Daughter Droplets Research Articles

A novel theoretical model of breakage rate and daughter size distribution for droplet in turbulent flows

A novel model for droplet breakage has been developed. In this model, several effective constraints of surface energy density increase combining the multiple breakage and the underlying turbulence were proposed. They exhibit a dependency on the original droplet size and the daughter droplets sizes, and reflect the difference between binary and higher order breakages. The possible non-exchangeability among the sizes of daughter droplets depends on the breakage process. Meanwhile, it can be accounted for by the proposed constraints. The breakage rate and daughter size distributions predicted by this model showed a good agreement with the available experimental data reported in the literature.

Active and Precise Control of Microdroplet Division Using Horizontal Pneumatic Valves in Bifurcating Microchannel

This paper presents a microfluidic system for the active and precise control of microdroplet division in a micro device. Using two horizontal pneumatic valves formed at downstream of bifurcating microchannel, flow resistances of downstream channels were variably controlled. With the resistance control, volumetric ratio of downstream flows was changed and water-in-oil microdroplets were divided into two daughter droplets of different volume corresponding to the ratio. The microfluidic channels and pneumatic valves were fabricated by single-step soft lithography process of PDMS (polydimethylsiloxane) using SU-8 mold. A wide range control of the daughter droplets’ volume ratio was achieved by the simple channel structure. Volumetric ratio between large and small daughter droplets are ranged from 1 to 70, and the smallest droplet volume of 14 pL was obtained. The proposed microfluidic device is applicable for precise and high throughput droplet based digital synthesis.

Generation of sub-femtoliter droplet by T-junction splitting on microfluidic chips

In the paper, sub-femtoliter droplets were easily produced by droplet splitting at a simple T-junction with orifice, which did not need expensive equipments, complex photolithography skill, or high energy input. The volume of the daughter droplet was not limited by channel size but controlled by channel geometry and fluidic characteristic. Moreover, single bead sampling and bead quantification in different orders of magnitude of droplet volumes were investigated. The droplets split at our T-junction chip had small volume and monodispersed size and could be produced efficiently, orderly, and controllably.

Droplet emission induced by ultrafast spreading on a superhydrophilic surface

A novel phenomenon is reported, wherein, if a mother droplet spreads faster than its critical velocity on a superhydrophilic surface, a smaller daughter droplet is emitted in a process that is controlled both dynamically and thermodynamically. Using a high-speed camera, we directly observed that while the lower part of the droplet spread, the upper part remained unchanged at first, and a temporary meniscus bridge formed in between. This meniscus bridge became unstable owing to capillary pressure, and broke when the lower part spread faster than its critical velocity, emitting the upper part as a daughter droplet. Through modeling and varying experimental parameters such as contact velocity, contact angle and surface structure, we determined that droplet emission could only be achieved by ultrafast spreading on superhydrophilic surfaces. The insights from these observations are helpful for the creation and application of special wettable surfaces.

Review on Applicable breakup/coalescence models in turbulent liquid-liquid flows

Liquid-liquid flows are common in process industries, particularly in turbulent systems. These systems are usually characterized by the diameter of the dispersed phase and are governed by external forces, deformation, breakup, and coalescence processes. In this review, the common methods and equations used to predict these phenomena will be discussed. First, deformation models in both laminar and turbulent flows containing single and multi-drop are considered. Then, the breakup process and models for these mechanisms are investigated. The coalescence process and collisions that may result in coalescence are also investigated. Coalescence efficiency is another factor that will be introduced in this review. Finally, daughter droplet size distribution is investigated considering both phenomenological and statistical models. Copyright © 2011-2013 by Walter de Gruyter GmbH.

Electrostatic charging and control of droplets in microfluidic devices

Precharged droplets can facilitate manipulation and control of low-volume liquids in droplet-based microfluidics. In this paper, we demonstrate non-contact electrostatic charging of droplets by polarizing a neutral droplet and splitting it into two oppositely charged daughter droplets in a T-junction microchannel. We performed numerical simulation to analyze the non-contact charging process and proposed a new design with a notch at the T-junction in aid of droplet splitting for more efficient charging. We experimentally characterized the induced charge in droplets in microfabricated devices. The experimental results agreed well with the simulation. Finally, we demonstrated highly effective droplet manipulation in a path selection unit appending to the droplet charging. We expect our work could enable precision manipulation of droplets for more complex liquid handling in microfluidics and promote electric-force based manipulation in 'lab-on-a-chip' systems.

How Does an Air Film Evolve into a Bubble During Drop Impact?

When a liquid drop impacts a solid surface, air is generally entrapped underneath. Using ultrafast x-ray phase-contrast imaging, we directly visualized the profile of an entrapped air film and its evolution into a bubble during drop impact. We identified a complicated evolution process that consists of three stages: inertial retraction of the air film, contraction of the top air surface into a bubble, and pinch-off of a daughter droplet inside the bubble. Energy transfer during retraction drives the contraction and pinch-off of a daughter droplet. The wettability of the solid surface affects the detachment of the bubble, suggesting a method for bubble elimination in many drop-impact applications.

Spreading and atomization of droplets on a vibrating surface in a standing pressure field

We report the first observation and analytical model of deformation and spreading of droplets on a vibrating surface under the influence of an ultrasonic standing pressure field. The standing wave allows the droplet to spread, and the spreading rate varies inversely with viscosity. In low viscosity droplets, the synergistic effect of radial acoustic force and the transducer surface acceleration also leads to capillary waves. These unstable capillary modes grow to cause ultimate disintegration into daughter droplets. We find that using nanosuspensions, spreading and disintegration can be prevented by suppressing the development of capillary modes and subsequent break-up.

Electrically Tunable Partial Coalescence of Oppositely Charged Drops

We report the existence of a critical ionic conductivity below which oppositely charged drops only partially coalesce. The extent of coalescence between dissimilarly sized water drops in oil can be tuned from complete coalescence at low electric field strengths to complete noncoalescence at high field strengths, thus providing external control over the daughter droplet size. Strikingly, the size and charge of the daughter droplet are both independent of the ionic conductivity. We present evidence suggesting the charge transfer is instead strongly influenced by convection associated with the capillary-driven penetration of a vortex into the larger drop, and we demonstrate that the size of the daughter droplet is consistent with a scaling model based on a balance between capillary-driven inertia and electrostatic repulsion.

Continuous generation of femtolitre droplets using multistage dividing microfluidic channel

We describe a novel method for generation of femtolitre-order monodisperse droplets using a multistage dividing microfluidic channel. A droplet is uniformly divided into 16 parts in a four-stage microfluidic channel without the need for external equipment. The droplets become smaller as the cross-junction part becomes narrower (range from 87.8 to 9.05 pL). Central micropillar structures at each bifurcation reduce the difference in the channel resistance throughout the microchannel between two side-channel that is divided by micropillar structures, which enables the equivalent division of femtolitre-order-volume droplets. After the fourth bifurcation, the minimum radius of a daughter droplet is 5 μm (ca. 524 fL) and the coefficient variation is 0.51%. The generation rate is 3800 droplets/s in a single-droplet generation line.

Low voltage picoliter droplet manipulation utilizing electrowetting-on-dielectric platforms

Picoliter droplets actuated on an electrowetting-on-dielectric (EWD) actuator are demonstrated. In this study, the physical scaling of electrodes for 33 μm and 21 μm EWD devices resulted in droplets of 12 pl and 5 pl being dispensed respectively in conjunction with 3 μm SU8 gaskets. The stacked multi-layer insulators in the actuators consisted of 200 nm tantalum pentoxide (Ta2O5) and 200 nm parylene C films deposited and coated with 70 nm of CYTOP. The voltages for dispensing droplets on chips without any external pressure sources are 17.1 Vrms and 22 Vrms for these two sets of devices. A 12 pl droplet can be split into two 6 pl daughter droplets at 18.7 Vrms with 33 μm electrode devices. Droplet manipulation is also demonstrated with paramagnetic beads and buffer solutions with proteins. In addition, electrodes with interlocking protrusions and special featured reservoir gasket are designed to facilitate droplet dispensing on these scaled EWD devices. In order to improve sealing of the two-piece sandwich EWD structure, a soft material, Norland Optical Adhesive (NOA), was coated on the top plate along with pressure on top. We demonstrate that based on fundamental theories and experiments, the dimensional scaling of EWD devices has not yet met a limitation as long as the EWD device can be sealed well.

Continuous-flow in-droplet magnetic particle separation in a droplet-based microfluidic platform

This paper presents a continuous-flow in-droplet magnetic particle separation in a droplet-based microfluidic device for magnetic bead-based bioassays. Two functions, electrocoalescence and magnetic particle manipulation, are performed in this device. A pair of charging metallic needles is inserted into two aqueous channels of the device. By electrostatic force, two different solutions can be merged to be mixed at a junction of droplet generation. The manipulation of magnetic particles is achieved using an externally applied magnetic field. The magnetic particles are separated by the magnetic field to one side of the droplet and extracted by splitting the droplet into two daughter droplets: one contains the majority of the magnetic particles and the other is almost devoid of magnetic particles. The applicability of the continuous-flow in-droplet magnetic particle separation is demonstrated by performing a proof-of-concept immunoassay between streptavidin-coated magnetic beads and biotin labelled with fluorescence. This approach will be useful for various biological and chemical analyses and compartmentalization of small samples.

Droplet dispensing in digital microfluidic devices: Assessment of long-term reproducibility

We report an in-depth study of the long-term reproducibility and reliability of droplet dispensing in digital microfluidic devices (DMF). This involved dispensing droplets from a reservoir, measuring the volume of both the droplet and the reservoir droplet and then returning the daughter droplet to the original reservoir. The repetition of this process over the course of several hundred iterations offers, for the first time, a long-term view of droplet dispensing in DMF devices. Results indicate that the ratio between the spacer thickness and the electrode size influences the reliability of droplet dispensing. In addition, when the separation between the plates is large, the volume of the reservoir greatly affects the reproducibility in the volume of the dispensed droplets, creating "reliability regimes." We conclude that droplet dispensing exhibits superior reliability as inter-plate device spacing is decreased, and the daughter droplet volume is most consistent when the reservoir volume matches that of the reservoir electrode.

Fission and fusion of droplets in a 3-D crossing microstructure

We demonstrate a 3-D crossing microstructure that has simple and versatile features for the fission and fusion of droplets. For their fission, the size of daughter droplets is readily controllable solely on modulating the ratio of flow rates at the inlets. We observed two distinct scenarios of droplet fission and propose dripping-like and squeezing-like mechanisms to explain such anomalous phenomena. Depending on the width of the outlet channel, the microstructure exhibits chronologically differentiated dynamics of droplet fusion and fission, leading to diverse droplet mixing. With this microstructure, droplets of diverse size and concentration can be accordingly produced from two individual droplets of distinct constituents. As the 3-D structure allows for both droplet dispersion and mixing, it is beneficially applicable for biochemical and biomedical applications such as drug dosing and drug delivery. Diverse droplet manipulations are realized with this 3-D crossing microstructure, shedding new light on droplet-based microfluidic systems.

Microfluidic platform for on-demand generation of spatially indexed combinatorial droplets

We propose a highly versatile and programmable nanolitre droplet-based platform that accepts an unlimited number of sample plugs from a multi-well plate, performs digitization of these sample plugs into smaller daughter droplets and subsequent synchronization-free, robust injection of multiple reagents into the sample daughter droplets on-demand. This platform combines excellent control of valve-based microfluidics with the high-throughput capability of droplet microfluidics. We demonstrate the functioning of a proof-of-concept device which generates combinatorial mixture droplets from a linear array of sample plugs and four different reagents, using food dyes to mimic samples and reagents. Generation of a one dimensional array of the combinatorial mixture droplets on the device leads to automatic spatial indexing of these droplets, precluding the need to include a barcode in each droplet to identify its contents. We expect this platform to further expand the range of applications of droplet microfluidics to include applications requiring a high degree of multiplexing as well as high throughput analysis of multiple samples.

Role of cohesive energy in droplet fragmentation

Using molecular-dynamics simulation, we investigate the fragmentation behavior of droplets after collision with a wall. We demonstrate that the ratio of the impact to the cohesive energy E(coh) of the droplet is the key quantity characterizing the droplet fragmentation process. To show this both van der Waals-bonded Ar and N(2) droplets and polar H(2)O droplets are studied. If the impact energy per molecule E<(0.35-0.4)E(coh), the droplet is reflected without fragmenting. Beyond that impact energy fragmentation of the droplet abruptly starts. At E=E(coh), the fragmentation process already results in a fine dispersal of the droplet into daughter droplets; the maximum fragment contains only less than 4% of the initial droplet mass and around one-third of the droplet has been shattered into isolated molecules. The disintegration process continuously increases with collision energy. These findings are relevant for the process of droplet fragmentation as used in the method of impact desolvation of electrosprayed microdroplets mass spectrometry.

Droplet breakup and viscosity-stratified flows in microchannels

The hydrodynamic coupling between droplets and viscous stratifications is examined in square microchannels. A segmented flow of droplets is injected into a viscosity-stratified flow region. The large difference in velocity between parallel streams having dissimilar viscosities produces a variety of droplet dynamics, including breakup into an array of daughter droplets. We characterize stable viscous stratifications generated using hydrodynamic focusing into a square microchannel and we present a general phase-diagram of droplet behavior. The capillary number is shown to influence both the morphology and dynamics of daughter droplets. In particular, the film thickness between droplets and walls is measured along with the droplet velocity. Deformable droplets significantly disrupt viscous stratifications at low Reynolds numbers and a plume is produced in the trail of the last daughter droplet. The formation and evolution of viscous fingers from the edges of high-viscosity stratifications are discussed. This study shows the possibility to displace high-viscosity oil with droplets in microgeometries.

Two-Dimensional Lattice Boltzmann Model for Droplet Impingement and Breakup in Low Density Ratio Liquids

AbstractA two-dimensional lattice Boltzmann model has been employed to simulate the impingement of a liquid drop on a dry surface. For a range of Weber number, Reynolds number and low density ratios, multiple phases leading to breakup have been obtained. An analytical solution for breakup as function of Reynolds and Weber number based on the conservation of energy is shown to match well with the simulations. At the moment breakup occurs, the spread diameter is maximum; it increases with Weber number and reaches an asymptotic value at a density ratio of 10. Droplet breakup is found to be more viable for the case when the wall is non-wetting or neutral as compared to a wetting surface. Upon breakup, the distance between the daughter droplets is much higher for the case with a non-wetting wall, which illustrates the role of the surface interactions in the outcome of the impact.

Analytical solution of the droplet breakup equation by the Adomian decomposition method

The droplet population balance equations (PBEs), which despite its importance rarely has an analytical solution. However, few cases with assumed functional forms of breakup rate, daughter droplet distribution exist, where most of these solutions are for the batch stirred vessel. A new framework for solving (PBEs) for batch and continuous systems is proposed in this work, which uses the Adomian decomposition method. This technique overcomes the crucial difficulties of numerical discretization and stability that often characterize previous solutions in this area. The technique used in this work has been tested for the droplet breakup equation. The solutions are presented for several cases, for which analytical solutions are available, for batch and continuous systems for droplet breakup in stirred vessels. In all cases, the predicted droplet size distributions converge exactly in a continuous form to that of the analytical solution.

Deformation and Breakup of Micro- and Nanoparticle Stabilized Droplets in Microfluidic Extensional Flows

Using a microfluidic flow-focusing device, monodisperse water droplets in oil were generated and their interface populated by either 1 μm or 500 nm amine modified silica particles suspended in the water phase. The deformation and breakup of these Pickering droplets were studied in both pure extensional flow and combined extensional and shear flow at various capillary numbers using a microfluidic hyperbolic contraction. The shear resulted from droplet confinement and increased with droplet size and position along the hyperbolic contraction. Droplet deformation was found to increase with increasing confinement and capillary number. At low confinements and low capillary numbers, the droplet deformation followed the predictions of theory. For fully confined droplets, where the interface was populated by 1 μm silica particles, the droplet deformation increased precipitously and two tails were observed to form at the rear of the droplet. These tails were similar to those seen for surfactant covered droplets. At a critical capillary number, daughter droplets were observed to stream from these tails. Due to the elasticity of the particle-laden interface, these drops did not return to a spherical shape, but were observed to buckle. Although increases in droplet deformation were observed, no tail streaming occurred for the 500 nm silica particle covered droplets over the range of capillary numbers studied.