Increased Drop Formation Frequency via Reduction of Surfactant

Article pubs.acs.org/Langmuir

Increased Drop Formation Frequency via Reduction of Surfactant Interactions in Flow-Focusing Microfluidic Devices Dimitris N. Josephides and Shahriar Sajjadi* Department of Physics, Kings College, London, U.K. ABSTRACT: Glass capillary based microfluidic devices are able to create extremely uniform droplets, when formed under the dripping regime, at low setup costs due to their ease of manufacture. However, as they are rarely parallelized, simple methods to increase droplet production from a single device are sought. Surfactants used to stabilize drops in such systems often limit the maximum flow rate that highly uniform drops can be produced due to the lowering interfacial tension causing jetting. In this paper we show that by simple design changes we can limit the interactions of surfactants and maximize uniform droplet production. Three flow-focused configurations are explored: a standard glass capillary device (consisting of a single round capillary inserted into a square capillary), a nozzle fed device, and a surfactant shielding device (both consisting of two round capillaries inserted into either end of a square capillary). In principle, the maximum productivity of uniform droplets is achieved if surfactants are not present. It was found that surfactants in the standard device greatly inhibit droplet production by means of interfacial tension lowering and tip-streaming phenomena. In the nozzle fed configuration, surfactant interactions were greatly limited, yielding flow rates comparable to, but lower than, a surfactant-free system. In the surfactant shielding configuration, flow rates were equal to that of a surfactant-free system and could make uniform droplets at rates an order of magnitude above the standard surfactant system.

■

INTRODUCTION Glass capillary microfluidic methods of creating monodisperse emulsions have in recent years shown great promise due to their ease and low cost of manufacture and the highly uniform emulsions they can produce.1−6 In their simplest form, they consist of a square cross-sectional glass capillary tube with inserted pulled micropipettes where the end of each acts as a fluid port. The formulation and morphology of the produced emulsions have the potential to be used in a wide number of applications (both commercial and academic), but due to the nature of the drop by drop formation method, i.e., every drop in the final emulsion is created consecutively, production rates are often small. Increasing the rate at which an emulsion of desired properties can be produced while keeping the simplicity of these devices is sought. The limiting factor often experienced when using these types of devices is when they move from dripping to jetting regimes at increased flow rates, dripping being associated with highly uniform emulsions and jetting characterized by an increase in polydispersity.7,8 When a formulation’s viscosity is increased, or its interfacial tension is decreased, jetting occurs at progressively lower flow rates. With these problematic formulations, flow rates must be reduced to sometimes unfavorable levels in order to maintain dripping and a tradeoff between monodispersity and production rates encountered.9 Increasing monodispersity at elevated flow rates has been the subject of many studies where different mechanical techniques have been employed to force a system which would normally form jets to form individual droplets. Methods used range from vibrating nozzles,10 pulsing feed pressure,11−13 and the use of electric fields,14 but these studies have required additional © 2014 American Chemical Society

means and equipment rather than seeking a purely microfluidic approach to address the problem. Abate et al. introduced the idea of a chaperoning fluid to induce dripping in problematic formulations consisting of both viscoelastic fluids and low interfacial tension systems.15 In such a technique, a third intermediate fluid is introduced between the dispersed and continuous phases to create core−shell drops. The droplet rupturing mechanism is then dominated by the continuous−intermediate phase interactions. A high interfacial tension or Newtonian intermediate phase can alleviate problems associated with low interfacial and nonNewtonian systems, respectively. This made the production of droplets feasible, but a drawback of this technique is the addition of a tertiary intermediate phase, which must be removed, can cause contamination and extra complexities. This report shows that by a simple formulation reconfiguration and geometry changes to a working flow-focused glass capillary based system involving surfactants (Figure 1A), one can change the interfacial dynamics to further increase the flow rate at which dripping will occur and thus increase the production rate of highly uniform emulsions. Surfactants in a microfluidic system, essential for drop stability, reduce the interfacial tension between phases and can increase the onset of jetting when compared to a pure (surfactant-free) system. We show two simple techniques that limit surfactant interactions, thus increasing the flow rates at which devices can be used before jetting occurs. The first technique involves delivering the Received: November 3, 2014 Revised: December 16, 2014 Published: December 17, 2014 1218

DOI: 10.1021/la504299r Langmuir 2015, 31, 1218−1224

Article

Langmuir

and “surfactant shielding” device (Figure 1B,C) consists of two cylindrical tapered glass capillaries inserted at opposite ends of a square cross-sectional glass capillary so that their nozzles are slightly apart but axially aligned; it is a common geometry used for creating core−shell emulsions. The dispersed phase is pumped through the end of the smaller cylindrical channel and the continuous phase pumped through both ends of the square channel. The final emulsion is collected from the end of the larger cylindrical collector channel. Using two ports for the continuous phase allows us to locally change the continuous phase’s properties in proximity of the drop generating nozzle where the phases have not had time to mix. Microfluidic cells were fabricated by using a pipet puller (Sutter P1000) to draw either one or two glass capillaries (i.d. 0.7 mm, o.d. 1 mm, World Precision Instruments) to fine tapered ends (nozzle diameter 2 mm). The highest flow rate data point of each experimental set was obtained at the point where the device entered the jetting regime, resulting in a sharp increase in both size and polydispersity. The marked increase in droplet size once jetting was induced was due to the widening geometry of the collection capillary tube. Similar to the phenomenon of a widening jet observed in coflow systems,22 as the jet moves downstream its velocity is reduced and therefore its diameter is increased. It was observed that the further away from the orifice jet rupture occurred, the larger the final drop diameter. All data points below the final jetting value in each case are obtained during dripping where highly uniform drops are created.

Figure 4. Measured droplet diameters and monodispersity for the nozzle fed flow-focused system while in the dripping regime.

Configuration A: Standard Flow Focused Device. In the standard flow focused configuration, characterized by a 1220

DOI: 10.1021/la504299r Langmuir 2015, 31, 1218−1224

Article

Langmuir Wed =

ρd ud 2Djet (1)

σ

where ρ, u, Djet, and σ denote density, plug velocity, jet diameter, and interfacial tension, respectively, and the subscript “d” denotes dispersed phase. The capillary number (Ca) describes the relative importance of viscous forces acting on a fluid’s interface compared to its interfacial tension, and it is defined as follows: μ uc Cac = c (2) σ where μ denotes dynamic viscosity and the subscript “c” denotes the continuous phase. If we calculate Wed and Cac for the three surfactant systems at the point jetting occurs and assuming equilibrated interfacial tension values, we obtain the values shown in Table 1. Table 1. Calculated Values of We and Ca at the Onset of Jetting Assuming Equilibrated Interfacial Tension system

Cac

Wed

Cac + Wed

Igepal SDS pure

0.122 0.049 0.029

0.300 0.240 0.576

0.423 0.289 0.606

We can see from the table that for the pure system jetting occurs when the summation of Wed and Cac is equal to about 0.6. As there is no dynamic interfacial effect in the pure system, we assume this to be the critical value for jetting within this geometry. When dealing with high frequency “drop by drop” methods of emulsion production containing surfactants, it is common to evaluate the effective interfacial tension of the drop at creation. This often is not an attempt to accurately measure the dynamic interfacial tension at the interface but rather a means to predict and make sense of output droplet diameters and dripping−jetting transition points that are not predicted well using equilibrated values. Depending on the chosen criteria for effective interfacial tension calculation, this normally yields values somewhere between the equilibrated and pure system values, where the higher the frequency, the closer the value is to the pure system. In the three microfluidic geometries used in these experiments, we evaluated the effective interfacial tensions as the value at which satisfies the system jetting at a critical Wed + Cac = 0.6. Effective interfacial tension values are calculated to be 1.05 and 3.6 mN/m for the Igepal and SDS systems, respectively. It may be surprising to note that the surfactant systems in this configuration seem to behave as if their interfacial tension values are below that of equilibrium, especially when taking into account the high frequency at which droplets are produced. For the Igepal system at the onset of jetting, droplets were being formed at ≈1000 Hz and for the SDS system ≈2000 Hz. These time scales are classically considered to be too quick for equilibrated values of interfacial tension to be achieved; for example, a 20 mM SDS solution was shown to take 0.05 s to reach equilibrium (air−water) in one study26 whereas droplets in our SDS system are created every 0.0005 s. The large interfacial area that is created in this form of flow focused configuration before drop formation, as can be seen in Figure 2A, certainly contributes to the explanation for such low effective interfacial tension values but does not explain how they could be below equilibrium. We must now ask the

Figure 5. Measured droplet diameters and monodispersity for the surfactant shielded flow-focused system while in the dripping regime.

dispersed phase feed geometry being much larger (≈1000 μm) than the collector nozzle geometry (≈100 μm), we can clearly see the effects of the different surfactants on the operating regions of the device. In the Igepal system (equilibrated interfacial tension = 1.5 mN/m) it is seen that uniform droplets can be created at dispersed flow rates ranging from 250 to 750 μL/h. For the SDS system (equilibrated interfacial tension = 7.5 mN/m) we see a rise in operating flow rates ranging from 500 to 1500 μL/h, and the pure system operates in the range of 5000−6000 μL/h. For all systems a linear droplet size decrease (≈90 to ≈70 μm) was observed with increasing dispersed flow until the onset of jetting occurred. Conceptually these results are unsurprisinga reduction in interfacial tension leading to an earlier onset of jetting.23 However, it is known that the dynamic effects of interfacial tension are of great importance in “drop by drop” emulsification systems where the high rate of drop production often means such devices operate at effective interfacial tensions much greater than their equilibrated values. We cannot directly measure the interfacial tension of the drop interface during production, but by calculating various dimensionless numbers at the onset of jetting, we may infer the magnitude. Predicting the point at which jetting will occur in microfluidic devices has been the subject of many studies and are well reviewed in the work of Nunes et al.24 No analytical method currently exists to do this,25 but it is assumed that jetting generally occurs when the summation of the Weber and capillary numbers are of order unity (frequently lower). The Weber number (We) describes the relative importance of a fluid’s inertia compared to its interfacial tension, and it is defined as follows: 1221

DOI: 10.1021/la504299r Langmuir 2015, 31, 1218−1224

Article

Langmuir

Figure 6. Top left: immediate coalescence downstream of a flow-focused device not containing any surfactants (Qd = 6000 μL/h). Top right: downstream droplets formed using a surfactant shielded flow-focused system. Rapid mixing of surfactants at the nozzle ensures droplets are protected from coalescence (Qd = 6000 μL/h). Middle: drop induced mixing of the two-part continuous phase (Qd = 4000 μL/h, Qc = 16 000 μL/h) Bottom: laminar flow of pure and surfactant containing continuous phases with no droplets present (Qc = 16 000 μL/h). It is observed that very little mixing occurs due to low Reynolds numbers.

the inclusion of a dispersed feed nozzle. Assuming this critical value to be the same for the surfactant systems, we can calculate the effective interfacial tension value to be 22.75 mN/m. It is not known why the two surfactant systems in this configuration behave so similarly, and a detailed analysis of the surfactant diffusion effects goes beyond the scope of this paper; however, one possible explanation is that even though SDS diffuses onto the interface faster (due to its lower molecular mass), it is less effective in decreasing the interfacial tension as it has a higher equilibrated interfacial tension value than Igepal co630. Configuration C: Surfactant Shielded Flow Focused Device. The surfactant shielded flow focused configuration uses the same physical geometry as the nozzle fed configuration, but in this case the continuous phase consists of two distinct parts. Pure water is introduced over the dispersed phase nozzle, and the surfactant laden continuous phase (4 wt % Igepal/SDS) is introduced over the collector nozzle. This has the effect of shielding the interfacial area from surfactants until drops have formed (the results for the pure system are therefore identical to the nozzle fed configuration). In this case, both the surfactant systems behaved very similarly to that of the pure system with the onset of jetting occurring at Qd = 6000 μL/h and a linear droplet reduction from ≈100 to ≈60 μm. The effective interfacial tension for all the systems can be said to be equal to that of the pure system (50 mN/m) which shows that negligible surfactant diffusion took place at the interface of the forming drops. This is by far the most desirable flow-focused configuration showing a 700% increase in maximum Qd compared to the standard flow-focused system and 50% increase compared to the nozzle fed system for the Igepal target emulsion (300% and 50% for the SDS target emulsion). Depending on the dominant forces in a given geometry and formulation, we can generalize the results above into two equations to predict the boundaries of performance increase of using a surfactant shielded system. By equating either a constant critical Ca or We number into eqs 1 and 2, we can derive

question, is the dynamic interfacial tension at the point of droplet creation indeed lower than equilibrium or just an artifact of our chosen effective interfacial tension criteria? Tipstreaming and tip-dropping are well-known phenomena in systems containing below and above CMC concentrations of surfactant, respectively. Originally observed in experiments where isolated droplets subjected to subcritical capillary number shear flows would rupture into many drops either through tip-streaming, where the droplet would assume a slender pointed shape and much smaller drops would detach from the points, or tip-dropping, where a slender pointed shape would from but much larger drops would detach. The effects of tip-streaming have been observed in flow focusing devices both at above and below CMC concentrations.27−30 The phenomenon occurs when hydrodynamic forces from the continuous phase act on the interface moving surfactant molecules to the front tip further concentrating the surfactant at the point of droplet formation. This further concentration of surfactant on the interface has been known to reduce interfacial tension to near zero values in some studied systems28 and could well explain the earlier than expected onset of jetting in our studied system. Configuration B: Nozzle Fed Flow Focused Device. In the nozzle fed flow focused configuration, characterized by a dispersed phase feed geometry being smaller (≈50 μm) than the collector nozzle geometry (≈100 μm), we can see a great improvement on the operational flow rates of the surfactant systems as compared to the standard flow focused geometry. Interestingly, the choice of surfactant seemed to make little difference as the onset of jetting and droplet sizes were found to be very similar. Both surfactant systems had operating flow rates ranging from ≈500 to 4000 μL/h, and the pure system operated in the range of 3000 to 6000 μL/h. For all systems, a linear droplet size decrease (≈100 to ≈60 μm) was observed with increasing dispersed flow until the onset of jetting occurred. The range of operational flow rates was increased by a factor of 3 for all systems in this configuration. The improvements observed in this configuration can be attributed to the greatly reduced interfacial area before drop formation occurs, as seen in Figure 2B. Again the pure system begins to jet at Qd = 6000 μL/h (Wed + Cac = 0.6) as the critical Weber and capillary number seem to be unaffected by

⎛Q ⎞ σpure ⎜⎜ shield ⎟⎟ = σeff ⎝ Q surf ⎠cap 1222

(3) DOI: 10.1021/la504299r Langmuir 2015, 31, 1218−1224

Article

Langmuir ⎛Q ⎞ ⎜⎜ shield ⎟⎟ = ⎝ Q surf ⎠ web

surfactant containing continuous phase at the collector nozzle orifice. This resulted in a large increase in feed rate (700% for the Igepal co630 and 300% for the SDS target emulsion) when compared to a standard configuration. The results show that unlike conventional thought on microfluidic drop generation,32 surfactant interactions may be important at high droplet production frequencies, and it is beneficial to try to limit these. Proposed techniques could also be incorporated in 2D planar microfluidic devices and systems involving cosolvents as well as surfactants.

σpure σeff

(4)

where the subscripts cap and web represent capillary and Weber dominant flow systems, respectively, and σpure and σeff represent the pure system interfacial tension and the effective interfacial tension of the comparable system. In systems where viscous forces dominate (high viscosities compared to mass flow rates), the maximum performance increase is expected, whereas if inertial forces dominate, we expect less of an improvement. Effective interfacial tensions could be derived experimentally or estimated from the dynamics of the surfactant system. One might argue that drops could be formed in the absence of surfactant using traditional microfluidic means, while surfactant incorporation can be carried out downstream to stabilize drops. This unfortunately can be problematic for various reasons. When droplets are formed in widening configurations (as in glass capillary based microfluidics), the velocity of the emulsion is quickly reduced after formation and droplets in the center stream are forced to crash into each other. Without the presence of a surfactant early on, droplets continue to coalesce forming larger and more polydisperse drops as they travel downstream (Figure 6). If we now consider a scenario where we have a nonwidening straight channel instead (as is common in 2D planar systems), one must contemplate how to introduce the surfactant downstream. If it is introduced in the microfluidic laminar environment, it is difficult to achieve a rapid mixing of the two aqueous phases;31 thus a longer channel would be required to allow time for diffusion. If an energy efficient method of creating uniform droplets is sought, the longer the channel, the more energy (pressure) is required to pump at a given flow rate. An example of the difficulties associated with micromixing in laminar flows is shown in Figure 6, where pure water and surfactant laden water are introduced into the collector channel of a microfluidic device with no dispersed phase. Because of the altered refracted index of the aqueous phases by the addition of surfactant, the interface between pure water and surfactant laden water is easily visible via transition light microscopy. One can clearly see that very little mixing between the two phases occurs downstream; however, if we compare this to the surfactant shielding configuration, very rapid mixing of the two aqueous phases occurs at the nozzle orifice. This is due to the perturbations in the continuous phase flow caused by drops passing through a narrowing region. This causes large regular time dependent changes in the radial flow direction of the continuous phase at the nozzle and greatly enhances surfactant mixing, protecting the drops from early coalescence.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (S.S.). Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We acknowledge the use made of Vision Research Phantom V710 which was borrowed from the EPSRC (Engineering and Physical Sciences Research Council) Engineering Instrument Pool.

■

REFERENCES

(1) Van Dijke, K. C.; Schroën, K. C. P. G. H.; Boom, R. M. Microchannel Emulsification: From Computational Fluid Dynamics to Predictive Analytical Model. Langmuir 2008, 24, 10107−10115. (2) Nisisako, T. Microstructured Devices for Preparing Controlled Multiple Emulsions. Chem. Eng. Technol. 2008, 31, 1091−1098. (3) Shah, R.; Shum, H.; Rowat, A.; Lee, D.; Agresti, J.; Utada, A.; Chu, L.; Kim, J.; Fernandeznieves, A.; Martinez, C. Designer Emulsions Using Microfluidics. Mater. Today 2008, 11, 18−27. (4) Chu, L.-Y.; Utada, A. S.; Shah, R. K.; Kim, J.-W.; Weitz, D. A. Controllable Monodisperse Multiple Emulsions. Angew. Chem., Int. Ed. 2007, 46, 8970−8974. (5) Utada, A. S. Monodisperse Double Emulsions Generated from a Microcapillary Device. Science 2005, 308, 537−541. (6) Vladisavljević, G. T.; Kobayashi, I.; Nakajima, M. Production of Uniform Droplets Using Membrane, Microchannel and Microfluidic Emulsification Devices. Microfluid. Nanofluid. 2012, 13, 151−178. (7) Utada, A.; Fernandez-Nieves, A.; Stone, H.; Weitz, D. Dripping to Jetting Transitions in Coflowing Liquid Streams. Phys. Rev. Lett. 2007, 99. (8) Nie, Z.; Seo, M.; Xu, S.; Lewis, P. C.; Mok, M.; Kumacheva, E.; Whitesides, G. M.; Garstecki, P.; Stone, H. A. Emulsification in a Microfluidic Flow-Focusing Device: Effect of the Viscosities of the Liquids. Microfluid. Nanofluid. 2008, 5, 585−594. (9) Josephides, D. N.; Sajjadi, S. Microfluidic Method for Creating Monodisperse Viscous Single Emulsions via Core−Shell Templating. Microfluid. Nanofluid. 2014, 1−8. (10) Huang, S.-B.; Wu, M.-H.; Lee, G.-B. Microfluidic Device Utilizing Pneumatic Micro-Vibrators to Generate Alginate Microbeads for Microencapsulation of Cells. Sens. Actuators, B 2010, 147, 755− 764. (11) Sauret, A.; Cheung Shum, H. Forced Generation of Simple and Double Emulsions in All-Aqueous Systems. Appl. Phys. Lett. 2012, 100, 154106. (12) Song, Y.; Shum, H. C. Monodisperse w/w/w Double Emulsion Induced by Phase Separation. Langmuir 2012, 28, 12054−12059. (13) Sauret, A.; Shum, H. C. Beating the Jetting Regime. Int. J. Nonlinear Sci. Numer. Simul. 2012, 13, 351−362. (14) Yeh, C.-H.; Lee, M.-H.; Lin, Y.-C. Using an Electro-Spraying Microfluidic Chip to Produce Uniform Emulsions under a DirectCurrent Electric Field. Microfluid. Nanofluid. 2012, 12, 475−484. (15) Abate, A. R.; Kutsovsky, M.; Seiffert, S.; Windbergs, M.; Pinto, L. F. V.; Rotem, A.; Utada, A. S.; Weitz, D. A. Synthesis of

■

CONCLUSIONS Standard flow focused techniques in glass capillary based microfluidics have been shown to be greatly affected by surfactants in terms of maximum production rates. It has been shown that by simple reconfiguration of the geometry and surfactant location, production rates can be greatly increased while still producing highly uniform and stable drops. The most effective way to increase production rates was by means of a surfactant shielding configuration. This is where continuous phase with no surfactant is passed over the dispersed phase nozzle during drop formation and quickly mixing with 1223

DOI: 10.1021/la504299r Langmuir 2015, 31, 1218−1224

Article

Langmuir Monodisperse Microparticles from Non-Newtonian Polymer Solutions with Microfluidic Devices. Adv. Mater. 2011, 23, 1757−1760. (16) Kakaç, S.; Kosoy, B.; Li, D.; Pramuanjaroenkij, A. Microfluidics Based Microsystems: Fundamentals and Applications; Springer Science & Business Media: New York, 2010. (17) Norton, M. M.; Brugarolas, T.; Chou, J.; Lee, D.; Bau, H. H. Ellipsoidal Particles Encapsulated in Droplets. Soft Matter 2014, 10, 4840. (18) Tan, Y.-C.; Cristini, V.; Lee, A. P. Monodispersed Microfluidic Droplet Generation by Shear Focusing Microfluidic Device. Sens. Actuators, B 2006, 114, 350−356. (19) Dendukuri, D.; Pregibon, D. C.; Collins, J.; Hatton, T. A.; Doyle, P. S. Continuous-Flow Lithography for High-Throughput Microparticle Synthesis. Nat. Mater. 2006, 5, 365−369. (20) Nisisako, T.; Torii, T. Microfluidic Large-Scale Integration on a Chip for Mass Production of Monodisperse Droplets and Particles. Lab. Chip 2008, 8, 287. (21) Sun, B. J.; Shum, H. C.; Holtze, C.; Weitz, D. A. Microfluidic Melt Emulsification for Encapsulation and Release of Actives. ACS Appl. Mater. Interfaces 2010, 2, 3411−3416. (22) Castro-Hernández, E.; Gundabala, V.; Fernández-Nieves, A.; Gordillo, J. M. Scaling the Drop Size in Coflow Experiments. New J. Phys. 2009, 11, 075021. (23) Chaurasia, A. S.; Josephides, D. N.; Sajjadi, S. Buoyancy-Driven Drop Generation via Microchannel Revisited. Microfluid. Nanofluid. 2014, 1−11. (24) Nunes, J. K.; Tsai, S. S. H.; Wan, J.; Stone, H. A. Dripping and Jetting in Microfluidic Multiphase Flows Applied to Particle and Fibre Synthesis. J. Phys. Appl. Phys. 2013, 46, 114002. (25) Herrada, M.; Gañań -Calvo, A.; Ojeda-Monge, A.; Bluth, B.; Riesco-Chueca, P. Liquid Flow Focused by a Gas: Jetting, Dripping, and Recirculation. Phys. Rev. E 2008, 78. (26) Kawale, D.; Van Nimwegen, A. T.; Portela, L.; Henkes, R. A. W. M.; Van Dijk, M. TU Delft: Applied Sciences: Multi-Scale Physics; TU Delft, Delft University of Technology. Influence of Dynamic Surface Tension on Foams: Application in Gas Well Deliquification, 2012. (27) Anna, S. L.; Mayer, H. C. Microscale Tipstreaming in a Microfluidic Flow Focusing Device. Phys. Fluids 2006, 18, 121512− 121512 − 13. (28) Eggleton, C. D.; Tsai, T.-M.; Stebe, K. J. Tip Streaming from a Drop in the Presence of Surfactants. Phys. Rev. Lett. 2001, 87, 048302. (29) Suryo, R.; Basaran, O. A. Tip Streaming from a Liquid Drop Forming from a Tube in a Co-Flowing Outer Fluid. Phys. Fluids 2006, 18, 082102. (30) Ward, T.; Faivre, M.; Stone, H. A. Drop Production and TipStreaming Phenomenon in a Microfluidic Flow-Focusing Device via an Interfacial Chemical Reaction. Langmuir 2010, 26, 9233−9239. (31) Lee, C.-Y.; Chang, C.-L.; Wang, Y.-N.; Fu, L.-M. Microfluidic Mixing: A Review. Int. J. Mol. Sci. 2011, 12, 3263−3287. (32) Predicting Sizes of Droplets Made by Microfluidic FlowInduced Dripping. Soft Matter, in press.

1224

DOI: 10.1021/la504299r Langmuir 2015, 31, 1218−1224