LETTER pubs.acs.org/Langmuir
Breakup of Double Emulsion Droplets in a Tapered Nozzle Jiang Li,†,‡ Haosheng Chen,*,§,|| and Howard A. Stone*,† †
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, United States School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China § State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
)
‡
ABSTRACT: When double emulsion droplets flow through a tapered nozzle, the droplets may break up and cause the core to be released. We model the system on the basis of the capillary instability and show that a droplet will not break up when the tilt angle of the nozzle is larger than 9°. For smaller tilt angles, whether the droplet breaks up also depends on the diameter ratio of the core of the droplet to the orifice of the nozzle. We verified this mechanism by experiments. The ideas are useful for the design of nozzles not only to break droplets for controlled release but also to prevent the droplet from rupturing in applications requiring the reinjection of an emulsion.
1. INTRODUCTION Microfluidic technologies have proven effective for the controlled generation and manipulation of droplets.13 The same methods can be used in a hierarchical fashion to make double, triple, and even higher-order multiple emulsions,46 which are useful in cosmetics, drug delivery, food processing, and the handling of hazardous materials, primarily because of their versatility in the encapsulation or controlled release of the innermost phase.7 Droplets can also be used as microcompartments for assays of cells in high-throughput screening,8,9 where droplets can be reinjected into another device for further manipulations after incubation. Confined geometries, such as tapered nozzles, are commonly used to control the velocity, perturb the flow, or align droplets. However, when a double emulsion droplet flows through a confined geometry, the droplet may break up and release the core.10 In some applications, the breakup of the droplet is desired for controlled release, but in other applications, it is necessary to prevent the droplet from rupturing in order to allow further processing steps, such as reinjection for further studies or the generation of higher-order multiple emulsions. The controlled breakup of single-phase droplets in confined geometries has been well studied both theoretically and experimentally.1114 On the contrary, the breakup of double emulsion droplets has been studied, with theoretical15 or numerical methods,16 mostly in unbounded flow. There are few studies on the deformation17 and the breakup10 of double emulsion droplets that flow through confined geometries, which are typical of microfluidics, primarily because of the large number of variables present in the systems. Therefore, an improved understanding of the breakup mechanism of double emulsion droplets will aid the design of nozzles either for controlled release or for reinjection in potential applications. In this work, we investigate the breakup of a double emulsion droplet from a geometrical point of view based on the theory of r 2011 American Chemical Society
the capillary instability. We provide a design criterion of the nozzle (i.e., the tilt angle) for manipulating double emulsions and then verify the criterion by experimental results for water-in-oilin-water (W/O/W) droplets passing through microcapillary nozzles with different tilt angles.
2. EXPERIMENTAL METHOD In our experiments, double emulsion droplets are first generated using a microcapillary device,2 collected in a syringe, and then rejected into another device through a tapered nozzle, as shown in Figure 1. The device for drop generation consists of three capillary tubes: an injection tube, a collection tube, and an outer tube. Both the injection and the collection tubes are cylindrical, and their tips are tapered using a pipet puller. The two tubes are inserted from opposite sides into the outer square tube and are aligned along the same axis. The three phases, which are referred to as the inner (core), middle (shell), and outer (carrier) phases, form a coaxial jet and generate monodisperse W/O/W droplets in a continuous aqueous carrier, as shown in Figure 1a. The core is pure water, with a density of Fi = 1000 kg 3 m3 and a viscosity of μi = 1 mPa 3 s; the shell is poly(dimethylsiloxane) (PDMS) oil containing a 2 wt % surfactant of Dow Corning 749 fluid and has a density of Fm = 970 kg 3 m3 and a viscosity of μm = 10 mPa 3 s; and the continuous carrier is an aqueous solution of 10 wt % poly(vinyl alcohol) (PVA) with a density of Fo = 1027 kg 3 m3 and a viscosity of μo = 20 mPa 3 s. The concentration of the surfactants has been chosen to achieve a stable double emulsion. The interfacial tension between the shell and the core is γim = 31.3 mN 3 m1, and that between the shell and the carrier is γom = 9.0 mN 3 m1, as measured by a tensiometer (Sigma 70, KSV Instruments Ltd.). In our experiments, the diameter D of the core ranges from 20 to 150 μm and the diameter of the double emulsion droplet ranges from 60 to 200 μm; the diameters are controlled by the flow rates of the different phases. Received: February 4, 2011 Revised: March 12, 2011 Published: March 18, 2011 4324
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Figure 1. Microcapillary devices used in the experiments. (a) Device used to generate double emulsion droplets. (b) Tapered nozzle used to manipulate the droplets. Scale bars are 200 μm. The collected W/O/W double emulsions are then reinjected with a syringe pump into a cylindrical capillary tube with a tapered nozzle (Figure 1b). The cylindrical capillary with an inner diameter of 600 μm is first tapered using a pipet puller, and the resulting tilt angle of the tapered tip is usually around 6 to 7°; the diameter of the orifice, d, is controlled by polishing the tip. The reinjection nozzle is then fitted into a square capillary tube, where the flow rate of water is fixed to 1000 μL 3 h1 and the flow rate Q of the reinjected double emulsion can be adjusted from 500 to 5000 μL 3 h1. The typical values of the Reynolds numbers at the orifice are Re = FoQ/μod ≈ 0.051, and the typical values of the capillary numbers, which compare viscous stresses to surface tension stresses, for the shell liquid at the orifice are Ca = μmQ/γimd2 ≈ 0.0020.5. A highspeed camera (Phantom V7.0) attached to a microscope is used to image the movement and deformation of the double emulsion droplets as they flow though the tapered tip, and the typical frame rates used in the experiments are 5004000 fps depending on the flow rate.
3. EXPERIMENTAL RESULTS To investigate the mechanism of the breakup of the double emulsions, we reinject two droplets, labeled I and II, with the same core sizes into the same tapered nozzle under the same flow rate (Figure 2). Droplet I breaks up inside the nozzle but droplet II does not, and the only difference between them is that the shell of droplet I is thicker than that of droplet II, as shown in Figure 2a,b, respectively. To understand this and similar observations, the behavior of the two droplets is divided into four stages, where in the first two stages the two droplets behave in a similar way. In the first stage, as the droplet flows into the nozzle, the shell deforms and forces the carrier phase into a thin annular film; when the local diameter of the nozzle is smaller than the diameter of the core, the core begins to deform and consequently slows the velocity of the droplet. The shell is then effectively separated into two parts by the deformed core, the upstream part and the downstream part, which are connected by a thin annular film of the shell liquid. As long as the leading edge of the shell is upstream from the orifice, we define the length of the downstream shell as h and the diameter of the nozzle at the meniscus as dr; see the geometrical model in Figure 2c. We now consider the experimental results in Figure 2a,b. The ratio h/dr of the downstream shell of droplet I is longer than that of droplet II, as shown in Figure 2a-1,b-1. In the second stage, the downstream shell drips out of the orifice while the upstream shell is almost stalled by the core, which effectively clogs
Figure 2. Comparison of the behaviors of two double emulsion droplets as they flow through the tapered nozzle. (a) Droplet I with a thicker shell breaks up, but (b) droplet II does not rupture. Arrows are drawn to indicate the main features of interest, and scale bars are 200 μm. (c) Geometrical model of the droplet as the leading edge of the shell reaches the orifice; the dashed circle indicates the position where the core starts to deform. the nozzle. Noticeable lobes of the carrier phase are observed near the meniscus between the core and the downstream shell, as indicated by the arrows in Figure 2a-2,b-2. In the third stage, the lobes, indicated by the arrow in Figure 2a-3, pinch off the thin thread of the shell inside the nozzle before the core reaches the orifice, while the thin thread of shell is still connected to the remainder of the droplet, as indicated by the arrow in Figure 2b-3. Finally, for the droplet with the larger shell in Figure 2a, the shell breaks up and the core is released, whereas for the smaller shell phase, the entire droplet in Figure 2b passes through the orifice without breakup. The appearance of the lobes of the continuous carrier phase and the small capillary number, Ca , 1, which indicates the dominance of surface tension stress relative to viscous stress, indicate that the RayleighPlateau capillary instability likely accounts for the breakup of the shell. In addition, we observed that the time needed for the downstream shell to flow out of the orifice is more than 4 times longer than that needed for a single-phase fluid, which means that the deformed core almost clogs the nozzle as the downstream shell is dripping out of the orifice. This evidence matches well with a description of a thin film that undergoes the RayleighPlateau-like instability.18,19 Moreover, the ratio of the interfacial tensions in our double emulsion system is γom/ γim = 0.29, which satisfies the condition for the formation of the lobes in which γom/γim < 0.6 ( 0.1.19 According to the RayleighPlateau instability, a cylindrical thread or thin film should break up into drops if its length exceeds its circumference, which is π times its diameter. Here, we apply this result approximately in our case because the tilt angle θ of the nozzle is small. Therefore, we expect that the shell will not break up provided that h arctan 2π The critical tilt angle of 9° means that the critical condition of the RayleighPlateau-like instability is satisfied when the size of the orifice reaches zero. For a tilt angle larger than 9°, the instability happens only when the size of the orifice has a negative value, which means that it should not happen. For those nozzles that have tilt angles smaller than 9°, the breakup of the shell fluid depends on the ratio D/d, where D is the diameter of the core and d is the diameter of the orifice of the nozzle. We define the distance to the orifice of the nozzle for the deforming core to pass through as H (Figure 2c). According to the geometrical model shown in Figure 2c, we have h H e dr D cos θ
ð4aÞ
H 1 ¼ D cos θ d 2 tan θ
ð4bÞ
According to eqs 1 and 4a, we predict stability as long as H/(Dcos θ) < π, which, combined with eq 4b, predicts that the shell will not break up if the ratio D/d satisfies D 1 < d 1 2π sin θ
ð5Þ
Equations 3 and 5 indicate that although the ratio h/dr is related to the length of the downstream shell, the breakup condition is independent of
4. FURTHER RESULTS AND DISCUSSIONS To verify the effect of the tilt angle of the nozzle and the diameter ratio of the core to the orifice on the breakup of the droplet, we obtained experimental results with two different nozzles, labeled A and B, with θA = 6.5° and θB = 9°, respectively. We focus on double emulsion droplets rather than other twophase flow problems. In addition, we focus on typical cases where the diameter ratio of the core to the orifice is smaller than 10 so that both the core and the shell have a finite length, even when the droplet is significantly deformed. The predicted breakup diagram for double emulsions according to eqs 3 and 5 is given by a plot of the critical diameter ratio D/d versus the tilt angle θ, as shown by the dashed curve in Figure 3a. In addition, in the Figure we have included the experimental results obtained with the two nozzles, and the results have also been repeated with different nozzles with the same tilt angles. For nozzle A with a tilt angle of θ = 6.5°, the theory predicts that droplets with D/d < 3.5 will not break up, while in the experiments the breakup of the shell did not happen for the droplets with D/d < 3.7, as indicated by open circles in Figure 3a. For nozzle B with a tilt angle of θ = 9°, no shell breakup is predicted, which is also validated by the experimental results in Figure 3a. All of the droplets that passed through nozzle B did so without the breakup of the shell; even a very large droplet with D/d = 7.5 was able to pass through nozzle B without breakup. We conclude that the theoretical predictions are in good agreement with the experiments. Because all of the experimental results match our predictions quite well, eqs 3 and 5 can be used as criteria for the design of nozzles in manipulating double emulsions. We also notice that the breakup of the shell is usually accompanied by the release of the core because after the breakup of the shell the daughter double emulsion droplet has a thin film of the shell liquid near the open orifice. The thin film ruptures easily, so the core is released. Consequently, we can also take advantage of this feature for applications of controlled release. In addition, our experimental results also show that the breakup of the shell is independent of the flow rate of the double emulsion, which is consistent with eqs 3 and 5. Moreover, we observed that the core may also be released without the breakup of the shell. This case happens only when the core is not large enough for the breakup of the shell and the Reynolds number (flow rate) is relatively small. Although the mechanism still needs to be studied further, it can be avoided by increasing the flow rate of the double emulsion to shorten the timescale for the droplet to flow entirely through the orifice. 5. CONCLUSIONS As a double emulsion droplet flows through a tapered nozzle, both the tilt angle of the nozzle and the diameter ratio of the core to the orifice influence the breakup of the shell. When the 4326
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deformation of the core significantly slows the upstream flow, the thin annular film of the continuous carrier undergoes the RayleighPlateau capillary instability, which results in the breakup of the shell. For a given core size within the droplet, increasing the tilt angle or the diameter of the orifice is useful for preventing large droplets from breaking up. For example, we can design a nozzle with a tilt angle of about 9° for an application involving reinjection so that double emulsions with a large range of drop diameters are able to flow through the nozzle without breakup.
’ AUTHOR INFORMATION Corresponding Author
*(H.C.) E-mail:
[email protected]. (H.A.S.) Tel: (609)258-9493. Fax: (609)-258-6109. E-mail:
[email protected].
’ ACKNOWLEDGMENT We thank Prof. David A. Weitz, Dr. Ho Cheung Shum, Dr. Jeffrey M. Aristoff, Dr. Ian Griffiths, and Dr. Andrew S. Utada for helpful conversations and the Weitz group at Harvard University for supporting the experiments. This work is supported by NSFC projects (nos. 50805008 and 50975158) and Fundamental Research Funds for the Central Universities (FRF-TP-09-013A). ’ REFERENCES (1) Shah, R. K.; Shum, H. C.; Rowat, A. C.; Lee, D.; Agresti, J. J.; Utada, A. S.; Chu, L. Y.; Kim, J. W.; Fernandez-Nieves, A.; Martinez, C. J.; Weitz, D. A. Mater. Today 2008, 11, 18–27. (2) Christopher, G. F.; Anna, S. L. J. Phys. D: Appl. Phys. 2007, 40, R319–R336. (3) Song, H.; Chen, D. L.; Ismagilov, R. F. Angew. Chem., Int. Ed. 2006, 45, 7336–7356. (4) Okushima, S.; Nisisako, T.; Torii, T.; Higuchi, T. Langmuir 2004, 20, 9905–9908. (5) Utada, A. S.; Lorenceau, E.; Link, D. R.; Kaplan, P. D.; Stone, H. A.; Weitz, D. A. Science 2005, 308, 537–541. (6) Abate, A. R.; Weitz, D. A. Small 2009, 5, 2030–2032. (7) Chu, L. Y.; Utada, A. S.; Shah, R. K.; Kim, J. W.; Weitz, D. A. Angew. Chem., Int. Ed. 2007, 46, 8970–8974. (8) Brouzes, E.; Medkova, M.; Savenelli, N.; Marran, D.; Twardowski, M.; Hutchison, J. B.; Rothberg, J. M.; Link, D. R.; Perrimon, N.; Samuels, M. L. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 14195–14200. (9) Clausell-Tormos, J.; Lieber, D.; Baret, J. C.; El-Harrak, A.; Miller, O. J.; Frenz, L.; Blouwolff, J.; Humphry, K. J.; Koster, S.; Duan, H.; Holtze, C.; Weitz, D. A.; Griffiths, A. D.; Merten, C. A. Chem. Biol. 2008, 15, 427–437. (10) Chen, H. S.; Li, J.; Shum, H. C.; Stone, H. A.; Weitz, D. A. Soft Matter 2011, 7, 2345–2347. (11) Anna, S. L.; Bontoux, N.; Stone, H. A. Appl. Phys. Lett. 2003, 82, 364–366. (12) Tan, Y. C.; Fisher, J. S.; Lee, A. I.; Cristini, V.; Lee, A. P. Lab Chip 2004, 4, 292–298. (13) Link, D. R.; Anna, S. L.; Weitz, D. A.; Stone, H. A. Phys. Rev. Lett. 2004, 92, 054503. (14) Menetrier-Deremble, L.; Tabeling, P. Phys. Rev. E 2006, 74, 035303. (15) Stone, H. A.; Leal, L. G. J. Fluid Mech. 1990, 211, 123–156. (16) Smith, K. A.; Ottino, J. M.; Cruz, M. O. Phys. Rev. Lett. 2004, 93, 204501. (17) Zhou, C.; Yue, P. T.; Feng, J. J. Int. J. Multiphase Flow 2008, 34, 102–109. (18) Newhouse, L. A.; Pozrikidis, C. J. Fluid Mech. 1992, 242, 193–209. (19) Bico, J.; Quere, D. J. Fluid Mech. 2002, 467, 101–127. 4327
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