Outer Droplet Research Articles

On the transport of a millimeter-sized compound droplet in a Poiseuille flow

The compound droplet consists of the inner and outer droplets. The outer droplet's ability to isolate the inner contents from its surroundings makes applications such as drug delivery, cell encapsulation, and cell sorting possible. Here, we experimentally explore the transport of the compound droplet at different Reynolds numbers, viscosity ratios, and volume ratios. Compound droplets have a longer dimensionless transport distance along the X-axis than single-phase droplets at Reynolds numbers from 44 to 366. When the Reynolds number is increased from 81.2 to 243.7, the dimensionless maximum transport distance of the compound droplet along the X-axis becomes 2.04 times. As the Re increases, the compound droplet deflection rate decreases continuously. For a constant initial velocity of the compound droplet, an increase in the viscosity ratio leads to an increase in the dimensionless velocity along the x axis with the compound droplet during transport. The maximum transport distance along the x-axis increases, and the deflection rate decreases as the inertial and viscous forces increase with increasing viscosity and dimension ratios. The chemical droplets become more stable as a result.

Numerical investigation of double emulsion formation in non-Newtonian fluids using double co-flow geometry

This paper uses the Volume of Fluid (VOF) method to simulate a double Co-Flow microfluidic device that can produce double emulsions in both Newtonian (water) and non-Newtonian fluids. The simulation is 2D axisymmetric and involves three phases. A model is evaluated in this study to examine how the size and double emulsion’s generation rate are impacted by factors such as phase velocity, viscosities, interfacial tension, and the rheological properties of non-Newtonian fluids. The model predicted the process of emulsification successfully in dripping and jetting regimes and predicted the impacts of phase velocity on the dimension and frequency of compound droplets. Increasing the flow rate of the inner phase causes the inner droplets to grow, while the outer droplet dimensions remain mostly unchanged. Vice versa, an increase in outer phase flow rate reduces compound droplet size. However, when the middle phase's flow rate is enhanced, the size of detached droplets in the inner and outer phases undergoes opposite changes, i.e., decreasing and increasing, respectively. The results showed that in non-Newtonian fluids, smaller droplets are formed compared to water, and the diameter of the double emulsions formed decreases with the rise in the viscosity at zero shear rate of the non-Newtonian fluid.

Interface coupling and droplet size under various flow-focusing geometry dimensions in double emulsion formation

The application performance of droplets, including the size and core-shell volumetric ratio of a double emulsion droplet, is investigated under various geometric sizes and flow rates in a flow-focusing capillary device. This study uses three-dimensional (3D) printing to create a novel substrate to assemble capillaries and make the inner dimension of the device tunable. Droplet generation is separated into two regions (uniform or non-uniform) based on the interface coupling shapes, where different generation modes are classified based on the rupture form of the multilayer interfaces. A map of the generation modes is established based on geometric size and flow conditions. In the dripping mode, interface coupling and its effect on generation are analyzed by the interface necking process for the two generation sub-modes (with/without a ball). The local capillary number of the double emulsion droplet is established for these sub-modes to analyze variations in the inner droplet volume, which helps propose the volume predictive model of inner and outer droplets.

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.

Temperature-Responsive Pickering Double Emulsions Stabilized by Binary Microgels.

Microgels are excellent emulsifiers that can self-assemble to reduce interfacial tension and form a steric barrier at an oil-water interface. Herein, we report a two-step emulsification approach to prepare oil-in-water-in-oil (O/W/O) Pickering double emulsions through the dispersion of microgels in two immiscible phases. The stabilization mechanism depends on the uneven distribution and adsorption of hydrophilic water-swollen microgels and hydrophobic octanol-swollen microgels on either outer water droplets or inner oil droplets. Our results reveal that binary microgels outperformed single microgels in terms of interfacial tension reduction and emulsion stabilization. Notably, the binary microgel-stabilized Pickering double emulsions show excellent temperature responsiveness owing to the intrinsic thermal sensitivity of microgels. Consequently, the selective and rapid release of encapsulated substances in different phases can be achieved through the adjustment of the ambient temperature.

Hydrodynamics during an immiscible compound droplet impact on a liquid pool

A numerical model based on the volume of fluid method is adopted to numerically study the hydrodynamics of an immiscible compound droplet impacting on a liquid pool. This numerical simulation achieves good agreement with the experimental results for both the evolutions of interface and cavity depth after droplet impact. By conducting the numerical simulation, three impact regimes are identified, namely, engulfment, bursting, and splashing, and a regime map with splashing threshold is plotted to quantitatively represent them. Under both bursting and splashing regimes, the inner and outer droplets have similar deformation behaviors during impact. The changes in impact velocity and inner droplet size have a greater effect on the hydrodynamic behaviors of the compound droplet under the bursting regime than that under the splashing regime. Larger inner droplet sizes can significantly reduce the deformation of the droplet and cavity. Moreover, to provide valuable guidance for controlling the compound droplet impacting on the liquid pool in the related real applications, a scaling correlation with a modified Weber number is proposed to predict the maximal spreading of the droplet.

A Tri‐Droplet Liquid Structure for Highly Efficient Intracellular Delivery in Primary Mammalian Cells Using Digital Microfluidics

Automated techniques for mammalian cell engineering are needed to examine a wide range of unique genetic perturbations especially when working with precious patient samples. An automated and miniaturized technique making use of digital microfluidics to electroporate a minimal number of mammalian cells (≈40 000) at a time on a scalable platform is introduced. This system functions by merging three droplets into a continuous droplet chain, which is called a triDrop. In the triDrop configuration, the outer droplets are comprised of high‐conductive liquid while an inner or middle droplet comprising of low‐conductivity liquid that contains the cells and biological payloads. In this work, it is shown that applying a voltage to the outer droplets generates an effective electric field throughout the tri‐droplet structure allowing for insertion of the biological payload into the cells without sacrificing long‐term cell health. This technique is shown for a range of biological payloads including plasmids, mRNA, and fully formed proteins being inserted into adherent and suspension cells which include primary T‐cells. The unique features of flexibility and versatility of triDrop show that the platform can be used for the automation of multiplexed gene edits with the benefits of low reagent consumption and minimal cell numbers.

Thermocapillary migration of a compound droplet on a substrate

We present a numerical study of the thermal migration of a compound droplet attached to a horizontal substrate. The different constant temperatures are applied to the left and right boundaries of the computational domain. The compound droplet contains one inner core. The problem is solved by using a front-tracking technique associated with the finite difference method. The investigated parameters include the radius ratio (Rio) of the inner droplet and the equivalent radius of the outer droplet (Rio varied in the range of 0.2 to 0.7), the viscosity ratio (μom) of the outer to middle fluids (μom varied in the range of 0.1 to 2.4), and the static contact angle θe (θe varied in the range of 60° to 120°). The results reveal that the inner droplet drives the compound droplet towards the hot region as its radius is sufficiently large (Rio≥ 0.6). The compound droplet moves towards the cold region as the value of Rio is less than 0.6. Increasing the viscosity of the outer fluid (by increasing μom) or θe causes the compound droplet to move towards the hot region. The trajectory of the centroid of the inner droplet is also investigated.

One-Step Generation of O/W/O Double Pickering Emulsions Utilizing Biocompatible Gliadin/Ethyl Cellulose Complex Particles as the Exclusive Stabilizer.

Double emulsions hold great potential for various applications due to their compartmentalized internal structures. However, achieving their long-term physical stability remains a challenging task. Here, we present a simple one-step method for producing stable oil-in-water-in-oil (O/W/O) double emulsions using biocompatible gliadin/ethyl cellulose complex particles as the sole stabilizer. The resulting O/W/O systems serve as effective platforms for encapsulating enzymes and as templates for synthesizing porous microspheres. We investigated the impact of particle concentration and water fraction on the properties of Pickering O/W/O emulsions. Our results demonstrate that the number and volume of inner oil droplets increased proportionally with both the water fraction and particle concentration after a 60-day storage period. Moreover, the catalytic reaction rate of the encapsulated lipase within the double emulsion exhibited a significant acceleration, achieving a substrate conversion of 80.9% within 15 min. Remarkably, the encapsulated enzyme showed excellent recyclability, enabling up to 10 cycles of reuse. Additionally, by utilizing the O/W/O systems as templates, we successfully obtained porous microspheres whose size can be controlled by the outer water droplet. These findings have significant implications for the future design of Pickering complex emulsion-based systems, opening avenues for extensive applications in pharmaceuticals, food, cosmetics, material synthesis, and (bio)catalysis.

Thermocapillary flow‐induced core release from double‐emulsion droplets in microchannels

AbstractThe use of double emulsions (DEs), which represent colloidal structures composed of droplets nested within droplets, can provide for unparallel droplet manipulation in droplet‐based microfluidic technology due to their unique core–shell structures. The controlled release of cores in DEs is of particular interest. However, this process remains poorly explored. In this work, the thermocapillary flow induced by a temperature gradient is used as a driving force to control the core release and the impacts of different linear temperature gradients, core diameters, shell diameter, and core/shell diameter ratios on the thermocapillary flow and core release characteristics of DE droplets consisting of a water‐in‐n‐hexadecane‐in‐water system within a cylindrical microchannel are investigated. Most of the core and shell diameter conditions considered result in a double‐core release process, where the inner droplet volume is partially ejected before the remaining core is rewrapped by the outer droplet, and the remaining inner droplet volume is ejected later during a second core release event. However, relatively small core diameters of 50 and 75 μm produce conditions where the full inner droplet volume is ejected during a single‐core release process. In addition, we provide empirical relationships for accurately determining the time at which core release initially occurs under given DE parameters as well as for precisely determining whether the applied conditions will lead to single‐ or double‐core release processes. Therefore, the results of this study provide insights enabling the development of accurate inner droplet release technologies under thermocapillary migration.

Electric-field-controlled deformation and spheroidization of compound droplet in an extensional flow

A 3-dimensional numerical model is developed by employing the electric current model and the phase-field method to investigate the electric-field-mediated compound droplet deformation and spheroidization in an extensional flow field (EFF). Based on this model, the detailed deformation morphologies of the compound droplet under different electrophysical properties are presented and the underlying electrohydrodynamics are clarified. Furthermore, the regime diagrams for quantificationally identifying different droplet deformation characteristics are summarized. In particular, the quantitative electrohydrodynamic criterion is obtained for achieving the droplet spheroidization in an EFF via the active electric field (EF) regulation. It is found that by applying a proper EF, the hydrodynamic force imposed by the EFF on the compound droplet and the flow-field-induced morphology deformation can be completely counterweighted. The deformation types and degrees of the compound droplet are determined by the fluids’ electrophysical parameters (especially the conductivity ratio R01 and permittivity ratio S01), EFF strength, and EF strength. Within the current research scope, the compound droplet can be restored to a spherical shape only when R01S01>1. Specifically, under a proper R01S01 (7≤ R01S01≤10 in the current simulation), the changing rate of the deformation of the outer droplet and inner droplet can match exactly and the two droplets can reach a spherical shape (i.e., S-S shape) simultaneously. Furthermore, the critical electric capillary number (CaE) for the compound droplet spheroidization is almost linearly related to the capillary number (Ca), which can be expressed as CaE=kCa. The factor k decreases with an increasing R01S01, so a larger R01S01 helps the compound droplet maintain its spherical shape.

Impact dynamics of compound drops of fluids with density contrast

The dynamics of compound drops impacting on a flat substrate is numerically investigated using a ternary-fluid diffuse-interface method, with the aim of assessing the effect of a density difference between the inner and outer droplets (denoted by $\lambda$ ) on the evolution of the interfaces. With the help of numerical simulations, we find that, at the intermediate stage of drop impact, the inner droplet exhibits a self-similar deformation at $\lambda =1$ and relatively high Weber number, and experiences more or less a uniform acceleration for various $\lambda$ . In particular, the acceleration magnitude at $\lambda \ne 1$ can be correlated with the acceleration at $\lambda =1$ and the Atwood number. When the inner droplet is denser than the outer one, a lamella occurs at the spreading front of the inner droplet. We present a scaling analysis of the thickness of the lamella, and the resultant theoretical prediction is in good agreement with numerical results. At the maximal spreading of the compound drop, a bulging structure is formed around the symmetry axis due to the presence of the inner droplet, thereby effectively reducing the liquid supply to the spreading front and leading to a decrease of maximal spreading ratio $\beta _{max}$ as compared with a pure drop. We proposed a corrected Weber number $We^*_\lambda$ by taking account of the combined effects of $\lambda$ , volume fraction of the inner droplet, Weber number and morphology of the compound drop. Integrating $We^*_\lambda$ with the universal model of $\beta _{max}$ for impacting pure drops, we successfully build up a new model for predicting the maximal spreading ratio of impacting compound drops with various $\lambda$ .

Numerical study of head-on collision of two equal-sized compound droplets

Although on-axis collisions between compound droplets are involved in numerous technological applications, no detailed investigation of such collisions is yet available. To address this problem, the present work uses an axisymmetric front-tracking method to numerically explore the dynamics of on-axis collisions of compound droplets that contain one or more inner droplets. Two identical droplets are placed symmetrically on the midplane of a computational domain and made to make contact with an initial colliding velocity. Various parameters such as the Reynolds number Re, the Weber number We, the size of the inner droplets, the interfacial tension ratio, and the eccentricity are considered. Three primary outcomes are observed: complete coalescence (CC), outer coalescence (OC), and rebound (R) for Re = 4–256 and We = 1–128. CC is when both the inner and outer droplets coalesce, whereas OC is when only the outer droplets coalesce. R is when the droplets come into contact and then bounce back. Increasing Re or decreasing We enhances the CC pattern, as does increasing the size of the inner droplets or the interfacial tension ratio. The influence of the initial distance between the droplets is also investigated. Finally, regime diagrams related to these patterns of collision are also presented.

Eccentricity-induced dielectrophoretic migration of a compound drop in a uniform external electric field

Eccentric compound drops, which are ubiquitous in many naturally inspired and engineering systems, can migrate under the sole presence of a uniform electric field, unlike the case of isolated single drops. Here, we report the migration of eccentric compound drops under a uniform electric field, imposed parallel to the line of centres of the constituting drops, by developing an approximate analytical model that applies to low Reynolds number limits under negligible droplet deformation, following axisymmetric considerations. In contrast to the sole influence of the electrohydrodynamic forces that has thus far been established to be emphatic for the eccentric configuration, here we report the additional effects induced by the dielectrophoretic forces to result in decisive manipulation in the drop migration. We show that the relative velocity between the inner and outer drops, which is a function of the eccentricity itself, dictates the dynamical evolution of the eccentricity variation under the competing electrohydrodynamic and dielectrophoretic interactions. This brings out four distinct regimes of the migration characteristics of the two drops based on their relative electro-physical properties. Our results reveal that an increase in eccentricity and the size ratio of the inner and outer droplets may induce monotonic or non-monotonic variation in the drop velocities, depending on the operating regime. We show how the interplay of various properties holds the control of selectively increasing or suppressing the eccentricity with time. These findings open up various avenues of electrically manipulative motion of encapsulated fluidic phases in various applications encompassing engineering and biology.

Modeling and simulation of the penetration of a compound droplet into a throat in a pore-throat structure

We present a theoretical and numerical study of a compound droplet flowing through a single pore-throat structure. By quantifying the capillary pressures in the pore and throat under various geometrical conditions, we derive a theoretical model to predict whether the compound droplet is able to penetrate into the throat in a pore-throat structure. Meanwhile, the lattice Boltzmann simulations are conducted to assess the capability and accuracy of the theoretical model. Through a combination of theoretical analysis and lattice Boltzmann simulations, we then investigate the effect of inner droplet size, compound droplet size, and surface wettability on the invasion behavior of a compound droplet. The results show that with increasing the inner droplet size or the compound droplet size, the compound droplet undergoes the transition from the state where the entire compound droplet can pass through the throat to the state where only a part of outer droplet penetrates into and blocks the throat. Although the theoretical predictions show good agreement with the simulation results for most of the cases investigated, it is found that the proposed theoretical model is not applicable to the cases in which the droplets are intermediate-wetting or wetting to the solid surface. This is because the shape of newly formed interface in the pore significantly deviates from the initial circle, which violates the assumption made in the derivation of the theoretical model.

Understanding the microfluidic generation of double emulsion droplets with alginate shell

The monodisperse double emulsions obtained by microfluidic method can serve as ideal templates for preparing core-shell alginate microcapsules, which have attracted much attention in biological applications, such as drug delivery systems and cell encapsulation, tissue engineering. However, the formation behavior and dynamic analysis of double emulsion with an alginate shell is still unclear due to the complex rheological behavior of alginate solutions. Herein, we employ a dual-coaxial microfluidic device to generate the high-quality double emulsion droplets with alginate shell, focusing on the effects of the fluid properties of alginate solution in the middle phase (viscosity, μm) and the fluid flow rate on the droplet formation mechanism. As the viscosity of the middle fluid (μm) increased, the size of compound droplets (D2) increased and the size of inner droplets (D1) decreased, and the break-up regimes occurred a dripping-to-jetting transition when μm = 160 mPa s. The number of encapsulated inner droplets can be predicted and precisely controlled by regulating the generation frequency of inner (f1) and outer droplets (f2). The breakup dynamics of the alginate thread are also analyzed by using the volume-of-fluid/continuum-surface-force (VOF/CSF) method. The results show that the pressure and velocity in the neck of pinch-off is lower in the jetting than that in the dripping regime. This study will provide useful guidance for the rational design and controllable preparation of core-shell alginate microcapsules.

Pinch-off dynamics of double-emulsion droplets with/without the influence of interfacial coupling effect

Pinch-off dynamics of double-emulsion droplets is experimentally studied. Pure liquid systems with different combinations of three-phase viscosities are considered to particularly reveal the thinning mechanisms and their variation characteristics when the interfacial coupling effect exists. The whole breakup process is analyzed at first, and the pinch-off stage governed by the interfacial tension is confirmed. The scaling law of the minimum neck width is constructed to make quantitative comparisons with the conventional theories obtained from single emulsions. The influence of the coupling effect on the thinning dynamics is discussed by sequentially varying the viscosity of one single phase of the liquid system. With the coupling effect, it is found that the rapid collapsing occurs in advance due to the superposition of the Laplace pressure differences at the minimum neck width. The thinning rate of the outer droplet follows that of the inner droplet until the breakup of the inner droplet, after which the thinning process of the outer droplet quickly coincides with the uncoupled case as the disturbances damp out by relatively high viscosity. On the contrary, the subsequent thinning dynamics would be changed when the low-viscosity liquid is used.

Experimental study on dynamics of double emulsion droplets flowing through the Y-shaped bifurcation

Dynamic behaviors of double emulsion droplets flowing through the Y-shaped bifurcation are experimentally studied and the influences of droplet length, droplet velocity, and liquid viscosity are particularly discussed. The flow patterns of double emulsion droplets are categorized by typical features in motion, namely the number of interfacial breakups and the coupling effect between interfaces. Critical conditions for the existence of the coupling effect are determined by the relative difference between the residence time of inner and outer droplets. Influences of the droplet length and velocity on the transition laws of flow patterns are summarized, and the corresponding dynamic mechanisms are discussed through characteristics of the interfacial deformations. Breakup conditions of inner and outer droplets are individually identified and their variations in liquid systems with different viscosity ratios are analyzed with the aid of the built theory of single emulsion droplets. Universal phase diagrams of the flow patterns are established by taking into account the physical parameters of both inner and outer droplets, which characterize all working forces including the viscous force, the squeezing force, the interfacial tension, and the coupling force that is the unique feature during the breakup of multiple interfaces.

A numerical study of a suspended compound droplet solidifying under forced convection

In this study, we numerically investigate the solidification process of a suspended compound droplet in a cold environment under forced convection by a front-tracking method. The compound droplet consisting of an inner gas core (i.e., inner bubble) surrounded by a phase-change liquid shell (i.e., outer droplet) starts solidifying from a nucleus at its bottom. The phase-change interface evolves upward to form the solid shell with an upper conical outer surface due to volume expansion. We monitor main parameters such as the Reynolds number (Re) in the range of 25–200, the Stefan number (St) in the range of 0.05–1.6, the inner-to-outer radius ratio (Rio) in the range of 0.2–0.7, the solid-to-liquid density ratio (ρs1) in the range of 0.8–1.2, the nucleus size (r0/R) in the range of 0.05–0.3, the initial eccentricity (ε0) in the range of -0.15–0.3 and the growth angle (ϕgr) in the range of 0°–15°. It is found that an increase in St, ρsl or a decrease in ϕgr leads to a decrease in the height of the solidified droplet. In contrast, an increase in Re, r0/R, ε0 or Rio has a minor effect on the drop height after complete solidification. In contrast to ρsl, which has less influence on the solidification time, the change in the value of these parameters considerably modifies the solidification time. The inner and outer aspect ratios of the solidified droplet are also revealed.

Numerical Investigation of Double Emulsion Droplets using Modified Flow Focusing Microfluidic Device for Drug Delivery

Double emulsion droplets generation is convenient for drug delivery applications since the core-shell template has the ability to increase the success of the target and release of the drug. In this study, the modified flow-focusing microfluidics device is proposed to generate double emulsion droplets with high monodispersity and high throughput, satisfying industrial needs. The W/O/W (water-in-oil-in-water) encapsulation template is a common combination in drug delivery. The research aims to analyze double emulsion droplets generation using the 2D Volume of Fluid (VoF) VoF approach, which is able to visualize flow regime, droplets average diameter, Coefficient of Variation (CoV), and droplets generation rate. Combination of water-in-olive oil-in-water was used as the working fluids. The diameter of the droplets, CoV, and generation rate was obtained using image processing. The simulation results showed that the injection model and the sudden expansion in the modified flow-focusing device successfully produced double emulsion droplets with two dripping instabilities. The narrowing jetting flow regime is obtained, including its droplets evolution. The average diameter for both outer and inner droplets were achieved with their CoV, including the generation rate. The outer and inner droplet's diameter generated can potentially be implemented for drug delivery, although the inner droplet's monodispersity must be further investigated. Nevertheless, the proposed device and the flow control were able to generate high-throughput double emulsion droplets.