Droplet Deformation Research Articles

Numerical investigation of water droplet collision dynamics on moving surfaces

This work presents a comprehensive numerical study on the dynamics of droplet collision on a moving solid surface with different wettabilities. Results of numerical simulations for the cases of both stationary and moving substrates are compared with the corresponding experimental results. The spreading of droplets, lamella formation, and recoil in dependence on droplet size, impact velocity, and motion of the surface are discussed in the present work. The results demonstrate that with large drops and high surface velocities, droplet deformation is strongly asymmetric due to the competition between normal and tangential forces. Also, detachment of the lamella becomes stronger by increasing the speed of the surface; hence, there is only a little recoiling contact with increased energy dissipation. In contrast, the smaller droplets had a quite stable spreading with no lamella breakup at all, which is evidence again for the decisive action of droplet size and kinetic energy in dynamics after impact. Among the other manifestations, the present study points out the formation of a central splash in the larger droplets. These facts increase awareness in droplet dynamics concerning moving surfaces with applications in optimizing the efficiency of industrial processes like inkjet printing, spray cooling, and surface coating technologies.

Scaling law for the critical voltage of a droplet on a surface in the presence of an external field

Using external fields to regulate the droplet shape and behavior has attracted considerable attention due to its wide range of practical applications. However, determining the complex flow phenomenon inside a droplet and its deformable boundary shape at equilibrium is a challenging physical and mathematical exercise. In the present work, we employ theoretical and experimental approaches to study the shape deformation of a sessile droplet on a substrate in the presence of an external electric field. Based on the theoretical model we propose, and by combining the finite element method with the gradient descent algorithm, we successfully determine the droplet shape by minimizing the total free energy of the system, viz., a combination of electrostatic energy, surface tension energy, and gravitational potential energy. We also perform scaling analyses and derive an empirical expression for the critical voltage, featuring a universal scaling exponent of 1/2 for the contact angle as a function of normalized volume. The master curve depicted by the empirical expression provides an excellent fit to both the experimental and numerical results.

Modeling Drop Atomization Using Computational Fluid Dynamics

Atomization, a process in which droplets break into smaller structures, is common in both natural and industrial contexts. The mechanisms of droplet deformation and breakup are often described through hydrodynamic instabilities, informed by experimental studies, theoretical developments, and simulations via Computational Fluid Dynamics (CFD). In this work, Direct Numerical Simulations (DNS) were employed to analyze droplet atomization under various conditions. Two models were considered for studying droplet deformation and breakup: one axisymmetric and the other threedimensional. The results showed that the deformation and fragmentation of the droplet are highly de- pendent on the Weber number. Additionally, an increase in the Weber number accelerates the onset of the fragmentation process. The three-dimensional (3D) simulations revealed perforations with a spatial distribution characterized by initial axial symmetry, which dissipates as fragmentation progresses. DNS proves valuable in such studies due to its ability to detect the droplets produced during atomization, enabling the measurement of their positions and velocities at each moment, which can be aggregated into statistical data.

Thermodynamics of an oblique droplet impinging on stationary water film

The flow and heat transfer of the oblique impact of a droplet on a stationary liquid film with various dimensionless thicknesses (01.0–0.5) are investigated experimentally and numerically. A superhydrophobic guideway is used to create the oblique impact of a droplet, which causes subsequent asymmetric crown structure and splashing. The thermal level set method is employed to capture the deformation and heat transfer of warm droplets' oblique impact on a cold liquid film. A parameter study of the effect of Weber number, oblique angle, and liquid film thickness on geometrical characteristics and wall heat flux is carried out. The results show that in the downstream direction, during the crown rising period, the radius is independent of the normal Weber number but increases for a larger tangential Weber number and a thinner liquid film. The maximum downstream crown height increases with an increase in the Weber number and exhibits a non-monotonic trend with the liquid film thickness. The heat transfer rate between the liquid film and surface decreases with larger oblique angles and thicker liquid films while having a poor dependence on the Weber number. In addition, the critical oblique angles for prompting splashing at different liquid film thicknesses are presented. Finally, modified thermodynamics models and splashing thresholds for the liquid film are developed to further enhance the understanding of aircraft icing.

Compound Surfactant System with Superior Oil Displacement Performance: Balanced Synergistic Effects from Oil-Water and Oil-Solid Interfaces.

The oil film formed by the adhesion of crude oil to the resin-asphalt adsorption layer is difficult to peel off due to the strong oil-solid interaction, which severely limits further improvements in oil recovery. Although conventional compound oil displacement systems can effectively reduce oil-water interfacial tension, facilitate oil droplet deformation, and alleviate the Jamin effect, they are insufficient in controlling the wettability of oleophilic rock surfaces. In this paper, sodium nonylphenol polyoxyethylene ether sulfate (NPES) and sodium lauric acid ethanolamine sulfonate (HLDEA) were compounded to construct an efficient oil displacement system that simultaneously achieves wettability control of lipophilic surfaces and ultralow oil-water interfacial tension. The HLDEA + NPES system reduces the interfacial tension to 3.8 × 10-3 mN·m-1 and enhances surface wettability control, with an underwater oil contact angle of 157.2°. The compound system can remain stable at high temperatures (up to 110 °C) and high salinity (1 × 105 mg·L-1 NaCl and 7 × 103 mg·L-1 Ca2+). The oil recovery rate increases by 28.7% compared with water flooding and surpasses by 7.8% compared with a commercial ultralow interfacial tension system (10-4 mN·m-1). The synergistic effect of HLDEA and NPES in the oil/water interface increases the interfacial modulus and phase angle, thereby improving the stability of the interfacial film. The synergistic adsorption of HLDEA and NPES in the oil/water interface creates a denser adsorption layer, achieving enhanced wettability control. The HLDEA + NPES system balances the interactions from the oil-water and oil-solid interfaces, achieving a synergistic effect of oil film peeling and oil droplet migration, thereby significantly improving the recovery rate.

Large-Eddy Simulation of Droplet Deformation and Fragmentation Under Shock Wave Impact

This study employs the large-eddy simulation (LES) approach, together with the hybrid volume of fluid—discrete phase model, to examine the deformation and breakup of a water droplet impacted by a traveling shock wave. The research investigates the influence of Weber number on transient deformation and breakup characteristics. Particular focus is given to the detailed analysis of sub-droplet-size distributions, which are frequently overlooked in existing studies, providing a novel insight into droplet fragmentation dynamics. The predicted deformation and breakup patterns of droplets in the shear breakup regime align well with experimental data, validating the computational approach. Notably, LES is able to reproduce the underlying physical mechanisms, highlighting the significant role of recirculation zones and the progression of Kelvin–Helmholtz instabilities in droplet breakup. Additionally, it is shown that higher Mach numbers significantly amplify both cross-stream and streamwise deformations, leading to earlier breakup at higher airflow pressures. Increasing the Weber number from 205 to 7000 results in 25% reduction in the average size of the sub-droplets, indicating the strong influence of aerodynamic forces on droplet fragmentation. This comprehensive analysis, while aligning with experimental observations, also provides new insights into the complex dynamics of droplet breakup under post-shock conditions, highlighting the robustness and applicability of the proposed hybrid Eulerian–Lagrangian formulation for such advanced applications in fluid engineering.

Reconsideration on the maximum deformation of droplets impacting on solid surfaces

AbstractDroplet impact on solid surfaces is widely involved in diverse applications such as spray cooling, self‐cleaning, and hydrovoltaic technology. Maximum solid‒liquid contact area yielded by droplet spreading is one key parameter determining energy conversion between droplets and surfaces. However, for the maximum deformation of impact droplets, the contact length and droplet width are usually mixed indiscriminately, resulting in unignored prediction errors in the maximum contact area. Herein, we investigate and highlight the difference between the maximum contact length and maximum droplet width. The maximum droplet width is never smaller than the maximum contact length, and the difference appears once the contact angle exceeds 90° (which becomes more significant on superhydrophobic surfaces), regardless of impact velocities, liquid viscosities, and system scales (from macroscale to nanoscale). A theoretical model analyzing the structure of the spreading rim is proposed to demonstrate and quantitatively predict the above difference, agreeing well with experimental results. Based on molecular dynamics simulations, the theoretical analysis is further extended to the scenario of nanodroplets impacting on solid surfaces. Reconsideration on the maximum deformation of impact droplets underscores the often‐overlooked yet significant difference between maximum values of contact length and droplet width, which is crucial for applications involving droplet‒interface interactions.

Droplet contact numbers and contact probabilities in liquid‐liquid dense‐packed zones

AbstractDense‐packed zones (DPZs) are crucial in designing equipment for liquid‐liquid phase separation processes, as the DPZ height affects apparatus size. This article presents an open‐access simulation approach to determine droplet contact numbers and probabilities, which are vital for modeling the deformation and coalescence of polydisperse droplets in a DPZ. The simulation is applied to three technical cases to assess how droplet size distribution (DSD) shapes impact contact numbers and probabilities. Sensitivity analysis reveals that broader DSDs and larger droplet classes lead to higher contact numbers. In contrast, contact probability is primarily determined by droplet class diameter and its number probability within the DSD, showing an almost linear relationship. These results highlight the significance of DSD shape and droplet class diameter in predicting droplet contact numbers and probabilities in DPZs, providing valuable insights for future modeling of liquid‐liquid phase separation.

Electrohydrodynamic effects on the viscoelastic droplet deformation in shear flows

Droplet deformation under shear flows is widely observed in many practical applications, including droplet-based microfluidics and emulsion processing, whereby the droplet usually exhibits viscoelastic characteristics. It has been shown that the performance of these applications is significantly influenced by the size and shape of the resulting droplets. Therefore, the underlying performance is directly tied to the precision and efficiency of viscoelastic droplet control. Previous studies demonstrate that the electric field is a straightforward and efficient way of manipulating fluid flows. However, the effects of an electric field on the viscoelastic droplet deformation remain unexplored. To this aim, this work investigates the electrohydrodynamic (EHD) control of viscoelastic droplets under shear flows using a hybrid numerical framework coupling the lattice Boltzmann method and finite difference method. Extensive simulations are conducted under various electrical properties, such as conductivity ratio R, permittivity ratio S, and electric field strength CaE. Focus is placed on the quantitative analysis of the viscoelastic droplet morphological metrics including deformation D and inclination angle θ. Phase diagrams of D, θ, and combined D and θ in the plane of R–S are developed, where four regions can be identified based on different droplet behaviors under an electric field. The mechanism of this phenomenon is presented by analyzing the distribution of the electric field, electric charge, and electrical force at different regions. It is further observed that the electric field strength CaE amplifies these effects, either suppressing or promoting the droplet deformation and rotation. While viscoelastic effects are considered, they are found to play a subdominant role compared to EHD forces in controlling or modifying droplet morphology. This study provides insights into the electrohydrodynamic (EHD) effects on the dynamics of viscoelastic droplets in shear flow, contributing to the development of active control strategies for viscoelastic droplets in microfluidic applications, including drug delivery and food processing.

Influence of liquid nitrogen droplet fragmentation and deformation on tracing in cryogenic wind tunnels

Influence of liquid nitrogen droplet fragmentation and deformation on tracing in cryogenic wind tunnels

Investigation on the transient solution for electrohydrodynamic deformation of droplets in a combined DC electric field and shear flow field

Investigation on the transient solution for electrohydrodynamic deformation of droplets in a combined DC electric field and shear flow field

ConvNet-based prediction of droplet collision dynamics in microchannels

The dynamics of droplet collisions in microchannels are inherently complex, governed by multiple interdependent physical and geometric factors. Understanding and predicting the outcomes of these collisions (whether coalescence, reverse-back, or pass-over) pose significant challenges, particularly due to the deformability of droplets and the influence of key parameters such as the density and viscosity of immiscible fluids, the initial offset between droplets, and the confined geometry of microchannels. Traditional methods for analyzing these collisions, including computational and experimental techniques, are time-consuming and resource-intensive, limiting their scalability for real-time applications. In this work, we explore a novel data-driven approach to predict droplet collision outcomes using convolutional neural network (CNN). CNN-based approaches present a significant advantage over traditional methods, offering faster, scalable solutions for analyzing large datasets with varying physical parameters. Using a lattice Boltzmann method for binary immiscible fluids, we numerically generated droplet collision data under confined shear flow. These data, represented as droplet shapes, serve as input to the CNN model, which automatically learns hierarchical features from the images, allowing for accurate and efficient collision outcome predictions based on deformation and orientation. The model achieves a prediction accuracy of 0.972, even on test datasets with density and viscosity ratios not included in the training. Our findings suggest that the CNN-based models offer improved accuracy in predicting collision outcomes while drastically reducing computational and time constraints. This work highlights the potential of machine learning to advance droplet dynamics studies, providing a valuable tool for researchers in fluid dynamics and soft matter.

Spreading and rebound of viscoelastic droplets on surfaces with hybrid wettability

Understanding viscoelastic droplet impact dynamics on solid surfaces is crucial for various industrial applications, including fuel injection, spray coating, inkjet printing, and microfluidics. This study investigates the behavior of a viscoelastic droplet impacting a solid substrate with different wettability properties characterized by different wall contact angles (WCA): hydrophilic (10°), hydrophobic (160°), and a hybrid surface that combines both properties (10°–160°). This study integrates the Oldroyd-B viscoelastic model with a dynamic contact angle framework to examine the effects of WCA and fluid relaxation time on droplet spreading and rebound behaviors. The findings reveal that surface wettability significantly influences droplet behavior during the spreading and rebound stages, affecting wetted area and droplet shape. On hydrophilic surfaces, droplets exhibit typical rebound behavior with partial attachment, while hydrophobic surfaces induce spreading with smaller contact areas and increased rebound. Notably, hybrid surfaces induce complex, asymmetric droplet dynamics markedly different from surfaces with homogeneous wettability. Increasing a droplet's relaxation time enhances spreading and reduces droplet deformation during the maximum rebound stage, particularly on the hydrophobic part of hybrid surfaces. In contrast, reduced relaxation times result in an increase in the height of the droplet during the rebound stage.

The Effects of Nanoparticle Surfactants on the Release Behavior of Trapped Droplet in Micro-pore Throat

The release of trapped droplets in pore-throat structures is of great significance to study multiphase flow in porous media. In this paper, the effects of nanoparticle surfactants on the release behavior of trapped droplets in micro-pore throat are investigated using microfluidic visualization system and fluorescence techniques. We demonstrate a droplet control technique in microchannel and observe the release states of trapped droplets in pore-throat. We obtain the phase diagram of droplet states and establish mathematical models describing the critical transition condition by mechanism analysis. Based on the force’s analysis on the trapped droplets, the breakup and release mechanisms are also obtained when droplets move through the pore-throat. In addition, this research reveals the effect of nanoparticle surfactants on droplet release behavior by analyzing the variation of droplet length with flow velocity and capillary number. Nanoparticle surfactants decreases the critical flow velocity of droplet release, while significantly increasing the critical capillary number and this phenomenon becomes more pronounced with increasing concentrations of nanoparticle surfactants. Fluorescence experiments further elucidate the mechanism by which nanoparticle surfactants inhibit the release of trapped droplets in pore-throat by inducing interfacial viscoelasticity. Nanoparticles react with polymers at the interface to form the viscoelastic film. This film-induced interfacial viscoelasticity hinders droplet deformation and increases the viscous resistance between droplets and wall, thereby impeding the release of trapped droplets in pore-throat.

An Acidic Media Pump with Ga‐Based Liquid Metal

AbstractMicropumps have an important influence on the field of microfluidics, with particular interest in pumps based on liquid metal that operate without mechanical moving parts. While previous research has primarily focused on pumping alkaline media, this article aims to advance the field by demonstrating a liquid metal pump suitable for acidic environments. A key strategy involves reducing the interfacial tension between the liquid metal and the surrounding solution through the addition of surface‐active anions (I−). Theoretical analysis first evaluates the effectiveness of this approach. These experimental results confirm that increasing KI concentrations leads to a decrease in interfacial tension, enabling the deformation and actuation of liquid metal droplets at lower voltages compared to acidic media alone. Subsequently, an acidic media pump is constructed, and various parameters influencing its performance are examined, including acidity, iodide anion concentration, voltage, frequency, and droplet volume. This research offers strategies for developing liquid metal pumps with high flow rates and low energy consumption, thereby expanding the application potential of liquid metal in microfluidics.

Numerical investigation of electrocoalescence-induced fluid demixing between parallel plates

The efficient separation of dispersed phase droplets from a continuous phase in multiphase flow systems is essential for industries such as petroleum refining, pharmaceuticals, and food production. Conventional methods, relying on gravitational and buoyancy forces, are often inadequate for small droplets due to their weak influence. Electrocoalescence, utilizing electrical forces to enhance droplet coalescence, has gained attention as a promising alternative. However, most studies have focused on simplified models, limited electrical potentials, or axis-symmetric configurations, overlooking the effects of varying electrical potentials on droplet behavior in complex flows. This study bridges that gap by developing a numerical solver that couples the phase-field method with the Navier-Stokes equations to simulate electrocoalescence of two-dimensional droplets in laminar phase flow between parallel plates. The solver provides detailed insights into multiphase flow dynamics, including contact line behavior and interface tracking under different electrical potentials. The novelty of this work lies in its systematic evaluation of how varying electrical potentials affect droplet deformation, separation time, and interface dynamics, which are often not fully addressed by standard commercial solvers. The findings indicated that increasing electrical potentials from 50 kV to 100 kV leads to droplet deformation, with the droplet deformation index (DDI) increasing from 0.35 to 0.52. Additionally, phase separation time decreases by 20%, from 0.15 seconds to 0.12 seconds, as electrical potential increases. The increasing electrical potentials lead to asymmetric droplet shapes and instability, accelerating separation by disrupting the formation of stable liquid bridges. These findings offer valuable insights into optimizing electrocoalescence processes for industrial applications. In this study, a multi-objective optimization process was conducted using the Non-dominated Sorting Genetic Algorithm II (NSGA-II), with the aim of minimizing droplet deformation and phase separation time. The optimization results revealed that the ideal initial contact angle for minimizing deformation was 123.45°, while the optimal contact angle for minimizing separation time was 145.67°. These results highlight the potential of optimizing system parameters to improve the efficiency and stability of electrocoalescence processes in various industrial applications.The current study provides a deeper understanding of the interaction between electrical forces and multiphase flow dynamics, laying the groundwork for advancements in phase separation technologies across various industries.

Aerodynamic interaction of rain and wind turbine blades: the significance of droplet slowdown and deformation for leading-edge erosion

Abstract. Leading-edge rain erosion is a severe problem in the wind energy community since it leads to blade damage and a reduction in annual energy production by up to a few percent. The impact speed of rain droplets is a key driver of the erosion rate; therefore, its precise computation is essential. This study investigates the aerodynamic interaction of rain droplets and wind turbine blades. Based on findings from the literature and an analysis of the relevant parameter space, it is found that the aerodynamic interaction leads to a reduction in the impact speed. Additionally, the rain droplets deform and break up as they approach the wind turbine blade. An existing Lagrangian particle model, developed for research in aircraft icing, is adapted, extended, and validated for leading-edge rain erosion to study the process in more detail. Results show that the droplet slowdown reduces predicted damage toward the tip of the blade by over 50 %. The model indicates that the aerodynamic blade interaction affects small droplets significantly more than large droplets. Due to this drop-size dependency, the damage accumulation is shifted toward higher-rain-intensity events. Additionally, the droplet impact speed is sensitive to the aerodynamic nose radius of the airfoil. Due to this sensitivity and its drop-size dependency, the slowdown effect provides interesting levers for erosion mitigation via blade design or operational adjustments. To conclude, the aerodynamic interaction between droplet and blade is non-negligible and needs to be taken into account in erosion lifetime models.

Optically Pumped and Electrically Switchable Microlaser Array Based on Elliptic Deformation and Q-Attenuation of Organic Droplet Oscillators.

Conventional laser panel displays are developed through the mass integration of electrically pumped lasers or through the incorporation of a beam steering system with an array of optically pumped lasers. Here a novel configuration of a laser panel display consisting of a non-steered pumping beam and an array of electrically Q-switchable lasers is reported. The laser oscillator consists of a robust, self-standing, and deformable minute droplet that emits laser through Whispering-Gallery Mode resonance when optically pumped. The laser oscillation is electrically switchable during optical pumping by applying a vertical electric field to the droplet. Electromagnetic and fluid dynamics simulations reveal the deformation of the droplet into a prolate spheroid under the electric field and associated attenuation of quality factor (Q-factor), leading to the halt of the laser oscillation. A 2 × 3 array of droplets is fabricated by inkjet printing as a prototype of a laser panel display, and it successfully achieves the pixel-selective switching of the oscillation.

Simulation of Single Droplet Deformation and Breakup in Shear Flow by the Phase-Field Lattice Boltzmann Method

Simulation of Single Droplet Deformation and Breakup in Shear Flow by the Phase-Field Lattice Boltzmann Method

The Deformation of a Liquid Metal Droplet Under Continuous Acceleration in a Variable Cross-Section Groove.

This paper constructs a numerical simulation model for the deformation of droplets in a variable cross-section groove of a liquid droplet MEMS switch under different directions, amplitudes, frequencies, and waveforms of acceleration. The numerical simulation utilizes the level set method to monitor the deformation surface boundary of the metal droplets. The simulation outcomes manifest that when the negative impact acceleration on the X-axis is 12.9 m/s2, the negative impact acceleration on the Y-axis is 90 m/s2, the negative impact acceleration on the Z-axis is 34.5 m/s2, and the metal droplet interfaces with the metal electrode. The droplet deformation under the effect of a sine wave acceleration signal in the X and Y directions is lower than that under impact acceleration, while in the Z direction, the deformation is higher than that under impact acceleration. The deformation of metal droplets under square wave acceleration is more pronounced than that under sinusoidal wave acceleration. The deformation escalates with the augmentation in square wave amplitude and dwindles with the reduction in square wave acceleration frequency. Furthermore, there exists a phase difference between the deformation curve of the metal droplet and the continuous acceleration signal curve, and the phase difference is dependent of the material properties of the metal droplet. This work elucidates the deformation of the liquid-metal droplets under continuous acceleration and furnishes the foundation for the continuous operation design of MEMS droplet switches.