Droplet Position Research Articles

Discrete dynamical model for the hydrodynamic analog of a quantum mirage

Recently discrete dynamical models of walking droplet dynamics have allowed for fast numerical simulations of their horizontal chaotic motion and consequently the long-time statistical distribution of the droplet position. We develop a discrete model for walkers on an elliptical corral with two dominant eigenmodes. These eigenmodes are excited periodically with each having random, but correlated, weights. At each iteration the model computes the horizontal propulsion of the droplet due to impacts with the fluid bath. The propulsion is calculated based on the interaction of the droplet and the wavefield produced by the eigenmode excitations, with the droplet being propelled perpendicular (rather than parallel) to the wave gradient. We record the long-time statistics, and remarkably for a dynamical system with some non-physical assumptions, they are qualitatively similar to that of experiments.

Optimizing contact angle changes for droplet actuation by optoelectrowetting (OEW): A numerical multi-parameter analysis

With the transition of fluid-capillary-based “Lab on a chip 1.0″ concepts in analytical chemistry to “Lab on a chip 2.0″ approaches relying on distinct fluid droplets (“digital microfluidics”, DMF), the need for reliable methods for droplet actuation has increasingly come into focus. One possible approach is based on “electrowetting on dielectric” (EWOD). This technique has the disadvantage that any possible desired later positions of the droplets on the chip have to be defined prior to chip realization because one of the EWOD electrode layers has to be structured accordingly. “Optoelectrowetting” (OEW) goes a step further in the sense that the later droplet positions do not have to be known before, and none of the electrode layers has to be structured. Instead, the electrical parameters of the layer sequence can be altered locally by an impinging (and movable) light spot. Although some research groups have succeeded in demonstrating OEW actuation of droplets, the optimization of the relevant parameters of the layer sequence and the droplet – at least half a dozen parameters altogether – is tedious and not straight-forward. In this contribution, for optimization purposes, the equations governing OEW are revisited and altered again, e.g., by numerical implementation of the experimentally well-known saturation of the contact angle change. Additionally, a Nelder-Mead algorithm is applied to find the parameters, on which the optimization has to focus to maximize contact angle changes and, thus, mechanical forces on the droplets. The numerical investigation yields diverse results, e.g., the finding that the droplet’s contact area on the dielectric layer has a strong influence on the contact angle change and the question whether the droplet is pulled or pushed. Moreover, the interplay between frequency and amplitude of the applied rectangular alternate voltage is important for optimization.

Sensing the Positions of Multi Droplets on a Piezoelectric Substrate Using a Smartphone Based on CIELab Color Model

A method for simultaneously sensing positions of multi droplets on a piezoelectric substrate was presented. A double D-value algorithm was presented to distinguish target droplets using CIELab color model. An application soft (app) was developed to sense positions of target droplets. In order to verify the presented method, black ink solution droplets on a 128°-YX LiNbO3 substrate were used to demonstrate for sensing droplets position. Results show that different number of target droplets can be distinguished and their positions can be simultaneously sensed. As an application, a 5 micro-liters black ink solution droplet was driven on the piezoelectric substrate by surface acoustic wave. Its position was sensed and its movement path was analyzed using developed app. In the meantime, the transporting velocity of the droplet was obtained, of which value is 0.33 mm/s from 6th second to 7th second at 27.5 dBm electric signal power.

Flow and Heat-Transfer Characteristics of Droplet Impingement on Hydrophilic Wires.

It is a common phenomenon that droplets collide with wires in industrial production, and their flow and heat-transfer behavior significantly impact the production efficiency. This article presents an experimental and numerical study on the impact of pure water droplets on hydrophilic stainless-steel wires. The dynamic behavior and solid-liquid heat-transfer law of droplet impacting the wire are emphatically analyzed. The impact position of the droplets has a significant effect on their morphology. Under the condition of low Weber number (We), eccentric impacts tend to cause droplets to separate from the wire. Additionally, both We and wire/droplet size ratio have noticeable effects on the droplet morphology. The smaller the We, the larger the wire/droplet size ratio, and the easier it is for droplets to be captured by wires. Conversely, as We increases and the wire-to-droplet size ratio decreases, some droplets become detached from the wire, primarily exhibiting a single-film falling mode. Furthermore, the impact morphology of droplets is influenced by the Ohnesorge number (Oh). The higher the Oh, the more inclined the droplet to develop a double-film falling mode. There is obvious field synergy in the process of droplet impacting on wire. The maximum heat flux is located at the three-phase contact line, while the minimum heat flux is observed at the bubble interface. The impact position of droplets influences the temperature distribution, although its impact on the magnitude of temperature variation is minimal.

Magnetically Actuated Surface Microstructures for Efficient Transport and Tunable Separation of Droplets and Solids

Efficient transportation of droplets (≈101–102 μL) and small solid objects (≈101–102 mm3) have important applications in many fields, such as microfluidics, lab‐on‐a‐chip devices, drug delivery, etc. A novel multifunctional surface consisting of a periodic array of micro‐lamellae from a soft magnetoactive elastomer on a plastic substrate is reported for these purposes. The physical origin of the propulsion is the bending of soft magnetic lamellae in nonuniform magnetic fields, which is also observed in uniform magnetic fields. The magnetoactive surface is fabricated using a facile and rapid method of laser ablation. The propulsion of items is realized using a four‐pole rotating magnet. This results in a cyclic lamellar fringe motion over the microstructured surface and brings an advantage of easy reciprocation of transport by rotation reversal. Two modes of object transportation are identified: “pushing” mode for precise control of droplet and solid positioning and “bouncing” mode for heavier solid objects transportation. A water droplet of 5 μL or a glass sphere with a 2.1 mm diameter can be moved at a maximum speed of 60 mm s−1. The multifunctionality of the proposed mechatronic platform is demonstrated on the examples of selective solid–liquid separation and droplet merging.

Dynamics of droplets entering ultrasonic standing wave field at different angles

We, herein, present dynamic behaviors of droplets entering an ultrasonic standing wave field (19 800 Hz) at different angles. In experiments, droplets’ motion is recorded by using a high-speed camera, and an in-house Python program is used to obtain droplet positions and morphological characteristics as functions of time. The experimental results indicate that when the sound intensity is lower than the instability intensity and higher than the levitation intensity, the vertically falling droplet will oscillate up and down based on the equilibrium position. Although the oscillation amplitude decays from 0.52Tl to 0.01Tl (Tl = λ/2, λ is the wavelength) under the action of viscous resistance, the oscillation frequency of the droplet remains unchanged. Meanwhile, as the droplet’s position oscillates, the acoustic radiation force on the droplet also periodically fluctuates, resulting in the acoustically forced oscillation of the droplet shape. In addition, when the droplet enters the sound field with a horizontal tilt angle θ of 15°, it undergoes a V-shaped translational motion, first descending and then ascending. As the sound pressure amplitude increases, the rebound position of the droplet advances. When the sound pressure amplitude reaches the instability value (7900 Pa), the droplet undergoes right-hand and left-hand disintegration during its descent and ascent, respectively. This instability is due to the acoustic radiation pressure distribution and the droplet’s V-shaped trajectory. This work comprehensively discussed the complex motion of moving droplets in the acoustic standing wave field, which may inspire revealing the spray motion in the liquid engine with high-intensity resonance.

Modeling Multivariate Spray Characteristics with Gaussian Mixture Models

With the increasing demand for efficient and accurate numerical simulations of spray combustion in jet engines, the necessity for robust models to enhance the capabilities of spray models has become imperative. Existing approaches often rely on ad hoc determinations or simplifications, resulting in information loss and potentially inaccurate predictions for critical spray characteristics, such as droplet diameters, velocities, and positions, especially under extreme operating conditions or temporal fluctuations. In this study, we introduce a novel approach to modeling multivariate spray characteristics using Gaussian mixture models (GMM). By applying this approach to spray data obtained from numerical simulations of the primary atomization in air-blast atomizers, we demonstrate that GMMs effectively capture the spray characteristics across a wide range of operating conditions. Importantly, our investigation reveals that GMMs can handle complex non-linear dependencies by increasing the number of components, thereby enabling the modeling of more complex spray statistics. This adaptability makes GMMs a versatile tool for accurately representing spray characteristics even under extreme operating conditions. The presented approach holds promise for enhancing the accuracy of spray combustion modeling, offering an improved injection model that accurately captures the underlying droplet distribution. Additionally, GMMs can serve as a foundation for constructing meta models, striking a balance between the efficiency of low-order approaches and the accuracy of high-fidelity simulations.

Flexible Patterned Electrohydrodynamic Jet Printing Using Orthogonal Deflection Electrodes.

Electrohydrodynamic jet (E-Jet) printing technology provides unmatched advantages in the fabrication of patterned micro/nanostructures. However, the rapid jets generated during printing can lead to localized droplet accumulation on complex structures due to the relatively slow motion control achieved with motorized translation stages, resulting in distorted patterns. To address this challenge, we introduce two jet-deflecting electrodes orthogonally placed on each other, which can rapidly change the electric field in the vicinity of the jet and thus flexibly adjust the flight trajectory of the fast jet to avoid the region where droplets have been deposited. In this way, the jet droplets are precisely controlled to generate high-fidelity microstructures with arbitrary predefined patterns on the stationary substrate. The maximum deflection distance of the jet droplets reaches several hundred microns. Furthermore, the positioning error of the printed structure is less than 3%. Moreover, we successfully obtained a diverse range of complex patterns by combining this technique with stage motion. This innovative printing technology not only enables the fabrication of complex patterned structures with high fidelity but also opens up exciting possibilities for new applications that require complete control of fast droplet positioning.

Inkjet printability of Celecoxib drug solutions

Abstract Inkjet printing is a versatile tool for the precise positioning of droplets that is used in many application areas such as 3D printing, biotechnology or pharmacy. This work focused on comparing the inkjet printability of different drug solutions of celecoxib (CLX), a non-steroidal anti-inflammatory drug, to produce drug depots in medical implants. CLX was dissolved in dimethyl sulfoxide (DMSO), poly(ethylene glycol) diacrylate (PEGDA) and a mixture of DMSO and PEGDA in a ratio of 1:1. The pure solvents and the drug solutions were inkjet printed using a Nanoplotter 2.1 with the NanoTip J printhead (GeSiM mbH, Radeberg, Germany). The voltage was varied from 60 V to 150 V using a step size of 5 V. Droplet volume and the trajectory of the droplets were investigated. For DMSO, DMSO-CLX, DMSO-PEGDA and DMSOPEGDA- CLX, reproducible droplet formation occurred with a droplet volume of approximately 300 pl - 500 pl and not more than one satellite droplet in a voltage range between 60 V to 80 V. Inkjet printing of PEGDA and PEGDA-CLX was not reproducible in the range of 60 V to 150 V. DMSO, DMSOPEGDA, DMSO-CLX and DMSO-PEGDA-CLX showed a high inkjet printability. In contrast, inkjet printability of PEGDA and PEGDA-CLX was very limited.

Locating a droplet on piezoelectric substrate based on a smartphone

In order to detect the position of a droplet on a piezoelectric substrate, a smartphone-based location method is developed. A transportation video is recorded and then analyzed using the smartphone. An algorithm for identifying the droplet in the captured image is presented, and the center distance of the droplet is calculated by analyzing the color information of the image. A black ink solution droplet is demonstrated for determining droplet position using a self-developed app. The results show that the droplet position is 201 pixels at the 11th second and its transportation velocity is 0.37 mm/s from the 2nd second to the 11th second at 27.5 dBm electric signal power.

Molecular dynamics simulation of oily wastewater treatment by air floatation

Molecular dynamics (MD) method was used to study the process of treating oily wastewater by air flotation. The bubbles generated by the machine combine the suspended oil droplets in the oily wastewater in the way of entrapment. In the process of upward movement, bubbles will collide with oil droplets suspended in water, the oil droplets will slightly deform on the surface of foam film, and the oil droplets will stick to the surface of foam film. Moreover, in the process of oil droplets floating up with bubbles, the foam film will further depress the position of oil droplets to the gas phase, and the closer oil droplets will coalesce in the depression, while the farther oil droplets will approach each other without coalescence.

Micropipette aspiration as a tool for single-particle X-ray imaging and diffraction.

A sample environment and manipulation tool is presented for single-particle X-ray experiments in an aqueous environment. The system is based on a single water droplet, positioned on a substrate that is structured by a hydrophobic and hydrophilic pattern to stabilize the droplet position. The substrate can support several droplets at a time. Evaporation is prevented by covering the droplet by a thin film of mineral oil. In this windowless fluid which minimizes background signal, single particles can be probed and manipulated by micropipettes, which can easily be inserted and steered in the droplet. Holographic X-ray imaging is shown to be well suited to observe and monitor the pipettes, as well as the droplet surface and the particles. Aspiration and force generation are also enabled based on an application of controlled pressure differences. Experimental challenges are addressed and first results are presented, obtained at two different undulator endstations with nano-focused beams. Finally, the sample environment is discussed in view of future coherent imaging and diffraction experiments with synchrotron radiation and single X-ray free-electron laser pulses.

Experimental analysis of droplet coalescence and transport mechanisms on a single vertical fiber

In mist filtration, fiber-based coalescers are an established form of filtering droplets contained in mist. The filtration process can be divided into different process steps, describing the impact of the droplets on fibers, the formation of fluid structures and the liquid transport. In order to investigate mechanisms inside depth filters on a microscopic level, investigations are often reduced to single fibers. In this work, the coalescence and transport mechanisms of axially distributed water droplets on a vertical fiber, subjected to gravity, are reported. This is done with the latest high-speed camera technology commercially available. Automated tracking of droplets is used for a frame-by-frame investigation of droplet position, size, and oscillation. Coalescence mechanisms describe the process of fluid formation. The first observed coalescence mechanism is identified by the coalescence of droplets contained in mist with an adhering droplet at the fiber. The second coalescence mechanism describes the coalescence of two closely spaced sessile droplets on a fiber. As a result, the newly formed droplet oscillates and can begin to drain. Furthermore, the coalescence process of a draining and sessile droplet is reported. Both the draining droplet and the second droplet involved in the coalescence event can be subject to oscillation. The given temporal high-resolution information about the droplet position and deformation improves the understanding of droplet coalescence on fibers and by that also its influence on transport processes and therefore droplet drainage. Observed transport mechanisms which take part in the drainage process are gravitational draining, droplet bouncing, and droplet sweeping.

Swirl-like Acoustofluidic Stirring Facilitates Microscale Reactions in Sessile Droplets.

Sessile droplets play a crucial role in the microreactors of biochemical samples. Acoustofluidics provide a non-contact and label-free method for manipulating particles, cells, and chemical analytes in droplets. In the present study, we propose a micro-stirring application based on acoustic swirls in sessile droplets. The acoustic swirls are formed inside the droplets by asymmetric coupling of surface acoustic waves (SAWs). With the merits of the slanted design of the interdigital electrode, the excitation position of SAWs is selective by sweeping in wide frequency ranges, allowing for the droplet position to be customized within the aperture region. We verify the reasonable existence of acoustic swirls in sessile droplets by a combination of simulations and experiments. The different periphery of the droplet meeting with SAWs will produce acoustic streaming phenomena with different intensities. The experiments demonstrate that acoustic swirls formed after SAWs encountering droplet boundaries will be more obvious. The acoustic swirls have strong stirring abilities to rapidly dissolve the yeast cell powder granules. Therefore, acoustic swirls are expected to be an effective means for rapid stirring of biomolecules and chemicals, providing a new approach to micro-stirring in biomedicine and chemistry.

Spray Printing of Porous Substrates from Nanosuspensions

In this work, we present and characterise an experimental setup that allows the generation of porous packings from nanosuspensions. By defined positioning and drying of solid-containing droplets, large-scale porous structures can be generated. Examples of such structures are shown and characterised. Operational challenges are presented, and it is discussed how they can be overcome to allow the maximum degree of freedom in packing generation.

Effect of the wetting behavior of water droplets on the output of a water-droplet-based electricity generator

Water-droplet-based electricity generators (DEGs) have attracted considerable attention owing to their simple metal substrate/dielectric/metal electrode structure and ability to generate high power instantaneously. However, their characteristics are significantly affected by the behavior of water droplets. In this study, to verify the relationship between water droplet movement and DEG output characteristics, we fabricated DEGs with two different structures. The electrodes were arranged vertically and horizontally with respect to the sliding direction of the water droplet, and DEG operation with different water droplet positions was verified. The results indicated that DEG output voltage varied according to water droplet behavior. Moreover, when the water droplet came in contact with an electrode, the wetting effect modified the shape of the droplet, thereby changing DEG output characteristics.

Improving agricultural robot patch-spraying accuracy and precision through combined error adjustment

Site-specific weed management (SSWM) involves precision spraying operations based on the spatial variability of weeds in the field. High spraying precision enables extensive economic and environmental benefits. We developed a high-precision patch-spraying robot system based on weed maps to conduct patch-spraying operations at the individual plant scale. The patch-spraying droplet deposition effect is evaluated by post-spraying droplet deposition images. The agricultural robot mainly consists of a walking chassis, spraying, and control systems. The walking chassis provides walking power and support for the suspended spraying system. Combining the static structural and dynamic error models of the robot improves patch-spraying accuracy and precision. Twelve patch-spraying simulations were carried out on the leveling site. Different correction methods and driving speeds were tested, with driving rates of 0.5, 1.0, and 1.5 m/s. Aerial images of the patch-spraying process were evaluated using pixel point-based discriminant statistics after operation completion. The droplet deposition coverage accuracy ranged from 95.9 to 98.8 %. The center of droplet deposition offset distance was 3.7–7.2 cm. Field results showed that the patch-spraying weed control rate based on individual plant scales (spraying precision ≤ 15 cm) was 94.2–98.1 %. In summary, the developed agricultural robot performs patch-spraying operations at the individual plant scale. Patch-spraying accuracy and precision are improved by modeling corrections for random errors. A general error correction method for the deposition position of fog droplets is explored to achieve precise droplet delivery in the walking state of plant protection operation equipment.

An adjoint method for control of liquid-gas flows using a sharp interface model

We present a computational, continuous adjoint framework for the control of liquid-gas flows using a sharp interface model. The two-phase Navier–Stokes equations are solved using a mass-conserving geometric Volume-of-Fluid method, while the adjoint equations consider a level set-based representation of the interface. To facilitate the accurate transport of a surface adjoint variable, a geometric surface transport method is formulated and applied. We verify our method by comparing adjoint-calculated gradients against analytical gradients or finite difference approximations. The method is then applied to a variety of benchmark two-phase flow problems, including the multi-dimensional inflow control of droplet position and optimal control of the initial velocity profile in a temporally evolving liquid-gas mixing layer.

Effect of incident direction and droplet position on dynamic and heat transfer behaviors of droplet impacting on super-hydrophilic cylindrical surface

Abnormal impact of droplet with different incident directions and positions can be found in evaporator, desalinator and nuclear engineering etc. The researches devoted to droplet abnormal impingement on a super-hydrophilic cylindrical surface are limited. In this paper, a numerical study of individual droplet impacting on super-hydrophilic cylindrical heated surface was conducted by applying VOF method. The incident direction and position of droplet were characterized by the impact angle φ and horizontal offset δx, the effect of which on dynamic and heat transfer behaviors was analyzed. Results show that there is an anisotropic spread during droplet impingement. Compared to no-offset vertical impact, the peaks of liquid film thickness for impact with an impact angle or horizontal offset are not the same at two edges of liquid film along circumferential direction. Impact angle or horizontal offset leads to a reduced contact area, a lower average temperature of liquid film and smaller total droplet input heat flow. For φ from 0° to 75° and δx from 0 mm to 5 mm, the maximum total droplet input heat flow decreases by 42.1% and 27.6% respectively. The local heat flux shows apparent fluctuations along the circumferential direction, and the high heat flux region is concentrated at a lower position in the circumferential direction of the cylinder for a larger φ or δx due to the auxiliary effect of gravity.

Position sensing of jetting droplets enabled by triboelectric nanogenerators

Inkjet printing, as a drop deposition technique, has been the subject of considerable scientific research and technological application; however, deposition positioning is typically realized by imaging techniques and its in-situ monitoring remains elusive. Here, we report a solid-liquid triboelectric nanogenerator (TENG) sensing technique for the position sensing of jetting droplets. Four single-electrode-mode TENG units cooperate to assemble a self-aware array to achieve droplet positioning based on the triboelectric output sum and ratio. The demonstration of the technique shows that the open-circuit voltage can be regarded as the key index to precisely characterize the deposition positioning of jetting droplets. The voltage-position characteristic curve is well explained by developing an equivalent-capacitor-set hypothesis, expressing the relationship between voltage and contact area. Moreover, we extend the work from one-dimensional to two-dimensional position sensing and develop an intelligent software platform for visualization, showing high accuracy with the maximum error of 0.164 mm. We believe this study to be the very first demonstration of solid-liquid TENGs for the position sensing of inkjet printing, paving the way for in-situ monitoring of intelligent devices such as additive manufacturing.