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Experimental study of double emulsion formation behaviors in a one-step axisymmetric flow-focusing device
Experimental Thermal and Fluid Science 103 (2019) 18–28
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Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Experimental study of double emulsion formation behaviors in a one-step axisymmetric flow-focusing device
T
⁎
Cheng Yua, Liangyu Wua,b, , Lei Lia, Meifang Liuc a
Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, China School of Hydraulic, Energy and Power Engineering, Yangzhou University, Yangzhou 225127, China c Laser Fusion Research Center, China Academy of Engineering Physics, Mianyang 621900, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Double emulsion Flow-focusing Microfluidics Dripping, jetting
Formation behaviors of double emulsions in the one-step axisymmetric flow-focusing microfluidic device are studied experimentally based on a visualization system. Typical droplet formation regimes are examined and the effects of the flow rates on droplet sizes and morphologies are discussed. Especially, a comparative study of the performance between the flow-focusing and co-flowing device is conducted. The results indicate that the dripping and jetting regimes appear during the double emulsion formation under one-step flow-focusing, in which the dripping regime includes two distinct generation modes namely synchronized dripping and asynchronized dripping. Squeezing from the outer interface leads to the collapse of the inner interface in the synchronized dripping regime. The formation regime, droplet sizes as well as their polydispersities are determined by the flow rate of the outer fluid, while the shell thickness depends on the flow rate ratio between the middle fluid and the inner fluid. Compared with the co-flowing system, deformation of the interfaces is enhanced by the hydrodynamic focusing effect in the flow-focusing system where faster production of double emulsions with smaller sizes is achieved.
1. Introduction The microfluidics has recently been the attractive subject of scientific investigation for microscale heat and mass transfer [1,2], and the microfluidic generated droplets have been found in a wide technical application in ICF [3,4], biomedical [5] and chemical engineering [6], etc. Among the microfluidic generated droplets, dispersed droplets in emulsions are ideal vessels for various processes such as mixing [7,8], reactions [9,10] and diagnostics of materials [11] and are especially effective due to the highly extended surface area. Through shielding the inner droplets inside an additional middle fluid, double emulsions [12–14] can provide extra flexibility. For example, slow release and high loading are achieved by encapsulating insulin inside double emulsions [15]. Conventionally, double emulsions are produced by two-step mixing [16] in a top-to-bottom way accompanied with violent oscillation [12]. Hence, the conventional methods are unsatisfying when droplet morphologies and size distributions are prescribed. In the past few years, the emergence of double emulsions via microfluidic approaches [17–19] have innovated plenty of applications, including drug delivery [20,21], functional material synthesis [22], biochemical
analysis [23] and thermal management [24–26]. Attribute to the bottom-to-top approach [27], bulk processes are circumvented in microfluidic devices that manipulation over individual droplet can be realized. To actively control the droplet formation processes, particular geometries have been utilized as droplet makers in microfluidic devices and can be classified into three main categories: T-junction [28], coflowing [29] and flow-focusing [30–32]. Combining the basic droplet makers, a variety of microfluidic devices have been proposed to produce double emulsions. A co-flowing counter-current flow-focusing device is assembled by Utada et al. [12] using aligned glass capillaries. The coaxial flow of the inner and middle fluid is focused by the outer fluid flowing from the opposite direction into the collection tube and ruptured into double emulsions with high degree of control. Generally, double emulsion droplets can be formed either following a two-step [33,34] or a one-step approach [35,36]. The inner droplets are generated at the first droplet maker and carried downstream by the middle fluid into the second droplet maker to be encapsulated in the two-step devices. Comprised of consecutive droplet makers, two-step approach is popular in the design of quasi-two-dimensional microfluidic devices
⁎ Corresponding author at: Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, China. E-mail address: [email protected] (L. Wu).
https://doi.org/10.1016/j.expthermflusci.2018.12.032 Received 10 August 2018; Received in revised form 21 December 2018; Accepted 31 December 2018 Available online 03 January 2019 0894-1777/ © 2019 Elsevier Inc. All rights reserved.
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is added to the outer fluid supply tube via a three way valve, which is connected to a storage tank of the outer fluid shown in Fig. 1(b). Photos of the droplets are taken above the collection vessel to measure the size of the droplets and fifty droplets are collected to examine the size distribution. To fabricate the PDMS brick and PDMS annulus, SYGRID 184 (Dow Corning Co., Shanghai, China) mixed with curing agent is cured in the mould for 4 h at 85 °C. 20 mPa·s and 500 mPa·s silicon oil are applied as the inner fluid and outer fluid respectively, and 5% (w/w) solution of Poly(vinyl alcohol) 1788 are used as the middle fluid purchased from Aladdin Biochemical Technology Co., Shanghai, China. The physical properties of the fluids are summarized in Table 1. PTFE tubes are used to transport the fluids into the microfluidic device from three separate syringe pumps (LSP02-1B, Longer Precision Pump Co., Baoding, China). A microscope (SZX7, Olympus, Tokyo, Japan) combined with a highspeed camera (500K-M2, Photron, Tokyo, Japan) dynamically records the phase interface information of emulsion in our experiment. A cold light source (DAK-C1-0408, Dongxiong Co., Foshan, China) is placed at the opposite of the microscope to provide illumination. The room temperature is set at 22 °C for all experiments.
[37] especially when soft lithography is employed [38]. However, droplet makers must be modified with alternating wettability to guarantee the formation of double emulsions [39]. On the other hand, the inner droplet and outer droplet are generated through the same droplet maker in one-step devices under particular outer fluid flow field. Since the inner fluid is always shielded by the middle fluid, the wettability of the device wall has less effect on the droplet formation process than the two-step device. In particular, one-step device is advantageous in producing double emulsions with ultra-thin shells [40,41]. Yet the application of one-step approach still requires a comprehensive understanding of the complex interactions between two nested interfaces involved during the formation of double emulsions. In the one-step devices, two distinct regimes are recognized as dripping and jetting which are determined by the interplay between viscous force, interfacial tension, and inertial force. The radii of the droplets and jets can be predicted as functions of the flow rate of the outer fluid [12]. The instability of compound jet focused by a sheath fluid into a chamber is examined by Lee et al. [42] based on a conventional flow cytometer. The flow rate ratio between the middle fluid and inner fluid determines the shape of the coaxial fluid cones, the morphology of the downstream jet and the resultant double emulsions. Synchronous jet breakup occurs when the reduced wave number is below a certain threshold that mononuclear compound droplets can be formed. Whereas several fundamentals are still waiting to be investigated such as the transition from dripping to jetting and the quantitative relations between the radii of droplets and flow rates of all three fluids. In addition, the comparison between the two typical axisymmetric geometry – co-flowing and flow-focusing – has not been clarified yet. Here we focus on revealing the underlying physics of double emulsion generated by one-step axisymmetric flow-focusing geometry. An experimental study is conducted based on a visualization system comprised of microscope and high-speed CCD. The characteristics of dripping and jetting regimes are investigated as well as the transition from dripping to jetting evoked by increasing the flow rate of the outer fluid. The effects of the flow rate of the inner and middle fluid are also discussed. Additionally, the droplet formation in the flow-focusing device is compared with that in a co-flowing device to reveal the effect of hydrodynamic focusing on the double emulsion morphology and regime transition behaviors.
3. Results and discussion Through adjusting the flow rates, double emulsions with diverse morphologies can be produced as illustrated in Fig. 2. The shell thickness can be adjusted continuously from 5% to 50% of the double emulsion radius. According to the experimental observation, the droplet formation regimes for the flow-focusing device are the dripping and jetting. 3.1. Dripping regime Two generation modes of dripping regime namely synchronized dripping (Fig. 3(a)) and asynchronized dripping (Fig. 3(b)) are observed under the low flow rate of the outer fluid. Double emulsions are produced at the vicinity or even upstream of the flow-focusing orifice under both modes. The evolution of the inner interface and outer interface is synchronized in the synchronized dripping while asynchronized in the asynchronized dripping. Note that the orifice is made of transparent PDMS, red dotted lines are added in all the experimental photos hereinafter to help to recognize the position and shape of the orifice. The bubbles inside the dotted lines are sealed in the PDMS annulus to locate the orifice and do not affect the fluid flow. The nondimensional time is calculated as τ = t/(R1/vi) in which t is the real flow time and vi = Qi/πR12 is the velocity of the inner fluid hereinafter. To quantitatively characterize the interfaces behavior, the evolution of the droplet lengths li and lo (distance from the inlets of the inner and middle fluid to the fronts of the inner and outer droplet respectively as illustrated in Fig. 4(a)) are measured and non-dimensionalized by the inner diameter of the outer tube as Li = li/2R3 and Lo = lo/2R3 in Fig. 4(b). Synchronized dripping occurs when the flow rate of the middle fluid is much smaller than the inner fluid. The formation of double emulsions possesses strong periodic characteristics and can be divided into two stages, growing and detaching, and the growing stage takes up more than 90% time of a droplet formation cycle. And the evolution of Li and Lo are highly synchronized as shown in Fig. 4(b). During the earlier stage of growing, the inner and outer droplets attach to the outlets of the steel capillaries, and Li and Lo increase linearly with time. This growth law of the droplet lengths is similar with those double emulsions formed in co-flowing streams [43]. As the front of the double emulsion moves downstream and enters the orifice, the fluids are accelerated due to a reduction in flow passage area. The outer fluid converges the middle and inner fluid and stretches the interfaces along the flow direction leading to the rapid increment of Li and Lo (τ > 11.47). Both inner and outer interfaces cannot maintain a spherical shape inside the orifice owing to the confinement as shown in
2. Experimental setup The axisymmetric flow-focusing microfluidic device used in this work (see Fig. 1(a)) is assembled through a simple fabrication strategy. Firstly, a polydimethylsiloxane (PDMS) brick with fluid passages and holes for the alignment of the tubes is molded. Then, a short steel capillary (outer diameter (OD): 1.6 mm, inner diameter (ID): 1.32 mm) that is pulled off from 16G dispensing needles is inserted into the middle of PDMS brick to serve as the flow passage of middle fluid. A long steel capillary (OD: 0.62 mm, ID: 0.34 mm) pulled off from 23G dispensing needle is inserted from one end of the PDMS brick to inject the inner fluid into the device. Finally, a transparent polymethyl methacrylate (PMMA) tube (OD: 6 mm, ID: 4 mm) mounted with a concentric PDMS annulus is inserted at the other end of the PDMS brick as the outer fluid channel. As shown in Fig. 1(a), the outer diameter of the PDMS annulus is the same as R3. The diameter of the orifice in the annulus Rori is 1.6 mm and the thickness of the annulus Δori is 1 mm. The PDMS annulus is located at the downstream of the steel capillaries outlets to induce the flow-focusing effect into the device and the distance from the exits of the needles to the annulus Lori is 1.25 mm. All fluids are flowing in the same direction coaxially and the inner fluid is embraced by the middle fluid entirely, so no modification of surface wettability is required in droplet generation. The experimental system is presented in Fig. 1(b). To control the droplet formation processes, the flow rate of one fluid is adjusted while the flow rates of the other two fluids are kept constant. To refill the outer fluid to the syringe, a branch 19
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Fig. 1. (a) Schematic of the flow-focusing device, (b) Experimental system. Table 1 Physical properties of the fluids at 22 °C.
Inner fluid Middle fluid Outer fluid
Material
Density (kg/m3)
Viscosity (mPa·s)
Interfacial tension coefficient with the middle fluid (mN/m)
Silicon oil PVA solution 5% (w/w) Silicon oil
963 1082 963
20 33 500
1.8
20
2.2
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Fig. 2. Samples of double emulsions produced by the flow-focusing device (the scale bar is 200 μm).
Hence, synchronized deformation of the interfaces is beneficial for the production of highly uniformed double emulsions. 3.2. Jetting regime Jetting is another class of flow regime that produces double emulsions at the end of a stretched co-axial jet under high flow rate of the outer fluid. Increase in the viscous force of the outer fluid leads to a spontaneous transition from dripping to jetting, where the dominant force turns from interfacial tension into viscous force. There is only one jetting regime observed in our experiment as shown in Fig. 6. Since the droplets are growing and detaching in a fully developed flow field, the evolution of Li and Lo are almost linear with time except for the short period at the beginning of a droplet formation circle caused by the retraction of interfaces after detaching. Compared to dripping, the periodicity in jetting regime is not strong, hence, wider distribution in both inner and outer droplet size are observed (Fig. 6(c)). However, double emulsions can be produced at a higher frequency by jetting, which is preferred in situations that require fast droplet generation. Also, jetting is easier to occur in flow-focusing devices than that in coflowing devices [44] since the local viscous force from the outer fluid is proportional to 1/Rorifice2.
Fig. 3. (a) Synchronized dripping and (b) asynchronized dripping.
Fig. 4 τ = 13.27. The increased shear effect promotes the development of a neck on the outer interface while the inner interface remains inflated under interfacial tension (see τ = 14.17 in Fig. 4). Once formed, the neck shrinks drastically and drain the fluid inside, indicating the end of the growing stage. In the detaching stage, the interfaces are deformed rapidly along the radial direction. The inner interface is squeezed by the outer interface and breaks into a single inner droplet that moves downstream rapidly. The outer interface breaks up soon afterwards. After the inner droplet detaches, the outer interface collapse fast and only a thin layer of middle fluid is occupied by the formation of the double emulsion, due to the large flow rate ratio between the inner and middle fluids. The synchronized dripping is ideal for producing double emulsions with high monodispersity and ultra-thin shell as shown in Fig. 4(c). Another dripping mode namely asynchronized dripping is observed when the flow rate of the middle fluid and inner fluid are of the same magnitude, as shown in Fig. 5(a). Differing from the synchronized dripping mode, the growing stage in the asynchronized dripping mode takes up about 60% time of a droplet formation cycle and the evolution of Li and Lo is asynchronous. As illustrated in Fig. 5(b), Li grows almost linearly with time during the growing stage while the evolution of Lo is obviously faster. This is caused by the sufficient injection of the middle fluid. When the front of the outer droplet enters the orifice the inner droplet is still growing upstream. The detaching stage begins with the development of a neck on the inner interface (see τ = 7.76 in Fig. 5(b)). The evolution of Li is accelerated in the detaching stage when the inner interface enters the orifice and the inner interface soon breaks up producing an inner droplet. The inner droplet is carried downstream by the middle fluid while the neck on the outer interface is developing. The narrowest position of the neck moves downstream due to the expansion of the inner interface upstream. The produced double emulsions have size distribution wider than those formed under synchronized dripping mode (Fig. 5(c)).
3.3. Effects of flow rates on double emulsion formation The flow rate directly determines the flow regimes of droplet formation in microfluidics. Effects of the flow rates of the outer fluid, middle fluid and inner fluid on droplet formation morphologies, droplet sizes and formation frequencies are all examined and analyzed in this paper. Note that, in situations when both double emulsion and single emulsions are produced, only droplet size and formation frequency of the double emulsions are counted (Figs. 6–8). The flow rate of the outer fluid Qo determines both the droplet formation regime and droplet sizes as presented in Fig. 7. The shell thickness relies on the flow rate ratio between the middle fluid and inner fluid. As stated above, the dripping regime occurs under a low flow rate of the outer fluid producing relatively big double emulsions under low frequency. When Qo is of the same magnitude as Qi + Qm (such as Qo = 5 mL/h), the double emulsions are packed downstream of the orifice after detaching. The outer fluid is not flowing fast enough to bring the double emulsions downstream and merging of the double emulsions is observed if no surfactant is added to the fluid system. The droplet size decreases with Qo while the variation of Ro is more sensitive to Qo than that of Ri for Qo < 50 mL/h. This is caused by the generation of middle fluid single droplet strings before the detachment of double emulsion. The decrement in the outer interface area results in the decaying of viscous force acting on the outer interface, hence, polydispersed droplets of the middle fluid are produced. Yet the droplet formation regime is still dripping and the double emulsions are monodispersed. The number of middle fluid droplets decreases when Qo > 70 mL/h as shown in Fig. 7(a) attributed to the transition from dripping to jetting. Behaviors of both dripping and jetting are observed in transitional regimes. The detaching position of the outer interface is dragged downstream of the orifice by the viscous force while the detaching 21
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Fig. 4. Synchronized dripping (Qi = 2.5 mL/h, Qm = 0.25 mL/h, Qo = 15 mL/h): (a) evolution of the interfaces, (b) evolution of droplet length, (c) size distribution of the inner and outer droplets.
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Fig. 5. Asynchronized dripping (Qi = 2.5 mL/h, Qm = 2.5 mL/h, Qo = 12.5 mL/h): (a) evolution of the interfaces, (b) evolution of the droplet length, (c) size distribution of the inner and outer droplets.
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Fig. 6. Jetting regime (Qi = 2.5 mL/h, Qm = 2.5 mL/h, Qo = 375 mL/h): (a) evolution of the interfaces, (b) evolution of droplet length, (c) size distribution of the inner and outer droplets.
downstream. The presence of inner interface acts as an obstructive effect in the transition from dripping to jetting. As Qo exceeds 125 mL/h, the viscous force from the outer fluid is sufficient to overcome both the interfacial tension of the inner and outer interface. As consequence, coaxial cones of the interfaces yield and the detaching of the inner droplet synchronize with the outer droplet resulting in no single droplet of the middle fluid. The double emulsions form a line at the axis after detaching (Qo = 140 mL/h) and then scattered downstream due to the deceleration of the outer fluid downstream of the orifice. Though the double emulsions are packed densely, the droplets are small and are
position of the inner interface is still at upstream of the orifice and the two interface can be retracted back to the inlets the double emulsion is formed. This indicates that the viscous force can overcome the interfacial tension of the outer interface but is insufficient to overcome the interfacial tension of the inner interface. Various patterns of transition from dripping to jetting are observed in our experiments (70 mL/ h < Qo < 260 mL/h). When Qo > 85 mL/h dumbbell shaped droplet is formed and breaks into one double emulsion and one single droplet of the middle fluid accompanied with several satellite droplets when flowing
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Fig. 7. Effect of flow rate of the outer fluid on droplet formation: (a) droplet formation patterns, (b) droplet size and polydispersity, (c) droplet formation frequency (Qi = 2.5 mL/h, Qm = 2.5 mL/h).
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Fig. 8. Effect of the flow rate ratio between the middle and inner fluids on droplet formation: (a) droplet formation patterns, (b) droplet size, (c) droplet formation frequency (Qo = 15 mL/h).
coefficient of the outer interface decreases. According to our previous numerical works [41], the viscosity ratio of the middle fluid to the inner one has little influence on the droplet size in the dripping regime. While in the jetting regime, the droplet size increases with the rise in this viscosity ratio. Obvious effects on the interface shapes can be expected when the interfacial tension ratio of the outer interface to the inner one varies. However, the droplet formation regime is not affected in a wide range from 1 to 10. An increase in the flow-rate ratio between the middle and inner fluid Qm/Qi leads to higher shear on the inner interface and more single droplets of the middle fluid which attribute to the decrement of Ro and Ri as well as slower droplet formation frequency, as illustrated in Fig. 8. Regarding the effect of Qm/Qi on double emulsion formation behaviors, lower Qm/Qi (Qm/Qi < 1) favors the formation of monodispersed double emulsions with ultra-thin shells under dripping regime when the growth of the inner droplet and outer droplet are synchronized. Meanwhile, the shell thickness Δ is insensitive to Qm/Qi. Unlike the outer fluid, the flow-rate ratio between the middle and inner fluids Qm/ Qi has little influence on the droplet formation regime over the entire range of Qm/Qi investigated, as illustrated in Fig. 8(a). Hence, it is favorable to control the size of the double emulsions with almost constant shell thickness and low polydispersity through adjusting Qm/Qi, when Qm/Qi < 1. When Qm/Qi > 1, a mismatch in the growth of inner and outer droplet occurs and of the quantity of the single droplets of the middle fluid decreases with Qm/Qi. The inertia of the middle fluid grows stronger with Qm/Qi that suppresses the deformation of outer interface resulting in the production of bigger droplets of the middle fluid and double emulsions with thicker shells. The formation frequency of double emulsions increases gradually with Qm/Qi.
carried downstream timely hence the collision between droplets do not lead to massive merging in this situation. The sudden decrement in the droplet size is observed since all double emulsions are formed inside the orifice under high shear. All of the droplets formed are double emulsions and the droplet formation frequency reaches the highest accordingly. As Qo exceeds 180 mL/h, coaxial jets are developed with the detaching position of both inner and outer droplets been dragged downstream of the orifice. A string of inner droplets come off the end of the jet before the outer interface break up and the number of inner droplets are not constant, which is determined by the fluctuation on the outer interface. Since the double emulsions are formed downstream the orifice with less intense shear, bigger droplets can be produced. The sudden increment in Ro is observed owing to the multiple inner droplets encapsulated and the formation frequency decreases abruptly with Qo. Steady jetting regimes are observed after Qo exceeds 260 mL/h when the local convective instability of the perturbation is formed. Based on the analytical work of Herrada et al. [45], the transition from dripping to jetting is related to the absolute/convective instability which is determined by the critical Weber number. Both Ro and Ri decrease with Qo in jetting regime while the variation is less drastic compared with that in the dripping regime. The shell thickness is not sensitive to Qo as well. Similar results are obtained in the co-flowing system [46]. Compared to dripping, the polydispersity of double emulsions formed in jetting is relatively higher, however, the size distribution still meets the requirement in situations that prefer fast droplet formation frequency. The transition from dripping to jetting will happen under a lower flow rate of the outer fluid due to relatively large viscous force when the viscosity of the outer fluid increases or the interfacial tension 26
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single-core double emulsions covers from 30 mL/h to 250 mL/h in the co-flowing device and the shell thickness decrease with Qo slightly. Alternate detaching of double emulsions and single droplets of the middle fluid is also observed in the co-flowing device after Qo exceeds 260 mL/h which is the transition mode from dripping to jetting indicating that the viscous force dominates over the interfacial tension. Compared with the co-flowing device, in spite of Qo, smaller double emulsions with thinner shells are produced in the flow-focusing device with higher production rate (Fig. 9(b)). This can be attributed to the local confinement and increased shear brought by hydrodynamic focusing. The size of the double emulsions decreases with Qo in both devices while Ro_coflow (outer droplet radius of the double emulsions formed in the co-flowing device) is more sensitive to Qo due to the decay of inner droplets encapsulated, especially under low Qo. The transition from dripping to jetting in the flow-focusing device happens under low Qo than that in the co-flowing device caused by the increasing in the viscous force at the orifice. Note that there is a unique mode namely the monosized dripping [47] in the flow-focusing system (Qo = 150 mL/h in Fig. 9a) which is different from the standard dripping and jetting mode. Monodisperse droplets are formed right behind the tapering meniscus with much smaller diameter than the orifice. A scaling law predicting the droplet diameter as a function of the governing parameters is derived by Cruz-Mazo et al. [47].
4. Conclusions An axisymmetric one-step flow-focusing microfluidic device is assembled to investigate the double emulsion formation behaviors in this paper. Combined with a microscope and high-speed CCD, a visualization study is conducted. The entire droplet formation processes of both dripping and jetting regimes are analyzed. The effects of the flow rates of all three phases are discussed as well. In addition, comparative experiments are carried out to examine the performance of flow-focusing and co-flowing devices. The conclusion can be summarized as follows: (1) Two distinct droplet generation modes of dripping regime – synchronized dripping mode and asynchronized dripping mode – with strict periodicity are recognized. In the synchronized dripping mode, the detaching of the inner and outer droplets is highly synchronized and squeezing from the outer interface leads to the pinching of the inner interface. Monodispersed double emulsions with ultra-thin shells can be produced by the synchronized dripping mode. While in the asynchronized dripping mode, the evolution of the inner and outer interface is asynchronized. Double emulsions produced by the asynchronized dripping mode have wider size distribution than those produced by the synchronized dripping mode. (2) The flow rate of the outer fluid Qo determines the double emulsions are formed either in dripping or jetting regime. The detaching position of the droplets is dragged downstream with increasing Qo accompanied with various transitional modes. The flow rate ratio between the middle and inner fluids Qm/Qi is found to have little effect on the droplet formation regime over the entire range of Qm/ Qi (0.25 ≤ Qm/Qi ≤ 4.5) investigated. (3) Compared with the co-flowing device, the hydrodynamic focusing effect in the flow-focusing device enhances the deformation of the interfaces and leads to the production of smaller double emulsions under higher frequency. Also, the transition from dripping to jetting is facilitated under the presence of hydrodynamic focusing effect.
Fig. 9. Comparison of the double emulsion formation between co-flowing microchannel and flow-focusing microchannel: (a) interface morphologies, (b) droplet sizes and polydispersities.
3.4. Comparison with the co-flowing device Axisymmetric co-flowing and flow-focusing devices have similar configurations in which the fluids flow coaxially. The co-flowing device can be regarded as a special flow-focusing device in which the intensity of hydrodynamic focusing is zero. Hence, the droplet formations of double emulsions in co-flowing and flow-focusing devices are compared under the same flow conditions to study the effect of hydrodynamic focusing. As shown in Fig. 9(a), multi-core double emulsions with polydispersed inner droplets are formed in the co-flowing device under dripping regime when Qo ≤ 20 mL/h while monodispersed double emulsions are formed in the flow-focusing device. In the absence of hydrodynamic focusing, the viscous force acting from the outer fluid is insufficient, so the outer droplet does not detach until the interfacial tension brings about the collapse of the neck which leads to encapsulation of numerous inner droplets. Dripping regime producing
Conflict of interest The authors declared that there is no conflict of interest.
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Acknowledgements
microfluidic spray dryer, Lab Chip 11 (2011) 2362–2368. [21] Y. Chen, X. Liu, Y. Zhao, Deformation dynamics of double emulsion droplet under shear, Appl. Phys. Lett. 106 (2015) 141601. [22] T. Nisisako, T. Torii, T. Higuchi, Novel microreactors for functional polymer beads, Chem. Eng. J. 101 (2004) 23–29. [23] M.T. Guo, A. Rotem, J.A. Heyman, D.A. Weitz, Droplet microfluidics for highthroughput biological assays, Lab Chip 12 (2012) 2146–2155. [24] W.-G. Liang, C. Yang, G.-Q. Wen, W. Wang, X.-J. Ju, R. Xie, L.-Y. Chu, A facile and controllable method to encapsulate phase change materials with non-toxic and biocompatible chemicals, Appl. Therm. Eng. 70 (2014) 817–826. [25] X. Liu, Y. Chen, M. Shi, Dynamic performance analysis on start-up of closed-loop pulsating heat pipes (CLPHPs), Int. J. Therm. Sci. 65 (2013) 224–233. [26] Y. Chen, C. Zhang, M. Shi, Y. Yang, Thermal and hydrodynamic characteristics of constructal tree-shaped minichannel heat sink, AIChE J. 56 (2010) 2018–2029. [27] S.L. Anna, N. Bontoux, H.A. Stone, Formation of dispersions using “flow focusing” in microchannels, Appl. Phys. Lett. 82 (2003) 364–366. [28] T. Thorsen, R.W. Roberts, F.H. Arnold, S.R. Quake, Dynamic pattern formation in a vesicle-generating microfluidic device, Phys. Rev. Lett. 86 (2001) 4163–4166. [29] C. Cramer, P. Fischer, E.J. Windhab, Drop formation in a co-flowing ambient fluid, Chem. Eng. Sci. 59 (2004) 3045–3058. [30] A.M. Ganan-Calvo, J.M. Gordillo, Perfectly monodisperse microbubbling by capillary flow focusing, Phys. Rev. Lett. 87 (2001) 274501. [31] A.M. Ganan-Calvo, Perfectly monodisperse microbubbling by capillary flow focusing: an alternate physical description and universal scaling, Phys. Rev. E 69 (2004) 027301. [32] P. Garstecki, I. Gitlin, W. DiLuzio, G.M. Whitesides, E. Kumacheva, H.A. Stone, Formation of monodisperse bubbles in a microfluidic flow-focusing device, Appl. Phys. Lett. 85 (2004) 2649–2651. [33] S. Okushima, T. Nisisako, T. Torii, T. Higuchi, Controlled production of monodisperse double emulsions by two-step droplet breakup in microfluidic devices, Langmuir 20 (2004) 9905–9908. [34] A. Perro, C. Nicolet, J. Angy, S. Lecommandoux, J.-F. Le Meins, A. Colin, Mastering a double emulsion in a simple co-flow microfluidic to generate complex polymersomes, Langmuir 27 (2011) 9034–9042. [35] Z.H. Nie, S.Q. Xu, M. Seo, P.C. Lewis, E. Kumacheva, Polymer particles with various shapes and morphologies produced in continuous microfluidic reactors, J. Am. Chem. Soc. 127 (2005) 8058–8063. [36] A.R. Abate, J. Thiele, D.A. Weitz, One-step formation of multiple emulsions in microfluidics, Lab Chip 11 (2011) 253–258. [37] R.K. Shah, H.C. Shum, A.C. Rowat, D. Lee, J.J. Agresti, A.S. Utada, L.-Y. Chu, J.W. Kim, A. Fernandez-Nieves, C.J. Martinez, D.A. Weitz, Designer emulsions using microfluidics, Mater. Today 11 (2008) 18–27. [38] A. Rotem, A.R. Abate, A.S. Utada, V. Van Steijn, D.A. Weitz, Drop formation in nonplanar microfluidic devices, Lab Chip 12 (2012) 4263–4268. [39] A.R. Abate, D.A. Weitz, High-order multiple emulsions formed in poly(dimethylsiloxane) microfluidics, Small 5 (2009) 2030–2032. [40] S.A. Nabavi, G.T. Vladisavljevic, V. Manovic, Mechanisms and control of single-step microfluidic generation of multi-core double emulsion droplets, Chem. Eng. J. 322 (2017) 140–148. [41] Y.P. Chen, L.Y. Wu, L. Zhang, Dynamic behaviors of double emulsion formation in a flow-focusing device, Int. J. Heat Mass Transf. 82 (2015) 42–50. [42] S.Y. Lee, C. Snider, K. Park, J.P. Robinson, Compound jet instability in a microchannel for mononuclear compound drop formation, J. Micromech. Microeng. 17 (2007) 1558–1566. [43] T.V. Vu, S. Homma, G. Tryggvason, J.C. Wells, H. Takakura, Computations of breakup modes in laminar compound liquid jets in a coflowing fluid, Int. J. Multiphase Flow 49 (2013) 58–69. [44] X. Liu, L. Wu, Y. Zhao, Y. Chen, Study of compound drop formation in axisymmetric microfluidic devices with different geometries, Colloids Surf. A – Physicochem. Eng. Aspects 533 (2017) 87–98. [45] M.A. Herrada, J.M. Montanero, C. Ferrera, A.M. GaÑÁN-Calvo, Analysis of the dripping–jetting transition in compound capillary jets, J. Fluid Mech. 649 (2010) 523–536. [46] P. Lu, L. Wu, X. Liu, Visualization study of oil-in-water-in-oil (O/W/O) double emulsion formation in a simple and robust co-flowing microfluidic device, Micromachines 8 (2017) 268. [47] F. Cruz-Mazo, J.M. Montanero, A.M. Gañán-Calvo, Monosized dripping mode of axisymmetric flow focusing, Phys. Rev. E 94 (2016) 053122.
The authors gratefully acknowledge the supports of the National Natural Science Foundation of China (Grant Nos. 51706194, U1530260 and U1737104) and the Natural Science Foundation of Yangzhou City (Grant No. YZ2017103). References [1] D. Li, Encyclopedia of Microfluidics and Nanofluidics, Springer Science & Business Media, 2008. [2] C.B. Zhang, Z.L. Deng, Y.P. Chen, Temperature jump at rough gas-solid interface in Couette flow with a rough surface described by Cantor fractal, Int. J. Heat Mass Transf. 70 (2014) 322–329. [3] E.M. Campbell, V.N. Goncharov, T.C. Sangster, S.P. Regan, P.B. Radha, R. Betti, J.F. Myatt, D.H. Froula, M.J. Rosenberg, I.V. Igumenshchev, W. Seka, A.A. Solodov, A.V. Maximov, J.A. Marozas, T.J.B. Collins, D. Turnbull, F.J. Marshall, A. Shvydky, J.P. Knauer, R.L. McCrory, A.B. Sefkow, M. Hohenberger, P.A. Michel, T. Chapman, L. Masse, C. Goyon, S. Ross, J.W. Bates, M. Karasik, J. Oh, J. Weaver, A.J. Schmitt, K. Obenschain, S.P. Obenschain, S. Reyes, B. Van Wonterghem, Laser-direct-drive program: promise, challenge, and path forward, Matter Radiat. Extremes 2 (2017) 37–54. [4] M. Liu, L. Su, J. Li, S. Chen, Y. Liu, J. Li, B. Li, Y. Chen, Z. Zhang, Investigation of spherical and concentric mechanism of compound droplets, Matter Radiat. Extremes 1 (2016) 213–223. [5] J. Wang, W. Gao, H. Zhang, M. Zou, Y. Chen, Y. Zhao, Programmable wettability on photocontrolled graphene film, Sci. Adv. 4 (2018). [6] D.-K. Sun, Y. Wang, A.-P. Dong, B.-D. Sun, A three-dimensional quantitative study on the hydrodynamic focusing of particles with the immersed boundary – lattice Boltzmann method, Int. J. Heat Mass Transf. 94 (2016) 306–315. [7] J.D. Tice, H. Song, A.D. Lyon, R.F. Ismagilov, Formation of droplets and mixing in multiphase microfluidics at low values of the Reynolds and the capillary numbers, Langmuir 19 (2003) 9127–9133. [8] F. Alberini, D. Dapelo, R. Enjalbert, Y. Van Crombrugge, M.J.H. Simmons, Influence of DC electric field upon the production of oil-in-water-in-oil double emulsions in upwards mm-scale channels at low electric field strength, Exp. Therm. Fluid. Sci. 81 (2017) 265–276. [9] H. Chen, Y. Zhao, J. Li, M. Guo, J. Wan, D.A. Weitz, H.A. Stone, Reactions in double emulsions by flow-controlled coalescence of encapsulated drops, Lab Chip 11 (2011) 2312–2315. [10] X. Liu, C. Zhang, W. Yu, Z. Deng, Y. Chen, Bubble breakup in a microfluidic Tjunction, Sci. Bull. 61 (2016) 811–824. [11] J. Wang, L. Sun, M. Zou, W. Gao, C. Liu, L. Shang, Z. Gu, Y. Zhao, Bioinspired shapememory graphene film with tunable wettability, Sci. Adv. 3 (2017) e1700004. [12] A.S. Utada, E. Lorenceau, D.R. Link, P.D. Kaplan, H.A. Stone, D.A. Weitz, Monodisperse double emulsions generated from a microcapillary device, Science 308 (2005) 537–541. [13] Y. Chen, X. Liu, M. Shi, Hydrodynamics of double emulsion droplet in shear flow, Appl. Phys. Lett. 102 (2013) 051609. [14] Y. Chen, X. Liu, C. Zhang, Y. Zhao, Enhancing and suppressing effects of an inner droplet on deformation of a double emulsion droplet under shear, Lab Chip 15 (2015) 1255–1261. [15] B. Mutaliyeva, D. Grigoriev, G. Madybekova, A. Sharipova, S. Aidarova, A. Saparbekova, R. Miller, Microencapsulation of insulin and its release using w/o/ w double emulsion method, Colloids Surf. A – Physicochem. Eng. Aspects 521 (2017) 147–152. [16] C. Goubault, K. Pays, D. Olea, P. Gorria, J. Bibette, V. Schmitt, F. Leal-Calderon, Shear rupturing of complex fluids: application to the preparation of quasi-monodisperse water-in-oil-in-water double emulsions, Langmuir 17 (2001) 5184–5188. [17] Y. Chen, W. Gao, C. Zhang, Y. Zhao, Three-dimensional splitting microfluidics, Lab Chip 16 (2016) 1332–1339. [18] Y. Chen, Z. Deng, Hydrodynamics of a droplet passing through a microfluidic Tjunction, J. Fluid Mech. 819 (2017) 401–434. [19] C. Zhang, Y. Chen, Z. Deng, M. Shi, Role of rough surface topography on gas slip flow in microchannels, Phys. Rev. E 86 (2012) 016319. [20] J. Thiele, M. Windbergs, A.R. Abate, M. Trebbin, H.C. Shum, S. Foerster, D.A. Weitz, Early development drug formulation on a chip: Fabrication of nanoparticles using a
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Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Experimental study of double emulsion formation behaviors in a one-step axisymmetric flow-focusing device
T
⁎
Cheng Yua, Liangyu Wua,b, , Lei Lia, Meifang Liuc a
Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, China School of Hydraulic, Energy and Power Engineering, Yangzhou University, Yangzhou 225127, China c Laser Fusion Research Center, China Academy of Engineering Physics, Mianyang 621900, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Double emulsion Flow-focusing Microfluidics Dripping, jetting
Formation behaviors of double emulsions in the one-step axisymmetric flow-focusing microfluidic device are studied experimentally based on a visualization system. Typical droplet formation regimes are examined and the effects of the flow rates on droplet sizes and morphologies are discussed. Especially, a comparative study of the performance between the flow-focusing and co-flowing device is conducted. The results indicate that the dripping and jetting regimes appear during the double emulsion formation under one-step flow-focusing, in which the dripping regime includes two distinct generation modes namely synchronized dripping and asynchronized dripping. Squeezing from the outer interface leads to the collapse of the inner interface in the synchronized dripping regime. The formation regime, droplet sizes as well as their polydispersities are determined by the flow rate of the outer fluid, while the shell thickness depends on the flow rate ratio between the middle fluid and the inner fluid. Compared with the co-flowing system, deformation of the interfaces is enhanced by the hydrodynamic focusing effect in the flow-focusing system where faster production of double emulsions with smaller sizes is achieved.
1. Introduction The microfluidics has recently been the attractive subject of scientific investigation for microscale heat and mass transfer [1,2], and the microfluidic generated droplets have been found in a wide technical application in ICF [3,4], biomedical [5] and chemical engineering [6], etc. Among the microfluidic generated droplets, dispersed droplets in emulsions are ideal vessels for various processes such as mixing [7,8], reactions [9,10] and diagnostics of materials [11] and are especially effective due to the highly extended surface area. Through shielding the inner droplets inside an additional middle fluid, double emulsions [12–14] can provide extra flexibility. For example, slow release and high loading are achieved by encapsulating insulin inside double emulsions [15]. Conventionally, double emulsions are produced by two-step mixing [16] in a top-to-bottom way accompanied with violent oscillation [12]. Hence, the conventional methods are unsatisfying when droplet morphologies and size distributions are prescribed. In the past few years, the emergence of double emulsions via microfluidic approaches [17–19] have innovated plenty of applications, including drug delivery [20,21], functional material synthesis [22], biochemical
analysis [23] and thermal management [24–26]. Attribute to the bottom-to-top approach [27], bulk processes are circumvented in microfluidic devices that manipulation over individual droplet can be realized. To actively control the droplet formation processes, particular geometries have been utilized as droplet makers in microfluidic devices and can be classified into three main categories: T-junction [28], coflowing [29] and flow-focusing [30–32]. Combining the basic droplet makers, a variety of microfluidic devices have been proposed to produce double emulsions. A co-flowing counter-current flow-focusing device is assembled by Utada et al. [12] using aligned glass capillaries. The coaxial flow of the inner and middle fluid is focused by the outer fluid flowing from the opposite direction into the collection tube and ruptured into double emulsions with high degree of control. Generally, double emulsion droplets can be formed either following a two-step [33,34] or a one-step approach [35,36]. The inner droplets are generated at the first droplet maker and carried downstream by the middle fluid into the second droplet maker to be encapsulated in the two-step devices. Comprised of consecutive droplet makers, two-step approach is popular in the design of quasi-two-dimensional microfluidic devices
⁎ Corresponding author at: Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, China. E-mail address: [email protected] (L. Wu).
https://doi.org/10.1016/j.expthermflusci.2018.12.032 Received 10 August 2018; Received in revised form 21 December 2018; Accepted 31 December 2018 Available online 03 January 2019 0894-1777/ © 2019 Elsevier Inc. All rights reserved.
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is added to the outer fluid supply tube via a three way valve, which is connected to a storage tank of the outer fluid shown in Fig. 1(b). Photos of the droplets are taken above the collection vessel to measure the size of the droplets and fifty droplets are collected to examine the size distribution. To fabricate the PDMS brick and PDMS annulus, SYGRID 184 (Dow Corning Co., Shanghai, China) mixed with curing agent is cured in the mould for 4 h at 85 °C. 20 mPa·s and 500 mPa·s silicon oil are applied as the inner fluid and outer fluid respectively, and 5% (w/w) solution of Poly(vinyl alcohol) 1788 are used as the middle fluid purchased from Aladdin Biochemical Technology Co., Shanghai, China. The physical properties of the fluids are summarized in Table 1. PTFE tubes are used to transport the fluids into the microfluidic device from three separate syringe pumps (LSP02-1B, Longer Precision Pump Co., Baoding, China). A microscope (SZX7, Olympus, Tokyo, Japan) combined with a highspeed camera (500K-M2, Photron, Tokyo, Japan) dynamically records the phase interface information of emulsion in our experiment. A cold light source (DAK-C1-0408, Dongxiong Co., Foshan, China) is placed at the opposite of the microscope to provide illumination. The room temperature is set at 22 °C for all experiments.
[37] especially when soft lithography is employed [38]. However, droplet makers must be modified with alternating wettability to guarantee the formation of double emulsions [39]. On the other hand, the inner droplet and outer droplet are generated through the same droplet maker in one-step devices under particular outer fluid flow field. Since the inner fluid is always shielded by the middle fluid, the wettability of the device wall has less effect on the droplet formation process than the two-step device. In particular, one-step device is advantageous in producing double emulsions with ultra-thin shells [40,41]. Yet the application of one-step approach still requires a comprehensive understanding of the complex interactions between two nested interfaces involved during the formation of double emulsions. In the one-step devices, two distinct regimes are recognized as dripping and jetting which are determined by the interplay between viscous force, interfacial tension, and inertial force. The radii of the droplets and jets can be predicted as functions of the flow rate of the outer fluid [12]. The instability of compound jet focused by a sheath fluid into a chamber is examined by Lee et al. [42] based on a conventional flow cytometer. The flow rate ratio between the middle fluid and inner fluid determines the shape of the coaxial fluid cones, the morphology of the downstream jet and the resultant double emulsions. Synchronous jet breakup occurs when the reduced wave number is below a certain threshold that mononuclear compound droplets can be formed. Whereas several fundamentals are still waiting to be investigated such as the transition from dripping to jetting and the quantitative relations between the radii of droplets and flow rates of all three fluids. In addition, the comparison between the two typical axisymmetric geometry – co-flowing and flow-focusing – has not been clarified yet. Here we focus on revealing the underlying physics of double emulsion generated by one-step axisymmetric flow-focusing geometry. An experimental study is conducted based on a visualization system comprised of microscope and high-speed CCD. The characteristics of dripping and jetting regimes are investigated as well as the transition from dripping to jetting evoked by increasing the flow rate of the outer fluid. The effects of the flow rate of the inner and middle fluid are also discussed. Additionally, the droplet formation in the flow-focusing device is compared with that in a co-flowing device to reveal the effect of hydrodynamic focusing on the double emulsion morphology and regime transition behaviors.
3. Results and discussion Through adjusting the flow rates, double emulsions with diverse morphologies can be produced as illustrated in Fig. 2. The shell thickness can be adjusted continuously from 5% to 50% of the double emulsion radius. According to the experimental observation, the droplet formation regimes for the flow-focusing device are the dripping and jetting. 3.1. Dripping regime Two generation modes of dripping regime namely synchronized dripping (Fig. 3(a)) and asynchronized dripping (Fig. 3(b)) are observed under the low flow rate of the outer fluid. Double emulsions are produced at the vicinity or even upstream of the flow-focusing orifice under both modes. The evolution of the inner interface and outer interface is synchronized in the synchronized dripping while asynchronized in the asynchronized dripping. Note that the orifice is made of transparent PDMS, red dotted lines are added in all the experimental photos hereinafter to help to recognize the position and shape of the orifice. The bubbles inside the dotted lines are sealed in the PDMS annulus to locate the orifice and do not affect the fluid flow. The nondimensional time is calculated as τ = t/(R1/vi) in which t is the real flow time and vi = Qi/πR12 is the velocity of the inner fluid hereinafter. To quantitatively characterize the interfaces behavior, the evolution of the droplet lengths li and lo (distance from the inlets of the inner and middle fluid to the fronts of the inner and outer droplet respectively as illustrated in Fig. 4(a)) are measured and non-dimensionalized by the inner diameter of the outer tube as Li = li/2R3 and Lo = lo/2R3 in Fig. 4(b). Synchronized dripping occurs when the flow rate of the middle fluid is much smaller than the inner fluid. The formation of double emulsions possesses strong periodic characteristics and can be divided into two stages, growing and detaching, and the growing stage takes up more than 90% time of a droplet formation cycle. And the evolution of Li and Lo are highly synchronized as shown in Fig. 4(b). During the earlier stage of growing, the inner and outer droplets attach to the outlets of the steel capillaries, and Li and Lo increase linearly with time. This growth law of the droplet lengths is similar with those double emulsions formed in co-flowing streams [43]. As the front of the double emulsion moves downstream and enters the orifice, the fluids are accelerated due to a reduction in flow passage area. The outer fluid converges the middle and inner fluid and stretches the interfaces along the flow direction leading to the rapid increment of Li and Lo (τ > 11.47). Both inner and outer interfaces cannot maintain a spherical shape inside the orifice owing to the confinement as shown in
2. Experimental setup The axisymmetric flow-focusing microfluidic device used in this work (see Fig. 1(a)) is assembled through a simple fabrication strategy. Firstly, a polydimethylsiloxane (PDMS) brick with fluid passages and holes for the alignment of the tubes is molded. Then, a short steel capillary (outer diameter (OD): 1.6 mm, inner diameter (ID): 1.32 mm) that is pulled off from 16G dispensing needles is inserted into the middle of PDMS brick to serve as the flow passage of middle fluid. A long steel capillary (OD: 0.62 mm, ID: 0.34 mm) pulled off from 23G dispensing needle is inserted from one end of the PDMS brick to inject the inner fluid into the device. Finally, a transparent polymethyl methacrylate (PMMA) tube (OD: 6 mm, ID: 4 mm) mounted with a concentric PDMS annulus is inserted at the other end of the PDMS brick as the outer fluid channel. As shown in Fig. 1(a), the outer diameter of the PDMS annulus is the same as R3. The diameter of the orifice in the annulus Rori is 1.6 mm and the thickness of the annulus Δori is 1 mm. The PDMS annulus is located at the downstream of the steel capillaries outlets to induce the flow-focusing effect into the device and the distance from the exits of the needles to the annulus Lori is 1.25 mm. All fluids are flowing in the same direction coaxially and the inner fluid is embraced by the middle fluid entirely, so no modification of surface wettability is required in droplet generation. The experimental system is presented in Fig. 1(b). To control the droplet formation processes, the flow rate of one fluid is adjusted while the flow rates of the other two fluids are kept constant. To refill the outer fluid to the syringe, a branch 19
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Fig. 1. (a) Schematic of the flow-focusing device, (b) Experimental system. Table 1 Physical properties of the fluids at 22 °C.
Inner fluid Middle fluid Outer fluid
Material
Density (kg/m3)
Viscosity (mPa·s)
Interfacial tension coefficient with the middle fluid (mN/m)
Silicon oil PVA solution 5% (w/w) Silicon oil
963 1082 963
20 33 500
1.8
20
2.2
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Fig. 2. Samples of double emulsions produced by the flow-focusing device (the scale bar is 200 μm).
Hence, synchronized deformation of the interfaces is beneficial for the production of highly uniformed double emulsions. 3.2. Jetting regime Jetting is another class of flow regime that produces double emulsions at the end of a stretched co-axial jet under high flow rate of the outer fluid. Increase in the viscous force of the outer fluid leads to a spontaneous transition from dripping to jetting, where the dominant force turns from interfacial tension into viscous force. There is only one jetting regime observed in our experiment as shown in Fig. 6. Since the droplets are growing and detaching in a fully developed flow field, the evolution of Li and Lo are almost linear with time except for the short period at the beginning of a droplet formation circle caused by the retraction of interfaces after detaching. Compared to dripping, the periodicity in jetting regime is not strong, hence, wider distribution in both inner and outer droplet size are observed (Fig. 6(c)). However, double emulsions can be produced at a higher frequency by jetting, which is preferred in situations that require fast droplet generation. Also, jetting is easier to occur in flow-focusing devices than that in coflowing devices [44] since the local viscous force from the outer fluid is proportional to 1/Rorifice2.
Fig. 3. (a) Synchronized dripping and (b) asynchronized dripping.
Fig. 4 τ = 13.27. The increased shear effect promotes the development of a neck on the outer interface while the inner interface remains inflated under interfacial tension (see τ = 14.17 in Fig. 4). Once formed, the neck shrinks drastically and drain the fluid inside, indicating the end of the growing stage. In the detaching stage, the interfaces are deformed rapidly along the radial direction. The inner interface is squeezed by the outer interface and breaks into a single inner droplet that moves downstream rapidly. The outer interface breaks up soon afterwards. After the inner droplet detaches, the outer interface collapse fast and only a thin layer of middle fluid is occupied by the formation of the double emulsion, due to the large flow rate ratio between the inner and middle fluids. The synchronized dripping is ideal for producing double emulsions with high monodispersity and ultra-thin shell as shown in Fig. 4(c). Another dripping mode namely asynchronized dripping is observed when the flow rate of the middle fluid and inner fluid are of the same magnitude, as shown in Fig. 5(a). Differing from the synchronized dripping mode, the growing stage in the asynchronized dripping mode takes up about 60% time of a droplet formation cycle and the evolution of Li and Lo is asynchronous. As illustrated in Fig. 5(b), Li grows almost linearly with time during the growing stage while the evolution of Lo is obviously faster. This is caused by the sufficient injection of the middle fluid. When the front of the outer droplet enters the orifice the inner droplet is still growing upstream. The detaching stage begins with the development of a neck on the inner interface (see τ = 7.76 in Fig. 5(b)). The evolution of Li is accelerated in the detaching stage when the inner interface enters the orifice and the inner interface soon breaks up producing an inner droplet. The inner droplet is carried downstream by the middle fluid while the neck on the outer interface is developing. The narrowest position of the neck moves downstream due to the expansion of the inner interface upstream. The produced double emulsions have size distribution wider than those formed under synchronized dripping mode (Fig. 5(c)).
3.3. Effects of flow rates on double emulsion formation The flow rate directly determines the flow regimes of droplet formation in microfluidics. Effects of the flow rates of the outer fluid, middle fluid and inner fluid on droplet formation morphologies, droplet sizes and formation frequencies are all examined and analyzed in this paper. Note that, in situations when both double emulsion and single emulsions are produced, only droplet size and formation frequency of the double emulsions are counted (Figs. 6–8). The flow rate of the outer fluid Qo determines both the droplet formation regime and droplet sizes as presented in Fig. 7. The shell thickness relies on the flow rate ratio between the middle fluid and inner fluid. As stated above, the dripping regime occurs under a low flow rate of the outer fluid producing relatively big double emulsions under low frequency. When Qo is of the same magnitude as Qi + Qm (such as Qo = 5 mL/h), the double emulsions are packed downstream of the orifice after detaching. The outer fluid is not flowing fast enough to bring the double emulsions downstream and merging of the double emulsions is observed if no surfactant is added to the fluid system. The droplet size decreases with Qo while the variation of Ro is more sensitive to Qo than that of Ri for Qo < 50 mL/h. This is caused by the generation of middle fluid single droplet strings before the detachment of double emulsion. The decrement in the outer interface area results in the decaying of viscous force acting on the outer interface, hence, polydispersed droplets of the middle fluid are produced. Yet the droplet formation regime is still dripping and the double emulsions are monodispersed. The number of middle fluid droplets decreases when Qo > 70 mL/h as shown in Fig. 7(a) attributed to the transition from dripping to jetting. Behaviors of both dripping and jetting are observed in transitional regimes. The detaching position of the outer interface is dragged downstream of the orifice by the viscous force while the detaching 21
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Fig. 4. Synchronized dripping (Qi = 2.5 mL/h, Qm = 0.25 mL/h, Qo = 15 mL/h): (a) evolution of the interfaces, (b) evolution of droplet length, (c) size distribution of the inner and outer droplets.
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Fig. 5. Asynchronized dripping (Qi = 2.5 mL/h, Qm = 2.5 mL/h, Qo = 12.5 mL/h): (a) evolution of the interfaces, (b) evolution of the droplet length, (c) size distribution of the inner and outer droplets.
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Fig. 6. Jetting regime (Qi = 2.5 mL/h, Qm = 2.5 mL/h, Qo = 375 mL/h): (a) evolution of the interfaces, (b) evolution of droplet length, (c) size distribution of the inner and outer droplets.
downstream. The presence of inner interface acts as an obstructive effect in the transition from dripping to jetting. As Qo exceeds 125 mL/h, the viscous force from the outer fluid is sufficient to overcome both the interfacial tension of the inner and outer interface. As consequence, coaxial cones of the interfaces yield and the detaching of the inner droplet synchronize with the outer droplet resulting in no single droplet of the middle fluid. The double emulsions form a line at the axis after detaching (Qo = 140 mL/h) and then scattered downstream due to the deceleration of the outer fluid downstream of the orifice. Though the double emulsions are packed densely, the droplets are small and are
position of the inner interface is still at upstream of the orifice and the two interface can be retracted back to the inlets the double emulsion is formed. This indicates that the viscous force can overcome the interfacial tension of the outer interface but is insufficient to overcome the interfacial tension of the inner interface. Various patterns of transition from dripping to jetting are observed in our experiments (70 mL/ h < Qo < 260 mL/h). When Qo > 85 mL/h dumbbell shaped droplet is formed and breaks into one double emulsion and one single droplet of the middle fluid accompanied with several satellite droplets when flowing
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Fig. 7. Effect of flow rate of the outer fluid on droplet formation: (a) droplet formation patterns, (b) droplet size and polydispersity, (c) droplet formation frequency (Qi = 2.5 mL/h, Qm = 2.5 mL/h).
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Fig. 8. Effect of the flow rate ratio between the middle and inner fluids on droplet formation: (a) droplet formation patterns, (b) droplet size, (c) droplet formation frequency (Qo = 15 mL/h).
coefficient of the outer interface decreases. According to our previous numerical works [41], the viscosity ratio of the middle fluid to the inner one has little influence on the droplet size in the dripping regime. While in the jetting regime, the droplet size increases with the rise in this viscosity ratio. Obvious effects on the interface shapes can be expected when the interfacial tension ratio of the outer interface to the inner one varies. However, the droplet formation regime is not affected in a wide range from 1 to 10. An increase in the flow-rate ratio between the middle and inner fluid Qm/Qi leads to higher shear on the inner interface and more single droplets of the middle fluid which attribute to the decrement of Ro and Ri as well as slower droplet formation frequency, as illustrated in Fig. 8. Regarding the effect of Qm/Qi on double emulsion formation behaviors, lower Qm/Qi (Qm/Qi < 1) favors the formation of monodispersed double emulsions with ultra-thin shells under dripping regime when the growth of the inner droplet and outer droplet are synchronized. Meanwhile, the shell thickness Δ is insensitive to Qm/Qi. Unlike the outer fluid, the flow-rate ratio between the middle and inner fluids Qm/ Qi has little influence on the droplet formation regime over the entire range of Qm/Qi investigated, as illustrated in Fig. 8(a). Hence, it is favorable to control the size of the double emulsions with almost constant shell thickness and low polydispersity through adjusting Qm/Qi, when Qm/Qi < 1. When Qm/Qi > 1, a mismatch in the growth of inner and outer droplet occurs and of the quantity of the single droplets of the middle fluid decreases with Qm/Qi. The inertia of the middle fluid grows stronger with Qm/Qi that suppresses the deformation of outer interface resulting in the production of bigger droplets of the middle fluid and double emulsions with thicker shells. The formation frequency of double emulsions increases gradually with Qm/Qi.
carried downstream timely hence the collision between droplets do not lead to massive merging in this situation. The sudden decrement in the droplet size is observed since all double emulsions are formed inside the orifice under high shear. All of the droplets formed are double emulsions and the droplet formation frequency reaches the highest accordingly. As Qo exceeds 180 mL/h, coaxial jets are developed with the detaching position of both inner and outer droplets been dragged downstream of the orifice. A string of inner droplets come off the end of the jet before the outer interface break up and the number of inner droplets are not constant, which is determined by the fluctuation on the outer interface. Since the double emulsions are formed downstream the orifice with less intense shear, bigger droplets can be produced. The sudden increment in Ro is observed owing to the multiple inner droplets encapsulated and the formation frequency decreases abruptly with Qo. Steady jetting regimes are observed after Qo exceeds 260 mL/h when the local convective instability of the perturbation is formed. Based on the analytical work of Herrada et al. [45], the transition from dripping to jetting is related to the absolute/convective instability which is determined by the critical Weber number. Both Ro and Ri decrease with Qo in jetting regime while the variation is less drastic compared with that in the dripping regime. The shell thickness is not sensitive to Qo as well. Similar results are obtained in the co-flowing system [46]. Compared to dripping, the polydispersity of double emulsions formed in jetting is relatively higher, however, the size distribution still meets the requirement in situations that prefer fast droplet formation frequency. The transition from dripping to jetting will happen under a lower flow rate of the outer fluid due to relatively large viscous force when the viscosity of the outer fluid increases or the interfacial tension 26
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single-core double emulsions covers from 30 mL/h to 250 mL/h in the co-flowing device and the shell thickness decrease with Qo slightly. Alternate detaching of double emulsions and single droplets of the middle fluid is also observed in the co-flowing device after Qo exceeds 260 mL/h which is the transition mode from dripping to jetting indicating that the viscous force dominates over the interfacial tension. Compared with the co-flowing device, in spite of Qo, smaller double emulsions with thinner shells are produced in the flow-focusing device with higher production rate (Fig. 9(b)). This can be attributed to the local confinement and increased shear brought by hydrodynamic focusing. The size of the double emulsions decreases with Qo in both devices while Ro_coflow (outer droplet radius of the double emulsions formed in the co-flowing device) is more sensitive to Qo due to the decay of inner droplets encapsulated, especially under low Qo. The transition from dripping to jetting in the flow-focusing device happens under low Qo than that in the co-flowing device caused by the increasing in the viscous force at the orifice. Note that there is a unique mode namely the monosized dripping [47] in the flow-focusing system (Qo = 150 mL/h in Fig. 9a) which is different from the standard dripping and jetting mode. Monodisperse droplets are formed right behind the tapering meniscus with much smaller diameter than the orifice. A scaling law predicting the droplet diameter as a function of the governing parameters is derived by Cruz-Mazo et al. [47].
4. Conclusions An axisymmetric one-step flow-focusing microfluidic device is assembled to investigate the double emulsion formation behaviors in this paper. Combined with a microscope and high-speed CCD, a visualization study is conducted. The entire droplet formation processes of both dripping and jetting regimes are analyzed. The effects of the flow rates of all three phases are discussed as well. In addition, comparative experiments are carried out to examine the performance of flow-focusing and co-flowing devices. The conclusion can be summarized as follows: (1) Two distinct droplet generation modes of dripping regime – synchronized dripping mode and asynchronized dripping mode – with strict periodicity are recognized. In the synchronized dripping mode, the detaching of the inner and outer droplets is highly synchronized and squeezing from the outer interface leads to the pinching of the inner interface. Monodispersed double emulsions with ultra-thin shells can be produced by the synchronized dripping mode. While in the asynchronized dripping mode, the evolution of the inner and outer interface is asynchronized. Double emulsions produced by the asynchronized dripping mode have wider size distribution than those produced by the synchronized dripping mode. (2) The flow rate of the outer fluid Qo determines the double emulsions are formed either in dripping or jetting regime. The detaching position of the droplets is dragged downstream with increasing Qo accompanied with various transitional modes. The flow rate ratio between the middle and inner fluids Qm/Qi is found to have little effect on the droplet formation regime over the entire range of Qm/ Qi (0.25 ≤ Qm/Qi ≤ 4.5) investigated. (3) Compared with the co-flowing device, the hydrodynamic focusing effect in the flow-focusing device enhances the deformation of the interfaces and leads to the production of smaller double emulsions under higher frequency. Also, the transition from dripping to jetting is facilitated under the presence of hydrodynamic focusing effect.
Fig. 9. Comparison of the double emulsion formation between co-flowing microchannel and flow-focusing microchannel: (a) interface morphologies, (b) droplet sizes and polydispersities.
3.4. Comparison with the co-flowing device Axisymmetric co-flowing and flow-focusing devices have similar configurations in which the fluids flow coaxially. The co-flowing device can be regarded as a special flow-focusing device in which the intensity of hydrodynamic focusing is zero. Hence, the droplet formations of double emulsions in co-flowing and flow-focusing devices are compared under the same flow conditions to study the effect of hydrodynamic focusing. As shown in Fig. 9(a), multi-core double emulsions with polydispersed inner droplets are formed in the co-flowing device under dripping regime when Qo ≤ 20 mL/h while monodispersed double emulsions are formed in the flow-focusing device. In the absence of hydrodynamic focusing, the viscous force acting from the outer fluid is insufficient, so the outer droplet does not detach until the interfacial tension brings about the collapse of the neck which leads to encapsulation of numerous inner droplets. Dripping regime producing
Conflict of interest The authors declared that there is no conflict of interest.
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Acknowledgements
microfluidic spray dryer, Lab Chip 11 (2011) 2362–2368. [21] Y. Chen, X. Liu, Y. Zhao, Deformation dynamics of double emulsion droplet under shear, Appl. Phys. Lett. 106 (2015) 141601. [22] T. Nisisako, T. Torii, T. Higuchi, Novel microreactors for functional polymer beads, Chem. Eng. J. 101 (2004) 23–29. [23] M.T. Guo, A. Rotem, J.A. Heyman, D.A. Weitz, Droplet microfluidics for highthroughput biological assays, Lab Chip 12 (2012) 2146–2155. [24] W.-G. Liang, C. Yang, G.-Q. Wen, W. Wang, X.-J. Ju, R. Xie, L.-Y. Chu, A facile and controllable method to encapsulate phase change materials with non-toxic and biocompatible chemicals, Appl. Therm. Eng. 70 (2014) 817–826. [25] X. Liu, Y. Chen, M. Shi, Dynamic performance analysis on start-up of closed-loop pulsating heat pipes (CLPHPs), Int. J. Therm. Sci. 65 (2013) 224–233. [26] Y. Chen, C. Zhang, M. Shi, Y. Yang, Thermal and hydrodynamic characteristics of constructal tree-shaped minichannel heat sink, AIChE J. 56 (2010) 2018–2029. [27] S.L. Anna, N. Bontoux, H.A. Stone, Formation of dispersions using “flow focusing” in microchannels, Appl. Phys. Lett. 82 (2003) 364–366. [28] T. Thorsen, R.W. Roberts, F.H. Arnold, S.R. Quake, Dynamic pattern formation in a vesicle-generating microfluidic device, Phys. Rev. Lett. 86 (2001) 4163–4166. [29] C. Cramer, P. Fischer, E.J. Windhab, Drop formation in a co-flowing ambient fluid, Chem. Eng. Sci. 59 (2004) 3045–3058. [30] A.M. Ganan-Calvo, J.M. Gordillo, Perfectly monodisperse microbubbling by capillary flow focusing, Phys. Rev. Lett. 87 (2001) 274501. [31] A.M. Ganan-Calvo, Perfectly monodisperse microbubbling by capillary flow focusing: an alternate physical description and universal scaling, Phys. Rev. E 69 (2004) 027301. [32] P. Garstecki, I. Gitlin, W. DiLuzio, G.M. Whitesides, E. Kumacheva, H.A. Stone, Formation of monodisperse bubbles in a microfluidic flow-focusing device, Appl. Phys. Lett. 85 (2004) 2649–2651. [33] S. Okushima, T. Nisisako, T. Torii, T. Higuchi, Controlled production of monodisperse double emulsions by two-step droplet breakup in microfluidic devices, Langmuir 20 (2004) 9905–9908. [34] A. Perro, C. Nicolet, J. Angy, S. Lecommandoux, J.-F. Le Meins, A. Colin, Mastering a double emulsion in a simple co-flow microfluidic to generate complex polymersomes, Langmuir 27 (2011) 9034–9042. [35] Z.H. Nie, S.Q. Xu, M. Seo, P.C. Lewis, E. Kumacheva, Polymer particles with various shapes and morphologies produced in continuous microfluidic reactors, J. Am. Chem. Soc. 127 (2005) 8058–8063. [36] A.R. Abate, J. Thiele, D.A. Weitz, One-step formation of multiple emulsions in microfluidics, Lab Chip 11 (2011) 253–258. [37] R.K. Shah, H.C. Shum, A.C. Rowat, D. Lee, J.J. Agresti, A.S. Utada, L.-Y. Chu, J.W. Kim, A. Fernandez-Nieves, C.J. Martinez, D.A. Weitz, Designer emulsions using microfluidics, Mater. Today 11 (2008) 18–27. [38] A. Rotem, A.R. Abate, A.S. Utada, V. Van Steijn, D.A. Weitz, Drop formation in nonplanar microfluidic devices, Lab Chip 12 (2012) 4263–4268. [39] A.R. Abate, D.A. Weitz, High-order multiple emulsions formed in poly(dimethylsiloxane) microfluidics, Small 5 (2009) 2030–2032. [40] S.A. Nabavi, G.T. Vladisavljevic, V. Manovic, Mechanisms and control of single-step microfluidic generation of multi-core double emulsion droplets, Chem. Eng. J. 322 (2017) 140–148. [41] Y.P. Chen, L.Y. Wu, L. Zhang, Dynamic behaviors of double emulsion formation in a flow-focusing device, Int. J. Heat Mass Transf. 82 (2015) 42–50. [42] S.Y. Lee, C. Snider, K. Park, J.P. Robinson, Compound jet instability in a microchannel for mononuclear compound drop formation, J. Micromech. Microeng. 17 (2007) 1558–1566. [43] T.V. Vu, S. Homma, G. Tryggvason, J.C. Wells, H. Takakura, Computations of breakup modes in laminar compound liquid jets in a coflowing fluid, Int. J. Multiphase Flow 49 (2013) 58–69. [44] X. Liu, L. Wu, Y. Zhao, Y. Chen, Study of compound drop formation in axisymmetric microfluidic devices with different geometries, Colloids Surf. A – Physicochem. Eng. Aspects 533 (2017) 87–98. [45] M.A. Herrada, J.M. Montanero, C. Ferrera, A.M. GaÑÁN-Calvo, Analysis of the dripping–jetting transition in compound capillary jets, J. Fluid Mech. 649 (2010) 523–536. [46] P. Lu, L. Wu, X. Liu, Visualization study of oil-in-water-in-oil (O/W/O) double emulsion formation in a simple and robust co-flowing microfluidic device, Micromachines 8 (2017) 268. [47] F. Cruz-Mazo, J.M. Montanero, A.M. Gañán-Calvo, Monosized dripping mode of axisymmetric flow focusing, Phys. Rev. E 94 (2016) 053122.
The authors gratefully acknowledge the supports of the National Natural Science Foundation of China (Grant Nos. 51706194, U1530260 and U1737104) and the Natural Science Foundation of Yangzhou City (Grant No. YZ2017103). References [1] D. Li, Encyclopedia of Microfluidics and Nanofluidics, Springer Science & Business Media, 2008. [2] C.B. Zhang, Z.L. Deng, Y.P. Chen, Temperature jump at rough gas-solid interface in Couette flow with a rough surface described by Cantor fractal, Int. J. Heat Mass Transf. 70 (2014) 322–329. [3] E.M. Campbell, V.N. Goncharov, T.C. Sangster, S.P. Regan, P.B. Radha, R. Betti, J.F. Myatt, D.H. Froula, M.J. Rosenberg, I.V. Igumenshchev, W. Seka, A.A. Solodov, A.V. Maximov, J.A. Marozas, T.J.B. Collins, D. Turnbull, F.J. Marshall, A. Shvydky, J.P. Knauer, R.L. McCrory, A.B. Sefkow, M. Hohenberger, P.A. Michel, T. Chapman, L. Masse, C. Goyon, S. Ross, J.W. Bates, M. Karasik, J. Oh, J. Weaver, A.J. Schmitt, K. Obenschain, S.P. Obenschain, S. Reyes, B. Van Wonterghem, Laser-direct-drive program: promise, challenge, and path forward, Matter Radiat. Extremes 2 (2017) 37–54. [4] M. Liu, L. Su, J. Li, S. Chen, Y. Liu, J. Li, B. Li, Y. Chen, Z. Zhang, Investigation of spherical and concentric mechanism of compound droplets, Matter Radiat. Extremes 1 (2016) 213–223. [5] J. Wang, W. Gao, H. Zhang, M. Zou, Y. Chen, Y. Zhao, Programmable wettability on photocontrolled graphene film, Sci. Adv. 4 (2018). [6] D.-K. Sun, Y. Wang, A.-P. Dong, B.-D. Sun, A three-dimensional quantitative study on the hydrodynamic focusing of particles with the immersed boundary – lattice Boltzmann method, Int. J. Heat Mass Transf. 94 (2016) 306–315. [7] J.D. Tice, H. Song, A.D. Lyon, R.F. Ismagilov, Formation of droplets and mixing in multiphase microfluidics at low values of the Reynolds and the capillary numbers, Langmuir 19 (2003) 9127–9133. [8] F. Alberini, D. Dapelo, R. Enjalbert, Y. Van Crombrugge, M.J.H. Simmons, Influence of DC electric field upon the production of oil-in-water-in-oil double emulsions in upwards mm-scale channels at low electric field strength, Exp. Therm. Fluid. Sci. 81 (2017) 265–276. [9] H. Chen, Y. Zhao, J. Li, M. Guo, J. Wan, D.A. Weitz, H.A. Stone, Reactions in double emulsions by flow-controlled coalescence of encapsulated drops, Lab Chip 11 (2011) 2312–2315. [10] X. Liu, C. Zhang, W. Yu, Z. Deng, Y. Chen, Bubble breakup in a microfluidic Tjunction, Sci. Bull. 61 (2016) 811–824. [11] J. Wang, L. Sun, M. Zou, W. Gao, C. Liu, L. Shang, Z. Gu, Y. Zhao, Bioinspired shapememory graphene film with tunable wettability, Sci. Adv. 3 (2017) e1700004. [12] A.S. Utada, E. Lorenceau, D.R. Link, P.D. Kaplan, H.A. Stone, D.A. Weitz, Monodisperse double emulsions generated from a microcapillary device, Science 308 (2005) 537–541. [13] Y. Chen, X. Liu, M. Shi, Hydrodynamics of double emulsion droplet in shear flow, Appl. Phys. Lett. 102 (2013) 051609. [14] Y. Chen, X. Liu, C. Zhang, Y. Zhao, Enhancing and suppressing effects of an inner droplet on deformation of a double emulsion droplet under shear, Lab Chip 15 (2015) 1255–1261. [15] B. Mutaliyeva, D. Grigoriev, G. Madybekova, A. Sharipova, S. Aidarova, A. Saparbekova, R. Miller, Microencapsulation of insulin and its release using w/o/ w double emulsion method, Colloids Surf. A – Physicochem. Eng. Aspects 521 (2017) 147–152. [16] C. Goubault, K. Pays, D. Olea, P. Gorria, J. Bibette, V. Schmitt, F. Leal-Calderon, Shear rupturing of complex fluids: application to the preparation of quasi-monodisperse water-in-oil-in-water double emulsions, Langmuir 17 (2001) 5184–5188. [17] Y. Chen, W. Gao, C. Zhang, Y. Zhao, Three-dimensional splitting microfluidics, Lab Chip 16 (2016) 1332–1339. [18] Y. Chen, Z. Deng, Hydrodynamics of a droplet passing through a microfluidic Tjunction, J. Fluid Mech. 819 (2017) 401–434. [19] C. Zhang, Y. Chen, Z. Deng, M. Shi, Role of rough surface topography on gas slip flow in microchannels, Phys. Rev. E 86 (2012) 016319. [20] J. Thiele, M. Windbergs, A.R. Abate, M. Trebbin, H.C. Shum, S. Foerster, D.A. Weitz, Early development drug formulation on a chip: Fabrication of nanoparticles using a
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