Droplet Evaporation Research Articles

On the Resolution Limit of Electrohydrodynamic Redox 3D Printing.

Additive manufacturing (AM) will empower the next breakthroughs in nanotechnology by combining unmatched geometrical freedom with nanometric resolution. Despite recent advances, no micro-AM technique has been able to synthesize functional nanostructures with excellent metal quality and sub-100 nm resolution. Here, significant breakthroughs in electrohydrodynamic redox 3D printing (EHD-RP) are reported by directly fabricating high-purity Cu (>98 at.%) with adjustable voxel size from >6µm down to 50 nm. This unique tunability of the feature size is achieved by managing in-flight solvent evaporation of the ion-loaded droplet to either trigger or prevent the Coulomb explosion. In the first case, the landing of confined droplets on the substrate allows the fabrication of high-aspect-ratio 50 nm-wide nanopillars, while in the second, droplet disintegration leads to large-area spray deposition. It is discussed that the reported pillar width corresponds to the ultimate resolution achievable by EHD printing. The unrivaled feature size and growth rate (>100 voxel s-1) enable the direct manufacturing of 30 µm-tall atom probe tomography (APT) tips that unveil the pristine microstructure and chemistry of the deposit. This method opens up prospects for the development of novel materials for 3Dnano-printing.

Modeling the evaporation and drying of two-component slurry droplets

In this paper, we present a mathematical model and numerical simulation for the evaporation and drying of a liquid droplet containing suspended solids, relevant to processes such as spray drying and spray pyrolysis in the food and pharmaceutical industries. The model comprises three stages: first is the evaporation of the liquid droplet consisting of solid particles, followed by the second stage starting with the formation of a porous crust around a wet-core region and, finally, the third stage with sensible heating of the dry particle. Using a finite difference method with a moving grid, we account for the moving interface between the crust and wet core. Our model incorporates spatial temperature variations and is validated against experimental data on colloidal silica droplet drying, showing good agreement. We examine model assumptions and analyze the impact of drying conditions on drying rate and final particle morphology. Along with the temperature and velocity of the drying gas, we also find that the shape of suspended solid particles inside the droplet and assuming continuum flow of vapor through the crust influence drying quality. Finally, we develop a regime map to predict whether the final particle will be solid or hollow based on operating conditions.

A novel phase-field lattice Boltzmann framework for diffusion-driven multiphase evaporation

Heat transfer and phase change phenomena, particularly diffusion-driven droplet evaporation, play pivotal roles in various industrial applications and natural processes. Despite advancements in computational fluid dynamics, modeling multiphase flows with large density ratios remains challenging. In this study, we developed a robust and stable conservative Allen–Cahn-based phase-field lattice Boltzmann method to solve the flow field equations. This method is coupled with the finite difference discretization of vapor species transport equation and the energy equation. The coupling between the vapor concentration and temperature field at the interface is modeled by the well-known Clausius–Clapeyron correlation. Our approach is capable of simulations under real physical conditions and is compatible with graphics processing unit architecture, making it ideal for large-scale industrial simulations. Three validation test cases are conducted to demonstrate the consistency of the presented model, including simulations of Stefan flow, the evaporation of suspended droplets containing water, acetone, and ethanol in the air, and the evaporation of a water sessile droplet on a flat surface. The results show that the model is able to predict the behavior and characteristics of each case accurately. Notably, our numerical results exhibit a maximum relative error of approximately 1% in simulations of Stefan flow. In the case of suspended droplet evaporation, the observed maximum difference between the calculated wet bulb temperatures and those derived from psychrometric charts is approximately 0.9 K. Moreover, our analysis of the sessile droplet reveals a good agreement between the results obtained by our model for the evaporative mass flux and those obtained from the existing models in the literature for different contact angles.

Evaporation characteristics of single free-falling liquefied natural gas droplet under different ambient conditions based on the VOF method

The evaporation characteristics of droplets is a fundamental issue for accurate depictions of moving liquefied natural gas (LNG) droplets and constantly changing ambient environment owing to intense heat, mass transfer, and momentum exchanges. In this study, a modified droplet evaporation model is developed to investigate the evaporation behavior of a single free-falling LNG droplet under various ambient conditions. The proposed model captures the droplet interface and calculates the mass transfer rate through the vapor concentration gradient using the volume of fluid method integrated with a smooth function. Evaporation experiments were conducted on a single free-falling LNG droplet to capture the evaporation process. The results indicate that it is acceptable to ignore the effect of the Stefan flow of a single free-falling LNG droplet. This study also examined the impact of different ambient conditions on evaporation characteristics. The results indicate that the evolution of the droplet diameter is mainly influenced by the ambient temperature because it affects the thermal properties of the surrounding gas and the distribution of the boundary layer. The temporal characteristics of the Nu and Sh numbers generally stabilize after a period of rapid decline. This study provides a theoretical basis for understanding the evaporation mechanisms of LNG droplets.

Droplet–droplet vapor-mediated interactions in confined environments

The evaporation of multiple droplets ensues ubiquitously in nature and industry. Vapor mediation caused by evaporating neighboring droplets is a demonstrated phenomenon that shows that droplets can interact with each other via the vapor in both open and confined configurations, i.e., the “shielding effect.” However, interactions between paired droplets in confined environments, more common in industrial processes, remain unexplored. In this Letter, we experimentally investigate the evaporation of water based paired sessile droplets on hydrophilic glass slides at different spacings in the absence and presence of an enclosed chamber. The results demonstrate that a confined environment significantly attenuates droplet evaporation, which intensifies with decreasing spacing between droplets. A 30%–82% increase in the droplet lifetime is found for the shortest distance studied in a confined environment, while results in an open environment are provided as a control. Both the local shielding effect and the global vapor accumulation due to confinement collaboratively induce such strong evaporation suppression. In addition, two well differentiated evaporation regimes ensue in a confined environment where the shielding effect initially dominates the evaporation suppression, whereas confinement governs the later evaporation stage. The later stage accounts for over 60% of the droplet lifetime. Such transition and further evaporation suppression, when compared to the classical shielding effect, highlights the importance of a confined environment in multiple droplet evaporation.

Numerical Study of Air–Vapor–Particle Flow in Gas Cyclone

AbstractThis paper presents a numerical study of the complex multiphase flow of air, vapor, and particles in an innovative gas cyclone called CAP cyclone. The air–vapor flow is modeled as a mixture by the Reynolds‐averaged Navier‐Stokes equations with the mixture species transport and the Eulerian wall film model using FLUENT. Particle flow is modeled by the Lagrangian particle tracking method and the condensational growth of particle droplets is modeled via a user‐defined function. The model is validated by reaching good agreement with experimental results. Flow field analysis shows that the added vapor does not change the major vortex characteristics in the cyclone, but the vapor distribution is not uniform. The vapor concentration is much higher in the upper part than in the lower part of the cyclone, leading to insufficient condensational growth in the lower part. A secondary vapor injection is proposed to improve the vapor concentration in the lower part, which is shown to be effective in improving the collection efficiency. The model and the results are helpful to the understanding and optimization of the CAP cyclone technology, and also the vapor and particle droplet flow in turbulent flows.

Three approaches to modelling heating and evaporation of monocomponent droplets

Three approaches to modelling the heating and evaporation of monocomponent droplets are compared. Firstly, the heat rate supplied to the droplets to raise their internal energy is calculated based on the observation that steady-state equations for heat and mass balance in the gas phase should lead to the same droplet evaporation rates. The direct calculation of the above-mentioned heat rate is used in the second approach; the value of this rate is then used for the estimation of the droplet evaporation rate using the Spalding heat transfer number. In the third approach, the same algorithm as in the second approach is used to calculate the heat rate but the mass evaporation rate in this approach is inferred from the coupled solution to the momentum, mass and energy conservation equations in the gas phase; the gas mixture density in this approach depends on temperature. The predictions of the numerical algorithms for these approaches are compared with experimentally observed time dependencies of the rates of change of radii and average temperatures of n-decane droplets at initial temperatures and radii equal to 300 K and 0.85 mm, respectively, placed in a gas at temperatures 500 K and 760 K. It is shown that the algorithm for the third approach predicts values which are close to the experimental data.

Dual-Functional Nanodroplet for Tumor Vasculature Ultrasound Imaging and Tumor Immunosuppressive Microenvironment Remodeling.

Accurately evaluating tumor neoangiogenesis and conducting precise interventions toward an immune-favorable microenvironment are of significant clinical importance. In this study, a novel nanodroplet termed as the nanodroplet-based ultrasound contrast agent and therapeutic (NDsUCA/Tx) is designed for ultrasound imaging and precise interventions of tumor neoangiogenesis. Briefly, the NDsUCA/Tx shell is constructed from an engineered CMs containing the tumor antigen, vascular endothelial growth factor receptor 1 (VEGFR1) extracellular domain 2-3, and CD93 ligand multimerin 2. The core is composed of perfluorohexane and the immune adjuvant R848. After injection, NDsUCA/Tx is found to be enriched in the tumor vasculature with high expression of CD93. When triggered by ultrasound, the perfluorohexane in NDsUCA/Tx underwent acoustic droplet vaporization and generated an enhanced ultrasound signal. Some microbubbles exploded and the resultant debris (with tumor antigen and R848) together with the adsorbed VEGF are taken up by nearby cells. This cleared the local VEGF for vascular normalization, and also served as a vaccine to activate the immune response. Using a syngeneic mouse model, the satisfactory performance of NDsUCA/Tx in tumor vasculature imaging and immune activation is confirmed. Thus, a multifunctional NDsUCA/Tx is successfully developed for molecular imaging of tumor neoangiogenesis and precise remodeling of the tumor microenvironment.

Unveiling photon-driven nonlinear evaporation via liquid drop interferometry.

We investigated photomolecular-induced evaporation, wherein photons cleave off water clusters near water-vapor interfaces, bypassing the typical thermal evaporation process. However, thermal-induced evaporation is the main bottleneck to precisely identify photon-induced evaporation. Liquid drop interferometry (LDI) resolved this bottleneck, utilizing evaporating water drops as an active element. Interestingly, we first observed near-total internal reflection, a nonlinear increase in evaporation attributed to photomolecular-induced evaporation, which had never been studied before, to the best of our knowledge. Furthermore, by generating a standing wave on a partially metallic polished prism, we uncovered an unexpected enhancement in evaporation coinciding with the wave reaching its maxima at the air-water (AW) interface, validating that photomolecular-induced evaporation is a surface phenomenon. Significantly, our noninvasive measurements have identified transient deformation height as a key indicator of photon-induced cluster breaking and increased evaporation, thus significantly advancing our understanding of photomolecular effects on water droplet evaporation.

Altering Mechanical and Dissolution Properties of Coffee Deposit by Adding Glucose.

Glucose modifies the mechanical stability of coffee films and facilitates their dissolution dynamics at the microscale, rendering glucose-coffee a valuable natural biomaterial system for studying pharmaceutical applications. We show the glucose-dependent inhibition of crack propagation during the evaporation of glucose-coffee droplets. The addition of glucose increases the hardness, stiffness, and shear modulus of films, as measured by surface nanomechanical testing. The glucose-coffee film dissolves faster and more evenly than the pure coffee film through interfaces. The water penetrates through well-dissolved glucose channels. The modified mechanical properties and adjustable dissolution time, coupled with edibility, position the glucose-modified coffee as an excellent candidate for developing pharmaceutical inks for personalized medicine droplet-based printing.

Experimental Study on the Influence of Microwave Energy Pulse Width and Duty Cycle on Evaporation and Ignition Characteristics of ADN-Based Liquid Propellant Droplets

This study investigates the evaporation and ignition characteristics of a single droplet of ammonium dinitramide (ADN)-based liquid propellant utilizing a waveguide resonant cavity device, in conjunction with a high-speed photographic imaging system and testing system. Experimental methods are employed to analyze the impact of microwave pulse width and duty cycle on the puffing and meicro-explosion phenomena of the droplet, as well as the delay time and duration of ignition. The experimental findings reveal that increasing the duty cycle enhances the ignition success rate and diminishes flame development time. Specifically, elevating the microwave duty cycle from 60% to 80% reduces the ignition delay time of the droplet from 132.8 ms to 88.1 ms, and the ignition duration from 23.1 ms to 19.9 ms. Furthermore, an increase in microwave energy pulse width expedites the combustion process of the flame and influences plasma generation. Increasing the pulse width of microwave energy from 20 µs to 40 µs prolongs the ignition delay time from 140.3 ms to 200.5 ms and extends the ignition duration from 56.7 ms to 77.8 ms. Additionally, it is observed that a higher duty cycle leads to a more pronounced puffing phenomenon that initiates earlier. In contrast, a higher pulse width results in a more pronounced puffing phenomenon that commences later. This study provides a thorough investigation into the microwave ignition mechanism of ADN-based liquid propellants, offering theoretical insights into the ignition and combustion stability of such propellants in microwave-assisted ignition systems.

Molecular dynamics simulation of micro-explosion of water-in-heavy oil emulsion droplets

Evaporation and micro-explosion of water-in-oil emulsion droplets composed of water and polycyclic aromatic hydrocarbons (PAHs) were characterized by molecular dynamics simulation at 300–600 °C and 0.2–1.5 MPa. The driving force for micro-explosion of emulsion droplets comes from the difference between environment temperature and boiling point of water. Also, the evaporation potential of oil phase has a significant influence on the intensity of micro-explosion. An increase in water droplet diameter within a certain range, an increase in environment temperature and a decrease in environment pressure are beneficial to increasing the probability and intensity of micro-explosion. After an intense micro-explosion, the number of oil molecules in the resulting child clusters can be less than 20 % of the initial number of oil molecules in the emulsion droplets. The time required for complete evaporation of emulsion droplets depends on the evaporation of the largest child cluster produced by micro-explosion.

Supersonic coaxial aerodynamic atomization dust removal technology

The high concentration of respirable dust pollution created during coal mining has long been known to be harmful to employee health. A water absorbing atomization device has certain advantages when spray trapping particle sizes of PM2.5–10. To further improve the PM0–2.5 trapping efficiency, supersonic coaxial pneumatic atomization dust removal technology has been developed. The effects of fog droplet characteristics on the instantaneous diffusion of dust were studied by numerical simulation and macro- and microexperiments for the first time, and the coupling characteristics of fog droplets and dust fields were obtained. The results show that with increasing aerodynamic pressure, the supersonic range extends along the axis toward the nozzle outlet, and the average velocity in the tube increases. Under different pressures, the droplet particle size in the supersonic coaxial atomizing nozzle is <6 μm and decreases with increasing aerodynamic pressure. When a droplet effuses from the nozzle, the transonic distribution of the flow field causes the droplet velocity to increase first and then decrease under the drag force. The droplet field characteristic distribution of supersonic coaxial atomization is determined by droplet evaporation, condensation, and migration. Under the same pressure, with increasing spray distance, the distribution of the droplet particle size increases in a stepwise manner, and the droplet velocity decreases according to an exponential function so that the droplet field produces a high-speed fine fog area. The range of droplets with higher velocities and smaller particle sizes is mainly influenced by migration and increases with increasing pressure. The coupling effect droplet field and dust field can be characterized by the instantaneous dispersion of dust and are determined by the distribution characteristics of the fog droplet field. The large range of high-speed fine fog produced by supersonic coaxial atomization technology easily traps respirable dust, and the classification efficiency of PM0–2.5 reaches 90%. In this study, a new dynamic microfog dust trapping technique was proposed, and a new method of instantaneous sampling combined with a microscopic dispersion test was adopted to characterize the temporal and spatial distributions of dust fields affected by fog droplet fields, reveal the generation of dynamic microfog and the mechanism of dust trapping, enrich the theory of fine dust trapping, and provide technical support for the safe production and utilization of coal.

Fluorescence Lifetime Measurement For Studying Evaporation Of Bi-Component Droplet

Sprays are essential in engineering applications like evaporators and combustion chambers. Predicting the evaporation of multi-component liquid droplets is complex due to changing composition and properties. Measuring droplet composition is challenging, with limited non-intrusive methods available. Raman spectroscopy faces hurdles like weak signals and interference. Intensity based Laser-Induced Fluorescence (LIF) requires optical models to interpret data due to varying droplet size and position. Fluorescent dyes in liquid mixtures are sensitive to temperature, complicating measurements. Fluorescence lifetime measurements offer a promising alternative, being an absolute quantity less affected by reabsorption. This study develops a novel method using fluorescence lifetime to analyze droplet composition, leveraging Time-Correlated Single Photon Counting (TCSPC) for precise measurements. Factors such as dye concentration, solvent polarity, and temperature sensitivity are investigated. Calibration curves for ethanol-water mixtures correlate fluorescence lifetime with volume fraction. Experimental setups use TCSPC and femtosecond lasers for dye excitation. Results show that fluorescence lifetime decreases linearly with solvent polarity and is influenced by temperature and dye concentration. High dye concentrations cause self-quenching, altering temperature sensitivity. The method was applied to study the evaporation of ethanol-water droplets under acoustic levitation. Findings indicate that evaporation rates slow as the water fraction increases, with initial measurements showing higher water content due to partial evaporation. This research introduces a novel technique for droplet compositional analysis using fluorescence lifetime, providing insights into optimizing measurement accuracy and advancing understanding in engineering and related fields.

Suppressing the Leidenfrost effect by air discharge assisted electrowetting-on-dielectrics

The Leidenfrost effect for a droplet on an over-heated substrate always results in a superhydrophobic state, significantly hindering the water evaporation for heat dissipation. Here, we demonstrate a strategy of air discharge assisted electrowetting-on-dielectrics (ADA-EWOD), overcoming this challenge. This strategy increases the solid surface free energy by generating air discharge near the three-phase contact line of the droplet and combines it with the electromechanical force to decrease the contact angle, which makes ADA-EWOD have stronger wetting capabilities than traditional electrically control methods that only rely on electromechanical force. The water contact angle on an over-heated surface (above 350 °C) is decreased from nearly 180° down to less than 10°. This superhydrophilicity at high temperature reduces the droplet lifetime by at least 10 times, well inhabiting the Leidenfrost effect. Furthermore, we use ADA-EWOD in droplet evaporation for heat dissipation, where a heated silicon wafer at 600 °C is cooled down to less than 200 °C within 20 s. We believe that the present work provides a perspective on suppressing the Leidenfrost effect, which may have important potential applications in the field of heat dissipation.

Evaporation and Fragmentation of the Electrified Droplets in the Polar Clouds during Spring Season as a Key Mechanism of the Ozone Depression Formation

This study focuses on the role of the charged particles in the formation of the springtime ozone depression in the polar atmosphere. Analysis of experimental data collected in the polar atmosphere indicates that the small charged particles, predominantly ion clusters, can play a key role in the ozone molecules destruction and springtime ozone depression. The formation of these particles increases strongly during the spring season in the process of evaporation and fragmentation of the cloud-charged droplets in the lower stratosphere and upper troposphere. Additionally, small charged particles can also affect the formation and accumulation of chlorine monoxide under cold conditions of the lower stratosphere. At the same time, the chlorine mechanism of ozone destruction cannot completely explain the ozone depression formation, which probably takes place not only inside the polar vortex in the lower stratosphere but outside it also, both at the altitudes of the lower stratosphere and upper troposphere. The assumption that the charged particles play an important role in the process of ozone depression formation was put forward by previous studies, but in this research work, this assumption has been additionally confirmed, which is the springtime growth of ion clusters concentration as a result of the droplet's evaporation and defragmentation in the polar atmosphere is a key mechanism of the ozone depression formation. We simulated the process of evaporation and fragmentation in the case of a 10-micron size droplet, which implies the possible catalytic cycles of ozone destruction with the ion clusters. For the first time, the role of the Earth's magnetic field and the Polar vortex wind in the unipolar charge accumulation on the cloud particles in the lower stratosphere and upper troposphere not only inside the Polar vortex but also outside of it was substantiated. This fact in our point of view can give rise to the large-scale springtime ozone depression, spreading over the midlatitudes, which size is vastly greater than it is commonly supposed.

Effects of the droplet size and engine size on two-phase kerosene/air rotating detonation engines in flight operation conditions

The numerical and experimental research of rotating detonation engines is usually conducted in ground environmental conditions. Although many breakthroughs have been made, there are still deficiencies in understanding engines operating in real flight conditions. In order to reveal the effect of engine size and initial kerosene droplet size on the rotating detonation engines in flight conditions, the Eulerian-Lagrangian model is adopted, and a series of two-phase kerosene/air rotating detonation cases are simulated in the conditions of Mach 5 and 24 km altitude. When 5 μm and 10 μm droplets are adopted, the RDE behaves like gaseous rotating detonations with clear cellular structures. When the 20 μm and 30 μm droplets are adopted, the rotating detonation waves tend to be divided into two layers and form the λ-shaped shock structure. The results indicate that droplet size and engine size influence detonation wave propagation and flow field mainly through droplet heat absorption and evaporation height. Increasing the engine sizes can promote the two-phase rotating detonation and broaden the initial diameter range capable of obtaining rotating detonation waves. However, as droplet size increases, the fresh mixture layer becomes stratified, with an upper layer predominantly comprising fuel vapor and a lower layer of fuel droplets, which results in an λ-shaped shock structure at the detonation front. The flight operation condition brings in differences in features such as detonation wave height and velocity deficit. The detonation height in flight conditions is higher than that in ground conditions. The most velocity deficit in flight conditions observed in our study is below 15 %, which is lower than the results (22.5 %) in ground operating conditions. These results indicate that the optimal design of the rotating detonation engine must consider the real operation conditions and the effect of engine sizes and droplet sizes.

Continuous spatial field confocal thermometry using lanthanide doped tellurite glass

Distinguishing between microscopic variances in temperature in both space and time with high precision can open up new opportunities in optical sensing. In this paper, we present a novel approach to optically measure temperature from the fluorescence of erbium:ytterbium doped tellurite glass, with fast temporal resolution at micron-scale localisation over an area with sub millimetre spatial dimensions. This confocal-based approach provides a micron-scale image of temperature variations over a 200 μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu $$\\end{document}m ×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes $$\\end{document} 200 μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu $$\\end{document}m field of view at sub-1 second time intervals. We test our sensing platform by monitoring the real-time evaporation of a water droplet over a wide field of view and track it’s evaporative cooling effect on the glass where we report a net temperature change of 6.97 K ± 0.03 K. This result showcases a confocal approach to thermometry to provide high temporal and spatial resolution over a microscopic field of view with the goal of providing real-time measures of temperature on the micro-scale.

Research on nonequilibrium plasma-assisted evaporation and ignition of n-decane droplet

To evaluate the nanosecond pulsed discharge plasma-assisted evaporation and ignition attributes of hydrocarbon fuel droplets, numerical models are established. The influences of nonequilibrium plasma on the characteristics of n-decane droplet evaporation and ignition are numerically studied through a loosely coupled method employing a one-dimensional (1D) fully transient model of droplet evaporation and ignition and a model of nanosecond pulse plasma discharge. The results show that the reaction rate of the initial phase of n-decane droplet ignition is increased by nonequilibrium plasma. In addition, both the evaporation and ignition of the droplet are accelerated. Increasing the reduced electric field of the discharge leads to decreases in the droplet ignition delay time, survival time, and shortening amplitude. The evaporative cooling effect, which occurs at the initial phase of droplet ignition and typically decreases the local temperature surrounding a droplet surface, is weakened by the plasma. As the reduced electric field increases, the time to generate a high-temperature zone (&amp;gt;1800 K) decreases, while its duration increases. The initial phase of n-decane droplet ignition, in which the flame temperature increases while the flame radius decreases, is strongly affected by the plasma during the initial ignition phase. However, the plasma has little impact on the peak flame temperature and the flame radius during the stable combustion phase of the droplet. According to reaction kinetics analysis, the plasma directly interferes with the elementary reactions R330 (nC10H22 + O = 3-C10H21 + OH) and R331 (nC10H22 + O = 2-C10H21 + OH) of n-decane/air combustion. Moreover, the dissociation and oxidation processes of intermediate products are accelerated. Then, the important reaction rates, which determine the ignition delay time, increase indirectly. Thus, the overall ignition delay time of the n-decane droplet is shortened.

Integration of Hertz–Knudsen–Schrage phase change in phase-field lattice Boltzmann method: Validation and parametric studies

The phase transition between liquid and vapor is of vital importance in daily life and industry. Given the importance of the lattice Boltzmann method (LBM), in particular the phase field method, in the simulation of two-phase flows, a robust LBM phase transition model is essential. This study introduces a novel approach by integrating the widely used, Hertz–Knudsen–Schrage (HKS) phase change rate into a conservative phase-field LBM. The phase-field and momentum equations are solved using the Boltzmann distribution function, whereas the energy equation is solved using the finite difference method. Once the necessary parameters for the calculation of the phase change rate are obtained, the corresponding source terms are incorporated into each equation. The model's validation is performed through a series of benchmark problems, including the one-dimensional Stefan problem, Nusselt's film condensation, bubble detachment, centered droplet evaporation, and sessile droplet evaporation. The results demonstrate favorable agreement between the LBM solution and analytical or empirical data. Furthermore, this study highlights the model's ability to approximate steady-state phenomena with minimal reliance on the phase change coefficient of the HKS theory. It also underscores the model's capacity to accurately capture transient phenomena by appropriately selecting values for this coefficient. In addition, parametric studies are conducted to investigate evaporation problems using the HKS theory for recognizing the effect of superheat, contact angle, and droplet size on evaporation. Finally, this model not only can detect trends and behaviors of phenomena but also can adapt empirical and analytical results with good agreement.