Droplet Length Research Articles

A microfluidic approach for controllable synthesis of TiO2 submicrospheres

TiO2 submicrospheres are used in dye-sensitized solar cells and Li-ion batteries to enhance energy conversion efficiency and volumetric performance. In this study, a microfluidic chip was designed for the realization of the continuous controllable synthesis of TiO2 submicrospheres. The chip utilizes two T-channels to discrete dispersed phases into droplets, and a Y-channel to fuse the two dispersed phase droplets. The droplets generation process, the influencing factors of droplet length and the fusion process of droplets were investigated. The effects of the flow rate ratio of titanium oxysulfate and ammonia solutions, microchannel geometrical profiles including the Y-channel entrance angle on the size of the synthesized TiO2 were studied. The length of the generated droplets was found to decrease with increasing continuous-phase flow rate, and increase with increasing dispersed-phase flow rate and microchannel cross-section area. When the flow rate ratio of titanium oxysulfate solution and ammonia solution was 1:1, the average diameter of TiO2 spheres synthesized was the smallest, around 300 nm. Increasing the microchannel cross-section and Y-channel entrance angle were beneficial in obtaining larger TiO2 submicrospheres. This proposed microfluidic strategy has the potential for applications required continuous synthesis of TiO2 submicrospheres with controllable sizes.

Modulating droplet electrohydrodynamics via the interplay of extensional flow and an alternating current electric field

Electric fields can be used to exert controlled time-varying forces on a droplet under progressive stretching in an extensional flow, allowing for its precise manipulation in various industrial and scientific applications, including microfluidics, materials science, and biological studies. However, the interaction between the combined extensional flow field and electric field may trigger a complex electrohydrodynamic response, as determined primarily by the capillary and viscous forces and the convection of surface charge. Here, we theoretically and computationally analyze the deformation and breakup of a droplet subjected to an alternating current (AC) electric field and uniaxial extensional flow. Our asymptotic theory, applicable in the small-deformation limit, quantifies the contributions of each applied field to the shape oscillations. Numerical simulations are employed to explore the dynamical evolution of the droplet in the nonlinear regime of variation in the capillary number. Our theoretical and numerical results are in excellent agreement, demonstrating that an AC electric field can significantly alter transient deformation depending on its magnitude and frequency. We identify the threshold frequency, dependent on the ratios of electrical properties, which can induce periodic oblate-prolate shape transitions. The interaction between viscous and electric stresses driving these transients is discussed. Contrary to intuition, strong electric fields greatly suppress shape oscillations, leading instead to large continuous elongations that eventually result in an end-pinching breakup mode, forming elongated bulbous-ended droplets. The breakup state, characterized by droplet length and shape at the onset of breakup, is determined by the field parameters and the physical properties of the fluids. Notably, the breakup state length and total breakup time have a non-monotonic relationship with the applied electric field frequency. The insights gained into the physics of oscillatory stable deformation and non-oscillatory unstable deformation offer new means of droplet manipulation in droplet-based micro-mechano-electrical systems that remained unexplored thus far.

Asymmetric droplet splitting in a T-junction under a pressure difference

In this paper, the phase-field multiphase lattice Boltzmann method is employed to simulate droplet breakup in a T-junction under different outlet pressures. Three behaviors of droplet breakup: non-breakup (flow pattern I), breakup with tunnels (flow pattern II), and breakup with permanent obstruction (flow pattern Ⅲ) are identified. The evolution of morphological characteristics of droplet breakup is quantitatively characterized, based on which the asymmetric splitting mechanisms and the influencing factors are clarified. Additionally, the factors influencing the droplet splitting volume ratio (VII/VI) are elucidated. The results indicate that there is a non-linear relationship between the VII/VI and the flow rate ratio. Moreover, the curve depicting the final VII/VI versus the initial droplet length exhibits a V-shape and has a minimum value. A conclusion is drawn that the Capillary number mainly influences flow pattern II, with the final VII/VI decreasing as the Capillary number increases. Additionally, for flow pattern III, the final VII/VI increases linearly with rising droplet size at low viscosity ratios, whereas it decreases linearly at high viscosity ratios. The growing outlet pressure difference enlarges the flow difference between the two branches, leading to an increase in the final VII/VI.

Universal Correlation for Droplet Fragmentation in a Microfluidic T-Junction.

Despite extensive research on droplet dynamics at microfluidic T-junction, for different droplet lengths and Capillary numbers, there remains limited understanding of their dynamics at different viscosity ratio. In this study, we adopt a modeling framework in a three-dimensional (3D) configuration to numerically investigate the droplet dynamics as it passes through a symmetric T-junction with varying Capillary numbers, droplet lengths, and viscosity ratios. We present a 3D regime map for the first time to demarcate the droplet breakup and no breakup regimes. Herein, we propose a simple surface equation accounting for the critical Capillary number for breakup, in terms of viscosity ratio and dimensionless droplet length. The proposed universal relationship aligns well with experimental and computational findings from the existing literature. Furthermore, we reveal a new droplet breakup characteristic at high viscosity ratio and high Capillary number where the droplet spreads almost twice its initial value before splitting. Overall, this research provides comprehensive understanding of droplet dynamics at the T-junction and has significant implications for several related applications, including the large-scale synthesis of microdroplets using microchannel networks.

Stretch-Controlled Branch Shape Microstructures for Switchable Unidirectional Self-Driven Spreading of Oil Droplets.

Unidirectional transport of liquids has attracted the attention of researchers in recent years for its wide application foreground. However, it is still a challenge to control the spreading of liquid, especially for oils with relatively high viscosity. In this paper, a flexible surface textured with branch-shaped microstructures is proposed. These asymmetric microstructures exhibit excellent unidirectional spreading behaviors for various oils. By suitably stretching the flexible surface to different stretch ratios, the spreading length of the oil droplets can be controlled. Moreover, the ongoing forward spreading of oil droplets can be suspended dynamically when the surface is stretched to 40%. Corresponding mechanism analysis demonstrates that surface stretching can narrow and close the microvalves between adjacent branches, which restrain the flow of the precursor film and the primary droplet. The switchable unidirectional spreading behavior enables the surface with such microstructures to be used for oil transportation, oil-water separation, and controllable lubrication.

A novel high-DPI and monodisperse droplet inkjet printhead with the piezoelectric cutter

High dots per inch (DPI) is the core index of inkjet printer, which is hindered by satellite ink droplet. Herein, we propose a novel high-DPI and monodisperse droplet inkjet printhead with the piezoelectric cutter. The as-established model has optimized the inkjet printhead structural parameters, actuating and cutting signal waveforms. The cutter element achieves moving the break-up point to the middle of the ink column, reducing the length of tail and generating a monodisperse droplet. Additionally, the cutter consistently reduces the droplet length with different ink properties including viscosity, density, surface tension, and contact angle, exhibiting high applicability. The research results provide an in-depth study on the design of high-DPI and monodisperse inkjet printheads, offering an efficient approach to improve inkjet printhead performance.

Taylor droplet breakup in T-type microchannels: A detailed flow analysis

The study of droplet break-up in microchannels can be used to improve designs for both biological or chemical microreactors and microfluidic devices e.g., heat exchangers and microchips. In this study, 3D computer simulations were carried out to investigate the detailed behavior of droplet breakup in a T-junction microchannel using the Volume of Fluid (VOF) and Level Set (LS) coupling methods (S-CLSVOF) implemented in OpenFoam. The evolution of droplet morphology and the rupture regimens were analyzed considering pressure results, velocity neck thickness, and tunnel width. The results show four rupture regimes for a range of capillary numbers and dimensionless initial droplet length of 0.005≤Ca≤0.055 and 1≤l0/w≤5. The stages of each rupture were also analyzed and compared with experimental and numerical results from literature. A detailed description of each step in the droplet breakup is also given, including analyses of the influence that the local pressure field and Laplace pressure have on the rupture processes. The 3D results reveal that the Laplace pressure decreases in the main channel due to continuous flux at the top and bottom of the 3D channel. This in turn, leads to a slight change in the rear curvature of the bubble. Laplace pressure is an important parameter that can be used to predict the opening tunnel point, large changes in curvature, and whether the droplet will breakup or not. Just before breakup, the 3D simulations captured a backflow near the neck, a region, characterized by pressure drops, and thus smaller breakup times.

Influence of triangular obstacles on droplet breakup dynamics in microfluidic systems

Microfluidic devices with complex geometries and obstacles have attracted considerable interest in biomedical engineering and chemical analysis. Understanding droplet breakup behavior within these systems is crucial for optimizing their design and performance. This study investigates the influence of triangular obstacles on droplet breakup processes in microchannels. Two distinct types of triangular obstructions, positioned at the bifurcation (case I) and aligned with the flow (case II), are analyzed to evaluate their impact on droplet behavior. The investigation considers various parameters, including the Capillary number (Ca), non-dimensional droplet length (L*), non-dimensional height (A*), and non-dimensional base length (B*) of the triangle. Utilizing numerical simulations with COMSOL software, the study reveals that the presence of triangular obstacles significantly alters droplet breakup dynamics. Importantly, the shape and location of the obstacle emerge as key factors governing breakup characteristics. Results indicate faster breakup of the initial droplet when the obstacle is positioned in the center of the microchannel for case I. For case II, the study aims to identify conditions under which droplets either break up into unequal-sized entities or remain intact, depending on various flow conditions. The findings identify five distinct regimes: no breakup, breakup without a tunnel, breakup with a tunnel, droplet fragmentation into unequal-sized parts, and sorting. These regimes depend on the presence or absence of triangular obstacles and the specific flow conditions. This investigation enhances our understanding of droplet behavior within intricate microfluidic systems and provides valuable insights for optimizing the design and functionality of droplet manipulation and separation devices. Notably, the results emphasize the significant role played by triangular obstacles in droplet breakup dynamics, with the obstacle’s shape and position being critical determinants of breakup characteristics.

CRISPR/Cas9-induced LEAP2 and GHSR1a knockout mutant zebrafish displayed abnormal growth and impaired lipid metabolism

Investigating the principles of fish fat deposition and conducting related research are current focal points in fish nutrition. This study explores the endocrine regulation of LEAP2 and GHSR1a in zebrafish by constructing mutantmodels andexamining the effects of the endocrine factors LEAP2 and its receptor GHSR1a on zebrafish growth, feeding, and liver fat deposition. Compared to the wild type (WT), the mutation of LEAP2 results in increased feeding and decreased swimming in zebrafish. The impact is more pronounced in adult female zebrafish, characterized by increased weight, length, width, and accumulation of lipid droplets in the liver.Incontrast, deficiency in GHSR1a significantly reduces the growth of male zebrafish and markedly decreases liver fat deposition.These research findings indicate the crucial roles of LEAP2 and GHSR1a in zebrafish feeding, growth, and intracellular fat metabolism. This study, for the first time, investigated the endocrine metabolic regulation functions of LEAP2 and GHSR1a in the model organism zebrafish, providing initial insights into their effects and potential mechanisms on zebrafish fat metabolism.

Experimental study of liquid–liquid dispersion patterns in T-inlet microchannels with different junction angles

Liquid-liquid two-phase flow in T-inlet microchannels with different junction angles (θ = 30°, 60°, 90°, 120° and 150°) was investigated experimentally. Four flow regimes of the dispersed phase were identified, i.e., parallel flow, jetting, dripping and squeezing, and the distribution of flow regimes for the dispersed phase corresponding to variations in the junction angle was plotted. The consequences of varying junction angle and flow conditions in the squeezing regime on the generated droplet size were analyzed. The results indicate that low capillary number and large flow rate ratio are conducive to the formation of large-size droplets. For constant flow conditions, junction angle θ = 90° is detrimental to the formation of squeezing microdroplets. The increase in microchannel junction angle causes the droplet size to decrease until θ > 90°, where the droplet size increases with the junction angle. On the basis of experimental results, the scaling law correlation equations containing the junction angle for predicting the droplet length and droplet volume are proposed, respectively. The predicted values match well with the experimental data. The results of this work contribute to the enhancement of the monodispersity of microdroplets and the precise control over a wide range of the generated droplet size by adjusting the junction angle.

A Novel Microfluidics Droplet-Based Interdigitated Ring-Shaped Electrode Sensor for Lab-on-a-Chip Applications.

This paper presents a comprehensive study focusing on the detection and characterization of droplets with volumes in the nanoliter range. Leveraging the precise control of minute liquid volumes, we introduced a novel spectroscopic on-chip microsensor equipped with integrated microfluidic channels for droplet generation, characterization, and sensing simultaneously. The microsensor, designed with interdigitated ring-shaped electrodes (IRSE) and seamlessly integrated with microfluidic channels, offers enhanced capacitance and impedance signal amplitudes, reproducibility, and reliability in droplet analysis. We were able to make analyses of droplet length in the range of 1.0-6.0 mm, velocity of 0.66-2.51 mm/s, and volume of 1.07 nL-113.46 nL. Experimental results demonstrated that the microsensor's performance is great in terms of droplet size, velocity, and length, with a significant signal amplitude of capacitance and impedance and real-time detection capabilities, thereby highlighting its potential for facilitating microcapsule reactions and enabling on-site real-time detection for chemical and biosensor analyses on-chip. This droplet-based microfluidics platform has great potential to be directly employed to promote advances in biomedical research, pharmaceuticals, drug discovery, food engineering, flow chemistry, and cosmetics.

Study on the adsorption mechanism of droplets on parallel flow interfaces in U-shaped microchannels

The adsorption process of deionized water droplets on the parallel flow interface between ionic liquid [BMIM][PF6] and mineral oil is investigated in U-shaped microchannels. Three flow patterns of the efficient adsorption, moderate adsorption, and inefficient adsorption based on the adsorption efficiency were observed. The dimensionless droplet length D/W > 0.72 is conducive to efficient adsorption of droplets. When droplet shape factor β > 1, the lubrication pressure generated within the curved liquid film has a more significant hindrance on the adsorption process, and the reverse lubrication pressure at the outlet of the liquid film is the main reason for the rupture of the liquid film. An increase in the velocity of phase interface A-B movement can lead to an increase in lubrication pressure. A correlation model is established between the dimensionless adsorption length L* and the dimensionless adsorption time t*, and the influence of Laplace pressure is analyzed.

Role of elasticity on polymeric droplet generation and morphology in microfluidic cross-junctions

Recently, our direct numerical simulations [Duan et al., Phys. Fluids 36, 033112 (2024)] showed that fluid elasticity affects the extension length and pinch-off time of the droplet formation process, thus changing the flow pattern. However, the effect of fluid elasticity on the morphology and properties of polymeric droplets is not yet fully understood. In this work, by analyzing the stretched state of the polymer macromolecule and the velocity distribution of the flow process, we find that the increase in fluid elasticity (characterized by the relaxation time) inhibits the contraction of the dispersed phase during droplet pinching and resists the effect of surface tension after droplet generation, which significantly affects the droplet geometry, volume, and generation frequency. The results demonstrate that the length and volume of polymeric droplets increase with the relaxation time of the polymer fluid, while the generation frequency decreases. Meanwhile, the effects of polymer viscosity and the superficial velocity ratio of the continuous to the dispersed phase on the droplets' morphology are investigated. The semi-empirical models for the length, volume, and generation frequency of polymeric droplets are developed for the first time by considering the elastic interaction. The purpose of our work is to provide a better understanding and experimental guidance for controlling the parameters of polymeric droplets with viscoelasticity of different shapes and sizes.

Experimental and numerical investigation of droplet flow mechanisms at fracture intersections

Understanding unsaturated flow behaviors in fractured rocks is essential for various applications. A fundamental process in this regard is flow splitting at fracture intersections. However, the impact of geometrical properties of fracture intersections on flow splitting is still unclear. This work investigates the combined influence of geometry (intersection angle, fracture apertures, and inclination angle), liquid droplet length, inertia, and dynamic wetting properties on liquid splitting dynamics at fracture intersections. A theoretical model of liquid splitting is developed, considering the factors mentioned above, and numerically solved to predict the flow splitting behavior. The model is validated against carefully-controlled visualized experiments. Our results reveal two distinct splitting behaviors, separated by a critical droplet length. These behaviors shift from a monotonic to a non-monotonic trend with decreasing inclination angle. A comprehensive analysis further clarifies the impacts of the key factors on the splitting ratio, which is defined as the percentage of liquid volume entering the branch fracture. The splitting ratio decreases with increasing inclination angle, indicating a decrease in the gravitational effect on the branch fracture, which is directly proportional to the intersection angle. A non-monotonic relationship exists between the splitting ratio and the aperture ratio of the branch fracture to the main fracture. The results show that as the intersection angle decreases, the splitting ratio increases. Additionally, the influence of dynamic contact angles decreases with increasing intersection angle. These findings enhance our understanding of the impact of geometry on flow dynamics at fracture intersections. The proposed model provides a foundation for simulating and predicting unsaturated flow in complex fractured networks.

Quantitative study of droplet generation by pressure-driven microfluidic flows in a flow-focusing microdroplet generator

To precisely control the size of droplets is of great importance for the applications of the droplet microfluidics. In a flow-focusing microdroplet generator, the pressure-driven microfluidic device is designed to control the flow rates of the fluids. For a specific geometry of the flow-focusing microchannel, a mathematical model of droplet formation is established, and the nonlinear relation between the droplet length and the driven-pressure ratio can be described by our model. For pressure-driven microfluidic flows, the nonlinear relation between the droplet length and the driving-pressure ratio is measured experimentally in the flow-focusing microchannel. Particularly, by using the closed-loop control method of droplet generation, good agreements are shown between the measured size of droplets and the predicted size of the droplets. As a result, the control precision of the droplet size can be increased drastically by the closed-loop control method of droplet generation. Consequently, monodisperse droplets of extremely small size can be produced in the flow-focusing microdroplet generator.

Experimental study of liquid aluminum droplet breakup characteristics based on a Drop-on-demand (DOD) magnetohydrodynamic actuation

In magnetohydrodynamic (MHD) drop-on-demand (DOD) actuation, Lorentz force generated in different excitation stages are exerted on the liquid metal jet to form a "push-pull" mechanism, which is crucial for generating accurate and repeatable metal droplets. In this study, the important parameters of the excitation current waveform in the magnetohydrodynamic (MHD) process, including the influence of the excitation voltage pulse width ratio and current amplitude on the velocity, energy, volume, and breakup length of aluminum droplets are studied. The conversion process of surface energy and kinetic energy during the formation and fall stage of liquid droplets is analyzed. The results show that the negative and positive excitation voltage pulse width ratio of the MHD pump has a significant effect on the droplet velocity, breakup time, size, and sphericity. The amplitude of the excitation current and Hartmann number has a significant impact on the generation of stable droplets. The results show that the single droplet ejection state can be achieved within the Ha number between 319.5 and 391.1. As the Ha number increases, the volume, length, kinetic energy and surface energy of the droplets at breakup time also increase. The size of droplets can be adjusted by changing the amplitude of excitation waveform.

Three‐dimensional simulation of dripping and jetting phenomenon in a flow‐focusing geometry

Abstract3D simulations have been achieved on a flow‐focusing geometry employing the VOF method to study the consequence of viscosity, surface tension, wettability, and geometry on drop generation for the dripping regime. Here the dispersed phase is the PDMS oil (polydimethylsiloxane), and the continuous phase is the water. Simulations were performed at different oil‐to‐water viscosity ratios of 3, 12, 27, and 50. The interfacial tension between PDMS oil and water is 0.0118 N/m. It has been abridged to 0.008 N/m, 0.005 N/m, and 0.002 N/m, and simulations were performed. The walls of the microchannel are considered to be PMMA surfaces. The contact angle of an oil droplet on the PMMA surface in the presence of water is 140°. The effect of wettability was shown at various contact angles (angle created by water droplet on the PMMA surface in the presence of oil) of 0°, 40°, 90°, 135° and 180°. The frequency of droplet generation (1/s), non‐dimensional droplet length (L/Wc), droplet volume (nl), and droplet velocity (m/s) have been calculated for each of the cases. A flow pattern map has been industrialized classifying the dripping and jetting regimes. A comparison between normal geometry and two constricted geometries (having different orifice lengths) based on the frequency of droplet, non‐dimensional drop length, drop volume, and drop velocity has been made for both dripping and jetting regimes. Prediction of simulated non‐dimensional droplet length has also been made using dimensional analysis.

Numerical investigation on flow regime transition mechanism and length prediction method of droplet in T-junction by electric field

Although droplet microfluidics has received attention and research in the fields of chemistry and materials in recent years, research on electric field modulation of microchannel droplets is currently fragmented. In this paper, the effect of electric field and flow rate ratio on the behavior of discrete-phase flow in systems with different viscosity ratios was simulated. Subsequently, we delineated the regions of slug flow, drip flow, jet flow, and parallel flow under different parameters according to the simulation results, and investigated the mechanism of electric field manipulating the transformation of the above four flow types by combining the velocity vector diagram with the force situation. Additionally, in order to fill the gap in methods for predicting droplet length in T-junction microchannels under the presence of electric field, we present a scaling law for predicting droplet length that couples the effects of electric field, velocity, and viscosity. And it was verified that the error of the model built based on this method is less than 12 % when the flow ratio is less than 1.

Flow pattern maps of double emulsions transporting through bifurcation microchannels.

The transportation behaviors of compound droplets in confined channels are widespread phenomena while the physical mechanisms are far from being completely unraveled. In this work, behaviors of double emulsions flowing through bifurcation microchannels are experimentally studied with the aim of building universal flow pattern maps. Three flow patterns are categorized according to different features of daughter droplets in terms of size, uniformity, and shell thickness. A detailed analysis of the dynamics of interfacial evolutions in different patterns is carried out and the coupling interaction between interfaces is found to affect the minimum tail distance during transportation. It is feasible to obtain the threshold of the occurrence of the coupling interaction, due to the different variation tendencies in the two states, which relies on three dimensionless parameters, i.e. droplet length, length ratio, and capillary number. Furthermore, a novel physical model is proposed to build the flow pattern map, with the two transition boundaries being expressed as different relationships in terms of the three identified parameters. The physical mechanisms are summarized with the aid of force analysis. An excellent agreement is shown between the model and experimental results in different liquid systems and bifurcation structures, indicating the generality of the proposed model.

Soft wetting: an analytical model for pillar topography- and softness-dependent droplet depinning force.

The extent to which a droplet pins on a textured substrate is determined by the dynamics of the contact line and the liquid-vapor interface. However, the synergistic contribution of contact line sliding and interface distortion to the droplet depinning force remains unknown. More strikingly, current models fail to predict the depinning force per unit length of droplets on soft pillar arrays. Therefore, we fabricate soft pillar arrays with varying geometrical dimensions and mechanical properties and measure the depinning forces per unit length by allowing droplets to evaporate on such substrates. We then analyze the decrease in excess Gibbs free energy of the apparent droplet caused by the detachment of the droplet boundary from the previously pinned pillars. In contrast to prior notions, based on the measured decreases in excess Gibbs free energy, we find that the coefficient, that governs the ratio of interface distortion's contribution to the depinning force to that of the sliding contact line, increases with a decrease in pillar packing density. By considering the combined contribution from contact line sliding, liquid-vapor interface distortion, and pillar deflection, we introduce an analytical model to predict the droplet depinning force per unit length and corroborate the model using experimental data reported in this and prior studies.