Droplet Trajectories Research Articles

Estimating infectious disease transmission risk: An analysis based on multi-scale modeling of respiratory droplet transport

In the present work, a multi-scale model is used to simulate the trajectory of exhaled droplets for different types of respiratory events. By estimating the saliva viral content, information on the exhaled droplet trajectory and size distribution are exploited to derive spatial maps of viral concentration. The maps are used to estimate the risk of infection by direct inhalation for a susceptible individual exposed to exhalations. Discriminating between the droplets falling to the ground and those remaining airborne, further estimates of the risks associated with fomite and airborne transmission routes are made possible. Simulations are based on an analytical model, recently developed by the authors, implementing the equations of droplet transport, evaporation, energy, and chemical composition. Turbulent dispersion is modeled with a random walk approach, whereas the droplets are released randomly within the exhalation time span and mouth/nose orifice cross section. Droplet transport within the respiratory cloud, a critical aspect in this kind of investigation, is evaluated by coupling the analytical model to the results of unsteady computational fluid dynamics simulations of the respiratory scenarios investigated, namely: mouth breathing, nose breathing, speaking, coughing, and sneezing. Results are compared to those obtained in a previous work where the respiratory cloud was simulated through a two-dimensional unsteady empirical model proposed by the authors based on momentum conservation. The multi-scale model provides better predictions of small droplet trajectories albeit at a higher computational cost. The risk maps provided constitute a useful tool for assessing prevention needs in controlling the spread of epidemics.

Numerical investigation on droplet lateral movement in post-dryout region

This paper presents a numerical study of droplet lateral movement and droplet deposition behaviors in the post-dryout region using the Discrete Particle Model (DPM) in ANSYS FLUENT. The investigation focuses on the analysis of droplet lateral movement, including single droplet trajectory, the statistic distribution and average value of droplets radial velocity, and droplet transverse between central and near wall regions. The single droplet trajectory shows the droplet dynamic behavior in the near wall region vividly. The droplet radial velocities are plotted as histogram to display the droplets statistic characteristics. The average value of droplets radial velocities toward the wall are plotted along the radial distance. In addition, to quantitatively display the size and evaporation effect on droplet deposition, three new parameters presenting overall movement behavior, i.e. droplet deposition mass flux, droplet deposition velocity as well as droplet entrainment velocity are introduced and derived from the CFD results. The comparison of results with varying initial droplet size indicates that droplets with smaller sizes exhibit higher average velocities toward the wall. A smaller initial droplet size leads to a higher deposition velocity, lower entrainment velocity, and thus a higher droplet deposition mass flux. The histogram of droplet radial velocities reveals that the droplet evaporation significantly reduces the number of droplets with small radial velocities toward the wall, resulting in a decrease in overall droplet deposition mass flux. Furthermore, through the comparison of overall movement behavior parameters, evaporation not only inhibits droplet motion toward the wall but also noticeably enhances droplet movement away from the wall. This inhibition effect on droplet deposition and enhancement effect on droplet entrainment become more pronounced with increasing evaporation intensity.

Spray Deposition and Drift as Influenced by Wind Speed and Spray Nozzles from a Remotely Piloted Aerial Application System

The phenomenal growth of remotely piloted aerial application systems (RPAASs) in recent years has raised questions about their impact on the off-target movement of plant protection products. The spray droplet spectrum is one of the important determining factors that govern droplet trajectories and off-target movement of pesticide particles. A field study was conducted to compare in-swath and downwind spray deposition on ground samplers from a 20 L RPAAS platform, equipped with three different nozzles, which provided fine, medium, and extra-coarse droplet spectra. A fluorescent dye was used as a tracer to determine spray deposition. Airborne spray droplets were measured at 10 and 20 m downwind. Downwind deposition measured on ground samplers showed that the extra-coarse nozzle received significantly fewer deposits than the medium or the fine nozzle. Similarly, the airborne deposition for the extra-coarse nozzle was significantly less compared to either the fine or the medium nozzle. Linear mixed effects modeling confirmed these results and showed that wind speed served as a covariate by refining the deposition differences among nozzles. Results indicated that spray drift from RPAAS platforms may be mitigated by using appropriate nozzles that produce larger droplet spectra. These results will provide aerial applicators with a better understanding of the best management practices to mitigate drift.

Focused deposition of levitated nanoscale Au droplets

We describe a method for depositing nanoscale liquid Au droplets, initially levitated in an ion trap in high vacuum, onto a remote substrate. A levitated Au nanosphere is melted, expelled from the trap, and maintained in the molten state, with a laser directed along the droplet trajectory, until it reaches the substrate and rapidly solidifies. During transit, the charged droplets are focused to a small region of the substrate with an electrostatic lens. After deposition, the substrate is removed from the vacuum chamber and imaged and analyzed by techniques such as electron microscopy and energy dispersive spectroscopy. Over 90% of launched particles are deposited on the substrate, and when the lens is focused, particles land in a region of diameter 120 μm after traversing a distance of 236 mm. Our technique is of value for analysis of materials prepared or processed while levitated that can be melted. Also, Au droplets may be useful as tracers for future experiments involving smaller projectiles or oriented solids.

Numerical study of the dynamic aggregation behaviors of oil droplets in the porous filter media consisting of basalt particles

Porous granular media based on the gravity-driven principle have been proven to be efficient for the separation of oil-water emulsions. However, the complexity of the relevant parameters and the intricate structure of porous media pose great challenges to the design and optimization of the separation process. In this study, the dynamic behavior of oil droplets within the porous structure was numerically analyzed based on the Euler-Euler model and the coupling of the two-phase flow and level set method. The oil-water separation efficiency and droplet trajectory were analyzed under different conditions, considering the deformation of the droplets, kinetic viscosity, and interactions among the droplets. The simulation results show the real-time movement, aggregation, and detachment of oil droplets within the porous filter. The results are useful for understanding the demulsification in a microscopic perspective and provide theoretical guidance for designing more efficient oil-water separation systems.

A multiphase flow model of water droplets dielectrophoretic-induced air dehumidification phenomena

Air humidity in indoor spaces plays a critical role in human comfort and health. Dehumidification systems are used for building humidity controls, but they can take significant energy consumption, especially in geographic locations with high outdoor humidity and warm climates. Consequently, there is a growing demand for innovative dehumidification processes that consume minimal energy. Dielectrophoretic air dehumidification represents one such promising approach. However, it has not garnered significant attention due to the absence of engineering models and simulation tools capable of evaluating its performance and limitations at large-scale airflows. A new numerical multiphase CFD model, which is also experimentally validated, is developed in a customized Reacting Foam solver based on OpenFOAM® version 9. The newly developed model seeks to decrease substantial energy consumption and lower costs by leveraging the dielectrophoretic phenomenon to regulate moisture levels in the air. The solver integrates a hybrid Eulerian-Lagrangian framework to track the droplet's trajectory and growth rate while solving the continuum equations for the moist air. An electrospray produces electrically charged droplets, which grow during their in-flight trajectories as water vapor condenses onto their surfaces. The role of electrostatic forces in promoting vapor condensation within a high-gradient electrical field is investigated, and the dielectrophoretic vapor nucleation process on charged water droplets is discussed. The CFD model was validated against results from the literature and from proof-of-concept experiments conducted by the authors, which showed a 2 % air dehumidification with a single electrospray and airflow rate of 5 cubic feet per minute. The simulation results indicated that augmenting the number of electrically charged spray droplets increased the dehumidification of the air to 25 %. The initial mean droplet diameter, the orientation of the injector and relative humidity significantly influence the assessment of dehumidification. Scaling up this approach to larger airflow volumes is identified as a potential future research direction.

Unsteady numerical simulations of aircraft icing based on the dynamic grid method

In this study, an unsteady numerical simulation method based on dynamic grids was established to solve unsteady aircraft icing processes. The dual-time step method was used to achieve the time advancement of the transient airflow and droplets fields. The droplets trajectory was calculated using the Euler method, which incorporates a supercooled large droplets model. The transient evolution of the water film and ice layer on the substrate surface was considered in the icing thermodynamic model. The accuracy of the unsteady method for ice-shape prediction was verified via comparison and analysis of numerical examples. Additionally, the rime and glaze ice formation processes were explored, and the coupling effects of ice horn growth and the air convective heat transfer coefficient, water collection coefficient, and water film flow on the substrate surface were studied. The ice shapes calculated by unsteady and quasi-steady methods were compared. The results indicated that the latter predicts a larger icing range than the former. Moreover, there may be more obvious distinctions between these two methods in predicting glaze ice.

Electrotaxis of Self-Propelling Artificial Swimmers in Microchannels.

Biological microswimmers alter their swimming trajectories to follow the direction of an applied electric field, exhibiting electrotaxis. We show that synthetic active droplet microswimmers also autonomously change swimming trajectories in microchannels, even undergoing "U-turns," in response to an electric field, mimicking electrotaxis. We exploit such electrotaxis, in the presence of an external flow, to robustly tune the swimming trajectory of active droplets between wall-adjacent, oscillatory, and channel centerline swimming. A general hydrodynamic model demonstrates that the electrotactic dynamics is governed by the electrical effects due to the swimmer's inherent surface charge, besides its motility, hydrodynamic wall interactions, and relative orientations of the electric field and imposed flow. Our study demonstrates a simple method for controlling active agents in complex geometries for microrobotic applications, like autonomous cargo delivery.

Low-Reynolds-number droplet motion in shear flow micro-confined by a rough substrate

A three-dimensional spectral boundary element method has been employed to compute for the dynamics of the droplet motion driven by shear flow near a single solid substrate with a rough surface. The droplet size is comparable with the surface features of the substrate. This is a problem that has barely been explored but with applications in biomedical research and heat management. This work numerically investigated the influences of surface roughness features, such as the roughness amplitude and wavelength, on the droplet deformation and velocities. We observe that a greater amplitude or wavelength leads to larger variations in droplet velocity perpendicular to the substrate. The droplet velocity along the substrate increases when the amplitude is reduced or when the wavelength increases. The effects of capillary number and viscosity ratios have also been studied. The droplet deformation and its velocity increases as we increase the capillary number, while the viscosity ratio shows a non-monotonic influence on the droplet behavior. The predicted droplet behaviors, including deformation, velocities, and trajectories, can provide physical insight, help to understand the droplet behavior in microfluidic devices without a perfectly smooth surface, and contribute in the design and operation of those devices.

Modeling the hundreds-of-nanoseconds-long irradiation of tin droplets with a 2 µm-wavelength laser for future EUV lithography

Abstract The properties of an extreme ultraviolet (EUV) source driven by hundreds-of-nanoseconds-long laser pulses of λ laser = 2 µm wavelength are investigated through radiation-hydrodynamic simulations. We show that single-pulse irradiation of 30 µm-diameter tin droplets can generate in-band energies ∼ 30 mJ directed in the 2π sr solid angle subtended by the collector mirror, yielding energies ∼100 mJ produced from 45 µm-diameter droplets. Time-integrated in-band EUV emission profiles, generated by taking Abel transforms of the local net in-band emissivity, reveal EUV source sizes in the axial (laser) direction × radial direction of ∼600 (1000) × 100 (150) µm2 for 30 (45) µm-diameter droplets. We find that approximately 74% of the total in-band emission is produced during the first half of the total propulsion distance irrespective of droplet size or laser intensity. Furthermore, we propose a one-dimensional analytical propulsion model to qualitatively explain the simulated droplet trajectory and to predict the time taken for the droplet to vaporize. These findings offer motivation for the development of high-power EUV sources based on single-pulse, hundreds-of-nanoseconds-long irradiation of tin droplets.

Modeling of Supercooled Large Droplet Physics in Aircraft Icing

This paper aims to investigate phenomena that are related to SLD conditions in aircraft icing including gravity, non-spherical droplets, droplet breakup and droplet splash using an in-house computational tool. The in-house computational tool involves four modules for the computation of the flow field, droplet trajectories, convective heat transfer coefficients and ice growth rates. Droplet trajectories are computed using the Lagrangian approach, while ice growth rates are calculated using the Extended Messinger Model. In order to extend the capabilities of the computational tool to include SLD-related phenomena, empirical models that represent SLD physics are implemented. An extensive study has been performed using MS317 and NACA0012 airfoils, that aims to bring out the relative importance of the SLD-related phenomena, particularly on water catch rates and ice formation. The results of the study pointed to some important new conclusions that may shed further light on SLD physics. For example, multiple droplet breakup has been observed under certain conditions and droplet breakup emerged as a more important effect than previously reported. It was also seen that droplet splash influences both the energy balance and the mass balance in the icing process, which has been shown to have an important effect on the final ice shape, especially for very large droplets.

Study on the impact of active intake air fluctuation on the performance and mass transfer of PEM Fuel Cell

Enhancing mass transfer is imperative for mitigating concentration polarization and thereby optimizing fuel cell performance. This study presents numerical investigation to explore the performance of a proton exchange membrane fuel cell, which involves implementation of actively controlled fluctuating mass fluxes at cathode inlet in order to achieve desirable mass transfer enhancement. The trajectories of liquid droplets within channel were predicted by employing volume of fluid method. The results revealed that the current density exhibits frequency-dependent fluctuations, aligning with input oscillations. A marginal increase in mean current density was observed with frequency amplified and the maximum power density with fluctuated flow increased by 3.9 % compared to that with steady flow inlet. A noteworthy and linear augmentation was evident with amplitude escalation. The mean current density surpassed 34.7 % of the steady current at the amplitude of 10. Beyond a frequency threshold of 1000 Hz, the fluctuating current density surpassed that of steady flow throughout the entire period, attributed to the time constant of gas transport within the gas diffusion layer. Moreover, fluctuation phenomenon of the pressure field within the fuel cell channel, which contributed to reinforced mass transfer and accelerated product alleviation in the region facing bipolar rib was identified during gas transport in the gas diffusion layer. Numerical simulations adopting the volume of fluid method revealed a heightened tendency for the disintegration and expulsion of liquid droplets in the channel attributable to fluctuating flow.

Sunflower-Inspired Superhydrophobic Surface with Composite Structured Microcone Array for Anisotropy Liquid/Ice Manipulation.

Precisely controlling the directional motion trajectories of droplets on anisotropic 3D functional surfaces has great application potential in self-cleaning, drug delivery, and droplet power generation, but it also faces huge challenges. Herein, inspired by the microcone structure in the heart of sunflowers, a nanoneedle-modified microcone array surface (NMAS)is reported. The surface is created using a combination of nanosecond laser direct engraving and electroforming and is subsequently fluorinated. Through programmable control of the laser spot, the geometric parameters and inclination angle of the microcone can be quickly and finely adjusted, thereby achieving precise control of the droplet bouncing trajectory. The results show that droplets can achieve programmable multiple bouncing behaviors on patterned functional surfaces, including gravity-defying hopping and directional water transport. It is worth noting that this functional surface has delayed freezing and anti-freezing effects. Furthermore, this functional surface has a wide range of potential applications, including surface self-cleaning, droplet capture, and droplet-based chemical microreactions, especially in the field of anti-icing operations. This opens up a new way for the directional transport of droplets on biomimetic functional surfaces.

AI-powered modular and general-purpose droplet processing system based on single-sided continuous optoelectrowetting chip

Single-sided continuous optoelectrowetting (SCOEW) is a versatile light-controlled digital microfluidic technology. However, the absence of automated algorithms for generating light patterns to manipulate droplets has constrained SCOEW chips to employing only pre-recorded sequences. This limitation hinders SCOEW platforms in effectively addressing common experimental challenges like droplet pinning. To overcome this issue, we have developed a set of algorithms for the automatic generation of droplet-driving light patterns. By integrating these algorithms with machine vision (using YOLOv3) to detect, locate, and classify droplets through video camera input, and employing a path-planning algorithm (A*) to optimize droplet trajectories, our system achieves intelligent functionalities. These include simultaneous manipulation of multiple droplets, automated merging based on color-coded droplet composition, obstacle avoidance, and resolution of potential droplet manipulation failures (such as droplet pinning). In a practical application, we implemented an intelligent loop-mediated isothermal amplification (LAMP) assay on the platform. This modular approach to droplet processing is easily adaptable to other SCOEW hardware, offering potential integration of customizable functionality. The result is a promising suite of portable tools for a variety of biochemical analysis application.

Film investigation of swirl-vane separator based on Euler grid approximation and coupled film method of Eulerian wall film and volume of fraction method

The movement of multiple liquid droplets within steam flow constitutes a commonplace and noteworthy phenomenon across a spectrum of disciplines, including environmental science, chemical engineering, and energy studies. To simulate the dynamic behavior of these droplets, the methodology of Euler grid approximation, along with the Eulerian wall film (EWF) coupled with the volume-of-fluid (VOF) method, was successfully employed to simulate the steam-liquid separation and liquid film processes within the swirl-vane separator. The trajectory of droplets within the gas phase field was constructed using the Euler grid approximation methodology, while the flow of liquid film formed by droplet–wall collision was modeled based on the coupled EWF and VOF liquid film model. The investigation of two-phase flow and liquid film flow within the swirl-vane separator under high temperature and pressure conditions was conducted utilizing the proposed model, with subsequent analysis of the pertinent characteristics of droplets and liquid film. Specifically, the thickness and velocity of the liquid film significantly increased with the increase in droplet mass flow rate, with larger droplets more prone to concentrate and form stable flow of thick liquid film. The study results may hold significant implications for the design, operation, and optimization of separators.

Modeling non-monotonic variation of plume angle with superheat index of flash boiling spray

There is an urgent need for modeling angles and widths of liquid jet with internal phase change, but existing semi-empirical models rely strongly on coefficient fitting and lack a thorough understanding of the additional phase-change physics. In the present work, we proposed a theoretical model to predict the non-monotonic variation of plume angle with the defined superheat index of flash boiling spray. Assuming that the plume angle is determined by the trajectories of tiny droplets in the perimeter of the spray, this model identifies the angle with the inverse tangent of the ratio of the streamwise and crosswise velocities of the tiny droplets. The streamwise velocity is determined by solving a one-dimensional two-phase flow within the channel, and the crosswise velocity is determined by modeling the burst of an equivalent bubble at the exit of the nozzle. Compared with the existing semi-empirical models, this model is free of fitting parameters, and it agrees well with the experimental data from a rectangular microchannel with discrepancies being sufficiently discussed. This model has the potential of being applied to modeling the plume angle of flash boiling sprays with different nozzle geometries in various atomization practices.

Pragmatic Prediction Model of Droplet Trajectory in a Turbine Cascade

Abstract Droplet deposition on a turbine cascade is important for the turbine system performance but its experimental analysis is difficult. Thus, the simulation of a droplet liquid phase in a gas flow field was studied to optimize turbine cascade design. However, the computational fluid dynamics (CFD)-based approach for such droplet problems requires enormous costs. Thus, the application of CFD simulation in the turbine blade's early-stage design is challenging, requiring iterative optimization for adjusting design with performance prediction. Therefore, this study proposed an analytical prediction method, having a reasonable cost and moderate accuracy, as an alternative to the whole multi-phase numerical simulation approach. The proposed method predicts droplet motion using the outline of the turbine blade and gas–liquid physical properties. Furthermore, the approach was validated by performing a three-dimensional Eulerian–Lagrangian simulation with low-pressure turbine blade T106. It was found that the droplet trajectories in the turbine cascade are governed by Stokes number. Furthermore, the streamlines of the gas flow were characterized by the shape of the turbine blade. The proposed model reproduced droplet trajectories obtained using CFD within an error margin of 10%. Consequently, it was concluded that the proposed analytical model is a promising approach to predict the droplet trajectory in a turbine cascade, obtained by the three-dimensional numerical simulation at a low cost.

Visualization of the Charging of Water Droplets Sprayed into Air.

Water droplets are spraying into air using air as a nebulizing gas, and the droplets pass between two parallel metal plates with opposite charges. A high-speed camera records droplet trajectories in the uniform electric field, providing visual evidence for the Lenard effect, that is, smaller droplets are negatively charged whereas larger droplets are positively charged. By analyzing the velocities of the droplets between the metal plates, the charges on the droplets can be estimated. Some key observations include: (1) localized electric fields with intensities on the order of 109 V/m are generated, and charges are expected to jump (micro-lightening) between a positively charged larger droplet and the negatively charged smaller droplet as they separate; (2) the strength of the electric field is sufficiently powerful to ionize gases surrounding the droplets; and (3) observations in an open-air mass spectrometer reveal the presence of ions such as N2+, O2+, NO+, and NO2+. These findings provide new insight into the origins of some atmospheric ions and have implications for understanding ionization processes in the atmosphere and chemical transformations in water droplets, advancing knowledge in the field of aerosol science and water microdroplet chemistry.

Interplay of chemotactic force, Péclet number, and dimensionality dictates the dynamics of auto-chemotactic chiral active droplets.

In living and synthetic active matter systems, the constituents can self-propel and interact with each other and with the environment through various physicochemical mechanisms. Among these mechanisms, chemotactic and auto-chemotactic effects are widely observed. The impact of (auto-)chemotactic effects on achiral active matter has been a recent research focus. However, the influence of these effects on chiral active matter remains elusive. Here, we develop a Brownian dynamics model coupled with a diffusion equation to examine the dynamics of auto-chemotactic chiral active droplets in both quasi-two-dimensional (2D) and three-dimensional (3D) systems. By quantifying the droplet trajectory as a function of the dimensionless Péclet number and chemotactic strength, our simulations well reproduce the curling and helical trajectories of nematic droplets in a surfactant-rich solution reported by Krüger et al. [Phys. Rev. Lett. 117, 048003 (2016)]. The modeled curling trajectory in 2D exhibits an emergent chirality, also consistent with the experiment. We further show that the geometry of the chiral droplet trajectories, characterized by the pitch and diameter, can be used to infer the velocities of the droplet. Interestingly, we find that, unlike the achiral case, the velocities of chiral active droplets show dimensionality dependence: its mean instantaneous velocity is higher in 3D than in 2D, whereas its mean migration velocity is lower in 3D than in 2D. Taken together, our particle-based simulations provide new insights into the dynamics of auto-chemotactic chiral active droplets, reveal the effects of dimensionality, and pave the way toward their applications, such as drug delivery, sensors, and micro-reactors.

Dynamic control of active droplets using light-responsive chiral liquid crystal environment

Microscopic active droplets are of interest since they can be used to transport matter from one point to another. In this work, we demonstrate an approach to control the direction of active droplet propulsion by a photoresponsive cholesteric liquid crystal environment. The active droplet represents a water dispersion of bacterial Bacillus subtilis microswimmers. When placed in a cholesteric, a surfactant-stabilized active droplet distorts the local director field, producing a point defect-hedgehog, with fore-aft asymmetry, and allows for the chaotic motion of the bacteria inside the droplet to be rectified into directional motion. When the pitch of the cholesteric confined in a sandwich-like cell is altered by light irradiation, the droplet trajectory realigns along a new direction. The strategy allows for a non-contact dynamic control of active droplets trajectories and demonstrates the advantage of orientationally ordered media in control of active matter over their isotropic counterparts.