyzed, and the effect of the forced convection intensity on the exclusion distance and Marangoni instability is explored. Our findings reveal that, during the stable flow stage, a single vortex flow pattern prevails, characterized by a circulating zone with low ethanol concentration within the droplets. However, in the Marangoni instability-driven flow (MIF) stage, a complex multi-vortex flow appears inside the droplets, with a heterogeneous ethanol distribution. Under the action of the Stefan flow, external forced convection cannot directly affect the flow inside the droplets through viscous shear but indirectly impacts the internal flow through heat and mass transfer. The temperature-dependence of physical properties significantly influences the internal flow and delays the onset of the MIF stage. Forced convection affects the heat and mass transfer by changing the thickness of the thermal and concentration boundary layers. Compared with BMD evaporation under natural convection, the heat and mass transfer rate are significantly higher under forced convection, particularly in the MIF stage.

Periodic Alignment of Binary Droplets via a Microphase Separation of a Tripolymer Solution under Tubular Confinement.

We report the spontaneous formation of a characteristic periodic pattern through the phase separation of a tripolymer solution comprising polyethylene-glycol (PEG)/dextran (DEX)/gelatin. When this tripolymer solution is introduced into a glass capillary with a PEG-coated inner surface, we observe the time-dependent growth of microphase separation. Remarkably, a self-organized, periodic alignment of DEX- and gelatin-rich microdroplets ensues, surrounded by a PEG-rich phase. This pattern demonstrates considerable stability, enduring for at least 8 h. The fundamental characteristics of the experimentally observed periodic alignment are successfully replicated via numerical simulations using a Cahn-Hilliard model underpinned by a set of simple, theoretically derived equations. We propose that this type of kinetically stabilized periodic patterning can be produced across a broad range of phase-separation systems by selecting appropriate boundary conditions such as at the surface within a narrow channel.