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Flow focusing geometry generates droplets through a plug and squeeze mechanism{ Downloaded by University of California - San Francisco on 20 November 2012 Published on 17 October 2012 on http://pubs.rsc.org | doi:10.1039/C2LC40938K

Philip A. Romero and Adam R. Abate* Received 17th August 2012, Accepted 16th October 2012 DOI: 10.1039/c2lc40938k

Microdroplets are typically generated by one of two microfluidic geometries, the T-junction and flow focusing. These two geometries are often thought to form drops through different mechanisms. Here, by directly measuring the pressures in the drop maker, we show that flow focus devices exhibit pressure fluctuations that are essentially identical to those found in T-junctions, suggesting that, in these devices and low-tomoderate capillary number, the drop formation process is also dominated by interfacial stresses and proceeds through a plugging–squeezing process. Microfluidic devices can form picolitre-volume droplets at kilohertz rates. Each droplet can be used to house a different chemical compound or cell, allowing massive numbers of independent reactions to be performed rapidly using a minimal amount of total reagent. The massive throughput of these systems makes them valuable for a broad range of biological studies, including for DNA analysis,1 rare cell detection,2 and the directed evolution of enzymes.3,4 A key consideration when applying these techniques to a particular biological application is choosing the best drop formation method for the task at hand. In microfluidics, there are two common methods for making droplets, T-junction5,6 and flow focus7 drop formation. These methods utilize different microchannel geometries, have different numbers of inlet ports, and may form droplets through distinct mechanisms. Theoretical work has identified three distinct mechanisms of drop formation: squeezing, dripping, and jetting.8 The squeezing mechanism proceeds as the emerging dispersed phase obstructs the flow of the continuous phase, causing its pressure to rise; this rise in pressure, in turn, allows the continuous phase to squeeze on the dispersed phase, pinching off a drop in the process. The dripping mechanism occurs when shear stresses overcome the interfacial tension, and drop breakup is caused by the shearing of the dispersed phase by the continuous phase. Finally, the jetting mechanism is characterized by the formation of long threads in the dispersed phase, which are broken due to the Plateau–Rayleigh instability. The squeezing mechanism is distinguished from the Department of Bioengineering and Therapeutic Sciences and California Institute for Quantitative Biosciences, University of California, San Francisco, California, USA. E-mail: [email protected] { Electronic supplementary information (ESI) available. See DOI: 10.1039/c2lc40938k

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other two by the existence of large pressure fluctuations in the continuous phase. Detailed theoretical descriptions of T-junctions suggest that, for the flow rates and Capillary numbers (Ca) that are most commonly used when applying these techniques, the drop formation process proceeds through the squeezing mechanism.6,8 This has been validated with recent simulation8 and experimental9 work that has shown pressure fluctuations during the drop breakup cycle in these devices. However, no comparable studies have been performed for flow focus devices and, as of yet, it is unknown whether similar pressure fluctuations exist in these devices and dominate their drop formation. In this communication, we present an experimental investigation of the pressures in a flow focus device during drop formation. Using Laplace sensors,9 pressure probes that allow fast, accurate, and localized measurements of pressures in microchannels, we measure the pressures in the droplet and continuous phases during drop formation. We find that, indeed, the pressures in these fluids fluctuate during the drop formation and that, moreover, these fluctuations are nearly identical to those of T-junctions. This indicates that flow focus devices, for the flow rates that are most commonly used when applying these techniques, also form droplets through a plugging–squeezing process. Our microfluidic devices are fabricated using soft lithography in poly(dimethylsiloxane).10 The devices consist of a flow focusing drop maker with channel dimensions of 25 mm in width and height. To form water-in-oil emulsions, we make our devices hydrophobic by perfusing their channels with Aquapel and then blowing them dry with air. The devices are then baked at 65 uC for 1 h. For the droplet fluid we use deionized water and for the continuous fluid the fluorinated oil HFE-7500, having a viscosity of 1.2 mPa s, which is close to that of water. We also use the ammonium carboxylate salt of Krytox FSL at 2 wt% as a surfactant to reduce interfacial tension and stabilize the drops. With this combination of solutions, we measure an interfacial tension of y4 mN m21. The pressures in the channels of the flow-focusing drop maker are measured with a Laplace sensor, which provides a fast, accurate, and localized measurement of pressure. A Laplace sensor is a channel that intersects the channel whose pressure is being measured (Fig. 1). The sensor channel is filled with a fluid that is immiscible with the fluid in which the pressure is to be measured, causing an interface to form between these fluids. The pressure This journal is ß The Royal Society of Chemistry 2012

Downloaded by University of California - San Francisco on 20 November 2012 Published on 17 October 2012 on http://pubs.rsc.org | doi:10.1039/C2LC40938K

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Fig. 1 Laplace sensors in a flow focusing drop maker. The dispersed fluid flows in from the left and the continuous phase from the top and bottom. Pressure is monitored at three locations: dispersed phase (Pd), continuous (Pc), and outlet (Pout). Fluid–fluid interfaces are identified using k-means image segmentation and circles are fit to each interface using least squares regression. The progression of the droplet breakup is given by the minimum width (w) of the emerging droplet in the channel intersection.

difference between the two phases can then be determined by the interface’s radius of curvature through the Laplace law DP~

2c r

where r is the interface’s radius of curvature and c is the interfacial tension. To measure the pressure fluctuations generated during flow focus drop formation, we use three Laplace sensors: dispersed phase (Pd), continuous phase (Pc), and the droplet output (Pout), as shown in Fig. 1. We record movies of the drop formation process and the motions of the Laplace sensor interfaces using a Phantom V7 fast camera at 31 250 fps. Each frame is segmented using k-means clustering and each interface is fit to a circle using least squares regression. The fit radius is used to determine the pressure difference between the two phases at each time point. In addition, we monitor the progression of the drop breakup by measuring the minimum width (w) of the droplet in the channel intersection, indicated by the white double-arrow in Fig. 1. Pressure time traces for hundreds of drop breakup events are generated and averaged over the drop breakup cycle (Fig. 2). The first half of the drop cycle (0 to 0.6 ms in Fig. 2) is marked by a droplet emerging from the dispersed phase inlet. The pressures in the continuous and dispersed phases are relatively constant, and the output pressure shows a significant decrease. The fluctuation in the outlet pressure from y0.4 to 0.6 ms is due to the drop from the previous cycle passing over the output Laplace sensor. In the third quarter of the drop cycle (y0.6 to 0.9 ms) the dispersed phase plugs the outlet channel. The pressure increases in the continuous phase, decreases in the dispersed phase, and increases in the outlet. In the final quarter of the cycle (y0.9 to 1.2 ms) the neck of the dispersed phase begins to collapse. The pressure of the continuous phase decreases, the dispersed phase increases, and the outlet remains constant. These pressure fluctuations, which we observe in our flow focusing geometry, are nearly identical to those we previously observed in the T-junction.9 The similarity of these fluctuations is shown by comparison with the dotted lines, which correspond to the pressure fluctuations for the T-junction rescaled by the drop formation period and pressure fluctuation amplitudes, Fig. 2(c–d). Importantly, both drop making This journal is ß The Royal Society of Chemistry 2012

Fig. 2 Average pressure fluctuations during the drop breakup cycle. (a) Microscopy images of drop formation in a flow focusing drop maker. (b) The progression of drop formation is monitored by the minimum width (w) of the droplet in the nozzle defined by the four corners of the channel intersection. This width is zero before the droplet front crosses the distal intersection boundary, quickly rises during plugging, and then returns back to zero during squeezing. (c) The pressure of the continuous phase is constant over the first half of the drop cycle and then increases as the droplet plugs the channel. The T-junction’s pressure with rescaled amplitude (2.36) and time (0.76) are shown as a dashed line. (d) The pressure of the dispersed phase is nearly the opposite of the continuous phase. It is constant over the first half of the cycle and then decreases during plugging. The rescaled dispersed T-junction pressure (7.1 6 amplitude, 0.7 6 time) is shown as a dashed line. (e) The pressure of the outlet channel shows a decrease as the droplet approaches it, a pulse (from y0.4 to 0.6 ms) as the droplet passes over it, and an increase as the droplet moves away. The rescaled T-junction data (0.6 6 amplitude, 0.7 6 time) is shown as a dashed line. The flow focusing and T-junction geometries show very similar pressure fluctuations in the continuous and dispersed inlet channels.

geometries show a pressure increase in the continuous phase as the dispersed phase plugs the channel. This pressure increase is indicative of a squeezing mechanism of droplet breakup for the flow focus device. Lab Chip, 2012, 12, 5130–5132 | 5131

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mechanism of drop breakup. These pressure fluctuations are nearly identical to those observed in the T-junction, suggesting that both geometries generate drops by the same mechanism, which depends largely on the capillary number of the flow. Our results demonstrate that, for the flow rates for which microfluidic drop formation is most commonly used, T-junction and flow focus drop makers behave nearly the same.

Downloaded by University of California - San Francisco on 20 November 2012 Published on 17 October 2012 on http://pubs.rsc.org | doi:10.1039/C2LC40938K

Acknowledgements

Fig. 3 Dependence on the capillary number (Ca). The pressure fluctuation |DP|max at each Ca is calculated as the difference between the minimum and maximum pressures. The pressure fluctuations in both the dispersed and continuous phases decrease with increasing Ca. At the lowest Ca tested (0.04), the curves become more flat, suggesting a transition to the squeezing regime.

To quantify the relative importance of flow stresses versus interfacial stresses, we analyze the drop breakup process at varying capillary numbers by adjusting flow rates. In the squeezing regime, simulations have shown the magnitude of the pressure fluctuation does not depend on the capillary number, while in the dripping regime the magnitude decreases with increasing capillary number.8 We therefore analyze the magnitude of the pressure fluctuations in the dispersed and continuous phases at five capillary numbers (Fig. 3). These curves show a decrease in the pressure fluctuation with increasing Ca, indicative of a dripping breakup mechanism. At the lowest Ca tested (0.04), the slopes of the curves become flatter, suggesting a transition to the squeezing regime. This is consistent with results from simulations that have shown the squeezing mechanism becomes dominant for Ca , 0.01.8 We have used Laplace sensors to measure the pressure fluctuations in the channels of a flow focusing drop maker. We found significant pressure fluctuations in the dispersed and continuous phases, which are typically associated with a squeezing

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We would like to thank Pascaline Mary for her help. This work was supported by startup funds from the Department of Bioengineering and Therapeutic Sciences, a Research Award from the California Institute for Quantitative Biosciences (QB3), the Bridging the Gap Award from the Rogers Family Foundation, and the UCSF/Sandler Foundation Program for Breakthrough Biomedical Research.

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This journal is ß The Royal Society of Chemistry 2012