Droplet Dynamics Research Articles

The Role of Re-Entrant Microstructures in Modulating Droplet Evaporation Modes

The evaporation dynamics of sessile droplets on re-entrant microstructures are critical for applications in microfluidics, thermal management, and self-cleaning surfaces. Re-entrant structures, such as mushroom-like shapes with overhanging features, trap air beneath droplets to enhance non-wettability. The present study examines the evaporation of a water droplet on silicon carbide (SiC) and silicon dioxide (SiO2) re-entrant structures, focusing on the effects of material composition and solid area fraction on volume reduction, contact angle, and evaporation modes. Using surface free energy (SFE) as an indicator of wettability, we find that the low SFE of SiC promotes quick depinning and contact line retraction, resulting in shorter CCL phases across different structures. For instance, the CCL phase accounts for 55–59% of the evaporation time on SiC surfaces, while on SiO2 it extends to 51–68%, reflecting a 7–23% increase in duration due to stronger pinning effects. Additionally, narrower pillar gaps, which increase the solid area fraction, further stabilize droplets by extending both CCL and constant contact angle (CCA) phases, while wider gaps enable faster depinning and evaporation. These findings illustrate how hydrophobicity (via SFE) and structural geometry (via solid area fraction) influence microscale interactions, offering insights for designing surfaces with optimized liquid management properties.

Influence of liquid–vapor phase change on the self-propelled motion of droplets on wettability gradient surfaces

Self-propelled motion of sessile droplets on gradient surfaces is key to the advancement of microfluidic, nanofluidic, and surface fluidic technologies. Precise control over droplet dynamics, which often involves liquid–vapor phase transitions, is crucial for a variety of applications, including thermal management, self-cleaning surfaces, biochemical assays, and microreactors. Understanding how specific phase changes like condensation and evaporation affect droplet motion is essential for enhancing droplet manipulation and improving transport efficiency. We use the thermal Navier–Stokes–Korteweg equations to investigate the effects of condensation and evaporation on the motion and internal dynamics of droplets migrating across a surface with a linear surface energy profile. The study focuses on the early dynamics of self-propelled motion of a phase changing droplet at sub-micron scale before viscous forces are comparable with the gradient forces. Our results demonstrate that phase change significantly affects the self-propelled motion of droplets by reshaping interfacial mass flux distributions and internal flow dynamics. Condensation increases droplet volume and promotes extensive spreading toward regions of higher wettability, while evaporation reduces both volume and spreading. These changes in droplet shape and size directly affect the driving forces of motion, augmenting self-propulsion through condensation and suppressing it during evaporation. Additionally, each phase change type generates distinct internal flow patterns within the droplet, with condensation and evaporation exhibiting unique circulatory movements driven by localized phase changes near the contact lines.

Efficiently and consistently energy-stable [formula omitted]-phase-field method for the incompressible ternary fluid problems

Ternary incompressible fluid flows extensively exist in atmospheric science, chemical engineering, and energy and power engineering, etc. The phase-field method is popular in multi-phase fluid modeling thanks to its efficient ability of interface capturing. This work aims to develop an energy dissipation law-preserving and temporally second-order accurate algorithm for a ternary phase-field fluid system. To establish a simple energy estimation, an adapted auxiliary variable approach is used to transform the original model into its equivalent form. Later, a second-order backward difference strategy is used to design the fully decoupled and linear time-marching scheme. To improve the consistency between original and modified discrete energy functionals, a practical energy correction technique is presented. We analytically prove the discrete energy dissipation property and show that the energy estimation can be easily established without considering the complex treatments of nonlinear and coupling terms. To facilitate the interested readers, we briefly describe the numerical implementation in each time step. The numerical tests indicate that the proposed method not only has desired accuracy, but also satisfies the energy stability even if a larger time step is used. Moreover, the proposed method can well simulate various ternary fluid phenomena, such as the liquid lens, phase separation, droplet dynamics, Kelvin–Helmholtz instability, and billowing cloud.

Experimental insights into droplet behavior on Van der Waals and non-Van der Waals liquid-impregnated surfaces

Droplet impact is a fascinating phenomenon that occurs when a liquid droplet collides with a surface. It is not only a fundamental area of scientific inquiry but also has practical implications across many industries and natural systems. The dynamics during droplet impact on liquid-impregnated surfaces (LIS) are of special interest because the properties of the surface and impregnated liquid may significantly change the impact outcome. We present a detailed study of the impact and subsequent retraction of liquid droplets on a liquid-impregnated surface using high-speed imagery. Square-shaped textures with varying post-spacings of 5, 20, and 30 μm on a silicon wafer were fabricated and functionalized using octadecyltrichlorosilane. Two different lubricants, silicone oil and hexadecane, were infused to investigate how their properties affect impact dynamics. Droplet impacts were investigated on these surfaces across a broad range of Weber numbers, i.e., (28–495). Additionally, we measured the stability of the LIS surface by calculating spreading coefficients and contact angles. The experiments revealed that the properties of the infused oil play an insignificant role in droplet dynamics, including spreading, rebound, and unique phenomena related to oil interaction with surface textures. This study provides insights into the intricate dynamics of droplet interactions with LIS, offering valuable contributions to understanding surface-wetting phenomena.

Computational Study of Dynamics of Compound Droplets in a Straight Micro Channel

Computational Study of Dynamics of Compound Droplets in a Straight Micro Channel

Effect of gamma-rays irradiation on wettability of sol–gel silica nanofilms

Silica nanofilms are often used as antireflection films due to their unique optical properties. In the national high-power laser systems, in order to reduce optical reflection, the silica films are covered on the final optical components. However, the gamma radiation generated during the operation of these systems alters the properties of the silica films on the optical components. While wettability serves as the cornerstone of dust and pollution prevention in engineering technology, it has garnered limited attention in the research of optical components for high-power laser devices. Hence, this paper delves into the surface wettability and intricate hydrodynamics of droplets on silica films, both before and after gamma ray irradiation. The findings reveal that as the irradiation dose increases, the surface energy of the silica film rises, rendering it more lyophilic. By analyzing the impact dynamics of droplets on the silica thin film, we conclude that gamma irradiation renders the silica film coating on optical element surfaces more susceptible to contamination.

Theoretical models from experiments on particle population in convective arrays

Studying suspensions of gold nanorods has provided valuable knowledge on variations in concentration and how nanoparticles behave. Analysis of UV–visible spectra has shown changes in both longitudinal and transverse peaks, indicating a reduction in nanoparticle absorption peaks as the nanoparticle concentration decreases in suspension. Furthermore, changes in droplet contact angles have elucidated a direct correlation between nanoparticle density and droplet dynamics, shedding light on the intricate interplay between concentration reduction and droplet behavior. Investigations into cetyltrimethylammonium bromide (CTAB-coated) gold nanorods have unraveled the complexities of depletion, electrostatic, and Van der Waals forces, offering valuable knowledge on the self-assembly mechanisms governing these nanomaterials. The examination of interactions within coffee stain rings has underscored the crucial role of nanoparticle density in nanostructure arrangements, influencing deposition patterns and contributing to a deeper understanding of volume fraction evolution in nanostructured systems. By establishing a quantitative framework for interpreting energy parameters and observing optimal fitting agreements with experimental data, this research provides a solid foundation for future endeavors aimed at elucidating nanomaterial behavior in suspended systems. This comprehensive overview lays the groundwork for tailored manipulation of gold nanorod properties, emphasizing the essential relationship between density and contact angle in shaping wetting phenomena and surface engineering practices.

Research on the dynamic characteristics of micro-scale droplet impact

Micro-scale droplet impact behavior is widely observed and holds critical significance in various fields such as inkjet printing, anti-icing, and spray cooling. However, current research has primarily focused on millimeter-scale droplets, leading to a lack of understanding regarding the dynamics of micro-scale droplets. To address this gap, our research systematically analyzed the impact and rebound behaviors of droplets of various sizes on microstructur surfaces, revealing the significant influence of droplet size on dynamic characteristics. The results revealed that micro-scale droplets exhibit markedly distinct morphological evolution during spreading, contraction, and rebound compared to millimeter-scale droplets. As droplet size decreases, the minimum rebound velocity threshold significantly increases, contact time extends substantially, and viscous dissipation becomes the primary energy loss mechanism in micro-scale droplets, resulting in a dramatic decrease in the restitution coefficient. Based on energy balance analysis, we developed a theoretical model to characterize the restitution coefficient of micro-scale droplets, demonstrating strong concordance with the experimental results. This research provides novel insights into the dynamic behavior of micro-scale droplets and offers theoretical support for surface design in diverse applications such as biomedical printing, aircraft anti-icing, and electronic device cooling.

The reverse-encapsulation and core-release process of a compound droplet under thermocapillary effects

This work demonstrates that a core-shell compound droplet can undergo separation into two different phase droplets or be transformed into a reverse-encapsulation droplet under the influence of thermocapillary effects. This study comprehensively investigates the thermocapillary effects on the migration, reverse-encapsulation, and core-release dynamics of compound droplets, with particular emphasis on the interactions among key dimensionless parameters, including the Marangoni number, Reynolds number, and the radius ratio of the inner to the middle fluid of a core-shell compound droplet. Using a reduction-consistent phase field model for incompressible N-phase flows, this research provides an in-depth analysis of the reverse-encapsulation and core-release processes of a compound droplet. The reverse-encapsulation process is characterized by three distinct stages: The initial acceleration stage, the encapsulation stage, and the post-transformation stage. Similarly, the core-release process also has three stages: The initial acceleration stage, the middle fluid contraction stage, and the independent movement stage. The results indicate that the Marangoni number has little influence on the migration velocity, while the tangential surface force (thermocapillary force) is the cause of these processes. The Reynolds number has a significant effect on the encapsulation dynamics, with higher values leading to slower and more turbulent processes. In addition, the radius ratio plays a critical role in determining the reverse-encapsulation and core-release processes, as well as migration behaviors. These findings advance our understanding of multiphase fluid dynamics and have significant implications for applications in microfluidics, targeted drug delivery, and advanced materials synthesis.

Mean field control of droplet dynamics with high-order finite-element computations

Liquid droplet dynamics are widely used in biological and engineering applications, which contain complex interfacial instabilities and pattern formation such as droplet merging, splitting and transport. This paper studies a class of mean field control formulations for these droplet dynamics, which can be used to control and manipulate droplets in applications. We first formulate the droplet dynamics as gradient flows of free energies in modified optimal transport metrics with nonlinear mobilities. We then design an optimal control problem for these gradient flows. As an example, a lubrication equation for a thin volatile liquid film laden with an active suspension is developed, with control achieved through its activity field. Lastly, we apply the primal–dual hybrid gradient algorithm with high-order finite-element methods to simulate the proposed mean field control problems. Numerical examples, including droplet formation, bead-up/spreading, transport, and merging/splitting on a two-dimensional spatial domain, demonstrate the effectiveness of the proposed mean field control mechanism.

Droplet Helical Motion on Twisted Fibers.

We investigate herein the impact of helical structures on the motion of asymmetrical droplets along vertically twisted fibers. The droplet adopts helical motion around the bundle driven by gravity. This complex motion can be manipulated by varying the twists turns of the fibers. When the droplet size is smaller than the characteristic length of the helix (pitch), the droplet adopts a predominant helical motion correlated to the groove of the twisted fibers. When the droplet size exceeds the pitch length, a mixed motion of intermittent vertical sliding and helical movement emerges. A model describes rotational and linear speeds as a function of the number of fiber twist turns. This research highlights the profound role of substructures in droplet dynamics, offering fresh insight into droplet manipulation or fiber-based devices.

Research on the Dynamic Spreading and Wettability Characteristics of Droplets on Coal Dust.

The dynamics of droplets spreading on surfaces have been extensively studied across various influencing factors, necessitating an exploration of their effect on wettability. Herein, the specific composition, size distribution, and contact angle of the coal dust preparation were characterized by a series of experiments to determine the conditions for the simulation. Meanwhile, the multiphase volume of the fluid method was implemented in the simulations, predicated on appropriate boundary conditions, and verified by a mesh independence test. The findings confirmed that the numerical approach for contact angle validation had a minor deviation, making it suitable for multiphase interface tracking. Besides, the typical wetting pattern of droplets was hereby identified into three stages, including the moving stage (stage I), the periodic wetting stage (stage II), and the balancing stage (stage III). The initial diameter could effectively increase the coverage area and spreading time for stage II. Obviously, the first amplitude of first maximum spreading diameter (D max-1) significantly increased with higher impact velocities, corresponding to an increase in kinetic energy. Despite the significant spreading effect of the falling height mainly on D max-1 and contact time, the increased trend of wetting efficiency was not obvious. However, the spreading factor and wetting efficiency decreased with increased roughness height. Finally, the difference in spreading wettability was illustrated based on the spreading wetting mechanism. The wetting efficiency of droplets on coal dust was remarkably influenced by the dynamic spreading behaviors of droplets. Overall, the findings from this study offer insights into the extent of spreading wetting that occurs before a droplet reaches an equilibrium state.

Spatio-temporal reconstruction of droplet impingement dynamics by means of color-coded glare points and deep learning

Abstract The present work introduces a deep learning approach for the three-dimensional reconstruction of the spatio-temporal dynamics of the gas–liquid interface on the basis of monocular images obtained via optical measurement techniques. The method is tested and evaluated at the example of liquid droplets impacting on structured solid substrates. The droplet dynamics are captured through high-speed imaging in an extended shadowgraphy setup with additional glare points from lateral light sources that encode further three-dimensional information of the gas–liquid interface in the images. A neural network is trained for the physically correct reconstruction of the droplet dynamics on a labeled dataset generated by synthetic image rendering on the basis of gas–liquid interface shapes obtained from direct numerical simulation. The employment of synthetic image rendering allows for the efficient generation of training data and circumvents the introduction of errors resulting from the inherent discrepancy of the droplet shapes between experiment and simulation. The accurate reconstruction of the three-dimensional shape of the gas–liquid interface during droplet impingement on the basis of images obtained in the experiment demonstrates the practicality of the presented approach based on neural networks and synthetic training data generation. The introduction of glare points from lateral light sources in the experiments is shown to improve the reconstruction accuracy, which indicates that the neural network learns to leverage the additional three-dimensional information encoded in the images for a more accurate depth estimation. By the successful reconstruction of obscured areas in the input images, it is demonstrated that the neural network has the capability to learn a physically correct interpolation of missing data from the numerical simulation. Furthermore, the physically reasonable reconstruction of unknown gas–liquid interface shapes for drop impact regimes that were not contained in the training dataset indicates that the neural network learned a versatile model of the involved two-phase flow phenomena during droplet impingement.

Bimodal Droplet-Based Electricity Generation Through Semi Cassini Oval Dynamic Morphology Control.

Droplet-based electricity generator (DEG) is the promising energy harvesting technology applicable in versatile scenarios. Despite numerous optimizations in DEG's materials and structures, few has paid attention to the droplet dynamics and morphology control. Here the droplet's spread-retraction dynamics and the resultant semi Cassini oval (SCO) morphology are reported, characterized by convex at both ends and concave in the middle. The lifted top electrode (LTE) is designed to respond to the dynamic SCO morphology in two steps: 1) LTE first contacts the leading edge of the spreading droplet, generating a negative voltage peak; 2) LTE second contacts the trailing edge of the retracting droplet, generating a positive voltage peak. In this way, bimodal electrical output is obtained, which exhibits 25% increase in peak-to-peak voltage and 33% increase in average power compared to the traditional DEG with only one voltage peak. These results prove that incorporating the droplet dynamics and morphology control into DEG design uplifts the energy harvesting limit from individual droplet. The proposed LTE-DEG inspires alternative route for DEG power enhancement by maximizing energy utilization of individual droplet from the perspective of droplet dynamic morphology design.

Experimental study on droplet dynamics behavior and combustion characteristics of high performance green propellant in electrical ignition mode

High performance green propellant represented by ammonium dinitramide-based liquid propellant and its new ignition method are the research hotspots of space propulsion in the 21st century. Exploring the complex multi-scale physical properties of multi-component ammonium dinitramide-based liquid propellant droplets in the electrical ignition mode has wide application significance for spray, propulsion system design and combustion control. The droplet dynamics behavior and combustion characteristics of propellant droplets at different ignition voltages were studied experimentally. The droplet dynamics behavior during the evaporation process, including violent volume oscillation, approximate steady-state expansion, contraction, secondary expansion, puffing and micro-explosion, have been determined by the generation, growth, and discharge of vapor bubbles. In the initial evaporation process, the heterogeneous nucleation is dominant. As the droplet is continuously heated, homogenization nucleation gradually dominates. The main physical and chemical mechanisms of bubble evolution driven by temperature involve methanol boiling, water overheating, ammonium dinitramide decomposition and combustion reaction between vapor molecules. Increasing the ignition voltage increases the droplet dynamics behavior and the combustion, but promotes the combustion instability. Increasing the ignition voltage increases the ignition delay time, puffing delay time, droplet lifetime, maximum temperature of droplet, and reduces the ignition critical diameter. It is proposed that the method of suppressing the droplet breakup dynamics at decomposition area and enhancing the droplet breakup dynamics at the combustion area are conducive to the combustion control of the thruster in electrical ignition mode. This research provides novel insight into the study of the electrical ignition mechanism of liquid fuels.

Simultaneous effects of capillary number, viscosity ratio, and contraction ratio on droplet dynamics in contraction microchannel

Abstract In droplet-based microfluidic systems, fluid properties, flow conditions, and channel geometry play crucial roles in the movement and manipulation of droplets. This study employs a three-dimensional numerical simulation method to investigate droplet dynamics in a contraction microchannel under the simultaneous influence of different factors, such as capillary number (Ca), viscosity ratio (λ), and contraction ratio (C). Specifically, a theoretical model is introduced for predicting the transition of droplets from trap to squeeze, and it is observed to be 〖Ca〗_I = f(C,λ). Meanwhile, droplet dynamics are investigated for the transition from squeeze to breakup for finding critical capillary number value (CaII). In addition, the critical viscosity ratio for the process from squeeze to breakup has been figured out by numerical results for a wide range of contraction ratios. Eventually, droplet dynamics including deformation, velocity ratio, and breakup during contraction microchannel are also quantitatively studied under the factors above.

Impact of density ratio on droplet dynamics in pulsating flow

Secondary atomization is extensively studied by investigating a droplet subjected to a steady air/gas stream. However, droplets are often subjected to unsteady or pulsating flows, such as in aero-engines or rockets, because of thermo-acoustic instabilities in the combustion chambers. The investigation focuses on the droplet dynamics and breakup in a pulsating flow for a range of density ratios (ρr), 1000 to 10, under sinusoidal airflow of different amplitudes and frequencies as compared to the dynamics in a steady flow. The volume of fluid multiphase model tracks the liquid–gas interface, and the governing equations are solved using the finite volume method. The two-dimensional axisymmetric pulsating simulations demonstrate accuracy comparable to the corresponding three-dimensional simulations at a much lower computational cost and are used for parametric studies. The droplets under the pulsating flow show a wavy surface, and larger vortex structures are observed during the deceleration period. At a high-density ratio (1000), pulsating flow enhances droplet deformation for a faster breakup, with the flow amplitude having more impact than its frequency. For a medium-density ratio (100), where breakup occurs under steady flow, droplet breakup is inhibited in the pulsating flow at low amplitude and high frequency. In the case of a low-density ratio (10), there is no breakup under steady flow, but pulsating flow promotes breakup, except at low amplitude and high frequency. The droplet breakup is always achieved for the highest amplitude, while lower frequencies push the liquid mass from the center of the droplet to the rim.

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.

The Influence of Gradient Patterned Design on Nanoshapes Deposition

Experimental exploration of surface modifications for nanoparticle patterning on hydrophilic set of stripes reveals unique patterns on gradient patterned designs. Combining theory with empirical data offers insights into droplet-induced assembly dynamics for gold nanorods and nanospheres mixture. The unique patterns and assembled arrays of nanospheres and nanorods has been evaluated and mapped with theoretical analytics. Gradient patterned surfaces demonstrate controlled particle deposition via precise manipulation of surface properties and complex energy interplay. Confinement effects induced by the surface design through engineered hydrophobic stripes that induce hydrodynamic flow play a critical role in guiding nanorods towards the center of the hydrophilic stripes, impacting wetting behavior and droplet dynamics. Such interplay of forces in suspension facilitates precise control over hydrodynamic confinement and capillary alignment. Study of theoretical models in this regard can play critical role in nanoparticle deposition, alignment, and shape separation effect.

Exploring mechanisms of asymmetric droplet impact dynamics on roughness gradient surface

Droplet impact on surfaces with varying roughness and wettability is a common phenomenon in both natural and industrial environments. While previous studies have primarily examined asymmetric droplet rebound driven by impact velocity or Weber number, the influence of surface structure and associated impact mode transitions has received less attention. In this study, molecular dynamics simulations and detailed analyses are employed to investigate the mechanisms governing droplet rebound on nanopillar arrays with gradient distributions. Results reveal that nanopillar height significantly influences rebound direction, with two distinct directional transitions occurring as the height increases. Additionally, the effects of surface structure and Weber number on impact patterns, rebound velocity, and contact time are systematically evaluated, with contact angle calculations shedding light on the underlying force mechanisms. A phase diagram is developed to illustrate the relationship between rebound direction, Weber number, and nanopillar height. The study further extends the analysis to substrates with bidirectional gradient distributions, demonstrating consistency with single-directional gradient results and validating the broader applicability of the findings. This research provides critical insights into droplet dynamics on roughness gradient surfaces, emphasizing the role of nanopillar height and impact mode in controlling droplet behavior and highlighting potential applications in the design of structured array surfaces.