Droplet Position Research Articles

Experimental investigation of the impact and freezing processes of supercooled water droplet on different cold curved surfaces

The impact of supercooled water droplets (SCWD) on aircraft cold surfaces constitutes a major cause of aircraft icing, posing a considerable threat to flight safety. Developing a safe, efficient, and energy-efficient anti-icing method necessitates an in-depth investigation of the icing mechanism of SCWD impacting cold curved surfaces. This study experimentally investigates the freezing behavior of SCWD on cold surfaces with diverse curvatures. The results show that the water droplet spreading factor (WDSF) significantly increases as surface curvature ranges from 0 to 125 while simultaneously decreasing the freezing time. Furthermore, the ice ring morphology from droplet freezing transitions from a raised crown shape to a concave cake shape at the center. Changing the impact position of droplet resulted in a marked increase in WDSF, a substantially reduced freezing time, and the emergence of strip icicles at the lower part. Additionally, this study examines the effects of Weber number (We = 459–650) and impact surface temperature (Tw = −30 °C–0 °C) on the impact freezing process. An increase in We leads to a higher WDSF and reduced freezing times, while lower surface temperatures decelerate droplet retraction, thereby shortening freezing time. At surface temperatures below −25 °C, Tw results in droplets splashing upon impact and rapidly freezing during the spreading stage. The findings of this research provide experimental insights crucial for developing aircraft anti-icing technology.

Dynamics of a droplet on the surfactant-infested free surface of another liquid

The dynamics of liquid droplets surfing over the surfactant-infested free surface of another liquid have been explored experimentally. We analyze the motion of oil droplets that has been initiated through the creation of a surface tension gradient resulting from the deposition of a drop of surfactant at the water surface contained in the petri dish. The experiments reveal that the location of surfactant deposition with respect to the droplet position influences its motion. Due to the presence of a surface tension gradient, the footprint area of the droplet reduces and its shape changes. We have studied the temporal variation in the velocity (|vx|) of the droplets in relation to their proximity to a wall. Based on the evolution of droplet shape and change in droplet velocity, the drop dynamics can be experimentally divided into four distinct zones. Results indicate that in zone-1, |vx| grows with t as |vx|≈tn, where n is between 0.8 and 1.0. The scaling argument shows that in this zone, the surface tension force dominates the drag force, and thereby, |vx| of the droplets increases linearly with t expressed as |vx|∝t. The experimental investigation and the scaling law exhibit a reasonable agreement. In zone-2, |vx| remains more or less constant, as it is postulated that the surface tension force balances the drag force. In zone-3, a decrease in surface tension force results in a deceleration of the droplets. In zone-4, the deceleration becomes more prominent as the droplet approaches the petri dish wall.

Analysis of the motion and deformation of water-in-oil emulsion droplets under the action of an electric field

Molecular dynamics simulations are used to study the aggregation dynamics of water-in-oil emulsion droplets under an electric field, and to analyze the effects of electric field strength, type, droplet position, and ionic concentration on their kinematic properties. The best droplet aggregation is observed at E=0.03V/Å for DC field condition, and E=0.045V/Å - 80ps for rectangular AC field condition. The rectangular alternating current (AC) field is able to merge the droplets farther away from the center of mass, but the two fields are not able to merge when the angle between the center of mass of the droplets and the electric field force is ≥35.54°. For different ion concentrations, t40N < t20N < t60N < t0N in the DC field and t20N < t40N < t0N < t60N in the rectangular AC field, and for the same ion concentration, the rectangular AC field takes longer time to merge.

Automated droplet manipulation enabled by a machine-vision-assisted acoustic tweezer

Automated droplet manipulation holds great significance for various biochemical applications, including but limited to heavy metal ions detection. Despite notable progress, contactless-acoustic-tweezer-based automated droplet manipulation on superhydrophobic surfaces is rarely reported. In this work, we introduce a machine-vision-assisted acoustic tweezer (MVAAT) for automated and contactless manipulation of droplets on a superhydrophobic surface. The MVAAT generates ultrasound standing waves between an ultrasonic transducer (UST) and a superhydrophobic surface, inducing acoustic radiation force to facilitate contactless droplet manipulation on the superhydrophobic surface. An industrial-camera-based machine vision system is employed for real-time detection and tracking of droplets, providing precise droplet positions for automated droplet transportation and merging via a UST equipped on a Cartesian robot. Experimental results demonstrate that the proposed MVAAT can transport droplets of various volumes on a superhydrophobic surface along planned paths at considerably high velocities exceeding one centimeter per second. Furthermore, with the vision feedback, the MVAAT can reliably and precisely transport a droplet to a target position, even if the droplet fails to follow the UST during its movement. Moreover, automated merging and patterning of multiple droplets are achieved, showcasing the versatility of the MVAAT. Last, the MVAAT is applied for fluorescence-based Cu2+ detection to showcase its potential for practical biochemical analyses. The proposed MVAAT significantly expands the capability of ultrasound for droplet manipulation on superhydrophobic surfaces, promising numerous practical applications in biology and chemistry.

High Frequency and Addressable Impedance Measurement System for On-Site Droplet Analysis in Digital Microfluidics

Digital microfluidics is a novel technique for manipulating discrete droplets with the advantages of programmability, small device size, low cost, and easy integration. The development of droplet sensing methods advances the automation control of digital microfluidics. Impedance measurement emerges as a promising technique for droplet localization and characterization due to its non-invasive nature, high sensitivity, simplicity, and cost-effectiveness. However, traditional impedance measurement approaches in digital microfluidics based on the high-voltage actuating signal are limited in sensing accuracy in practical applications. In this paper, we propose a novel droplet impedance sensing system for digital microfluidics by introducing a low-voltage and addressable measurement circuit, which enables impedance measurement over a wide frequency range. The proposed measurement system has also been used for detecting the droplet composition, size, and position in a digital microfluidic chip. The improved impedance sensing method can also promote the applications of the digital microfluidic, which requires high accuracy, real-time, and contactless sensing with automatic sample pretreatment.

Satellite droplet formation and its inertial separation in integrated microchannels

The breakup of filament is often accompanied by the formation of satellite droplet, which affects the uniformity of droplets, and inertial microfluidic technology is usually used to separate droplets of different sizes. In this study, different filament breakup modes are observed, and the variation of satellite droplet size with operating conditions are analyzed. Based on the experimental results, predictive model for the satellite droplet size is proposed. To better control the separation of particles with different sizes, the focusing and separation process of main and satellite droplets in microdevices are investigated by numerical simulation. It is found that increasing the fluid flow rate, the width of microchannel and rear cavity, and reducing the satellite droplet size are all beneficial for the separation of droplets of different sizes. At last, models for predicting the focusing positions of main and satellite droplets in rear cavity are established, and an integrated microfluidic device is proposed.

Magnetically-responsive microwall arrays with path-guide for directional transportation of droplets

This research provides a comprehensive exploration of the development and characterization of magnetically responsive microwall arrays (MRMAs), presenting a novel approach to precise droplet manipulation. The proposed fabrication process involves microscale wall arrays created using carbonyl iron particles embedded in polydimethylsiloxane through a replica molding process. The MRMAs demonstrate a unique response to magnetic fields, enabling precise control over droplet movement. Through superhydrophobic coatings and meticulously adjusted magnetic fields, the system facilitates the efficient movement of droplets along predefined routes, achieving outstanding accuracy in droplet directionality and positioning. The experiments highlight the capability of MRMAs to merge differently colored droplets, underscoring their potential in long-distance droplet transportation. The results suggest applications in microfluidic systems, lab-on-a-chip devices, and targeted drug delivery, marking a significant advancement in microfluidic research.

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.

Reaction-Driven Diffusiophoresis of Liquid Condensates: Potential Mechanisms for Intracellular Organization.

The cellular environment, characterized by its intricate composition and spatial organization, hosts a variety of organelles, ranging from membrane-bound ones to membraneless structures that are formed through liquid-liquid phase separation. Cells show precise control over the position of such condensates. We demonstrate that organelle movement in external concentration gradients, diffusiophoresis, is distinct from the one of colloids because fluxes can remain finite inside the liquid-phase droplets and movement of the latter arises from incompressibility. Within cellular domains diffusiophoresis naturally arises from biochemical reactions that are driven by a chemical fuel and produce waste. Simulations and analytical arguments within a minimal model of reaction-driven phase separation reveal that the directed movement stems from two contributions: Fuel and waste are refilled or extracted at the boundary, resulting in concentration gradients, which (i) induce product fluxes via incompressibility and (ii) result in an asymmetric forward reaction in the droplet's surroundings (as well as asymmetric backward reaction inside the droplet), thereby shifting the droplet's position. We show that the former contribution dominates and sets the direction of the movement, toward or away from fuel source and waste sink, depending on the product molecules' affinity toward fuel and waste, respectively. The mechanism thus provides a simple means to organize condensates with different composition. Particle-based simulations and systems with more complex reaction cycles corroborate the robustness and universality of this mechanism.

Dynamic label-free analysis of SARS-CoV-2 infection reveals virus-induced subcellular remodeling

Assessing the impact of SARS-CoV-2 on organelle dynamics allows a better understanding of the mechanisms of viral replication. We combine label-free holotomographic microscopy with Artificial Intelligence to visualize and quantify the subcellular changes triggered by SARS-CoV-2 infection. We study the dynamics of shape, position and dry mass of nucleoli, nuclei, lipid droplets and mitochondria within hundreds of single cells from early infection to syncytia formation and death. SARS-CoV-2 infection enlarges nucleoli, perturbs lipid droplets, changes mitochondrial shape and dry mass, and separates lipid droplets from mitochondria. We then used Bayesian network modeling on organelle dry mass states to define organelle cross-regulation networks and report modifications of organelle cross-regulation that are triggered by infection and syncytia formation. Our work highlights the subcellular remodeling induced by SARS-CoV-2 infection and provides an Artificial Intelligence-enhanced, label-free methodology to study in real-time the dynamics of cell populations and their content.

Numerical assessment of the drag force and Nusselt number during droplet impingement onto a particle

The dynamics of droplet impingement onto solid particles play a crucial role in various engineering applications, yet a fundamental understanding of the intricate momentum and heat transfer characteristics within the processes remains unclear. In this work, we numerically investigate and quantify the drag force and Nusselt (Nu) number during the process using a volume of fraction model. After model validations, it is employed to simulate the processes of molten iron ore spreading over a coke particle for demonstration. The results show that the drag force exhibits rapid initial growth, followed by significant fluctuations marked by two peaks, ultimately decreasing to a low value. The Nu number undergoes a sharp ascent to an immediate peak, followed by a two-stage decline with varying rates. Furthermore, the effect of three key operating parameters is quantified. The comparative analysis unveils that a larger droplet size significantly contributes to an augmented drag force, especially during the first peak. The Nu numbers under various droplet sizes follow a similar trajectory, rising and then decreasing until the wetter surface reaches the maximum. The larger droplets show a slower Nu number decrease. A higher initial droplet position can remarkably increase the drag force and Nu number with more rapid fluctuations. Conversely, the effect of gas velocity under the symmetrical and steady flow field is limited and can be practically disregarded. The present work reveals the fundamental characteristics of momentum and heat transfer process during droplets impact particles.

Inversion of Stabilized Large Droplet Clusters.

We investigate the spontaneous rearrangement of microdroplets in a self-assembled droplet cluster levitating over a thin locally heated water layer. The center-to-periphery droplet diameter ratio (the "inversion coefficient") controls the onset of the inversion. Larger droplets can squeeze between smaller ones due to increased drag force on them from the air-vapor flow. In smaller clusters, the rotation of the droplets plays an important role since larger droplets rotating with the same angular velocity (dependent on the rotor of the airflow field) have higher viscous friction force with the liquid layer. It is desirable to avoid cluster inversion in experiments where individual droplet positions should be traced.

Deterministic Single-Row-Droplet Catalyst Formation for Uniform Growth Integration of High-Density Silicon Nanowires.

Planar silicon nanowires (SiNWs), grown by using low temperature catalytic approaches, are excellent 1D channel materials for developing high-performance logics and sensors. However, a deterministic position and size control of the metallic catalyst droplets, that lead to the growth of SiNWs, remains still a significant challenge for reliable device integration. In this work, we present a convenient but powerful edge-trimming catalyst formation strategy, which can help to produce a rather uniform single-row of indium (In) catalyst droplets of Dcat = 67 ± 5 nm in diameter, with an exact one-droplet-on-one-step arrangement. This approach marks a significant achievement in self-assembled catalyst formation and offers a foundation to attain a reliable and scalable growth of density SiNW channels, via an in-plane solid-liquid-solid (IPSLS) mechanism, with a uniform diameter down to Dnw = 35 ± 4 nm, and do not rely on high-precision lithography techniques. Prototype SiNW-based field effect transistors (FETs) are also fabricated, with a high Ion/Ioff current ratio and small subthreshold swing of >107 and 262 mV·dec-1, respectively, indicating a reliable new routine to integrate a wide range of SiNW-based logic, sensor, and display applications.

Effect of initial droplet position on coalescence-induced jumping on superhydrophobic surfaces with micropillar arrays

Coalescence-induced droplet jumping holds great potential for applications such as water harvesting, self-cleaning, and the thermal management of electronic devices. This study investigates the impact of the droplet's initial position on coalescence-induced jumping on superhydrophobic surfaces with micropillar arrays. Numerical simulations are conducted to examine the differences in droplet jumping at various initial positions with uniform and nonuniform micropillar distributions, and the effects of the droplet's initial position on its velocity and pressure distribution are analyzed. The findings indicate that altering the initial position produces an asymmetric distribution of the high-pressure region at the droplet's base and the pressure at the solid–liquid contact surface during the contraction of the liquid bridge. This asymmetry allows the droplet to jump away from the surface with both vertical and horizontal components of velocity, and to be transported in the horizontal direction. Furthermore, numerical simulations with various initial droplet positions and radii demonstrate that the direction of the horizontal jumping velocity is influenced by both the offset distance and the direction of the initial droplet position, and that the impact of the initial position decreases as the relative size of the droplet with respect to the micropillars increases. The droplet jumping velocity, direction, and horizontal transport distance can be controlled by adjusting the initial droplet position and size. This work reveals the mechanism of coalescence-induced droplet jumping on superhydrophobic surfaces with micropillar arrays and provides an important reference for practical applications.

Non-frontal coalescence jumping of a rolling and a static droplet

The possibility of coalescence between rolling and static droplets is greater than that of static droplets. Due to the randomness of the velocity direction of rolling droplets and the position of static droplets, rolling and static droplets are more prone to non-frontal coalescence. Most studies focused on static droplets or head-on coalescence jumping, while non-frontal coalescence is poorly understood. In this work, we experimentally and numerically study the head-on and non-frontal coalescence of a rolling droplet and a static one. Furthermore, to measure the jumping characteristics of merged droplets, a “single camera defocusing imaging measurement” (SCDIM) method was proposed to obtain a 3D trajectory of the jumping droplet. For non-frontal coalescence, the morphological evolution of the merged droplet rotates counterclockwise during the coalescence process. The direction of horizontal jumping velocity deviates towards the rolling droplet. The non-frontal deviation and initial velocity determine whether rotation can occur and its strength. The higher initial velocity has a negative impact on the jumping velocity in the Z direction with the increase of non-frontal deviation, while the deviation angle could be negligible. As the non-frontal deviation ratio increases, the dominant mechanism of coalescence jumping is gradually transferred from the impact effect to the contraction of the merged droplets. Different from jumping velocity in the Z direction, the horizontal jumping velocity is approximately proportional to the dimensionless initial velocity.

Modeling of a liquid nitrogen droplet evaporating inside an immiscible liquid pool

Evaporation of liquid nitrogen in another immiscible liquid occurs in many industrial applications. Existing oversimplified one-dimensional (1D) quasi-steady models, although can quantitatively predict the evaporation rate by introducing an empirical fitting parameter, rely on configurations inconsistent with experimental observation so more rigorous models are required to get in-depth physical insights and improve modeling capability. This study proposes a 2D quasi-steady-state theoretical model, free of fitting parameters, that predicts the bubble growth rate and estimates the heat transfer rate for a liquid nitrogen droplet evaporating inside a liquid pool within the spherical bubble regime. The droplet's shape and position within a spherical bubble are determined by the equilibrium between the gravitational force and the upward pressure force resulting from the vapor flow between the droplet and the pool. The vapor layer thickness is calculated to be on the order of 10 microns. Notably, the primary contribution to heat transfer arises from the lower portion of the droplet, leading to local heat flux values up to approximately six times higher at the bottom compared to the top. The predicted bubble growth is quantitatively consistent with experimental data within the capillary spherical bubble regime. Furthermore, the overall heat transfer rate Q exhibits a distinct scaling relationship with the volume ratio between the bubble and droplet, yielding Q∼(Vb/Vd)−0.1.

Numerical simulation of rime ice accretion on airfoil using rigid sphere model

A 2D/3D numerical model for rime ice shape prediction is developed by combining the rigid sphere model (RSM) and computational fluid dynamics (CFD), and its characteristics are investigated. In the RSM, the ice accretion is modeled based on first principles with little physical modeling. The ice particle on an airfoil is described as a rigid sphere, and the ice shape is represented as a collection of rigid spheres. We use a non-body-fitted hierarchical Cartesian grid-based CFD solver so that complex ice shape represented by RSM can be handled. The tree data of the hierarchical Cartesian grid is also used for fast search of droplet positions. In addition, multiple ice particles are modeled as one large particle to reduce the number of trajectory calculations. The sensitivity of several parameters in the calculation is studied in 2D. Subsequently, 3D ice accretion analysis on NACA0012 airfoil using the RSM is performed for the first time. The simulation results are compared with those of the wind-tunnel experiments conducted at NASA. Although the RSM is a simple ice accretion model, reliable results are obtained in both 2D and 3D calculations.

Flow-Driven Self-Propulsion of Oil Droplet on a Surfactant Solution Surface, as Observed by Time-Resolved Interfacial Tension and Surface Flow Speed Measurements.

The imbalanced force of the interfacial tension applied to an object has often been taken into account in the analysis of the motion mechanism of self-propelled systems. However, heterogeneous distributions of the interfacial tension also cause Marangoni flows, and these flows also contribute to the self-propulsion through the viscous force. The contribution of such flows has not been observed directly, while the interfacial tension difference has been measured in some systems. In this study, simultaneous measurements of the interfacial tension and surface flow speed of the unidirectional self-propelled motion of a butyl salicylate (BS) droplet in a circular channel on a sodium dodecyl sulfate (SDS) aqueous solution were achieved by the quasi-elastic laser scattering method. The droplet position was also recorded by observing its fluorescence excited by a UV light. The BS droplet speed dependence of the interfacial tension and surface flow speed were measured by varying the initial BS concentration codissolved in the SDS aqueous solution. As a result, a periodic decrease of the interfacial tension and a periodic increase of the speed of both forward and backward flows were observed when the droplet passed the sampling position of the time-resolved measurements. When they were converted to the distribution in space of the droplet position, no droplet speed dependence of the interfacial tension difference between the front and rear of the droplet was observed. On the other hand, the speed of both forward and backward flows increased as the droplet speed increased. By analysis of the above results with a simplified model, it was clarified that the forward flow driven by the interfacial tension gradient at the droplet front is actually important in the mechanism of the unidirectional self-propelled motion of a droplet.

Optimizing Optical Dielectrophoretic (ODEP) Performance: Position- and Size-Dependent Droplet Manipulation in an Open-Chamber Oil Medium.

An optimization study is presented to enhance optical dielectrophoretic (ODEP) performance for effective manipulation of an oil-immersed droplet in the floating electrode optoelectronic tweezers (FEOET) device. This study focuses on understanding how the droplet's position and size, relative to light illumination, affect the maximum ODEP force. Numerical simulations identified the characteristic length (Lc) of the electric field as a pivotal factor, representing the location of peak field strength. Utilizing 3D finite element simulations, the ODEP force is calculated through the Maxwell stress tensor by integrating the electric field strength over the droplet's surface and then analyzed as a function of the droplet's position and size normalized to Lc. Our findings reveal that the optimal position is xopt= Lc+ r, (with r being the droplet radius), while the optimal droplet size is ropt = 5Lc, maximizing light-induced field perturbation around the droplet. Experimental validations involving the tracking of droplet dynamics corroborated these findings. Especially, a droplet sized at r = 5Lc demonstrated the greatest optical actuation by performing the longest travel distance of 13.5 mm with its highest moving speed of 6.15 mm/s, when it was initially positioned at x0= Lc+ r = 6Lc from the light's center. These results align well with our simulations, confirming the criticality of both the position (xopt) and size (ropt) for maximizing ODEP force. This study not only provides a deeper understanding of the position- and size-dependent parameters for effective droplet manipulation in FEOET systems, but also advances the development of low-cost, disposable, lab-on-a-chip (LOC) devices for multiplexed biological and biochemical analyses.

Controlled preparation of droplets for cell encapsulation by air-focused microfluidic bioprinting

Microfluidics is a facile platform that manipulates fluids for the production of droplets, particles, and microcapsules. However, the application of microfluidics is limited to the manipulation of the droplet position and the presence of a continuous oil phase, which needs to be removed for biomedical applications. Here, we used air as the continuous phase and developed a facile method for droplet generation and patterning by air-focused microfluidic three-dimensional (3D) droplet printing (AFMDP). By tuning the viscous drag of a focused air flow, monodisperse droplets with tunable size were generated in a microfluidic device, and droplet patterns were designed by combining the control system of the 3D printer. When using droplets as templates, hydrogel particles were prepared by AFMDP and crosslinked in a CaCl2 bath. These hydrogel particles were proven to be good carriers for the cell culture, controlled release, and immune therapy using chimeric antigen receptor (CAR) T cells. Cell viability and activity results confirmed that encapsulation of CAR-T cells in hydrogel particles did not compromise their cell activity and functionality but facilitated their manipulation and cell culture. Therefore, the AFMDP system provided a versatile platform for the design of droplets, particles, and microcapsules for biomedical applications.