Secondary Droplets Research Articles

Breakup of an isolated surface-adhering water droplet by an impinging jet flow

The study explored the depinning and breakup of a single surface-mounted droplet exposed to an impinging slot jet flow. Distilled water droplets of 50, 100, 200, 300, 400, 500, and 600 μl were tested on an anodized aluminum substrate in the impinging slot jet facility whose velocity was ramped from zero to 20 m/s at a range of accelerations. The breakup process comprised three distinctive consecutive stages: depinning, necking, and breakup. An aggregate analysis of the data from the present investigation and the results of previous studies is used to deduce that the Weber number at which depinning occurs was roughly constant for all tested conditions, whereas the Weber number at breakup followed a power-law relationship with the Ohnesorge number. The observed power law relation for surface-mounted droplets is similar to the trend reported earlier for critical conditions demarcating breakup regimes for free-falling droplets. During breakup, it was observed that larger originating droplets shed larger percentages of their volumes into secondary droplets, with higher flow accelerations exacerbating this effect. The majority of the formed secondary droplets had a higher critical depinning Weber number compared to the critical breakup Weber number. Consequently, for applications requiring the complete removal of surface-deposited droplets, it is beneficial to utilize shear flows at lower accelerations and maximum Weber numbers below critical breakup conditions.

Droplet-Scale Combustion Analysis of Third-Generation Biodiesel–Diesel Blends

Biodiesel derived from waste cooking oil (WCO) and animal fats is a promising alternative to fossil fuels, offering environmental benefits and renewable energy potential. However, a detailed understanding of its combustion characteristics at the droplet scale is essential for optimizing its practical application. This study investigates the combustion behavior of biodiesel–diesel blends (B5, B10, B15, B20, B25, B50, B75) and neat fuels (B0 and B100) by analyzing combustion rates, pre-ignition time, burning time, droplet morphology, and puffing characteristics. The results demonstrate that biodiesel concentration strongly influences combustion dynamics. Higher blends (B50, B75) exhibit enhanced steady combustion rates due to increased oxygen availability, while lower blends (B5–B25) experience stronger puffing events, leading to greater secondary droplet formation. The global combustion rate follows a non-linear trend, peaking at B10, decreasing at B25, and rising again at B50 and B75. Pre-ignition time increases with biodiesel content, while burning time exhibits an inverse relationship with combustion rate. Four distinct puffing mechanisms were identified, with lower blends producing finer secondary droplets and higher blends forming larger droplets. Puffing characteristics were evaluated based on puffing occurrences, intensity, and effectiveness, revealing that puffing peaks at B25 in occurrence and at B10 in intensity, while higher blends (B50, B75) exhibit notable puffing effectiveness. This study addresses a critical research gap in droplet-scale combustion of WCO and animal fat-derived biodiesel across a wide range of blend ratios (B5–B75). The findings provide key insights for optimizing biodiesel formulations to improve fuel spray atomization, ignition stability, and combustion efficiency in spray-based combustion systems, such as diesel engines, gas turbines, and industrial burners, bridging fundamental research with real-world applications.

Prediction of the Atomization Process in Respimat® Soft MistTM Inhalers Using a Volume of Fluid-to-Discrete Phase Model.

This study investigates the atomization process in Respimat® Soft MistTM Inhalers (SMIs) using a validated Volume of Fluid (VOF)-to-Discrete Phase Model (DPM) to simulate the transition from colliding liquid jets to aerosolized droplets. Key parameters, including colliding jet inlet velocity, surface tension, and liquid viscosity, were systematically varied to analyze their impact on the atomization, i.e., aerosolized droplet size distributions. The VOF-to-DPM simulation results indicate that higher jet inlet velocities enhance ligament fragmentation, producing finer and more uniform droplets while reducing total atomized droplet mass. The relationship between surface tension and atomization performance in colliding jet atomization is not monotonic. Reducing surface tension plays a complex dual role in the atomization process. On the one hand, lower surface tension enhances the likelihood of liquid jet breakup into a liquid sheet, leading to the formation of smaller ligaments under the same airflow conditions and shear forces. This increases the probability of generating more secondary droplets. On the other hand, reduced surface tension also destabilizes the liquid surface shape, decreasing the formation of fine, high-sphericity droplets in regimes where surface tension is a dominant force. Viscosity also influences atomization through complex mechanisms, i.e., lower viscosity reduces resistance to ligament breakup but promotes droplet interactions and coalescence, while higher viscosity suppresses ligament fragmentation, generating larger droplets and reducing atomization efficiency. The validated VOF-to-DPM framework provides critical insights for enhancing the performance and efficiency of inhalation therapies. Future work will incorporate nozzle geometry, jet impingement angles, and surfactant effects to better understand and optimize the atomization process in SMIs, focusing on achieving preferred droplet size distributions and emitted doses for enhanced drug delivery efficiency in human respiratory systems.

Droplet impact on inclined substrates under a non-uniform electric field

Droplet impact on inclined substrates under electric fields is a common behavior in electrostatic demisting applications, and understanding the droplet dynamics of this process is important for improving the performance of demisters. This study investigated the droplet impact dynamics on inclined substrates within a non-uniform electric field. Using high-speed imaging, the effects of voltage (U), substrate inclination (θ), and impact velocity (v) on the droplet behaviors were analyzed. The results revealed that at higher voltages, an upward ejection or pinch-off from the liquid column occurred during the recoiling stage, while the maximum dimensionless spreading diameter D*max increased with the voltage up to U ≤ 12 kV, then sharply decreased due to the droplet ejection for U > 12 kV. It was found that the electric field also intensified the droplet oscillation, with the maximum recoiling height H*max positively correlated with U. The secondary droplet ejection volume fraction η increased with the increase in U, decreased with the increase in both θ and D0, and peaked at v = 0.77 m/s. Furthermore, a critical threshold for the ejection or pinch-off and a predictive model for D*max were developed, incorporating electric Bond number (BoE), Weber number (We), and θ. Based on a profound comprehension of the electrohydrodynamic mechanisms governing the droplet impact on inclined substrates, these findings provide appropriate operating conditions to avoid the droplet pinch-off and ejection, improving the efficiency of electrostatic demisters.

Splashing correlation for single droplets impacting liquid films under non-isothermal conditions

The droplet impact phenomenon onto liquid films is predominant in a variety of modern industrial applications, including internal combustion engines and cooling of electronic devices. These are characterised by heat and mass transfer processes, such as evaporation, condensation and boiling. However, studies regarding droplets and liquid films under non-isothermal conditions are scarce in the literature and do not explore temperature-dependent phenomena. Due to this, the main objective of this work is to evaluate the influence of temperature on the splashing occurrence of single droplets impinging onto liquid films under the presence of a heat flux. The crown evolution is evaluated qualitatively to provide insight regarding breakup mechanisms. Water, n-heptane and n-decane are the fluids considered for the current study, as these provide a wide range of thermophysical properties and saturation temperatures. The splashing dynamics are evaluated by varying the droplet impact velocity and dimensionless temperature of the liquid film. Qualitative results show that an increase in the liquid film temperature leads to the transition from spreading to splashing, which is less evident for fuels in comparison with water. For water and n-heptane, the formation of cusps on the crown rim is promoted, which is associated with ligament breakup. For n-decane, the crown rims are relatively homogeneous in terms of shape and size, whereas the atomisation process varies a function of the liquid film temperature. Visually, the secondary droplets exhibit a greater size in comparison with lower temperatures. Transitional regimes display some irregularities, such as splashing suppression/reduction, which require further attention. In terms of splashing correlation, the authors propose to develop a non-splash/splash boundary for both iso- and non-isothermal conditions. Results show that the splashing threshold is dependent on the thermophysical properties and the dimensionless temperature of the liquid film.

Non-Newtonian fluid droplet impact dynamics on thin liquid films

Droplet impact on liquid films is a ubiquitous phenomenon in nature and many industrial applications. The present study highlights the impact dynamics of viscoelastic droplets on thin films of water and the same viscoelastic fluid as the droplet. In this experimental study, we have highlighted the variations in the impact dynamics that arise due to the non-Newtonian effects. The ejection of secondary droplets from the crown rim normally observed in the case of Newtonian droplet impacts on water films is suppressed, in the case of non-Newtonian droplet impacts on water films. Due to the fluid elasticity, the Rayleigh–Plateau instability-induced ejection of secondary droplets from the crown rim is inhibited. Long-lasting slender liquid filaments resembling beads-on-a-string structures are observed in the case of viscoelastic droplet impact on water films. However, when the drop and film are of the same viscoelastic fluid, such filaments are not observed during the crown formation stage. Subsequently, we have characterized the geometrical features of the crown and the regime maps of various outcomes of the droplet impact dynamics. It is observed that the elasticity of the liquid suppresses the crown growth and secondary droplet formation. The dependence of the impact dynamics on Weber number (We), polymer concentration in terms of elasticity number (El), Bond number (Bo), and film thickness (h*) are also highlighted in the form of regime maps. It is observed that secondary droplet ejection does not take place on an increase in Bond number and film thickness for both water and viscoelastic films.

Spray interaction in adjacent GCSC injector elements: role of droplet collision and secondary droplet breakup

Spray interaction in adjacent GCSC injector elements: role of droplet collision and secondary droplet breakup

Splash on a liquid pool: coupled cavity–sheet unsteady dynamics

Splashes from impacts of drops on liquid pools are ubiquitous and generate secondary droplets important for a range of applications in healthcare, agriculture and industry. The physics of splash continues to comprise central unresolved questions. Combining experiments and theory, here we study the sequence of topological changes from drop impact on a deep, inviscid liquid pool, with a focus on the regime of crown splash with developing air cavity below the interface and crown sheet above it. We develop coupled evolution equations for the cavity–crown system, leveraging asymptotic theory for the cavity and conservation laws for the crown. Using the key coupling of sheet and cavity, we derive similarity solutions for the sheet velocity and thickness profiles, and asymptotic prediction of the crown height evolution. Unlike the cavity whose expansion is opposed by gravitational effects, the axial crown rise is mostly opposed by surface tension effects. Moreover, both the maximum crown height and the time of its occurrence scale as ${\textit {We}}^{5/7}$ . We find our analytical results to be in good agreement with our experimental measurements. The cavity–crown coupling achieved enables us to obtain explicit estimates of the crown splash spatio-temporal unsteady dynamics, paving the way to deciphering ultimate splash fragmentation.

Fragmentation from inertial detachment of a sessile droplet: implications for pathogen transport

Fragmentation of a fluid body into droplets underlies many contamination and disease transmission processes where pathogens are transported in a liquid phase. An important class of such processes involves formation of a fluid ligament and its destabilization into droplets. Inertial detachment (Gilet & Bourouiba, J. R. Soc. Interface, vol. 12, 2015, 20141092) is one of these modes: upon impact on a sufficiently compliant substrate, the substrate's motion can transfer its impulse to a contaminated sessile drop residing on it. The fragmentation of the sessile drop is efficient at producing contaminated ejected droplets with little dilution. Inertial detachment, particularly from substrates of intermediate wetting, is also interesting as a fundamental fragmentation process on its own merit, involving the asymmetric stretching of the sessile drop under impulsive axial forcing with one-sided pinning due to the substrate's intermediate wetting. Our experiments show that the radius, $R_{tip}$ , of the tip drop ejected become insensitive to the Bond number value for $Bo>1$ . Here, $Bo$ quantifies the inertial effects via the relative axial impulsive acceleration compared with capillarity. The time, $t_{tip}$ , of tip-drop breakup is also insensitive to $Bo$ . Combining experiments, theory and validated numerics, we decipher the selection of $R_{tip}$ and its sensitivity to the surface-wetting and substrate foot dynamics. Using asymptotic theory in the large $Bo$ limit for which the thin-film/slender-jet approximations hold, we derive a reduced physical model that predicts $R_{tip}$ consistent with our experiments. Finally, we discuss how pathogen physical properties (e.g. wetting and buoyancy) within the sessile drop determine their distribution in the tip and secondary fragmentation droplets.

Nonspherical Particle Stabilized Emulsions Formed through Destabilization and Arrested Coalescence.

To form nonspherical emulsion droplets, the interfacial tension driving droplet sphericity must be overcome. This can be achieved through interfacial particle jamming; however, careful control of particle coverage is required. In this work, we present a scalable novel batch process to form nonspherical particle-stabilized emulsions. This is achieved by concurrently forming interfacially active particles and drastically accelerating emulsion destabilization through addition of electrolyte. To achieve this, surfactant-stabilized oil-in-water emulsions in the presence of dopamine were first produced. These emulsions were then treated with tris(hydroxymethyl)aminomethane hydrochloride buffer to both simultaneously initiate polymerization of dopamine in the emulsion continuous phase and reduce the Debye length of the system, thus accelerating droplet coalescence while forming surface-active particles. The concentration of buffer and imposed shear was then systematically varied, and the behavior at the interface was studied using pendent drop tensiometry and interfacial shear rheology. It was found that polydopamine nanoparticles formed in the emulsion continuous phase adsorbed to the reducing interface during coalescence, resulting in anisotropic droplets formed via arrested coalescence. Greater shear rates resulted in accelerated coalescence and formation of secondary droplets, whereas lower shear rates resulted in thicker interfacial films. The efficacy of this method was further demonstrated with a second system consisting of sodium dodecyl sulfate as the surfactant and polypyrrole particles, which also resulted in nonspherical droplets for optimized conditions.

Secondary size distributions for single drop impacts at high wall superheat

The impingement of liquid sprays on hot walls is used extensively in both spray-cooling systems and in combustor fuel injection applications. At low and moderate wall temperatures, the secondary size distributions have been reported in the literature. For high wall superheat conditions, particularly for real multicomponent fuels, this secondary size distribution has received less attention. Understanding the resultant size distribution for a spray-wall impact is key to capturing vaporization and local mixture for fuel-spray impingement. In this study, single drop impacts for a range of single-component (n-decane) and multicomponent jet fuel (F-24) are characterized through dual-view imaging. Secondary droplets are captured for impact Weber numbers of 100–600 and wall temperatures spanning the nucleate and film boiling (Leidenfrost) regimes. Imaging through a transparent sapphire substrate is used to capture the impact phenomena and impact-induced breakup of impacting drops. We report empirical correlations for the secondary droplet size for single-component (n-decane) and multicomponent (F-24) liquid fuels with varying wall temperature to provide validation datasets for spray-wall simulations.

Enhanced spray-wall interaction model for port fuel injection under medium load conditions

This study presents an Eulerian-Lagrangian framework for the numerical analysis of spray dynamics, with a focus on droplet movement, spray-wall interactions, and the effects of varying injection parameters associated with port fuel injection (PFI) system. A grid-independent criterion is introduced to optimize mesh analysis for accurate predictions of fuel penetration length. The size distribution of secondary droplets is described using a probability density function, and statistical optimization is subsequently implemented to estimate their mean size. This probabilistic approach enhances the Lagrangian wall film (LWF) model, leading to accurate predictions of the Sauter mean diameter (SMD) at a given radial width (Rw), with results closely matching experimental data. For 8.0mm≤Rw≤24.0mm, the maximum SMD of 21.67 μm corresponds to Rw=14.0,mm, while the smallest SMD of 12.68 μm is computed for a radial position of Rw=24.0mm. The numerical investigation quantifies the role of spray-wall interactions in determining the trajectory of fuel distribution, particularly in the formation of wall films and the relative spatio-temporal diesel concentration (F/A) %. The study explores aspects such as droplet size variations, heat transfer during evaporation, and film behavior under different injection pressures, providing insights into the multiphysical characteristics of spray-wall systems. Near the impingement site (2.0mm≤Rw≤4.0mm), the plume height (Hw) slightly decreases with an increase in injection pressure. While the CFD methodology in this current work has been primarily developed for automotive engineering sector (PFI engines), it also has potential applications in areas such as additive manufacturing, hydropower engineering, climate science, and environmental engineering.

Mechanisms of Secondary Spreading and Micro Droplet Formation on Steel

Abstract A new theory for secondary spreading based on the wetting theory of thin films is presented. It explains how micro droplets within the spreading zone and the primary droplet retain their shape, although connected by a thin electrolyte film and how humidity and salt concentration affect the growth rate of micro droplets. The trigger for secondary spreading, polarization or alkalization, is identified by using droplets of sodium hydroxide solution. Secondary spreading thus occurs on steel from pH 13.5 without corrosion or external polarization. The limiting pH value found explains why secondary spreading on steel only occurs when certain salts are used. 
The effect of the substrate is investigated by changing the microstructure of the steel. By comparing the sizes of micro droplets and micro structural phases and by scanning electron microscopy/energy-dispersive X-ray analysis measurements of the spreading zone, the existence of an electrolyte film connecting the micro droplets is supported. Ecorr potential profiles of secondary spreading droplets of sodium chloride solution on steel acquired by means of SKP are used to assess the contribution of secondary spreading to the total corrosion current, which is estimated to be low compared to that of the cathodic zone at the edge of the droplet

Droplet impact outcomes of emulsions on smooth and microstructured surfaces

This study explores the impact dynamics of emulsion droplets, with a dispersed phase of either silicone oil, toluene, or heptane, and water as the continuous phase, on both smooth and microstructured surfaces fabricated via photolithography. By preparing emulsions without surfactants, we isolated the effects of surface morphology and liquid properties on droplet behavior. We characterized the rheology of the emulsions and their droplet size distributions. The impact dynamics were recorded using a high-speed camera in a shadowgraph configuration, with analysis performed through image processing techniques. Our results indicate that at higher impact velocities, water exhibits the largest spreading diameter (dmax) on smooth surfaces, while emulsions with higher dispersed phase concentrations show reduced spreading due to increased energy dissipation. On microstructured surfaces, denser structures enhance resistance to spreading and trigger complex phenomena such as Worthington jets and secondary droplets, which are not observed on smooth surfaces. Additionally, we observed a transition in bouncing behavior for the silicone oil 50 cSt 20 v/v% emulsion on Glaco-coated surfaces, attributed to the infiltration of silicone oil into the Glaco microstructure, creating a suction force that prevents bouncing. These findings offer valuable insights for optimizing industrial processes like inkjet printing and pesticide application, where precise control of droplet behavior is crucial.

APPLICATION OF NEURAL NETWORKS TO ANALYZE THE BEHAVIOR OF LIQUID PHASE PARTICLES IN THE ELEMENTS OF FLOW PATHS OF TURBOMACHINES

The article discusses the issue of using neural networks to analyze the nature of the movement of droplets in the interblade channels of turbomachines. An experimentally verified computational model was used to analyze the parameters affecting the process under study. A set of 23 independent parameters was identified. They included both regime parameters and geometric ones. The presented set of parameters uniquely determines the behavior of a liquid particle moving through the channels of turbomachine cascades. The applicability of neural networks to analyze the behavior of droplets in the interblade channels of turbomachines is considered. For this purpose, a neural network was created that predicts the proportion of secondary droplets formed during the interaction of primary moisture with the surface of a turbine blade.

Liquid film breakup pattern and optimization of vane-type separator

Liquid film breakup pattern and optimization of vane-type separator

Predicting Leidenfrost Temperature and Effects of Impact Conditions on Droplet Size Distribution in Film-Boiling Regime

Abstract The interaction of a droplet with a solid wall is relevant in various engineering applications. The properties of the resulting secondary droplets are determined by the wall temperature, ambient pressure, impact momentum, and impact angle. This paper presents a comprehensive characterization of drop–wall interactions and the subsequent atomization as a function of the combined effects of such parameters. A drop–wall interaction model is derived for F-24 liquid fuel droplets using smoothed particle hydrodynamics (SPH). F-24 is a derivative of Jet-A aviation fuel with military additives, and it is the focus of this study due to its common use in military applications. The model can predict different impact outcome regimes (deposition, rebound, contact-splash, and film-splash) for different ambient pressures, wall temperatures, and impact parameters. The model also addresses the effect of ambient pressure on the Leidenfrost behavior. Size distributions of secondary droplets are compared for vertical and nonvertical impacts of F-24 droplets on superheated surfaces in the film-boiling regime. The nondimensional Sauter mean diameter (SMD) of the secondary droplets varies based on the position in the impact plane for all the nonvertical impacts but remains almost unchanged for vertical impacts. The zone of leading direction for nonvertical impact consists of larger secondary droplets, and the size decreases toward the zone of trailing direction. An empirical relation is proposed to represent this trend. This research sheds light on successive droplet impacts by studying the effects of impact frequency on SMD evolution. The results are compared to single droplet impact cases for different fuels and Weber numbers. The size of secondary droplets for successive impacts is observed to be nearly indistinguishable from that of single droplet vertical impacts.

The numerical analysis of complete and partial electrocoalescence in the droplet-layer system employing the sharp interface technique for multiphase-medium simulation

The numerical analysis of complete and partial electrocoalescence in the droplet-layer system employing the sharp interface technique for multiphase-medium simulation

Leidenfrost effect in the flash vaporization of hydrogen peroxide and water mixtures

The Leidenfrost effect, a phenomenon where a droplet levitates on a heated surface due to rapid vaporization, has been extensively studied with various liquids. However, the behavior of binary mixtures, specifically those involving hydrogen peroxide (H2O2) and water, remains relatively unexplored. This study investigates such mixtures, focusing on the ejection dynamics of secondary droplets under different temperatures and solution concentrations. High-speed imaging is used to capture the evolution of droplets upon impacting a hot surface. The results reveal a significant increase in droplet fragmentation and ejection with increasing temperature and hydrogen peroxide concentration. Droplet ejection volume increased by a factor of 2.5 when the temperature was 60 °C over the Leidenfrost point, while it increased by a factor of 1.7 when comparing a solution of 10% wt. H2O2 up to a concentration of 50%. A comprehensive analysis of the observed phenomena is proposed. The impact of hydrogen peroxide's thermal decomposition on systems such as H2O2 vapor decontamination enclosures is revealed. The main difficulty in obtaining highly concentrated H2O2 gas is attributed to the Leidenfrost effect ejecting secondary droplets.

Phase changes in burning precursor-laden single droplets leading to puffing and micro-explosion

When producing metal-oxide nanoparticles via flame spray pyrolysis, precursor-laden droplets are ignited and undergo thermally induced disintegration, called ‘puffing’ and ‘micro-explosion’. In a manner that is not fully understood, these processes are associated with the formation of dispersed phases inside the droplets. This work aims at visualizing the interior of precursor-laden burning single droplets via diffuse back illumination and microscopic high-speed imaging. Solutions containing iron(III) nitrate nonahydrate (INN) and tin(II) 2-ethylhexanoate (Sn-EH) were dispersed into single droplets of sub-100 μm diameter that were ignited by passing through a heated coil. At low precursor concentration, 50% of the INN-laden droplets indicate a gas bubble of about 5 μm diameter in the center of the droplet. The bubble persists for several hundred microseconds at a similar size. In almost all of these cases, the bubble expands at some point and the droplet ends up in a micro-explosion. In some of these instances, the droplet’s surface shows spatial brightness modulations, i.e., surface undulations, indicating the formation of a viscous shell. With increasing INN concentration, the fraction of droplets showing surface undulations, gas bubbles, and micro-explosions drastically decreases. This may be associated with a more rigid viscous shell and reduced mobility of bubbles. Bright incandescent streaks originating from the disrupting INN-laden droplets, may indicate sub-micrometer droplets or particles from within the droplets or formed in the gas phase. In contrast, Sn-EH-laden droplets show very fast disruptions, typically less than 10 μs from first visible deformation to ejection of secondary droplets. Bubbles and surface undulations were not observed.Graphical abstract