Article Cite This: Langmuir XXXX, XXX, XXX-XXX
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Droplet Formation by Rupture of Vibration-Induced Interfacial Fingers Sze Yi Mak,†,‡ Youchuang Chao,†,‡ Shakurur Rahman,† and Ho Cheung Shum*,†,‡ †
Department of Mechanical Engineering, The University of Hong Kong, Pok Fu Lam 999077, Hong Kong HKU-Shenzhen Institute of Research and Innovation (HKU-SIRI), Shenzhen, Guangdong 518000, China
‡
S Supporting Information *
ABSTRACT: By imposing vibration to a core-annular flow of an aqueous twophase system (ATPS) with ultralow interfacial tension, we observe a liquid finger protruding from the interface of an expanding jet. We find that the protruded finger breaks up only when its length-to-width ratio exceeds a threshold value. The breakup follows a constant wavelength-to-width ratio that is consistent with that of breakup under Rayleigh-Plateau instability. The mechanism is applicable to aqueous two-phase systems with a large range of viscosity ratios. The protruded finger can break up into small droplets that are monodisperse in size, controllable in generation frequency under a wide range of flow rates. This work suggests a way to generate small water−water droplets with high monodispersity and production rate from a single nozzle.
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INTRODUCTION The interface of a core-annular flow is usually smooth because of the presence of interfacial tension. The undulation of the jet surface, as induced by vibration, can give rise to finger-like liquid protrusions. The Rayleigh−Plateau instability amplifies the undulation of these fingers, resulting in drop formation.1−5 However, for a jet with an ultralow interfacial tension on the order of μN/m, such as that of an aqueous−aqueous interface,6 the jet breakup process is slow and difficult to control.7,8 Valve control9−11 and pressure control12,13 have been implemented in microfluidic devices to produce water−water droplets. However, the production rate is extremely low (typically on the order of Hz) and thus is not desired for mass production. Active approaches have been sought to control the droplet formation and enhance the throughput of droplet generation.14 For instance, external forcing has been imposed to accelerate the breakup process. Mechanical vibrations have been applied to accelerate the growth of Rayleigh− Plateau instability and to corrugate aqueous−aqueous jet interfaces.15−17 Besides mechanical perturbation, electrohydrodynamic actuations have been imposed to induce breakup of aqueous−aqueous jets. Examples are piezo-electric bending8,18,19 and driving induced by electric potential difference,20,21 both of which facilitate breakup only at a low frequency. Hence, a high throughput approach for microfluidic generation of all-aqueous droplets is still lacking. Apart from inducing jet breakup, perturbation has also been applied to generate complex structures.22 Double emulsions have been generated by integrating mechanical perturbation into a microfluidic device with designated wettability of the nozzle wall.23 Another example of complex fluid structure is jet corrugation by flow oscillation and mechanical perturbation.24−26 While all of the above interfacial actuations © XXXX American Chemical Society
manipulate the overall jet, localized manipulation has advantages of generating finer and more complex fluid structures. Wettinginduced droplet near the microchannel wall has been observed experimentally; however, the mechanism is unknown and the droplet formation is uncontrolled.27 Swirling of stratified jet has shown localized features but does not lead to breakup due to the miscibility of the phases.28,29 In this work, we apply a mechanical perturbation to achieve an unstable interfacial folding structure that ruptures under optimum conditions. In each cycle of perturbation, the interface folds and develops a finger which protrudes locally into the jet phase. If the aspect ratio of the finger exceeds a threshold value, the finger breaks up to form a droplet inside the jet phase. Such perturbation-induced rupture is localized because the perturbation only causes the finger to break but not the overall jet. Surprisingly, the rupturing finger adopts a wavelength-to-width ratio which is consistent with that of the jet breakup induced by Rayleigh−Plateau instability. The diameter of droplets is typically a few times smaller than the nozzle as a result of local rupture along the jet interface. For example, the generated droplets have a diameter of around 10 μm, with a uniform size distribution, for nozzles with diameters on the order of tens of micrometers. Moreover, the folding follows the frequency of the applied vibration, which is typically in the range of a hundred hertz to kilohertz. We show that this method works for a wide range of flow rate conditions applicable to the typical Special Issue: Early Career Authors in Fundamental Colloid and Interface Science Received: July 28, 2017 Revised: October 2, 2017
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DOI: 10.1021/acs.langmuir.7b02633 Langmuir XXXX, XXX, XXX−XXX
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RESULTS AND DISCUSSION Finger Protrusion Induced by Vibration. Inspired by interfacial ripples under hydrodynamic fluctuations17,25 and sawtooth corrugation by sound vibration,26 we study the evolution of the corrugated interface and discover a regime where the
Figure 1. Vibration-induced local rupture of a jet interface: (a) schematic drawing; (b) optical image. Scale bar is 100 μm. (c) Magnified view of panel b. Scale bar is 20 μm. L and w are defined as the length and width of the finger.
experimental setup. Our work demonstrates a robust method to induce jet breakup locally for rapid generation of small aqueous− aqueous emulsions.
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EXPERIMENTAL SECTION
Fabrication of Microfluidic Device. We fabricated microfluidic device using glass capillaries. We tapered the round glass capillary (with an outer diameter of 1 mm) to a desired nozzle size ranging from 20 to 100 μm and inserted it into a square capillary (with an inner dimension of 1.05 mm). We glued the connecting parts with epoxy. The capillary inlets were connected via plastic tubings to syringes. Experimental Setup. We injected the inner and outer phases into the round capillary and the square capillary, respectively. We pumped the fluid from the syringe using syringe pump (LSP01−2A, Longer Pump) at a flow rate ranging from 0.01 mL/h to 100 mL/h. To oscillate the inner fluid of the coflow to generate a jet with interfacial fingers, we applied vibration using a loud speaker. The vibration of the membrane of a loud speaker (SPA2210, Philips) was transmitted through the contact with the plastic tubing that held the inner fluid. We programmed the membrane of the loud speaker to vibrate at controlled frequency and amplitude. The folding structure adopts a shape of a protruded finger with a characteristic length L and width w. We monitored the jet interface using an inverted microscope (AE2000, Motic) coupled to a high speed camera (FASTCAM SA4, Photron). Preparation of Aqueous Two-Phase System (ATPS). The aqueous two-phase system was formed by dissolving two types of solute in deionized water. At sufficiently high concentration, two immiscible aqueous solutions were obtained. In our experiments, the solutes were polymers and salts, namely, poly(-ethylene glycol) (PEG, Mw = 4000 or 8000) (5−19 wt %), sodium citrate dihydrate (10−15 wt %), tripotassium phosphate (10 wt %), sodium carbonate (6−7 wt %), and Dextran T500 (10 wt %).30 Measurement of Fluid Properties. We used six ATPSs in our experiments; they are named as ATPS I, II, III, IV, V, and VI. All aqueous two-phase systems in our experiments have a viscosity μ ranging from 1 to 200 mPa·s (μVISC, RheoSense). A spinning drop tensiometer (SITE100, Krüss) was used to measure the ultralow interfacial tension, which is typically within the range of O(1−102) μN/m. Some viscosity and interfacial tension values were obtained from measurements done in previous works.31 The fluid properties of the six ATPSs are listed in Table S1 in Supporting Information 1.
Figure 2. Interfacial corrugations and fingering of ATPS I with increasing applied vibration amplitude: (a) smooth interface, (b) folding, (c) fingering, (d) finger rupturing, and (e) multiple fingering. Scale bars are 100 μm.
Figure 3. A plot of fingering length L against width w for ATPS I. Blue diamonds and red squares refer to the “Breakup” and “No Breakup” regimes. The dotted line dividing the two regimes is obtained by the support vector method (SVM). It has a slope of 10, with a classification error of 2%. The black hollow symbols indicate the support vectors. The protruded fingers break up when the L/w ratio is sufficiently large. B
DOI: 10.1021/acs.langmuir.7b02633 Langmuir XXXX, XXX, XXX−XXX
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Langmuir corrugation develops fingers along the interface and the fingers eventually break up into droplets within the main jet. We apply an external vibration to a microfluidic coflow of an aqueous two-phase system with a low interfacial tension to study the instability of the interfacial folding. Interestingly, the interface can fold and protrude into the jet phase, resulting in a protruded finger of the continuous phase (Figure 1a). We monitor the evolution of the finger penetrating into the jet phase. The process begins with the formation of finger on the interface and is followed by subsequent breakup; the droplet formed flows along with the jet phase (See Movie S1 in the Supporting Information). A typical microscopic image capturing the instance of local interfacial rupture is shown in Figure 1b,c.
Local Rupture of Jet Interface. We apply a vibration of 200 Hz to ATPS I and gradually tune up the vibration amplitude. The microscope images of ATPS I under different vibration amplitudes are displayed in Figure 2. Without perturbation, the expanding jet is smooth and fairly steady (Figure 2a). After imposing a small-amplitude perturbation, we observe interfacial folding (Figure 2b). Further increasing the vibration amplitude will lead to squeezing of the continuous phase into the jet phase to form a finger. We define L and w as the length and width of the finger, as illustrated in Figure 1c. The finger decays and disappears if L is small (Figure 2c). This is regarded as the “No Breakup” regime. In contrast, in the “Breakup” regime where L is large, the finger does not retract, instead it is carried by the flow and eventually
Figure 4. (a) A plot of wavelength λ against jet width w of the breakup of PEG-in-salt core-annular flows. The microscope images in red and blue boxes illustrate the definition of wavelength λ and jet width w of (b) the protruded finger and (c) the main jet. Scale bars are 100 μm. In the plot, red diamonds denote the breakup of the protruded finger, and blue squares indicate the breakup of main jet. ATPS III is used. Viscosity ratio μ1/μ2 = 13.9, where subscripts 1 and 2 refer to the breakup phase and the continuous phase, respectively. The dotted line marks the predicted wavelength using Tomotika’s model34 for ATPS III with a viscosity ratio of 13.9. It has a slope of 8.2.
Figure 5. Relation between λ/w and μ1/μ2. (a) Table of six different ATPSs and their values of viscosity and viscosity ratio. (b) Plot of λ/w against μ1/μ2. The black solid line is the theoretical relationship predicted for breakup by the viscosity-modified Rayleigh−Plateau instability.34 C
DOI: 10.1021/acs.langmuir.7b02633 Langmuir XXXX, XXX, XXX−XXX
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annulus and that of the core, respectively. Using Tomotika’s model for the viscosity-modified Rayleigh−Plateau instability,34 we calculate the λ/w ratio responsible for the jet breakup to be 8.2, which is in close approximation to the value of 8.4 we obtained for the protruded finger breakup. We further confirm our hypothesis by varying the viscosity ratio μ1/μ2 over a decade from 4.7, 7.4, 13.9, 22.5, 34.0 to 42.1 (Figure 5a). As the viscosity ratio is increased, breakup takes place at a larger λ/w ratio. Remarkably, the λ/w ratio for each of the fluid pair obtained is found in quantitative agreement with the prediction made by the model (Figure 5b). Based on this
breaks up (Figure 2d). A droplet is sheared off from the aqueous− aqueous interface and is embedded in the main jet. The folding features and the subsequent droplets formed follow a threedimensional trajectory, as indicated by the droplets sequentially becoming out of focus in Figure 2d. The formed droplets flow downstream and remain encapsulated by the jet phase within the field of view. As the vibration amplitude further increases, multiple protruded fingers are developed, yielding more droplets (Figure 2e). For ATPS I, we observe breakup when L becomes higher than (33.4 ± 0.8) μm, while w remains fairly constant at (5.3 ± 0.2) μm. To identify the parameters controlling the breakup of the finger, we tune the perturbation frequency and amplitude, and observe the breakup for ATPS I. Measuring the length L and width w of the finger, we find that the finger breaks up when it exceeds a critical length-to-width ratio, as indicated by the slope of the boundary separating the “Breakup” and “No Breakup” regions in Figure 3. The boundary is obtained using the support vector method (SVM).32 For ATPS I, the linear classifier is a straight line with a slope of 10.33 The phase diagram of another aqueous two-phase system (ATPS III) is shown in Figure S2 in Supporting Information 3. For ATPS III, the boundary that separates the two regimes is a line with a slope of 4. Based on the phase diagram of the two ATPSs, breakup occurs above a critical length-to-width ratio of the protruded finger, for which the value is potentially influenced by fluid properties of the ATPSs. Mechanism of the Rupture of Finger. For the cases of a finger exceeding a critical L/w ratio, a wave is developed on the finger. This wave grows with time and eventually results in the pinch-off of the protruded finger. The evolution of the wave on the interfacial finger is shown in Movie S2 and Figure S3 in Supporting Information 4. Additionally, we observe a breakup with a uniform periodicity into droplets with a uniform size distribution. Hence, we hypothesize that the finger breaks up at a specific wavelength λ. To test this hypothesis, we vary the finger width w from 2.8 to 11.2 μm and capture the wavelength λ formed along the interface of the protruded finger of ATPS III. We find that the protruded PEG-rich finger breaks up at a particular wavelength-to-width ratio (λ/w = 8.4), as shown by the red diamonds in Figure 4a. This result strongly suggests a wavelength-dependent breakup mechanism. To better understand the breakup of the protruded finger, we mimic the same situation of a protruded PEG-rich phase in a continuous salt-rich phase using a simple core-annular flow. We conduct experiments using a simple core-annular flow with the PEG-rich phase as the core and the salt-rich phase as the annulus (Figure 4c). Essentially, the PEG-in-salt main jet is an up-scaled analogue to the PEG-in-salt protruded finger. In this classical jet breakup experiment, we vary the width of the main jet by about 10-fold from 44.9 to 341.4 μm. As the jet width increases, the wavelength corresponding to breakup increases linearly while keeping λ/w constant. The wavelength-to-width ratio of the protruded finger is the same as that in case of a simple core-annular flow, as shown by the blue squares collapsing to the dotted line in Figure 4a. This result suggests a strong universal wavelength-dependent breakup mechanism in both the protruded finger and simple core-annular flow. Since both the breakup of the protruded finger and the simple core-annular flow follow the same λ/w ratio, we hypothesize that the protruded finger breaks up due to the Rayleigh-Plateau instability. For the fluid pair (ATPS III) we use, the viscosity ratio μ1/μ2 is 13.9, where μ1 and μ2 refer to the viscosity of the
Figure 6. (a) A plot of frequency of droplet generation against frequency of applied vibration. Over the range, the frequency of droplet generation matches with the frequency of applied vibration. The straight line is fdroplet = f vibration. The droplet generation frequency is the average value from four separate measurements; error bars are included. (b) Plot of droplet diameter against frequency of applied vibration. The inner and outer flow rates are kept constant at 1 mL/h and 5 mL/h, respectively. Over the range of the applied vibration from 200 to 1000 Hz, the droplets diameter decreases monotonically as the frequency increases. The droplet diameter is the average value from 20 separate measurements; error bars are included. The fitting curve is D = 24.9e−0.002f_vibration. (c) A plot of droplet size distribution. We measured the diameter of 200 droplets. The red line is the Gaussian fit. Droplets have a mean size of (14.4 ± 0.2) μm with a c.v. of 3%. D
DOI: 10.1021/acs.langmuir.7b02633 Langmuir XXXX, XXX, XXX−XXX
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In addition, we find that the perturbation only affects the local rupture of the interface, but posts no noticeable effect on the global rupture of the jet interface. Hence, this method can decouple the local breakup form the global breakup. With this approach, we can form core−shell emulsions with tunable ratios of core-to-shell size and number, and controllable generation frequency of the core droplets (see Supporting Information 5). Apart from precise control of generation frequency, the size of the droplet is also tunable. As we increase the frequency of the applied vibration from 200 to 1000 Hz, the droplet diameter decreases monotonically from 17 to 3 μm (Figure 6b). The generated droplets are not only small, but also uniform in size. For example, under the application of a vibration at 200 Hz and 0.1 A, the droplet size is (14.4 ± 0.2) μm (Figure 6c). The coefficient of variation (c.v.) is as low as 3%, suggesting a low polydispersity. Operating Range of Controlled Interfacial Rupture. To determine the operation range, we systematically change the outer and inner flow rates (0.2 mL/h < Qo < 50 mL/h and 0.05 mL/h < Qi < 2 mL/h). The flow behavior is classified into
result, we conclude that the Rayleigh−Plateau instability is responsible for the breakup of the protruded finger. Controlled Rapid Generation of Monodisperse Droplets. This work has implication to rapid generation of aqueous− aqueous emulsions with controllable generation frequency, tunable size in the range of microns, and high monodispersity. We can control the frequency of droplet generation through the frequency of perturbation. As we increase the frequency of the applied vibration, the frequency of droplet generation increases linearly. Over the range of the applied frequency from 100 to 1000 Hz, the droplets are generated at the same frequency as the applied vibration (Figure 6a). For example, when a vibration with f vibration = 300 Hz is applied to ATPS III, the droplets are generated at a rate of fdroplet = (299.8 ± 0.6) Hz. The natural breakup frequency of an aqueous−aqueous jet is extremely slow, typically below 10 Hz.8 With the applied perturbation, we are able to induce the formation of a thin protruded finger at the desired rate. Essentially, we can boost the frequency of droplet generation by 100 times, as compared to typical hydrodynamic breakup using flow rate control.
Figure 7. Operating flow range. (a) Phase diagram of three regimes for ATPS III under a vibration with f = 200 Hz and Avibration = 0.05 A. “Folding”, “Folding and Droplet Breakup” and “Backflow” are marked by symbols of triangle, circle and plus. In the “Folding” regime, the jet interface folds to form fingers that do not break up. In the “Folding and Droplet Breakup” regime, the fingers break up to form droplets. In the “Backflow” regime, a vortex is formed due to the extremely large velocity difference between the inner and outer phase; hence a backflow of one phase is observed. Without a clear and smooth interface, neither folding nor droplet breakup is observed in the “Backflow” regime. Keeping Qi = 1 mL/h, droplets can be formed as Qo changes by 100 times, from (b) 0.5 mL/h, (c) 2 mL/h, (d) 5 mL/h, (e) 10 mL/h, (f) 20 mL/h, to (g) 50 mL/h. As the outer flow rate increases, the jet width decreases. Scale bar is 100 μm. E
DOI: 10.1021/acs.langmuir.7b02633 Langmuir XXXX, XXX, XXX−XXX
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three distinct regimes, named as “Backflow”, “Folding” and “Folding and Droplet Breakup” (Figure 7a). The “Folding and Droplet Breakup” regime spans over two decades in Qo, indicating that our approach has a large operable range and thus is versatile. Interfacial fingers rupture only when the inner flow rate Qi is larger than 0.2 mL/h, which is equivalent to a mean velocity of the inner phase vi on the order of mm/s. For all the breakups of fingers in our experiments, the width of the main jet is larger than the size of nozzle, as shown in Figure 7b−g. Since the nozzle size is less than one-tenth of the channel size, the crosssectional area of the inner phase is much smaller than that of the outer phase. We therefore calculate the initial velocity contrast vi/vo at the exit of nozzle, where vi and vo refer to the initial mean velocity of the inner and the outer phases, respectively. We find that droplet generation using our approach works for a wide range of velocity contrast, O(1) < vi/vo < O(102), suggesting that the feasible operating flow conditions are not limited to a microfluidic setting. Since vi/vo is always greater than O(1) in the “Folding and Droplet Breakup” regime, the jet phase is always flowing at a higher velocity than the continuous phase. Hence, the jet phase increases in diameter as it flows downstream. Given the parabolic velocity profile in a coflow system, the protruded finger entering the velocity field of the inner phase is inevitably and vastly accelerated. Hence, parabolic velocity profile with a large vi/vo ratio favors the rupture of the protruded finger. The resultant vibration-induced droplets can be extracted by inserting a collection tube to the outlet of the channel (see Supporting Information 6).
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.7b02633. ATPSs used in the experiments, finger protrusion induced by vibration, phase diagram of ATPS I, evolution of the wave on the interfacial finger, decoupling rupture of the interfacial finger and of the overall jet, extraction of vibration-induced droplets embedded within the jet phase, and periodic dewetting of the inner phase from the inner wall of the nozzle (PDF) Movie S1: Finger protrusion induced by vibration (AVI) Movie S2: Evolution of the wave on the finger (AVI) Movie S3: Periodic dewetting of the inner phase from the inner wall of the nozzle (AVI)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Ho Cheung Shum: 0000-0002-6365-8825 Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank Dr. Alban Sauret for valuable discussions. This research was supported by the General Research Fund (No. HKU 719813E, 17304514, 17306315 and 17329516) and the Collaborative Research Fund (C6004-14G) from the Research Grants Council of Hong Kong, the General Program (No. 21476189/ B060201) and the Major Research Plan (No. 91434202) from the National Natural Science Foundation of China, as well as the Seed Funding Programme for Basic Research (No. 201411159038, 201511159280) from the University of Hong Kong.
CONCLUSION We use the interfacial-fingering strategy to generate aqueous− aqueous droplets. The dependence of the λ/w aspect ratio on the viscosity ratio suggests that the protruded finger breaks up under the Rayleigh−Plateau instability. While the focus of this study is on the rupture process of interfacial fingers, future study may explore the generation of interfacial fingers. We suggest that the interfacial fingering can be initiated from either corrugation of the interface due to flow rate variation25,26 or periodic dewetting of the inner phase from the inner wall of the nozzle (see Movie S3 in the Supporting Information). While previous studies have demonstrated vibration-induced breakup of the main jet of oil−water systems,23,35 we show that localized interfacial finger formation can be achieved for ATPSs, possibly due to the different wettability of the two-phase systems. In summary, our work demonstrates a robust method to control droplet formation in low interfacial tension systems. For aqueous two-phase systems with a low interfacial tension, hydrodynamic droplet formation is typically slow in the dripping regime36 and uncontrollable in the jetting regime.3,37 The resulting droplets are often large and polydisperse. Our approach enables controlled generation of aqueous−aqueous droplets with a significant enhancement in the droplet generation rate, and a high monodispersity due to the natural selection of the breakup wavelength. Traditional droplet formation from breakup of the main jet produces droplets with size close to the nozzle dimension.4,38 By contrast, the rupture of protruded finger yields droplets much smaller than the nozzle size. Our approach shows great promise in the fabrication of complex materials templated from all-aqueous multiphase flows.
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ABBREVIATIONS ATPS, aqueous two-phase system REFERENCES
(1) Rayleigh, L. On the Capillary Phenomena of Jets. Proc. R. Soc. London 1879, 29 (196−199), 71−97. (2) Eggers, J.; Villermaux, E. Physics of liquid jets. Rep. Prog. Phys. 2008, 71 (3), 036601. (3) Guillot, P.; Colin, A.; Ajdari, A. Stability of a jet in confined pressure-driven biphasic flows at low Reynolds number in various geometries. Phys. Rev. E 2008, 78 (1), 016307. (4) Utada, A. S.; Fernandez-Nieves, A.; Gordillo, J. M.; Weitz, D. A. Absolute Instability of a Liquid Jet in a Coflowing Stream. Phys. Rev. Lett. 2008, 100 (1), 014502. (5) Eggers, J.; Villermaux, E. Physics of liquid jets. Rep. Prog. Phys. 2008, 71 (3), 036601. (6) Song, Y.; Sauret, A.; Shum, H. C. All-aqueous multiphase microfluidics. Biomicrofluidics 2013, 7 (6), 061301. (7) Ren, Y.; Liu, Z.; Shum, H. C. Breakup dynamics and dripping-tojetting transition in a Newtonian/shear-thinning multiphase microsystem. Lab Chip 2015, 15 (1), 121−134. (8) Geschiere, S. D.; Ziemecka, I.; van Steijn, V.; Koper, G. J. M.; Esch, J. H. V.; Kreutzer, M. T. Slow growth of the Rayleigh-Plateau F
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Langmuir instability in aqueous two phase systems. Biomicrofluidics 2012, 6 (2), 022007. (9) Lai, D.; Frampton, J. P.; Sriram, H.; Takayama, S. Rounded multilevel microchannels with orifices made in one exposure enable aqueous two-phase system droplet microfluidics. Lab Chip 2011, 11 (20), 3551−3554. (10) Moon, B.-U.; Jones, S. G.; Hwang, D. K.; Tsai, S. S. H. Microfluidic generation of aqueous two-phase system (ATPS) droplets by controlled pulsating inlet pressures. Lab Chip 2015, 15 (11), 2437− 2444. (11) Dang, V. B.; Kim, S.-J. Water-head-driven microfluidic oscillators for autonomous control of periodic flows and generation of aqueous two-phase system droplets. Lab Chip 2017, 17 (2), 286− 292. (12) Moon, B.-U.; Abbasi, N.; Jones, S. G.; Hwang, D. K.; Tsai, S. S. H. Water-in-Water Droplets by Passive Microfluidic Flow Focusing. Anal. Chem. 2016, 88 (7), 3982−3989. (13) Moon, B.-U.; Hwang, D. K.; Tsai, S. Shrinking, Growing, and Bursting: Microfluidic Equilibrium Control of Water-in-Water Droplets. Lab Chip 2016, 16, 2601. (14) Schmid, L.; Franke, T. SAW-controlled drop size for flow focusing. Lab Chip 2013, 13 (9), 1691−1694. (15) Sauret, A.; Shum, H. C. Beating the Jetting Regime. Int. J. Nonlinear Sci. Numer. Simul. 2012, 13, 351. (16) Sauret, A.; Shum, H. C. Forced generation of simple and double emulsions in all-aqueous systems. Appl. Phys. Lett. 2012, 100 (15), 154106. (17) Sauret, A.; Spandagos, C.; Shum, H. C. Fluctuation-induced dynamics of multiphase liquid jets with ultra-low interfacial tension. Lab Chip 2012, 12 (18), 3380−3386. (18) Ziemecka, I.; van Steijn, V.; Koper, G. J. M.; Rosso, M.; Brizard, A. M.; van Esch, J. H.; Kreutzer, M. T. Monodisperse hydrogel microspheres by forced droplet formation in aqueous two-phase systems. Lab Chip 2011, 11 (4), 620−624. (19) Ziemecka, I.; van Steijn, V.; Koper, G. J. M.; Kreutzer, M. T.; van Esch, J. H. All-aqueous core-shell droplets produced in a microfluidic device. Soft Matter 2011, 7 (21), 9878−9880. (20) Song, Y. S.; Choi, Y. H.; Kim, D. H. Microextraction in a tetrabutylammonium bromide/ammonium sulfate aqueous two-phase system and electrohydrodynamic generation of a micro-droplet. Journal of Chromatography A 2007, 1162 (2), 180−186. (21) Choi, Y. H.; Song, Y. S.; Kim, D. H. Droplet-based microextraction in the aqueous two-phase system. Journal of Chromatography A 2010, 1217 (24), 3723−3728. (22) Song, Y.; Shum, H. C. Monodisperse w/w/w Double Emulsion Induced by Phase Separation. Langmuir 2012, 28 (33), 12054−12059. (23) Li, J.; Mittal, N.; Mak, S. Y.; Song, Y.; Shum, H. C. Perturbationinduced droplets for manipulating droplet structure and configuration in microfluidics. J. Micromech. Microeng. 2015, 25 (8), 084009. (24) Shum, H. C.; Sauret, A.; Fernandez-Nieves, A.; Stone, H. A.; Weitz, D. A. Corrugated interfaces in multiphase core-annular flow. Phys. Fluids 2010, 22 (8), 082002. (25) Li, Z.; Mak, S. Y.; Sauret, A.; Shum, H. C. Syringe-pumpinduced fluctuation in all-aqueous microfluidic system implications for flow rate accuracy. Lab Chip 2014, 14 (4), 744−749. (26) Mak, S. Y.; Li, Z.; Frere, A.; Chan, T. C.; Shum, H. C. Musical Interfaces: Visualization and Reconstruction of Music with a Microfluidic Two-Phase Flow. Sci. Rep. 2015, 4, 6675. (27) Cubaud, T. Wetting and lubricating film instabilities in microchannels. Phys. Fluids 2009, 21 (9), 091103. (28) Cubaud, T.; Mason, T. G. Swirling of Viscous Fluid Threads in Microchannels. Phys. Rev. Lett. 2007, 98 (26), 264501. (29) Hu, X.; Cubaud, T. Inertial destabilization of highly viscous microfluidic stratifications. Physical Review Fluids 2016, 1 (4), 044101. (30) de Oliveira, C. C.; Coimbra, J. S. d. R.; Zuniga, A. D. G.; Martins, J. P.; Siqueira, A. M. d. O. Interfacial Tension of Aqueous Two-Phase Systems Containing Poly(ethylene glycol) and Potassium Phosphate. J. Chem. Eng. Data 2012, 57 (6), 1648−1652.
(31) Chao, Y.; Mak, S. Y.; Shum, H. C. The transformation dynamics towards equilibrium in non-equilibrium w/w/o double emulsions. Appl. Phys. Lett. 2016, 109 (18), 181601. (32) Vapnik, V. N. The Nature of Statistical Learning Theory; Springer-Verlag New York, Inc.: New York, 1995; p 188. (33) Gunn, S. R. Support vector machines for classification and regression. ISIS Technical Report 1998, 14, 85−86. (34) Tomotika, S. On the Instability of a Cylindrical Thread of a Viscous Liquid Surrounded by Another Viscous Fluid. Proc. R. Soc. London, Ser. A 1935, 150 (870), 322−337. (35) Tan, S. H.; Maes, F.; Semin, B.; Vrignon, J.; Baret, J.-C. The Microfluidic Jukebox. Sci. Rep. 2015, 4, 4787. (36) Mak, S. Y.; Chao, Y.; Shum, H. C. The dripping-to-jetting transition in a co-axial flow of aqueous two-phase systems with low interfacial tension. RSC Adv. 2017, 7 (6), 3287−3292. (37) Wang, K.; Xie, L.; Lu, Y.; Luo, G. Generation of monodispersed microdroplets by temperature controlled bubble condensation processes. Lab Chip 2013, 13 (1), 73−76. (38) Utada, A. S.; Fernandez-Nieves, A.; Stone, H. A.; Weitz, D. A. Dripping to Jetting Transitions in Coflowing Liquid Streams. Phys. Rev. Lett. 2007, 99 (9), 094502.
G
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