Droplet Trajectories Research Articles

Droplet Transportation on Liquid-Infused Asymmetrically Structured Surfaces by Mechanical Oscillation and Viscosity Control.

The transportation of droplets on solid surfaces has received significant attention owing to its importance in biochemical analysis and microfluidics. In this study, we propose a novel strategy for controlling droplet motion by combining an asymmetric structure and infused lubricating oil on a vibrating substrate. The transportation of droplets with volumes ranging from 10 to 90 μL was realized, and the movement speed could be adjusted from 1.45 to 10.87 mm/s. Typical droplet manipulations, including droplet transportation along a long trajectory and selective movement of multiple droplets, were successfully demonstrated. Through experimental exploration and theoretical analysis, we showed that the adjustment of droplet transport velocity involves an intricate interaction among the Ohnesorge number, droplet volume, and input amplitude. It can potentially be used for the more complex manipulation of liquid droplets in microfluidic and biochemical analysis systems.

Analysis of Grinding Flow Field under Minimum Quantity Lubrication Condition

The flow field around the grinding wheel prevents grinding fluid from entering the grinding area, which deteriorates machining conditions and reduces the quality of the workpiece. MQL (Minimum Quantity Lubrication) grinding uses compressed gas to improve the ability of the grinding fluid to pass through the flow field of the grinding wheel so that a small amount of the grinding fluid can meet the cooling and lubrication requirements and reduce the cost of using grinding fluid. In this study, we investigated the flow field of grinding wheels under MQL conditions and obtain the rules that influence factors such as grinding fluid flow rate, grinding wheel linear speed and compressed gas pressure affect the flow rate of grinding fluid. The simulation method was used to simulate the flow field of the grinding wheel and the trajectory of the grinding fluid droplets. The simulation results show that these factors are important ones affecting the effective flow rate of grinding fluid. Meanwhile, the experimental results verify that these factors have the same influence pattern on the effective flow rate and grinding temperature.

Hammerstein–Wiener Model Identification for Oil-in-Water Separation Dynamics in a De-Oiling Hydrocyclone System

To reduce the environmental impact of offshore oil and gas, the hydrocarbon discharge regulations tend to become more stringent. One way to reduce the oil discharge is to improve the control systems by introducing new oil-in-water (OiW) sensing technologies and advanced control. De-oiling hydrocyclones are commonly used in offshore facilities for produced water treatment (PWT), but obtaining valid control-oriented models of hydrocyclones has proven challenging. Existing control-oriented models are often based on droplet trajectory analysis. While it has been demonstrated that these models can fit steady-state separation efficiency data, the dynamics of these models have either not been validated experimentally or only describe part of the dynamics. In addition to the inlet OiW concentration, they require the droplet size distribution to be measured, which complicates model validation as well as implementation. This work presents an approach to obtain validated nonlinear models of the discharge concentration, separation efficiency, and discharge rate, which do not require the droplet size distribution to be measured. An exhaustive search approach is used to identify control-oriented polynomial-type Hammerstein–Wiener (HW) models of de-oiling hydrocyclones based on concentration measurements from online OiW monitors. To demonstrate the effectiveness of this modeling approach, a PI controller is designed using the Skogestad internal model control (SIMC) tuning rules to control the discharge OiW concentration directly. The identification experiment emulates an offshore PWT system with installed OiW monitors, which is realistic with the legislative incentive to include online OiW discharge measurements. The proposed approach could enable the application of OiW-based control on existing offshore PWT facilities, resulting in improved de-oiling performance and reduced oil discharge.

Framework reinforced orderly-woven superhydrophobic metal–carbon composites for efficient emulsion separation in harsh environments

The primary barrier to the widespread use of super-wetting materials is the surface's limited resistance to physical damage, which leads to poor mechanical qualities. In this study, framework-reinforced orderly-woven superhydrophobic metal spiral coil-carbon fibers composites (SMSC-CFsC) with a durable uniform micro-structure were prepared by nested carbon fibers into metal spiral coils cleverly and woven them into a three-dimensional porous material innovatively. The separation purity of the prepared metal–carbon composites on several commonly used industrial lubricating oil emulsions was better than 99.90 % and the flux was greater than 1000 L/m2h. More significantly, computational fluid dynamics was used to establish a simulation model for emulsion separation that revealed the real-time dynamic motion trajectory and volume changes of water droplets. Additionally, even after high-temperature, compression, wear, and corrosion experiments, it still showed dependable separation purity and stable flux. As a result, it has been demonstrated that the proposed metal–carbon composite has a long oil–water separation service life in harsh environments and has great potential for developing efficient and durable emulsion separation materials.

Droplet Rolling Transport on Hydrophobic Surfaces Under Rotating Electric Fields: A Molecular Dynamics Study.

Driving droplets by electric fields is usually achieved by controlling their wettability, and realizing a flexible operation requires complex electrode designs. Here, we show by molecular dynamics methods the droplet transport on hydrophobic surfaces in a rolling manner under a rotating electric field, which provides a simpler and promising way to manipulate droplets. The droplet internal velocity field shows the rolling mode. When the contact angle on the solid surface is 144.4°, the droplet can be transported steadily at a high velocity under the rotating electric field (E = 0.5 V nm-1, ω = π/20 ps-1). The droplet center-of-mass velocities and trajectories, deformation degrees, dynamic contact angles, and surface energies were analyzed regarding the electric field strength and rotational angular frequency. Droplet transport with a complex trajectory on a two-dimensional surface is achieved by setting the electric field, which reflects the programmability of the driving method. Nonuniform wettability stripes can assist in controlling droplet trajectories. The droplet transport on the three-dimensional surface is studied, and the critical conditions for the droplet passing through the surface corners and the motion law on the curved surface are obtained. Droplet coalescence has been achieved by surface designs.

Effect of film properties on droplet impact on suspended films

Understanding the dynamics and underlying mechanisms of droplet impact on suspended films is crucial for controlling droplet motion. In this study, we conducted experiments to investigate droplet impact on suspended films and examined the typical phenomena and corresponding Weber number domains. We explored the effects of changing sodium dodecyl sulfate (SDS) concentration and glycerol content on the surface tension and dynamic viscosity of the films. Additionally, we elucidated the characteristics of film deformation and droplet trajectory. An energy analysis was performed, considering the droplet kinetic energy (Ek0), surface energy increment of the film (ΔEfs), and viscous dissipation (Evis). The results demonstrate that as the SDS concentration increases, the upper critical Weber number (Wecru) between bouncing and passing decreases, while the lower critical Weber number (Wecrl) between coalescence and bouncing first decreases and then increases. For droplet bouncing, increasing the SDS concentration makes the films more susceptible to deformation, whereas increasing the glycerol content enhances film rigidity. Moreover, increasing the SDS concentration and glycerol content leads to higher energy losses, resulting in a reduction in the maximum bouncing height (hbdmax). Regarding droplet passing, the passing velocity (Vpd) increases with increasing SDS concentration. For films without SDS, Vpd increases with increasing glycerol content, while for films with SDS, Vpd decreases. The different impact modes are categorized based on the dimensionless energy parameter E* = Ek0/(ΔEfs + Evis). We have successfully predicted the critical height thresholds (Hd0crl and Hd0cru) and established a relationship of We* = f (Re*, Bo*) that aligns well with experimental results.

Immiscible thermoplastic polymer blends with alternative layered encapsulation structure: Modeling and processing

“Encapsulation” is a common phenomenon during polymer melting processing, which supplied great opportunities for fabricating high-performance polymer products. In this work, two immiscible polymers, high density polyethylene (HDPE) and polyketone (PK), were used for preparing polymer blends with viscous encapsulation structures. Moreover, the effects of interfacial tension, viscosity ratio, and shear rate on the phase morphology evolution of HDPE/PK blends were investigated by numerical simulation and high-pressure capillary extrusion (HCE). Meanwhile, the formation mechanisms of HDPE/PK alternating layered encapsulation structure were explored by tracking the trajectory of PK droplets via numerical simulation. The results show that an alternative layered encapsulation structure of HDPE/PK was formed under the shear rate from 50 to 1000 s−1 with the interfacial tension over 1.35 mN/m. Moreover, it was found that the revealed mechanism in HCE was also applicable to the injection molding process. Therefore, this unique “microstructure-intelligent prediction-control” strategy of polymer blends is suitable for the industrial processing of high-performance polymer blends for desired applications.

A two-dimensional model for jet splashing rainfall intensity distribution in dam discharge based on laboratory experiments

Flood discharge atomization is a phenomenon of water droplets and mist diffusion caused by dam discharge, which brings heavy rainfall around the dam. The unnatural rainfall is harmful to the safe operation of hydropower stations and the stability of slopes. Jet splashing is the most important factor in the formation of flood discharge atomization. The splashing rainfall intensity and diffusion region are highly dependent on the jet impingement conditions. In this study, a two-dimensional splashing model is derived that describes the splashing rainfall distribution when a jet impinges on a plunge pool surface in terms of the jet impingement conditions. Given the close relationship between the splashing rainfall intensity distribution and the motion trajectories of droplets, it is hypothesized that certain droplet trajectories can accurately represent the distribution of rainfall intensity. The characteristic ejection angle of splashing droplets and the splashing diffusion coefficient are introduced to estimate the characteristic trajectories of droplets. Experimental data from laboratory tests are used to estimate the parameters of the splashing model. The current predictions are compared with the data from laboratory tests and prototype observations. The results suggest that the model accurately predicts the relative rainfall intensity at the upper region of the predicted curves, which corresponds to approximately 1/10 of the total height of the ideal parabola.

Programmable Droplet Bouncing on Bionic Functional Surfaces for Continuous Electricity Generation

AbstractThe natural phenomenon of droplets bouncing on various surfaces holds remarkable potential for applications like water transportation, self‐cleaning, antifreezing, etc. However, achieving precisely controlled patterned droplet bouncing on functional surfaces with accurately controlled factors like bouncing velocity and trajectory in three dimensions remains a formidable challenge. In this context, a concept of bionic hydrophobic functional surfaces composed of mushroom‐like microstructures is introduced. These microstructures are crafted using the projection microstereolithography (PµSL) based 3D printing technique, subsequently coated with a hydrophobic spray. By finely adjusting the geometric attributes and inclination angles of these micromushrooms, the ability is gained to meticulously manipulate the bouncing velocity and trajectory of water droplets. The most optimal performance is demonstrated by a droplet exhibiting a maximal jumping distance and height respectively of 2.5 and 7.1 mm with 50° inclined micromushrooms. Notably, these specially designed micromushrooms orchestrate diverse behaviors in droplet bouncing, encompassing patterned bouncing, antigravity jumps, and directional water transportation. Additionally, the functional surface's adaptable self‐cleaning capability facilitates the harnessing of energy from rainfall on large surfaces, offering potential applications in realms, such as self‐cleaning mechanisms, droplet capture, water conveyance, and clean energy generation.

Effect of electric field intensity on droplet fragmentation in oil-in-water-in-oil (O/W/O) emulsions: A molecular dynamics study

Oil-in-water-in-oil (O/W/O) emulsions commonly exist in crude oil treatment, food processing, pharmaceuticals, and cosmetics; however, few related studies have been conducted. To reveal the fragmentation mechanism of droplets in O/W/O emulsions, the behavior of complex droplets under different electric field intensities was investigated using a molecular dynamics method. It was found that the deformation of the intermediate phase (water) and the internal phase (hexane) increased dramatically with the electric field intensity, and the two phases separated when E ≥ 1.1 V∙nm−1, indicating that the complex droplets had been simplified into two simple liquids. Observation of the droplet trajectory shows that the deformation of the internal phase was smaller than that of the intermediate phase, and the internal oil droplet moved toward the high electric potential position. Furthermore, we elaborated the interactions between different phases at the molecular level by means of weak interactions and radial distribution function analysis, and their magnitudes were as follows: Cl− - Na+ > Na+ - Water > Water - Hexane. The electric fragmentation mechanism of the complex droplets was investigated, which provides theoretical guidance for the treatment of O/W/O emulsions by electrodehydration.

Performance Improvement of Kerosene Fuelled Scramjet Combustor Through Modified Fuel Injection - A Cfd Study

Full scale kerosene fuelled scramjet combustor of a hypersonic air-breathing vehicle is numerically explored for two different fuel injection systems. A commercial software CFXTASCflow has been used for the reacting flow computation within the combustor. Three dimensional Navier-Stokes equations are solved along with k-ε turbulence model to analyse the flow field. Eddy Dissipation Model (EDM) with fast rate chemical kinetics is used for combustion modeling. Lagrangian Particle Tracking Method (LPTM) has been used to simulate the trajectory of the kerosene droplets. Kerosene is injected from the struts. Reacting flow simulations have been carried out for the fuel equivalence ratio of 1.0. The overall flow characteristics in the combustor are presented through the distribution of various thermochemical parameters at different cross sections. Kerosene which is injected in liquid phase completely vaporizes within the combustor. Considerable improvement in the performance in terms of thrust and combustion efficiency is observed with the modified fuel injection system.

Effect of the Weber number on the coalescence of relatively moving droplets in an electric field: A molecular dynamics study

Herein, the movement of two non-centric droplets in hexane was studied using a molecular dynamics method to understand the microscopic coalescence mechanism of droplets with an initial velocity in an electric field. Unlike previous studies, this study overcame the limitations in experimental conditions and conventional analytical tools to understand the mechanism of droplet coalescence under the coupling effect of electric and velocity fields at the molecular level. This has implications for the development of inkjet printing technology and microfluidics. The analysis of droplet trajectories and centroid distances revealed that the Weber number can be divided into three ranges according to the three modes of droplet behaviour: incomplete coalescence, complete coalescence and non-coalescence. At a low Weber number (We < 1), the inhomogeneous distribution of ions in droplets causes the fragmentation of droplets that are not completely coalesced. The interaction energy and weak interaction analysis shows that hydrogen bonds between water molecules are the strongest, followed by van der Waals interactions, which is very prominent in the first and second coordination layers. Hexane and water molecules exhibit van der Waals interactions. As the Weber number increases from 0 to 5, the total interaction energy between two droplets increases, and the number of hydrogen bonds increases. A decrease in the total interaction energy, number of hydrogen bonds, radial distribution function and coordination number in a single droplet shows that increasing the Weber number loosens the single droplet and simultaneously promotes the coalescence of two droplets. However, when We > 5, the total interaction energy and number of hydrogen bonds between droplets are zero, and the two droplets do not merge. This is because the angle between the electric field and centreline of the droplets is so large that the electric field cannot horizontally act upon the droplets. This study provides a fundamental guide for studying the mechanism of droplet coalescence under the coupling effect of electric and flow fields.

Thermodynamic properties of oil droplets in oil-injected screw compressors and their influencing factors

As a typical positive displacement compressor, screw compressors are widely used in various industrial fields with a fast-growing trend, especially with the boost of the application of oil injection technology. The oil injection process inside the screw compressor is complicated and difficult to be captured by direct observation experiment, so is the accompanying heat transfer process. On the basis of single particle dynamics, the Lagrangian method is used to establish a spatial kinematic model of oil droplets in the simplified chamber of an oil-injected screw compressor, the droplet trajectory is analyzed. The relationship between the oil droplet diameter, injection velocity and temperature and the free flight time of oil droplets in the compression chamber is obtained. In order to investigate the liquid-gas two-phase flow after oil injection, the Level Set Method is adopted to simulate the oil distribution in the compression chamber. The impacting process of oil droplet on a hot wall is simulated, the influence of oil injection parameters such as the injection speed, temperature difference, droplet diameter, and the initial velocity on the heat transfer between oil droplets and hot gas and the wall is analyzed theoretically. For the simulated cases studied, the oil droplet diameter has the greatest effect on the gas-liquid heat transfer, while the temperature difference plays a greater role in the heat transfer between the oil droplet and the hot wall than other factors. The research in this paper helps to further understand and accurately predict the heat transfer process in oil-injected screw compressors, which is important for improving the energy efficiency of screw compressor.

The transport performance of condensate droplets on inclined superhydrophobic surfaces

Coalescence-induced droplet jumping on superhydrophobic surfaces has significant potential for various applications, such as enhanced condensation, water harvesting, self-cleaning, and thermal management of electronic devices. Existing research focuses primarily on the coalescence and jumping of two or more droplets on the horizontally placed superhydrophobic surface, but the transport behavior of condensate droplets caused by coalescence-induced jumping on the inclined superhydrophobic surface is insufficiently understood. In this work, we investigate the impact of the surface inclination angle on the dynamic behavior of condensate droplets and derive the relationship between the transport distance, transport height, jumping direction of droplets, and the surface inclination angle. Additionally, we establish a droplet motion equation to describe the trajectory of droplets after they jump off the surface. Furthermore, we demonstrate the phenomenon of multi-hop jumping on the inclined superhydrophobic surface, which can increase the droplet transport distance, and the established mathematical model can better predict the multi-hop jumping transport distance. This work exposes the effect of superhydrophobic surface inclination angle on droplet dynamics and droplet directional transport performance, which has significant implications for the application of droplet jumping.

RETRACTED: Influence of indoor relative humidity on the number concentration, size distribution, and trajectory of sneeze droplets: Effects on social distancing guidelines

RETRACTED: Influence of indoor relative humidity on the number concentration, size distribution, and trajectory of sneeze droplets: Effects on social distancing guidelines

On a model-based approach to improve intranasal spray targeting for respiratory viral infections

The nasopharynx, at the back of the nose, constitutes the dominant initial viral infection trigger zone along the upper respiratory tract. However, as per the standard recommended usage protocol (“Current Use”, or CU) for intranasal sprays, the nozzle should enter the nose almost vertically, resulting in sub-optimal nasopharyngeal drug deposition. Through the Large Eddy Simulation technique, this study has replicated airflow under standard breathing conditions with 15 and 30 L/min inhalation rates, passing through medical scan-based anatomically accurate human airway cavities. The small-scale airflow fluctuations were resolved through use of a sub-grid scale Kinetic Energy Transport Model. Intranasally sprayed droplet trajectories for different spray axis placement and orientation conditions were subsequently tracked via Lagrangian-based inert discrete phase simulations against the ambient inhaled airflow field. Finally, this study verified the computational projections for the upper airway drug deposition trends against representative physical experiments on sprayed delivery performed in a 3D-printed anatomic replica. The model-based exercise has revealed a new “Improved Use” (or, IU) spray usage protocol for viral infections. It entails pointing the spray bottle at a shallower angle (with an almost horizontal placement at the nostril), aiming slightly toward the cheeks. From the conically injected spray droplet simulations, we have summarily derived the following inferences: (a) droplets sized between 7–17 μm are relatively more efficient at directly reaching the nasopharynx via inhaled transport; and (b) with realistic droplet size distributions, as found in current over-the-counter spray products, the targeted drug delivery through the IU protocol outperforms CU by a remarkable 2 orders-of-magnitude.

Superhydrophobic wire-cotton woven porous material with excellent durability for emulsion separation

Superhydrophobic materials have been extensively investigated for their ability to separate oil/water mixtures, but their fragile durability has limited further development in this field. In this study, a durable superhydrophobic wire-cotton-based material (SWCM) was prepared by weaving metal wire and cotton fiber and modifying it with a mixed poly(vinyl phenol) (PVPh)/1,3-phenylene bisoxazoline (PBO) solution, which exhibits both macro-frame and micro-aperture. The SWCM demonstrates remarkable separation efficiency (greater than99.98 %) for a variety of water-in-oil emulsions using only gravity drive. More importantly, computational fluid dynamics (CFD) simulations were conducted to investigate the separation mechanism of SWCM, revealing dynamic trajectory and volume changes of water droplets in real-time. Moreover, the micro-aperture, protected by the macro-frame, can withstand hundreds of impacts and abrasions and still maintain reliable separation efficiency. Under the encapsulation of micro-apertures, the macro-frame exhibits excellent corrosion resistance and can maintain stable superhydrophobicity even after long-term immersion in different harsh solutions. Due to its excellent durability, the SWCM can maintain a long service life in oil–water separation in complex environments. Therefore, the presented SWCM has great potential in the development of durable and efficient materials for emulsion separation.

From Microscopic Droplets to Macroscopic Crowds: Crossing the Scales in Models of Short-Range Respiratory Disease Transmission, with Application to COVID-19.

Short-range exposure to airborne virus-laden respiratory droplets is an effective transmission route of respiratory diseases, as exemplified by Coronavirus Disease 2019 (COVID-19). In order to assess the risks associated with this pathway in daily-life settings involving tens to hundreds of individuals, the chasm needs to be bridged between fluid dynamical simulations and population-scale epidemiological models. This is achieved by simulating droplet trajectories at the microscale in numerous ambient flows, coarse-graining their results into spatio-temporal maps of viral concentration around the emitter, and coupling these maps to field-data about pedestrian crowds in different scenarios (streets, train stations, markets, queues, and street cafés). At the individual scale, the results highlight the paramount importance of the velocity of the ambient air flow relative to the emitter's motion. This aerodynamic effect, which disperses infectious aerosols, prevails over all other environmental variables. At the crowd's scale, the method yields a ranking of the scenarios by the risks of new infections, dominated by the street cafés and then the outdoor market. While the effect of light winds on the qualitative ranking is fairly marginal, even the most modest air flows dramatically lower the quantitative rates of newinfections.

Directional self-motion of nanodroplets driven by controlled surface wetting gradients

The self-propelled movement of droplets is essential for numerous applications. To obtain a microscopic insight on the self-propelling dynamics of droplets, droplet movement under different surface wettability gradients needs to be studied. In this study, a method is proposed to control the droplet motion using a continuous surface wettability gradient via molecular dynamics simulation. The effects of single gradient, continuous gradient, and nonlinear complex wetting gradient on the self-propelling dynamics of droplets are investigated. The results show that the droplet motion can be driven in a directional way by carefully designing the wetting gradient surface. On a single wetting gradient surface, the droplet speed increases with the wettability gradient. On a linear continuous wetting gradient surface, the droplet trajectory is consistent with the gradient direction. On a complex wetting gradient surface, the droplet trajectory can be a circle, a sine function curve, or a U-shaped curve. By ingeniously designing the wetting gradient surface, the proposed method for the self-propelled movement of droplets can be extended to more interesting paths. This study presents a microscopic perspective on the directional self-propelled movement of droplets on surfaces with wettability gradient and provides guidance for the application of droplet directional transport.

Kinetic analysis of a freely rising droplet in water during collision with the horizontal wall

An in-depth analysis of the kinetics of the collision between freely rising oil droplets in water in the range of Re = 4.64–463.3 was carried out to understand the physical mechanism and detailed kinetics of the interaction between the oil droplets and wall. The results show that when oil droplets with Re ≥ 27.8 hit the wall vertically at terminal velocities, a “dimple-like” water film is formed near the wall, which significantly affects the pressure distribution within the water film, the oil–water interfacial shear force, and forces on oil droplet. A coupled model describing water film thickness and pressure accurately captures the kinetic behavior of water film drainage near the wall. The film-induced force based on lubrication theory can reasonably predict the motion trajectory of oil droplets near the wall and dominate the motion of oil droplets colliding with the wall. The motion phase diagram with (Re, We) as the control parameter was established to quickly identify the droplet motion rule under different liquid–liquid density ratios.