Daughter Droplets Research Articles

On-Chip Droplet Splitting with High Volume Ratios Using a 3D Conical Microstructure-Based Microfluidic Device.

This work reports a simple microfluidic method for splitting a mother droplet into two daughter droplets with high and precise volume ratios. To achieve this, a droplet-splitting microfluidic device embedded with a three-dimensional (3D) conical microstructure is fabricated, in which the high splitting ratios of monodisperse mother droplets are achieved. The volume ratio of the split daughter droplets can reach up to 265. In addition, we examined factors that affect the splitting ratio of the daughter droplets and found that the ratio is affected by the flow rates of the two individual outlet channels, the injection length of the conical microstructure, and the diameter of the original mother droplets. Numerical simulations of these parameters were conducted to gain a clearer understanding of the splitting behavior. The proposed droplet splitting device with a conical microstructure enables on-chip sample extraction and droplet volume control, which can be a powerful tool for various droplet-based applications in microfluidic devices such as viral infectivity assays and sequencing heterogeneous populations.

Modulating outcomes of oil drops bursting at a water–air interface

Recent studies have shown that capillary waves generated by the bursting of an oil drop at the water–air interface produces a daughter droplet inside the bath, while a part of it floats above it. Successive bursting events produce next generations of daughter droplets, gradually diminishing in size until the entire volume of oil rests atop the water–air interface. In this work, we demonstrate two different ways to modulate this process by modifying the constitution of the drop. First, we introduce hydrophilic clay particles inside the parent oil drop and show that it arrests the cascade of daughter droplet generation preventing it from floating over the water–air interface. Second, we show that bursting behavior can be modified by a compound water–oil–air interface made of a film of oil with finite thickness and design a regime map, which displays each of these outcomes. We underpin both of these demonstrations by theoretical arguments providing criteria to predict outcomes resulting therein. Finally, all our scenarios have a direct relation to control of oil–water separation and stability of emulsified solutions in a wide variety of applications, which include drug delivery, enhanced oil recovery, oil spills, and food processing, where a dispersed oil phase tries to separate from a continuous phase.

Splitting of double-core solid-in-water-in-oil droplet in a microfluidic Y-junction

Solid particle-encapsulated droplets have significant applications in biochemistry, advanced materials, and inertial confinement fusion (ICF) experiments. However, there is a problem of encapsulating two solid cores in a single droplet during the preparation of single-core droplets, which reduces the utilization efficiency. In this study, an effective microfluidic approach for continuous splitting of solid-in-water-in-oil droplets encapsulating double solid cores is developed. Visualization experiments are conducted to analyze the movements of solid cores and evolution of liquid–liquid interface during the splitting. The results show that the squeezing stage during the splitting process is shortened due to the presence of solid cores. The splitting mechanisms were also revealed by analyzing the interaction forces between the solid cores and aqueous phase. The force analysis of the aqueous phase showed that sum of squeezing and shear force could overcome the interfacial tension, ensuring the successful splitting of the double-core droplets. The force analysis of the solid cores revealed that the motion of the core could be divided into three typical stages: deceleration, hitting and separation. The combined effect of the aqueous phase, channel wall, and interfacial forces ensured the stable separation of the two solid cores. The length distribution of the daughter droplets exhibited excellent monodispersity. The microfluidic method proposed in this work would effectively improve the controlled preparation efficiency of solid-in-water-in-oil droplets.

Composite liquids under high-power heating: superheat of water in micro-explosion of water-in-fuel droplets

Abstract The article analyses the degree of water superheating with respect to the liquid-vapour equilibrium line in experiments on the micro-explosion of a composite droplet comprised of two immiscible liquids. The analyses were carried out for water-in-fuel drops under conditions of high-power heating. This degree is compared with the mechanical effect of droplet decay, involving the formation of daughter droplets. Our attention was drawn to the smallness of the degree of superheating preceding the decay. A model of the boiling up of such a droplet is constructed taking into account the sources of premature boiling up of water inherent in micro-explosive experiments. The dependencies of the boiling up temperature of water on the heating rate obtained in the model turned out to be in accordance with the experimental data across a wide range of heating rates. A hypothesis about the local superheating of the transition layer, which is not detected in the experiment, is formulated. Thus, a step has been taken to clarify the essence of the mismatch of the degree of superheating of water recorded by macroscopic equipment along with a completely satisfactory generation of daughter droplets serving as the basis for advanced fuel technology.

Bursting of Underwater Oil Drops.

For decades, two main facets of underwater oil spills have been explored extensively-the rise of oil drops and resulting evolution of the oil slick at the air-water interface. We report on the bursting of rising oil drops at an air-liquid interface which precedes slick formation and reveal a counterintuitive bulge reversal that releases a daughter oil droplet inside the bulk as opposed to upward-shooting jets observed in bursting air bubbles. By unraveling the underlying physics we show that daughter droplet size and bulk liquid properties are correlated and their formation can be suppressed by an increase in the bulk viscosity.

On the onset of splashing of liquid metal drops in a viscous non-oxidizing environment

This Letter explores the onset of splashing of liquid metal drops and the underlying phenomenological reasons using a numerical approach. Validation is performed using experimental measurements, threshold splashing parameters, and by comparing splashing patterns. A significant observation is made: The ejection of the daughter droplet occurs toward the center of the mother drop instead of radially ejecting it outward. In the presence of a viscous medium, a significantly higher ejection angle of the daughter droplet between 90° and 130° is measured, compared to an air medium (average ejection angle of ∼10.6°). This work opens new avenues for further exploration of the broader topic of drop impact on a surface in viscous environments.

Experimental study of dynamic behavior of impacting droplets on vibrating super-hydrophobic surfaces

The dynamic behaviors of droplets impacting on a vibrating solid surface are complex and interesting, as the differences in the initial phase angle can result in various droplet behaviors. The dynamic behavior of free-falling droplets impacting vibrating superhydrophobic substrates was investigated via high-speed photography. The effects of the initial phase angle (φ), Weber number (We), and vibration frequency (f) on the morphology evolution and energy dissipation were analyzed. Herein, 12 initial phase angles were selected as variables to investigate the evolution of droplet morphology with various initial phase angles. The effect of different initial phase angles on the maximum spreading diameter of droplets can cause variations of over 10%. The initial phase angles enhancing or restricting the droplet spreading were quantitatively defined. The Weber number and initial phase angle which can produce daughter droplets are obtained quantitatively. Meanwhile, a correlation between dimensionless spreading coefficient and dimensionless time was established for various vibration frequencies (f), revealing the effects of f on the maximum spreading diameter of droplet. Furthermore, a mathematical relationship for predicting the maximum spreading diameter of droplet impacting on a vibrating substrate was established based on the derivation of energy conservation. The error of the prediction mathematical model was proved to be less than 2% by the experimental results. These results provide fundamental understanding of droplet impacting on a vibration wall and could be useful for related engineering applications.

Coalescence of non-spherical drops with a liquid surface

We employ three-dimensional numerical simulations to explore the impact dynamics of non-spherical drops in a deep liquid pool by varying the aspect ratios (Ar) and Weber numbers (We). We observe that when a non-spherical drop is gently placed on a liquid pool, it exhibits a partial coalescence phenomenon and the emergence of a daughter droplet for Ar>0.67. In contrast to the prolate (Ar<1) and spherical drops (Ar=1), an oblate (Ar>1) drop with a high aspect ratio encapsulates air in a ring-like bubble within the pool and emerges a liquid column that undergoes Rayleigh–Plateau capillary instability, leading to the formation of two daughter droplets with complex shapes. When the parent drop is impacted with finite velocity, our observations indicate that increasing the Weber number leads to elevated crater heights on the free surface for all aspect ratios. A prolate drop produces a less pronounced wave swell and exhibits a prolonged impact duration owing to its negligible impact area. Conversely, an oblate drop generates a much wider wave swell than spherical and prolate drops. We analyze the relationship between rim formation dynamics and the kinetic and surface energies of the system. Finally, we establish an analogy by comparing the dynamics of a freely falling non-spherical drop, undergoing topological oscillations during its descent from a height, with the impact dynamics of parent drops of various shapes striking the liquid surface with an equivalent velocity. Our investigation involving non-spherical drops contrasts the extensive studies conducted by various researchers on the impact of a parent spherical drop just above the free surface of a liquid pool.

Soft colloidal monolayers with reflection symmetry through confined drying.

Colloidal monolayers serve as fundamental building blocks in fabricating diverse functional materials, pivotal for surface modifications, chemical reactivity, and controlled assembly of nanoparticles. In this article, we report the formation of colloidal monolayers generated by drying an aqueous droplet containing soft colloids confined between two hydrophilic parallel plates. The analysis of the kinetics of evaporation in this confined mode showed that: (i) for a significant portion of the drying time, the drops adopt a catenoid configuration; (ii) in the penultimate stage of drying, the catenoid structure undergoes division into two daughter droplets; (iii) the three-phase contact line remains pinned at a specific location while it continuously slips at all other locations. The interplay between interface-assisted particle deposition onto the solid substrate and the time evolution of particle concentration within the droplet during evaporation results in unique microstructural features in the deposited patterns. Notably, these deposit patterns exhibit reflection symmetry. The microstructural features of the dried deposits are further quantified by calculating the particle number density, inter-particle separation, areal disorder parameter, and bond orientational order parameter. The variation of these parameters for deposits formed under different conditions, such as by altering the spacing between parallel plates and the concentration of microgel particles in the droplet, is discussed.

Generation, control, and application of stable bubbles in a hypersonic acoustic system.

Bubble-based microfluidics has been applied in many fields. However, there remains a need for a facile and flexible method for stable bubble generation and control in a microchannel. This paper reports a hypersonic acoustic system that can generate and release functional stable bubbles in a microchannel in an on-demand manner. It was found that the hypersonic frequency in this system played a vital role in the generation and control of bubbles. Specifically, a nanostructurally enhanced acoustic resonator was used to generate highly localized ultrahigh-frequency acoustic waves that ensured the feasibility and rapidity of bubble generation. Simultaneously, the acoustothermal effect of hypersound was harnessed to effectuate precise control over the bubble size. In addition, high-throughput droplet splitting was performed to confirm the stability of bubbles and their functionality in micromanipulation. The results showed that a mother droplet could be split controllably into a desired number of daughter droplets with specific volume ratios. In summary, the hypersonic acoustic system was demonstrated to be capable of on-demand-generation of stable bubbles in a microfluidic context and thus may extend the bubble-based applications.

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.

Experimental study on droplet breakup in an orifice jet mixer

AbstractThe droplet breakups in an orifice jet mixer are studied to gain a deeper understanding of the breakup mechanism and establish breakup models used as population balance model source terms for accurate predictions. The breakup process and details are captured in situ using a high‐speed photomicrography system. Experiments are performed with different levels of pressure drop and mother droplet size. A complete breakup process consists of several different sub‐breakup events, hence the cascade breakup definition is adopted to determine statistical results. High breakup frequency is achieved under high pressure drop and small mother droplet size. The average number of daughter droplets is 102–105 and is positively correlated with the pressure drop and mother droplet size. The daughter droplet size distribution has a tailing phenomenon and is mainly affected by the pressure drop. New breakup models based on the above features are established and predict well with the experimental results.

Daughter oil droplet entrainment by oil-coated bubble bursting

Compound bubbles with a liquid coating in another continuous immiscible bulk phase are ubiquitous in a wide range of natural and industrial processes. Their formation, rise and ultimate bursting at the air–liquid interface play crucial roles in the transport and fate of natural organic matter and contaminants. However, the dynamics of compound bubbles has not received considerable attention until recently. Here, inspired by our previous work (Yang et al., Nat. Phys., vol. 19, 2023, pp. 884–890), we investigate the entrainment of daughter oil droplets in bulk water produced by a bursting oil-coated bubble. We document that the size of the entrained daughter oil droplet is affected by the oil coating fraction and the bulk liquid properties. We rationalize this observation by balancing the viscous force exerted by the extensional flow produced by bubble bursting with the capillary force resisting the deformation of the oil coating, and considering the subsequent end-pinching process which finally entrains the daughter oil droplets. We propose a scaling analysis for the daughter oil droplet size that well captures the experimental results for a wide range of oil coating fractions and Ohnesorge numbers of the bulk liquid. In addition, we discuss the non-monotonic variation of daughter droplet size with the Ohnesorge number, and show the eventual absence of daughter droplets because of the strong viscous effect in the high-Ohnesorge-number regime. Our findings may advance the fundamental understanding of compound bubble bursting and provide guidance and modelling constraints for bubble-mediated contaminant transport in liquids.

Liquid distribution after head-on separation of two colliding immiscible liquid droplets

Equally sized droplets made of the same liquid are known to either bounce, coalesce, or separate under collision. Comparable outcomes are observed for immiscible liquids with bouncing, encapsulation instead of coalescence, and separation with two or more daughter droplets. While the transitions between these regimes have been described, the liquid distribution arising from separation remains poorly studied, especially in the case of head-on collisions, for which it cannot be predicted. This distribution can be of three types: either two encapsulated droplets form (single reflex separation), or a single encapsulated droplet plus a droplet made solely of the encapsulating liquid emerge, the latter being found either on the impact side (reflexive separation) or opposite to it (crossing separation). In this paper, a large number of experimental and simulation data covering collisions with partial and total wetting conditions and Weber and Reynolds numbers in the ranges of 2–720 and 66–1100, respectively, is analyzed. The conditions leading to the three liquid distributions are identified and described based on the decomposition of the collision in two phases: (i) radial extension of the compound droplet into a lamella and (ii) its relaxation into an elongated cylindrical droplet. In accordance with these two phases, two dimensionless parameters, Λ=ρi/ρoWei−1/2 and N=νo/νi σo/σio, are derived, which are built on the collision parameters and liquid properties of the encapsulated inner droplet (i) and the outer droplet (o) only. The combination of these two parameters predicts the type of liquid distribution in very good agreement with both experimental and numerical results.

Magnetic Janus origami robot for cross-scale droplet omni-manipulation

The versatile manipulation of cross-scale droplets is essential in many fields. Magnetic excitation is widely used for droplet manipulation due to its distinguishing merits. However, facile magnetic actuation strategies are still lacked to realize versatile multiscale droplet manipulation. Here, a type of magnetically actuated Janus origami robot is readily fabricated for versatile cross-scale droplet manipulation including three-dimensional transport, merging, splitting, dispensing and release of daughter droplets, stirring and remote heating. The robot allows untethered droplet manipulation from ~3.2 nL to ~51.14 μL. It enables splitting of droplet, precise dispensing (minimum of ~3.2 nL) and release (minimum of ~30.2 nL) of daughter droplets. The combination of magnetically controlled rotation and photothermal properties further endows the robot with the ability to stir and heat droplets remotely. Finally, the application of the robot in polymerase chain reaction (PCR) is explored. The extraction and purification of nucleic acids can be successfully achieved.

Hydrodynamic behavior of liquid flow in a rotating packed bed

Rotating Packed Bed (RPB) technology has emerged as a promising technology for reducing carbon footprint of various petrochemical processes by leveraging the HiGee field-induced mass transfer enhancement and allow for better capture of greenhouse gases. Despite its potential, there are still significant challenges that hinder the effective utilization of RPB technology in process intensification. Specifically, the hydraulics of liquid and gas phases within RPB packings present a significant challenge. In this study, 2D – VOF approach is employed to study the behavior of liquid droplets impacting on single rotating wire and on a whole rotating wire mesh within a Rotating Packed Bed (RPB). A comprehensive computational fluid dynamics (CFD) model is developed to analyze the influence of rotating speed, liquid velocity, and droplet diameter on the dynamics of liquid droplets. The boundaries of splashing – no splashing and dripping – capture breakup modes were validated for a single rotating wire and identified for wire mesh in RPBs by constructing the corresponding regime maps. This is achieved thanks to a new data processing algorithm that applies the principle of neighborhood aggregation. The proposed data processing algorithm helps reconstruct the regime maps for the various breakup phenomena within RPBs. The results show that the splashing mechanism reproduces higher-velocity detached daughter droplets, while the momentum-induced dripping mechanism results in low velocity daughter droplets. The results also reveal that the deposited liquid film with the wires has a key role in enhancing the splashing phenomena in RPBs. The radial distribution of diameter and velocity of liquid droplets in RPB is also analyzed in light of the droplet impact dynamics. The increase in the average liquid velocity with radial direction was attributed to the increase of splashed drops, which led to a bigger number of high-velocity droplets. The conclusions of this study can be used to help improve the dynamics of the two-phase flow within RPBs through a better packing design and flow conditions.

Droplet dynamics in asymmetric microfluidic junctions

Droplet-based microfluidics has received increasing interest over the last two decades, due to its extensive applications in drug delivery, cell encapsulation, protein crystallization, biochemical synthesis and high-throughput screening. As one of the key units in the microfluidic channels, asymmetric microfluidic junctions provide more opportunities to control and organize the droplets with different sizes, however, few studies have been reported to explore the effect of the junction angle on droplet behaviour in the asymmetric junctions. This work presents a numerical investigation of the droplet behaviour in asymmetric microfluidic junctions. The effect of the junction angle on the droplet breakup is explored in detail. Droplet breakup and non-breakup are found in asymmetric junctions. In the regime of the asymmetric breakup, the volume of the daughter droplet in the uphill branching channel is always larger than that in the downhill branching channel. Interestingly, in the regime of non-breakup, droplets are sorted into the uphill or downhill branching channels, suggesting that this asymmetric junction could be used for passive droplet sorting. The physical mechanisms behind droplet breakup and sorting are explored. Both the junction angle and the initial tip-to-tip length of the droplet play essential roles in the droplet behaviour in the asymmetric junctions. A phase diagram of the droplet behaviour is presented in this work. A scaling model is proposed to predict the transition between the breakup and non-breakup of the droplets in the asymmetric junctions.

Magnetic digital microfluidic manipulation with mobile surface energy traps capable of releasable droplet dispensing

Magnetic digital microfluidics (MDM) is a technology that manipulates droplets on an open surface with magnetic force for lab-on-a-chip (LOC) applications. MDM is capable of dispensing droplets of desired volume using surface energy traps (SETs); however, the daughter droplets dispensed by this approach cannot be released from the SET for subsequent microfluidic manipulation. This is a major disadvantage compared to the electrowetting-on-dielectrics (EWOD)-based digital microfluidics which is capable of releasable droplet dispensing. In this work, a polydopamine-coated thin magnet is introduced to MDM as a mobile SET for droplet manipulation, and for the first time, releasable droplet dispensing is accomplished on the MDM platform. In addition, the mobile SET is capable of all-terrain droplet transport regardless of the surface condition and rapid droplet transport via a unique droplet slingshot mechanism. The mobile SET-enabled MDM platform is able to match the functionality of the EWOD-based digital microfluidic system in terms of droplet dispensing and release, which will significantly expand the applicability and acceptability of MDM technology in biosensing, in vitro diagnostics, and many other biomedical applications.

Impact of hybrid surfaces on the droplet breakup dynamics in microgravity slug flow: A dynamic contact angle analysis

Microfluidic devices, which enable precise control and manipulation of fluids at the microscale, have revolutionized various fields, including chemical synthesis and space technology. A comprehensive understanding of fluid behavior under diverse conditions, particularly in microgravity, is essential for optimizing the design and performance of these devices. This paper aims to investigate the effects of discontinuous wettability on droplet breakup structures under microgravity conditions using a microchannel wall. The approach we adopt is underpinned by the volume-of-fluid methodology, an efficient technique renowned for its accurate resolution of the fluid interface in a two-phase flow. Furthermore, a modified dynamic contact angle model is employed to precisely predict the shape of the droplet interface at and near the wall. Our comprehensive model considers influential parameters such as slug length and droplet generation frequency, thereby providing crucial insights into their impact on the two-phase interface velocity. Validated against existing literature data, our model explores the impact of various configurations of discontinuous wettability on breakup morphology. Our findings highlight the significance of employing a dynamic contact angle methodology for making accurate predictions of droplet shape, which is influenced by the wall contact angle. Emphasis is placed particularly on the effects of slug length and droplet generation frequency. Notably, we demonstrate that the use of a hybrid surface at the junction section allows for precise control over the shape and size of the daughter droplets, contrasting with the symmetrical division observed on uniformly hydrophilic or superhydrophobic surfaces. This study contributes valuable insights into the complex dynamics of the droplet breakup process, which has profound implications for the design and optimization of microfluidic devices operating under microgravity conditions. Such insights are further poised to augment applications in space exploration, microreactors, and more.

The dynamic behavior of a droplet flows through a constricted splitting channel: a lattice Boltzmann study

In this paper, a lattice Boltzmann method is used to simulate the dynamic behavior of a droplet flows through a constricted channel, where an obstacle is placed in the center of the constricted channel to split the droplet. The method is first used to simulate the effect of the capillary number on the volume of the divided daughter droplets. Results show that the volume difference between the daughter droplets above and below the obstacle increases as increases. We also find that reducing the capillary number is conducive to the droplet splitting into two daughter droplets with similar volume. The method is then used to simulate the influence of the viscosity ratio on the droplet flows through a constricted channel. As increases, the volume difference between the daughter droplets above and below the obstacle decreases. Finally, the influence of the confinement ratio on the evolution of the droplet morphology is investigated. With increase in , the volume difference between the daughter droplets above and below the obstacle increases. When , the droplet does not break up and completely enters the bottom channel. Comparing with the converging-diverging and ratchet channels, the constricted splitting channel is more conductive to the breakup of the droplet neck.