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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 22 — Oct. 22, 2012
  • pp: 24450–24464
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Measuring the pressures across microfluidic droplets with an optical tweezer

Yuhang Jin, Antony Orth, Ethan Schonbrun, and Kenneth B. Crozier  »View Author Affiliations


Optics Express, Vol. 20, Issue 22, pp. 24450-24464 (2012)
http://dx.doi.org/10.1364/OE.20.024450


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Abstract

We introduce a novel technique that enables pressure measurements to be made in microfluidic chips using optical trapping. Pressure differentials across droplets in a microfluidic channel are determined by monitoring the displacements of a bead in an optical trap. We provide physical interpretation of the results. Our experiments reveal that our device has high sensitivity and can be operated over a wide range of pressures from several Pascals to several thousand Pascals.

© 2012 OSA

1. Introduction

Microfluidic techniques have been in rapid development in recent years and have found numerous applications in physics, chemistry, biology and interdisciplinary studies [1

1. T. Squires and S. Quake, “Microfluidics: Fluid physics at the nanoliter scale,” Rev. Mod. Phys. 77(3), 977–1026 (2005). [CrossRef]

,2

2. D. Mark, S. Haeberle, G. Roth, F. von Stetten, and R. Zengerle, “Microfluidic lab-on-a-chip platforms: requirements, characteristics and applications,” Chem. Soc. Rev. 39(3), 1153–1182 (2010). [CrossRef] [PubMed]

]. The transport and manipulation of emulsions, especially microfluidic droplets, are at the heart of many devices [3

3. S.-Y. Teh, R. Lin, L.-H. Hung, and A. P. Lee, “Droplet microfluidics,” Lab Chip 8(2), 198–220 (2008). [CrossRef] [PubMed]

5

5. A. B. Theberge, F. Courtois, Y. Schaerli, M. Fischlechner, C. Abell, F. Hollfelder, and W. T. S. Huck, “Microdroplets in microfluidics: An evolving platform for discoveries in chemistry and biology,” Angew. Chem. Int. Ed. Engl. 49(34), 5846–5868 (2010). [PubMed]

], and the extra pressure caused by droplets is often a key factor in their design and functionality [6

6. R. Seemann, M. Brinkmann, T. Pfohl, and S. Herminghaus, “Droplet based microfluidics,” Rep. Prog. Phys. 75(1), 016601 (2012). [CrossRef] [PubMed]

,7

7. C. N. Baroud, F. Gallaire, and R. Dangla, “Dynamics of microfluidic droplets,” Lab Chip 10(16), 2032–2045 (2010). [CrossRef] [PubMed]

]. For example, some “digital” microfluidic devices use droplets or bubbles as logic signals and rely heavily on the extra pressure that they provide to control logic gates and switches [8

8. L. F. Cheow, L. Yobas, and D.-L. Kwong, “Digital microfluidics: Droplet based logic gates,” Appl. Phys. Lett. 90(5), 054107 (2007). [CrossRef]

,9

9. M. Prakash and N. Gershenfeld, “Microfluidic bubble logic,” Science 315(5813), 832–835 (2007). [CrossRef] [PubMed]

]. As a result, the successful design and operation of droplet logic is based upon accurate knowledge of the pressure differentials across droplets of different sizes and in various flow conditions. In addition, droplet-based single cell analysis [10

10. J. Q. Boedicker, L. Li, T. R. Kline, and R. F. Ismagilov, “Detecting bacteria and determining their susceptibility to antibiotics by stochastic confinement in nanoliter droplets using plug-based microfluidics,” Lab Chip 8(8), 1265–1272 (2008). [CrossRef] [PubMed]

,11

11. P. Mary, L. Dauphinot, N. Bois, M.-C. Potier, V. Studer, and P. Tabeling, “Analysis of gene expression at the single-cell level using microdroplet-based microfluidic technology,” Biomicrofluidics 5(2), 24109 (2011). [CrossRef] [PubMed]

], biochemical assays [12

12. W. Y. Zhang, W. Zhang, Z. Liu, C. Li, Z. Zhu, and C. J. Yang, “Highly parallel single-molecule amplification approach based on agarose droplet polymerase chain reaction for efficient and cost-effective aptamer selection,” Anal. Chem. 84(1), 350–355 (2012). [CrossRef] [PubMed]

,13

13. T. Hatakeyama, D. L. Chen, and R. F. Ismagilov, “Microgram-scale testing of reaction conditions in solution using nanoliter plugs in microfluidics with detection by MALDI-MS,” J. Am. Chem. Soc. 128(8), 2518–2519 (2006). [CrossRef] [PubMed]

] and microparticle syntheses [14

14. C.-H. Chen, R. K. Shah, A. R. Abate, and D. A. Weitz, “Janus particles templated from double emulsion droplets generated using microfluidics,” Langmuir 25(8), 4320–4323 (2009). [CrossRef] [PubMed]

,15

15. T. Rossow, J. A. Heyman, A. J. Ehrlicher, A. Langhoff, D. A. Weitz, R. Haag, and S. Seiffert, “controlled synthesis of cell-laden microgels by radical-free gelation in droplet microfluidics,” J. Am. Chem. Soc. 134(10), 4983–4989 (2012). [CrossRef] [PubMed]

] present a considerable challenge for device miniaturization, since the large actuating pressure necessary to sustain the flow of an ensemble of droplets in high throughput experiments is demanding for the design of micropumps that can be integrated on the chip [16

16. D. J. Laser and J. G. Santiago, “A review of micropumps,” J. Micromech. Microeng. 14(6), R35–R64 (2004). [CrossRef]

]. Furthermore, some technologies use bubbles or droplets to disturb the laminar flow patterns that occur at low Reynolds numbers and thereby accelerate micromixing processes in the continuous phase [17

17. P. Garstecki, M. A. Fischbach, and G. M. Whitesides, “Design for mixing using bubbles in branched microfluidic channels,” Appl. Phys. Lett. 86(24), 244108 (2005). [CrossRef]

,18

18. P. Garstecki, M. J. Fuerstman, M. A. Fischbach, S. K. Sia, and G. M. Whitesides, “Mixing with bubbles: a practical technology for use with portable microfluidic devices,” Lab Chip 6(2), 207–212 (2006). [CrossRef] [PubMed]

]. The altered pressure distribution resulting from bubbles has an impact on the velocity and residence time of the other bubbles, as well as the continuous phase in the mixing units, and can therefore affect the quality and efficiency of mixing. Last, evaluation of pressure perturbations due to droplets and other emulsions in underground pores is key to enhanced oil recovery [19

19. S. Cobos, M. S. Carvalho, and V. Alvarado, “Flow of oil–water emulsions through a constricted capillary,” Int. J. Multiph. Flow 35(6), 507–515 (2009). [CrossRef]

], and microfluidic devices provide an ideal platform to mimic such porous environments and measure this pressure in a laboratory.

A variety of techniques to measure pressure changes or pressure differentials in microfluidic channels have been reported. Examples include membrane-based devices, which electrically [20

20. L. Wang, M. Zhang, M. Yang, W. Zhu, J. Wu, X. Gong, and W. Wen, “Polydimethylsiloxane-integratable micropressure sensor for microfluidic chips,” Biomicrofluidics 3(3), 34105 (2009). [CrossRef] [PubMed]

] or optically [21

21. M. J. Kohl, S. I. Abdel-Khalik, S. M. Jeter, and D. L. Sadowski, “A microfluidic experimental platform with internal pressure measurements,” Sens. Actuators A Phys. 118(2), 212–221 (2005). [CrossRef]

24

24. A. Orth, E. Schonbrun, and K. B. Crozier, “Multiplexed pressure sensing with elastomer membranes,” Lab Chip 11(22), 3810–3815 (2011). [CrossRef] [PubMed]

] characterize the pressure-induced deformation of a thin membrane serving as part of the channel wall, or track the displacement of microparticles due to membrane deformation [25

25. K. Chung, H. Lee, and H. Lu, “Multiplex pressure measurement in microsystems using volume displacement of particle suspensions,” Lab Chip 9(23), 3345–3353 (2009). [CrossRef] [PubMed]

]. However, these methods are in general not appropriate for measuring pressure differentials due to droplets, since deformation of the membrane alters the simple rectangular geometry of the channel cross section, rendering it difficult to interpret and model results for droplets. Also, membrane-based devices are often associated with tricky or expensive fabrication techniques, such as multilayer soft lithography [20

20. L. Wang, M. Zhang, M. Yang, W. Zhu, J. Wu, X. Gong, and W. Wen, “Polydimethylsiloxane-integratable micropressure sensor for microfluidic chips,” Biomicrofluidics 3(3), 34105 (2009). [CrossRef] [PubMed]

,22

22. W. Song and D. Psaltis, “Imaging based optofluidic air flow meter with polymer interferometers defined by soft lithography,” Opt. Express 18(16), 16561–16566 (2010). [CrossRef] [PubMed]

25

25. K. Chung, H. Lee, and H. Lu, “Multiplex pressure measurement in microsystems using volume displacement of particle suspensions,” Lab Chip 9(23), 3345–3353 (2009). [CrossRef] [PubMed]

] and reactive ion etching [21

21. M. J. Kohl, S. I. Abdel-Khalik, S. M. Jeter, and D. L. Sadowski, “A microfluidic experimental platform with internal pressure measurements,” Sens. Actuators A Phys. 118(2), 212–221 (2005). [CrossRef]

]. An alternative scheme for pressure sensing involves connecting microchannels to sealed air chambers and relating pressure to the volume of trapped air [26

26. N. Srivastava and M. A. Burns, “Microfluidic pressure sensing using trapped air compression,” Lab Chip 7(5), 633–637 (2007). [CrossRef] [PubMed]

]. Glass channels, however, are required in this scenario as poly(dimethylsiloxane) (PDMS), the flexible material popularly used for microfluidics, is air permeable. The need for glass channels reduces the flexibility and increases the cost. Recently, the use of external commercial pressure taps to measure extra pressure caused by droplets has been demonstrated [27

27. B. J. Adzima and S. S. Velankar, “Pressure drops for droplet flows in microfluidic channels,” J. Micromech. Microeng. 16, 1504–1510 (2016).

]. A limitation of this approach is that such external pressure gauges are usually not integration-friendly. That the distance between adjacent connections is several millimeters or more means that the total pressure differential can only be measured across a number of droplets, rather than across a single droplet. Finally, optical interface tracking is also employed to measure pressure fluctuations of multiphase flows [28

28. M. Abkarian, M. Faivre, and H. A. Stone, “High-speed microfluidic differential manometer for cellular-scale hydrodynamics,” Proc. Natl. Acad. Sci. U.S.A. 103(3), 538–542 (2006). [CrossRef] [PubMed]

,29

29. S. A. Vanapalli, A. G. Banpurkar, D. van den Ende, M. H. G. Duits, and F. Mugele, “Hydrodynamic resistance of single confined moving drops in rectangular microchannels,” Lab Chip 9(7), 982–990 (2009). [CrossRef] [PubMed]

]. While detecting pressure differential across single droplets has been successful [29

29. S. A. Vanapalli, A. G. Banpurkar, D. van den Ende, M. H. G. Duits, and F. Mugele, “Hydrodynamic resistance of single confined moving drops in rectangular microchannels,” Lab Chip 9(7), 982–990 (2009). [CrossRef] [PubMed]

], high throughput measurements might still be difficult: the geometry of these devices prohibits continuous measurement of single droplets at a high speed, since the droplets inevitably disturb the fluid-fluid interface, whose position serves as a pressure comparator.

2. Working principle

The shape of the cross section of the side channel is invariant along its length. Therefore at any given point in the cross section, the local fluid velocity v is linearly dependent on the volume flow rate Q in the channel. Furthermore, Eq. (1) implies a linear relation between Δx and v. Consequently, there is a linear dependence between the bead displacement Δx and flow rate Q. The proportionality coefficient can be determined from a calibration process, which is described in a later section.

Pressure-driven flows at low Reynolds numbers in a network of microfluidic channels are analogous to voltage-driven currents in an electrical circuit [34

34. H. Bruus, Theoretical Microfluidics (Oxford University Press, 2008).

]. Ohm’s law states that the electric current through a conductor is proportional to the voltage difference across it via its electrical resistance. Similarly, the flow rate Q in the side channel is proportional to the pressure differential ΔP across it via its hydraulic resistance Rh:
ΔP=RhQ,
(2)
The hydraulic resistance of the side channel Rh depends on channel geometry and can be approximated well by
Rh12μLw3h(10.63w/h)
(3)
where L denotes the total length of the segmented side channel, and w and h are the width and height (w < h in our design) of the side channel, respectively [34

34. H. Bruus, Theoretical Microfluidics (Oxford University Press, 2008).

].

In our experiments, we measure the bead displacement as droplets pass through the main channel. We then convert this to the flow rate Q in the side channel using the calibration data (discussed in a later section). We calculate the hydraulic resistance of the side channel Rh using Eq. (3). The pressure differential ΔP across the side channel, which is also equal to the pressure differential across the main channel containing the droplets, is then calculated by multiplying Q with Rh, as shown in Eq. (2).

3. Experimental

3.1 Device fabrication and experimental set-up

Photolithography and soft lithography are currently enabling PDMS-based microfluidic devices to be fabricated with short turnaround time [35

35. D. C. Duffy, J. C. McDonald, O. J. A. Schueller, and G. M. Whitesides, “Rapid prototyping of microfluidic systems in poly(dimethylsiloxane),” Anal. Chem. 70(23), 4974–4984 (1998). [CrossRef] [PubMed]

]. Following the standard protocols of these techniques, we fabricate the master in SU8 photoresist on a silicon wafer, and replicate it in PDMS [31

31. P. Tabeling, translated by S. Lin, Introduction to Microfluidics (Oxford University Press, 2005).

]. The PDMS replica is then oxidized in an oxygen plasma chamber at 80 W for 20 seconds, and bonded to a cover glass to form the channels. The bonded device undergoes a further oxidation in oxygen plasma at 80 W for 40 minutes, creating hydrophilic functional groups (e.g. silanol groups –SiOH) on the PDMS surface [36

36. M. J. Owen and P. J. Smith, “Plasma treatment of polydimethylsiloxane,” J. Adhes. Sci. Technol. 8(10), 1063–1075 (1994). [CrossRef]

,37

37. S. Bhattacharya, A. Datta, J. M. Berg, and S. Gangopadhyay, “Studies on surface wettability of poly(dimethyl) siloxane (PDMS) and glass under oxygen-plasma treatment and correlation with bond strength,” J. Microelectromech. Syst. 14(3), 590–597 (2005). [CrossRef]

]. The water-wetting nature is required for stable production of droplets with water as the continuous phase [3

3. S.-Y. Teh, R. Lin, L.-H. Hung, and A. P. Lee, “Droplet microfluidics,” Lab Chip 8(2), 198–220 (2008). [CrossRef] [PubMed]

,6

6. R. Seemann, M. Brinkmann, T. Pfohl, and S. Herminghaus, “Droplet based microfluidics,” Rep. Prog. Phys. 75(1), 016601 (2012). [CrossRef] [PubMed]

].

A microscope image of the fabricated device is presented in Fig. 2(a)
Fig. 2 (a) Microscope image of the device. A droplet is flowing in the main channel. The little dots are polystyrene beads. The red line denotes the length of the main channel, and the segmented green line denotes the length of the side channel. (b) Microscope image of the integrated 30 µm × 30 µm flow focusing nozzle. The oil phase (hexadecane) is broken into droplets around the nozzle by squeezing and by shear forces that arise from its encounter with water.
. The length of the segmented side channel, denoted by the green line in Fig. 2(a), is designed to be 240 µm. The width of the side channel measures 30 µm. The main channel is 200 µm long, as denoted by the red line in Fig. 2(a), and is 60 µm wide. All channels have a depth of 40 µm. These geometries enable calculation of the channels’ hydraulic resistances by Eq. (3). The two channels have a hydraulic resistance ratio of 1: 4.7. This guarantees that droplets will only enter the main channel, and not interfere with the optical trapping in the side channel.

Water and hexadecane oil (viscosity µ = 3.0 mPa⋅s at 298 K [38

38. D. S. Viswanath, T. K. Ghosh, D. H. L. Prasad, N. V. K. Dutt, and K. Y. Rani, Viscosity of Fluids (Springer, Dordrecht, 2007).

]) with 1.5 wt% surfactant (Span 80) are injected simultaneously into the device by pressurizing the fluids in syringes (Hamilton 25 µL) connected to two inlets with syringe pumps (NE-300, New Era Pump Systems Inc., and 11 Plus, Harvard Apparatus). Polystyrene beads with a diameter of 2 µm are dispersed in the water phase. At this size, the beads will not significantly alter the profile of fluid velocity in the channels. Oil droplets in water are generated by a flow focusing structure incorporated into the chip, similar to that introduced by Anna et al. [39

39. S. L. Anna, N. Bontoux, and H. A. Stone, “Formation of dispersions using flow focusing in microchannels,” Appl. Phys. Lett. 82(3), 364–366 (2003). [CrossRef]

], as illustrated in Fig. 2(b). The size of the nozzle is designed to be 30 µm × 30 µm. De-ionized water flows to the nozzle concurrently from the upper and lower channels, whereas hexadecane enters from the left branch. Around the nozzle, the oil phase is squeezed by the counter-flowing water and broken into droplets [40

40. P. Garstecki, H. A. Stone, and G. M. Whitesides, “Mechanism for flow-rate controlled breakup in confined geometries: a route to monodisperse emulsions,” Phys. Rev. Lett. 94(16), 164501 (2005). [CrossRef] [PubMed]

]. The size of droplets can be controlled by tuning the flow rates of the two phases [3

3. S.-Y. Teh, R. Lin, L.-H. Hung, and A. P. Lee, “Droplet microfluidics,” Lab Chip 8(2), 198–220 (2008). [CrossRef] [PubMed]

,6

6. R. Seemann, M. Brinkmann, T. Pfohl, and S. Herminghaus, “Droplet based microfluidics,” Rep. Prog. Phys. 75(1), 016601 (2012). [CrossRef] [PubMed]

,7

7. C. N. Baroud, F. Gallaire, and R. Dangla, “Dynamics of microfluidic droplets,” Lab Chip 10(16), 2032–2045 (2010). [CrossRef] [PubMed]

]. Nevertheless, at the extremely low flow rates (several µL per hour) we are working with, the size of droplets is polydisperse, likely because of the fluctuations of squeezing forces and flow rates around the flow focusing junction. This contrasts with the monodispersity observed in some studies performed at higher flow rates [38

38. D. S. Viswanath, T. K. Ghosh, D. H. L. Prasad, N. V. K. Dutt, and K. Y. Rani, Viscosity of Fluids (Springer, Dordrecht, 2007).

].

The microfluidic chip is placed in a modified optical tweezer system [41

41. ThorLabs model OTKG/M.

], as shown in Fig. 3(a)
Fig. 3 (a) Illustration of the modified optical tweezer system. The microfluidic device connected to syringe pumps is sandwiched between two lenses. Laser beam from a diode is collimated by the collimation lenses (CL), reflected by a dichroic mirror (DM) and a mirror (M), and focused into the channel by the bottom lens (100 × magnification). Illumination from a light-emitting diode (LED) is collected by another CL, passes through a DM, and arrives at the chip through the top lens (10 × magnification). The 100 × lens images the trapped bead onto the bottom CCD camera through a relay lens (RL). The 10 × lens images the parallel channels onto the top CCD camera through another RL and a shortpass filter (SP) that blocks the laser beam. (b) Trapped bead imaged by the 100 × lens. (c) Parallel channels imaged by the 10 × lens. Laser light scattered by the trapped bead is visible in the side channel.
. The core part of our experimental set-up is the pair of microscope lenses sandwiching the microfluidic chip. A near-infrared laser (λ = 975 nm, emitted power P = 200.0 mW) is focused into the side channel by an oil immersion lens (Nikon, NA = 1.25, 100 ×), forming the optical trap. The fluctuation of the laser power is less than 0.5 mW, so a nearly constant trapping stiffness can be expected. The fluid velocity varies quadratically across the microchannel [34

34. H. Bruus, Theoretical Microfluidics (Oxford University Press, 2008).

]. Thus, to ensure consistency in measurements, the bead is always trapped at a position that is equidistant to vertical side channel walls and just touches the bottom cover glass. This position is manually controlled by the micrometers on the sample stage holding the microfluidic chip. The same lens also images the bead onto a CCD camera (DFK 21AU04, The Imaging Source), as shown in Fig. 3(b), allowing determination of bead position. Another objective lens (Nikon, NA = 0.30, 10 × ) is used for bright field imaging of the device with light from a white light emitting diode (LED) onto another CCD camera (DMK 21AU04, The Imaging Source), as shown in Fig. 3(c). Despite the fact that the image quality is adversely affected by aberration incurred by the PDMS, the resolution is sufficient for determination of the size of droplets passing through the main channel. The two cameras work concurrently at 30 frames per second, and videos from the two are synchronized by noting the frame in which the LED illumination is switched on. The position of the bead is obtained in each frame imaged by the 100 × lens by locating its centroid. Specifically, we identify pixels above a brightness threshold in the center of the bead image, and calculate their average position.

3.2 Device calibration

As mentioned in the Working Principle section, a calibration process is necessary to quantitatively establish the linearity between the bead displacement x and the pressure differential ΔP shared by the parallel channels. To do this, we fabricate a chip containing a channel that has the same cross sectional geometry as the side channel, but is 10 mm long. This chip is placed in the optical tweezer set-up, and water containing polystyrene beads with a 2 µm diameter is flowed into it. A bead is trapped with a laser power of 200.0 mW at the same position in the channel cross section as mentioned before, i.e. equidistant to vertical side channel walls and just touching the bottom cover glass. This consistency in bead position ensures that in calibration the bead position x varies linearly with the flow rate Q, and that the calibration result can be applied to subsequent pressure measurements with the bead trapped at the same position (to be discussed in the following sections). Although this trapped bead may alter the profile of fluid velocity in the channel, this effect occurs in both the calibration results and the subsequent measurements. It is therefore not expected to adversely affect the accuracy of our device. This ensures that all the parameters in calibration match those in experiments for pressure measurement. Flow rates ranging from 1 to 8 µL⋅hr−1 are applied, and position of the trapped bead is measured for each from images obtained with the 100 × objective lens. At each flow rate, the bead position is averaged over a period of 13.33 s, which corresponds to 400 video frames i.e. 400 measurements of bead position. The standard deviation of the bead position within this period of time is found to be δx = 18 nm. The results are plotted in Fig. 4
Fig. 4 Calibration results for trapping in water, i.e. relation between bead position and water flow rate in a channel with a cross section identical to that of the side channel. Blue dots: experimental data; red line: linear fit.
, and demonstrate the anticipated linear dependence of bead position on flow rate. A linear fit is carried out, shown as the red line in Fig. 4, and gives a slope of 37.3 nm/(µL⋅hr−1). The data quantifies the variation of bead position x with the flow rate Q in the channel. Here, the bead position x refers to the distance of the bead center from the left edge of the image cropped from Fig. 3(b) for analysis. This means that an arbitrary offset exists and that the fit is not expected to pass through the origin. It is therefore the slope, rather than the absolute bead position, that is relevant for calibration purposes. One possible concern would be that the focused laser heats the water, modifying its viscosity [32

32. D. J. Acheson, Elementary Fluid Dynamics (Oxford University Press, 1990).

], and that this effect is highly dependent on flow rate due to its influence on heat dissipation. If that were the case, the relationship between x and Q would be non-linear. That the observed relationship is linear implies that the heating effect of the focused laser is not problematic.

Since the profile of fluid velocity for laminar flow in the channel only depends on the total flow rate and on the geometry of its cross section and does not vary with its length [34

34. H. Bruus, Theoretical Microfluidics (Oxford University Press, 2008).

], this result also applies to the much shorter side channel used in the droplet experiments. The quantitative relationship we obtain between bead displacement Δx and flow rate Q enables calculation of pressure differential ΔP from measured bead position by combining this calibration result with Eqs. (2) and (3), as described in the Working Principle section.

4. Results and discussion

4.1 Extra pressure of hexadecane droplets in water

In this section, we demonstrate the measurement of the extra pressure due to hexadecane droplets in water. Water is supplied to the device with a syringe pump at a flow rate of 6.0 µL⋅hr−1, and hexadecane at 2.5 µL⋅hr−1. Hexadecane droplets are produced at the integrated flow focusing nozzle (Fig. 2(b)). This pattern of droplet generation is robust, a result of the channel walls being hydrophilic after the plasma treatment. As droplets flow through the main channel, the computer records the images obtained by the two CCD cameras through the two lenses at a frame rate of 30 Hz. The droplets are of varied sizes, presumably as a result of natural fluctuations in the squeezing and shear forces at the flow focusing nozzle.

Video frames imaged through the 10 × lens (e.g. Fig. 3(c)) enable us to determine the length of each droplet passing through the main channel. Synchronization of this video with the data in Fig. 5(a) provides an opportunity for us to analyse the dynamics of pressure fluctuation in detail and its correspondence to the events in the main channel. For instance, this analysis reveals that in Fig. 5(a), the time interval between 4.73 s and 4.90 s (i.e. the peak denoted by a green arrow) corresponds to a single droplet whose length is 165 µm. The extra pressure during this droplet’s presence in the main channel takes an average of 5.35 Pa. We find that most pronounced peaks in Fig. 5(a) correspond to single droplets traversing in the main channel. Negative extra pressures are observed before and after many peaks. This is attributed to the fact that the droplet temporarily blocks the inlet or the outlet of the side channel before its entry into, or exit from, the main channel. This blockage lowers the flow rate in the side channel, and yields a pressure differential smaller than that in the standard water-only case. Occasionally, two closely-spaced droplets arrive at the parallel channel structure. In this scenario, the bead displacement no longer represents the extra pressure caused by the droplet in the main channel, since a second droplet in the vicinity may partially block the side channel and interfere with the flow. This results in a wider peak or some irregularly shaped structure in Fig. 5(a), e.g. the plateau around 2.83 s (denoted by a yellow arrow). These events are readily identified, however, from the video recorded using the 10 × lens.

Compiling the measured size and extra pressure for each droplet, we obtain the relation between extra pressure and droplet length, plotted in Fig. 5(b). The droplets range in size from ~75 µm to ~185 µm. The extra pressure they cause ranges from ~2.5 Pa to ~6.3 Pa. From Fig. 5(b), it can be seen that there is a positive correlation between the two quantities. The lack of a definitive theory concerning the extra pressure of droplets in rectangular channels makes it difficult for us to compare our data rigorously with theoretical predictions. Instead, we will refer to some basic intuition and a simple model in the literature to qualitatively discuss the factors affecting the extra pressure of droplets.

The pressure differential across a droplet originates from viscous dissipation and capillary forces, if no surfactant is present [7

7. C. N. Baroud, F. Gallaire, and R. Dangla, “Dynamics of microfluidic droplets,” Lab Chip 10(16), 2032–2045 (2010). [CrossRef] [PubMed]

,29

29. S. A. Vanapalli, A. G. Banpurkar, D. van den Ende, M. H. G. Duits, and F. Mugele, “Hydrodynamic resistance of single confined moving drops in rectangular microchannels,” Lab Chip 9(7), 982–990 (2009). [CrossRef] [PubMed]

]. The former comes from the fluid pressure induced by viscous stresses of the dispersed phase. For hexadecane droplets in water, an increase in length substitutes water for a more viscous fluid, hexadecane, leading to more viscous dissipation in the channel and generating a larger extra pressure. Simple models for this pressure differential ΔPbody make the assumption that the droplet body fills the entire channel cross section, and that flow in both phases is laminar [7

7. C. N. Baroud, F. Gallaire, and R. Dangla, “Dynamics of microfluidic droplets,” Lab Chip 10(16), 2032–2045 (2010). [CrossRef] [PubMed]

,29

29. S. A. Vanapalli, A. G. Banpurkar, D. van den Ende, M. H. G. Duits, and F. Mugele, “Hydrodynamic resistance of single confined moving drops in rectangular microchannels,” Lab Chip 9(7), 982–990 (2009). [CrossRef] [PubMed]

]. Under these assumptions, ΔPbody can be approximated by using the formulae for single-phase laminar flows.

The second contribution to pressure across a droplet is primarily an effect of Laplace pressure [7

7. C. N. Baroud, F. Gallaire, and R. Dangla, “Dynamics of microfluidic droplets,” Lab Chip 10(16), 2032–2045 (2010). [CrossRef] [PubMed]

]. The non-uniform thickness of lubrication films between a droplet in motion and channel walls gives rise to asymmetric caps [7

7. C. N. Baroud, F. Gallaire, and R. Dangla, “Dynamics of microfluidic droplets,” Lab Chip 10(16), 2032–2045 (2010). [CrossRef] [PubMed]

]. Intuitively, the upstream cap is “pushed” by the continuous phase and thus becomes flatter, i.e. less curved. This implies that the curvature-dependent pressure jump across the upstream interface is smaller and cannot fully compensate for the pressure drop across the downstream interface. Consequently, the capillary forces at droplet caps always yield a positive extra pressure ΔPcaps across the droplet. Our intuition is that an increase in droplet length leads to enlarged difference in curvature between the two caps, as a stronger pushing force from the continuous phase might be necessary for a longer droplet, and such force is primarily exerted on the upstream cap. However, the variation between the curvatures of the caps of the hexadecane droplets seems too small to be detected from the microscope images we obtain. Later in the paper we show data on the differences in curvature between the end caps of droplets of different lengths, but these are water droplets in hexadecane moving at higher speeds.

The picture above only represents a complete description of the mechanisms when no surfactant is present in either phase. However, we add surfactant into the dispersed phase. This facilitates generation of hexadecane droplets by reducing the interfacial tension between the two phases. Surfactant is known to alter the mechanism described above and provide additional contribution for pressure differential across a droplet [7

7. C. N. Baroud, F. Gallaire, and R. Dangla, “Dynamics of microfluidic droplets,” Lab Chip 10(16), 2032–2045 (2010). [CrossRef] [PubMed]

,42

42. M. J. Fuerstman, A. Lai, M. E. Thurlow, S. S. Shevkoplyas, H. A. Stone, and G. M. Whitesides, “The pressure drop along rectangular microchannels containing bubbles,” Lab Chip 7(11), 1479–1489 (2007). [CrossRef] [PubMed]

]. This considerably complicates the interpretation for experimental data, and essentially prevents us from comparing our results rigorously and quantitatively with theories.

4.2 Device sensitivity

In droplet experiments, however, slight fluctuations in flow rate exist, amplifying the uncertainty in the pressure measurements. The finite number of frames during the passage of one droplet also contributes to the uncertainty. Data in Fig. 5(a) can be used to coarsely evaluate the combined effect of all sources of error when we plot Fig. 5(b). We find that in those data, the standard deviation in bead position for water-only situations is δx = 13 nm within 7 frames, the typical duration for the passage of a droplet in the main channel. This corresponds to an uncertainty of δP = 0.49 Pa.

The ability of device to work in the low pressure range (several Pascals) with high sensitivity is unique compared with other existing techniques, which usually work in the range of hundreds of Pascals and above [21

21. M. J. Kohl, S. I. Abdel-Khalik, S. M. Jeter, and D. L. Sadowski, “A microfluidic experimental platform with internal pressure measurements,” Sens. Actuators A Phys. 118(2), 212–221 (2005). [CrossRef]

28

28. M. Abkarian, M. Faivre, and H. A. Stone, “High-speed microfluidic differential manometer for cellular-scale hydrodynamics,” Proc. Natl. Acad. Sci. U.S.A. 103(3), 538–542 (2006). [CrossRef] [PubMed]

]. Furthermore, this sensitivity can be easily improved by either increasing the frame rate or taking measures to stabilize the flow rates.

4.3 Modified design and experimental protocols for measuring extra pressure of water droplets in hexadecane

In this section and the next, we reverse the two phases, dispersing water droplets in a continuous hexadecane phase. We use our device to measure the pressure perturbations caused by water droplets. In addition, we run the experiments at higher flow rates.

We are motivated to do this for several reasons. First, our device has great flexibility in the design of its geometry and the pressure range over which it operates. We demonstrate how the device design can be readily modified to accommodate higher flow rates, and achieve measurement of a pressure differential above 1 kPa. Second, water (the dispersed phase) has smaller viscosity than hexadecane (the continuous phase). This viscosity contrast tends to decrease the pressure differential across the channel containing a water droplet in hexadecane, while capillary forces always contribute positively to extra pressure. Thus by performing experiments on water droplets in hexadecane, we can differentiate the effect of viscous dissipation in droplet body from that of capillarity around droplet caps, as these mechanisms affect the pressure differential in different ways. Last, the relative strength of viscous to capillary forces can be expressed by the dimensionless capillary number Ca = µV/σ [7

7. C. N. Baroud, F. Gallaire, and R. Dangla, “Dynamics of microfluidic droplets,” Lab Chip 10(16), 2032–2045 (2010). [CrossRef] [PubMed]

], where µ is the fluid viscosity of the more viscous phase, V is the characteristic fluid velocity, and σ is the interfacial tension between the two fluid phases. ΔPbody is shown to linearly depend on Ca, whereas ΔPcaps is found to vary as Ca2/3 [7

7. C. N. Baroud, F. Gallaire, and R. Dangla, “Dynamics of microfluidic droplets,” Lab Chip 10(16), 2032–2045 (2010). [CrossRef] [PubMed]

,42

42. M. J. Fuerstman, A. Lai, M. E. Thurlow, S. S. Shevkoplyas, H. A. Stone, and G. M. Whitesides, “The pressure drop along rectangular microchannels containing bubbles,” Lab Chip 7(11), 1479–1489 (2007). [CrossRef] [PubMed]

]. This indicates that ΔPbody grows at greater rate with Ca than ΔPcaps does, and is therefore expected to be the more important factor at larger Ca values. In a given channel, a higher flow rate results in higher fluid velocities and a larger capillary number. Higher flow rates should therefore enable us to better manifest the viscous effects and the viscosity contrast of the two phases.

Optical trapping of a bead in hexadecane in the side channel is feasible only when the flow velocity is sufficiently low. With the channel cross sectional area taken into consideration, this corresponds to a flow rate of several microliters per hour. To maintain a high flow rate (needed for a large capillary number) in the main channel and to simultaneously enable optical trapping in the side channel, a larger ratio of hydraulic resistances between the two channels must be realized, so that the flow rate in the side channel is only a very small fraction of the total. In order to do this, we elongate the side channel and fold it into a serpentine shape, as shown in Fig. 6(a)
Fig. 6 (a) Modified channel structure. This illustration shows the actual geometry of the main channel (440 µm in length) and the segmented side channel (7.2 mm in length). The inset displays the bead trapped in the center of the side channel. (b) Microscope image of portion of the parallel channels showing the top parts of the side channel segments. A laser spot scattered by the trapped bead can be seen in the center of the side channel. (c) Microscope image of the integrated 60 µm × 60 µm T junction that generates water droplets in hexadecane. Squeezing and shear forces break the water phase into droplets around the nozzle. (d) Calibration results for trapping in hexadecane, i.e. relation between bead position and hexadecane flow rate in a channel whose cross section matches that of the side channel. Blue dots: experimental data; red line: linear fit.
. Figure 6(b) is a microscope image of part of the fabricated parallel structures. Limited by the field of view, this image only shows some of the upward and downward sections of the side channel. The length of the main channel in this modified device is 440 µm, and the length of the serpentine side channel measures 7.2 mm. The widths of the main and side channels are 50 µm and 20 µm, respectively. All the channels are 30 µm in depth. Using Eq. (3), we calculate that the ratio of the hydraulic resistance of the side channel to that of the main channel is ~100: 1, with the assumption that the two convey the same single-phase flow. This large hydraulic resistance ratio allows for optical trapping and pressure measurements at high flow rates. Despite the altered geometry, the device works under the same principle: the bead displacement Δx is proportional to the pressure differential ΔP across the main and side channels.

The channel’s inner surfaces need to be hydrophobic or lipophilic for robust generation of water droplets in hexadecane [3

3. S.-Y. Teh, R. Lin, L.-H. Hung, and A. P. Lee, “Droplet microfluidics,” Lab Chip 8(2), 198–220 (2008). [CrossRef] [PubMed]

,6

6. R. Seemann, M. Brinkmann, T. Pfohl, and S. Herminghaus, “Droplet based microfluidics,” Rep. Prog. Phys. 75(1), 016601 (2012). [CrossRef] [PubMed]

]. We adopt the sol-gel approach developed by Abate et al. [44

44. A. R. Abate, J. Thiele, M. Weinhart, and D. A. Weitz, “Patterning microfluidic device wettability using flow confinement,” Lab Chip 10(14), 1774–1776 (2010). [CrossRef] [PubMed]

] to make the channel walls hydrophobic. Briefly, we prepare a mixture of 1 mL tetraethylorthosilicate (TEOS), 1 mL methyltriethoxysilane (MTES), 0.5 mL (heptadecafluoro-1,1,2,2-tetrahydrodecyl) triethoxysilane, 2 mL trifluoroethanol and 1 mL 3-(trimethoxysilyl)propyl methacrylate as the sol-gel solution. 0.5 mL of this solution is combined with 0.9 mL methanol, 0.9 mL trifluoroethanol, and 0.1 mL aqueous HCl, pH 2, and heated at 85 °C for ~2 minutes with intermittent shaking. The mixture is then diluted with methanol with a 1: 5 ratio of sol-gel to methanol. The mixture is flowed into the channels immediately after plasma bonding, and then we heat the device at 180 °C to evaporate the sol-gel. The remaining sol-gel coated on channel walls render them highly hydrophobic without appreciably modifying the cross sectional geometry.

We do not add surfactant to either phase in order to reduce the complexity of the origins of pressure across droplets. However, the large interfacial tension (~41 mN/m) [45

45. M. L. J. Steegmans, A. Warmerdam, K. G. P. H. Schroën, and R. M. Boom, “Dynamic interfacial tension measurements with microfluidic Y-junctions,” Langmuir 25(17), 9751–9758 (2009). [CrossRef] [PubMed]

] between pure water and hexadecane makes it rather difficult to generate droplets in a controllable manner. To overcome this problem, we add 25 wt% ethanol into water, reducing the interfacial tension to σ = ~17 mN/m. This value is estimated via linearly interpolating the data reported by Steegmans et al [45

45. M. L. J. Steegmans, A. Warmerdam, K. G. P. H. Schroën, and R. M. Boom, “Dynamic interfacial tension measurements with microfluidic Y-junctions,” Langmuir 25(17), 9751–9758 (2009). [CrossRef] [PubMed]

]. We use a T junction nozzle, similar to that introduced by Thorsen et al. [46

46. T. Thorsen, R. W. Roberts, F. H. Arnold, and S. R. Quake, “Dynamic pattern formation in a vesicle-generating microfluidic device,” Phys. Rev. Lett. 86(18), 4163–4166 (2001). [CrossRef] [PubMed]

], to generate water droplets in hexadecane, as shown in Fig. 6(c), since we find that for our device the T junction water droplet-maker has better performance than a flow focusing structure. The size of the nozzle is enlarged to 60 µm × 60 µm to obtain larger droplets [3

3. S.-Y. Teh, R. Lin, L.-H. Hung, and A. P. Lee, “Droplet microfluidics,” Lab Chip 8(2), 198–220 (2008). [CrossRef] [PubMed]

,6

6. R. Seemann, M. Brinkmann, T. Pfohl, and S. Herminghaus, “Droplet based microfluidics,” Rep. Prog. Phys. 75(1), 016601 (2012). [CrossRef] [PubMed]

,7

7. C. N. Baroud, F. Gallaire, and R. Dangla, “Dynamics of microfluidic droplets,” Lab Chip 10(16), 2032–2045 (2010). [CrossRef] [PubMed]

]. In Fig. 6(c), hexadecane is flowing from the left to the right; water arrives from the upper channel and is broken into droplets at the nozzle. We use syringes with a larger volume (Hamilton 250 µL) to pump the fluids at high flow rates. To capture the dynamics of pressure variation, we also replace the previously used cameras with faster ones (Grasshopper, Point Grey for low magnification microscopy, and acA2000-340km, Basler for high magnification microscopy). The emitting power of the trapping laser is increased to 300.0 mW. A calibration process similar to that described for optical trapping in water is carried out in a channel whose cross section matches that of the modified side channel. The calibration curve is plotted in Fig. 6(d). Each data point is the averaged bead position during 4 s, which contains 3600 video frames i.e. 3600 measurements of bead position. The standard deviation of the bead position during this period of time is δx = 19 nm. A linear fit of the data in Fig. 6(d) shows a slope of 104 nm/(µL⋅hr−1).

4.4 Extra pressure of water droplets in hexadecane

In this section we present experimental data on the extra pressure resulting from water droplets in hexadecane. The experiments start by injecting hexadecane and water at a total flow rate of 100.0 µL⋅hr−1. This gives an average flow velocity of v = 18.5 mm/s in the main channel (if we ignore the sharing of flow rate in the side channel), and a capillary number Ca = 0.0033. Under this condition, the water droplets in hexadecane we obtain are highly monodisperse in size. To obtain a range of droplets of various sizes, we modify the flow rates of the two phases, but maintain a total flow rate of 100.0 µL⋅hr−1 to ensure that the capillary number is constant. As before, the trapped bead is imaged by the 100 × lens onto the bottom camera, and the oil droplets in the main channel are imaged by the 10 × lens onto the top camera. The videos recorded by the cameras are used to determine the bead displacement and droplet length throughout the experiment. As before, averaged bead position is converted to extra pressure using the calibration results. Next, we fix the total flow rate at 80.0 µL⋅hr−1 and repeat the measurement process described above, thereby obtaining the extra pressure vs droplet size for a capillary number of 0.0026. Last, we fix the flow rate at 50.0 µL⋅hr−1, and obtain data at a capillary number of 0.0016. These results for three different capillary numbers are summarized in Fig. 7
Fig. 7 Dependence of extra pressure on water droplet length at different capillary numbers. A non-monotonic behavior of extra pressure is found. Blue circles: data at Ca = 0.0033; green squares: data at Ca = 0.0026; red diamonds: data at Ca = 0.0016. The orange arrow denotes the threshold droplet length for Ca = 0.0033.
. We find that extra pressure is no longer monotonic with droplet length. The extra pressure is initially positively correlated to length for smaller droplets. When droplets are further lengthened, the extra pressure then decreases with droplet length. For example, at Ca = 0.0033, the extra pressure increases with droplet length when droplets are shorter than a threshold value of ~240 µm (denoted by the orange arrow in Fig. 7), but is negatively correlated to length for droplets longer than that.

The same trend is observed for the other two capillary numbers. From Fig. 7 it can also be seen that the threshold length shifts to larger values when capillary number decreases, but this observation looks less definitive than the non-monotonic behavior of extra pressure. These results are found to be qualitatively consistent with those observed by Vanapalli et al [29

29. S. A. Vanapalli, A. G. Banpurkar, D. van den Ende, M. H. G. Duits, and F. Mugele, “Hydrodynamic resistance of single confined moving drops in rectangular microchannels,” Lab Chip 9(7), 982–990 (2009). [CrossRef] [PubMed]

].

We interpret the results in Fig. 7 by referring again to the aforementioned effects of viscous dissipation and capillary forces. For water droplets in hexadecane, viscous dissipation tends to result in a smaller pressure differential across the main channel, because the dispersed phase is lower in viscosity. On the other hand, capillary forces always contribute a positive pressure. We believe that capillary forces are primarily responsible for the increase of extra pressure with length for shorter droplets. To be more specific, below the threshold length, we suggest that an increase in size results in the continuous phase exerting a stronger pushing force on the droplet, which in turn results in a larger difference between the curvature of upstream and downstream caps. The Laplace pressure around the caps therefore gives a larger positive contribution to the pressure across the longer droplet. This mechanism can be directly observed from the microscope images of the droplets. Figure 8(a)
Fig. 8 (a) Microscope images of water droplets with different sizes. The scale bar applies to all the four droplets. (b) Radii of curvature on the image plane for the droplets displayed in (a). It can be observed that the upstream caps become less curved when droplet length increases, and this curvature change is less remarkable for larger droplets. The curvature of downstream ones does not vary with length.
displays images of four droplets of different lengths. In the Fig., the flow is from the left to the right with Ca = 0.0033. It can be clearly observed that the upstream cap becomes flatter and less curved as the droplet length increases. To quantify the curvature of the caps we fit a circular arc to the image of water/hexadecane interface. The radius of curvature of the cap in the image plane is then approximated by the radius of this arc. As shown in Fig. 8(b), the radius of curvature of the upstream cap increases with increasing droplet length, whereas the downstream cap has a nearly constant radius of curvature. The data of Fig. 8(b) confirms our physical interpretation, but is unfortunately insufficient for a quantitative estimation of the extra pressure contributed by capillary effects. This is because at any point on a curved interface, two radii of curvature exist. A quantitative evaluation of Laplace pressure would therefore require knowledge of both principal radii.

Moreover, it can be noted in Fig. 8(b) that the radii of curvature of both caps vary little with droplet length when the length is above a certain value. We believe that within this range, capillary forces cease to play the major role, and viscosity contrast dominates the relation between extra pressure and droplet length. For such droplets, elongation in length does not generate much more difference between the curvatures of the caps, but brings more water with lower viscosity into the main channel. Accordingly, an increase in length within this range primarily yields less viscous dissipation in the channel, and thereby results in a decrease in extra pressure, as observed in Fig. 8(a). It is worth noting that although the critical length above which curvature no longer changes significantly in Fig. 8(b) (~370 µm) does not seem to match the threshold length in Fig. 7 (e.g. ~240 µm for Ca = 0.0033), it still captures the basic physics governing the behavior of extra pressure for highly elongated droplets.

To summarize this section, we demonstrate the operation of our device at higher pressures and larger capillary numbers, and measure the extra pressure of water droplets in hexadecane under such conditions. Our results exhibit a competition between viscous and capillary forces. Such a competition gives rise to the observed non-monotonic relation between extra pressure and droplet length.

5. Conclusion

In this paper we have introduced a novel technique for pressure measurement in microfluidics by incorporating optical trapping. Our device is governed by a simple working principle, and can be readily fabricated with standard approaches. We employ the device to measure the extra pressure caused by hexadecane droplets in water and water droplets in hexadecane. We provide physical interpretation for the data obtained. The results demonstrate the effects of both viscous dissipation and capillary forces.

The experimental results demonstrate the high sensitivity and broadly adjustable pressure range of the device. These are a consequence of the fact that the channel geometry can be readily modified. In particular, our device can be used in the low pressure range of several Pascals, which might be difficult to access using other techniques. Inherent to the operating principle is the fact that tuning the trapping stiffness is a means for varying the dynamic range of the device. This can be done by adjusting the emitting power of the laser, or via other techniques, e.g. integration of plasmonic optical trapping structures into the microfluidic channel [47

47. K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Trapping and rotating nanoparticles using a plasmonic nano-tweezer with an integrated heat sink,” Nat Commun 2, 469 (2011). [CrossRef] [PubMed]

49

49. K. Wang, E. Schonbrun, and K. B. Crozier, “Propulsion of gold nanoparticles with surface plasmon polaritons: Evidence of enhanced optical force from near-field coupling between gold particle and gold film,” Nano Lett. 9(7), 2623–2629 (2009). [CrossRef] [PubMed]

]. The latter could also facilitate the trapping of sub-micron particles, suitable for pressure measurement in channels with smaller geometries.

Understanding the extra pressure brought about by micro-droplets is important to various devices and topics, such as droplet-based microfluidic logic, droplet-facilitated biochemical assays, syntheses and mixing, and extraction of residual oil in reservoirs. Furthermore, the simple design, easy fabrication and tuneable pressure range could expand applications of our technique to other areas. For example, our device should be able to measure the pressure required to squeeze cells through constrictions. This information may be of use in medical diagnostics [50

50. H. W. Hou, Q. S. Li, G. Y. H. Lee, A. P. Kumar, C. N. Ong, and C. T. Lim, “Deformability study of breast cancer cells using microfluidics,” Biomed. Microdevices 11(3), 557–564 (2009). [CrossRef] [PubMed]

]. Finally, we anticipate that multi-trap optical tweezing [51

51. E. Schonbrun, R. Piestun, P. Jordan, J. Cooper, K. D. Wulff, J. Courtial, and M. Padgett, “3D interferometric optical tweezers using a single spatial light modulator,” Opt. Express 13(10), 3777–3786 (2005). [CrossRef] [PubMed]

], possibly with microfabricated diffractive lenses [52

52. E. Schonbrun, C. Rinzler, and K. B. Crozier, “Microfabricated water immersion zone plate optical tweezer,” Appl. Phys. Lett. 92(7), 071112 (2008). [CrossRef]

,53

53. E. Schonbrun, A. R. Abate, P. E. Steinvurzel, D. A. Weitz, and K. B. Crozier, “High-throughput fluorescence detection using an integrated zone-plate array,” Lab Chip 10(7), 852–856 (2010). [CrossRef] [PubMed]

], could be used, thereby enabling pressure measurements to be performed simultaneously in multiple channels and a higher data throughput.

Acknowledgment

This work was supported by the Advanced Energy Consortium via the Bureau of Economic Geology at the University of Texas at Austin.

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P. Garstecki, H. A. Stone, and G. M. Whitesides, “Mechanism for flow-rate controlled breakup in confined geometries: a route to monodisperse emulsions,” Phys. Rev. Lett. 94(16), 164501 (2005). [CrossRef] [PubMed]

41.

ThorLabs model OTKG/M.

42.

M. J. Fuerstman, A. Lai, M. E. Thurlow, S. S. Shevkoplyas, H. A. Stone, and G. M. Whitesides, “The pressure drop along rectangular microchannels containing bubbles,” Lab Chip 7(11), 1479–1489 (2007). [CrossRef] [PubMed]

43.

W. P. Wong and K. Halvorsen, “The effect of integration time on fluctuation measurements: calibrating an optical trap in the presence of motion blur,” Opt. Express 14(25), 12517–12531 (2006). [CrossRef] [PubMed]

44.

A. R. Abate, J. Thiele, M. Weinhart, and D. A. Weitz, “Patterning microfluidic device wettability using flow confinement,” Lab Chip 10(14), 1774–1776 (2010). [CrossRef] [PubMed]

45.

M. L. J. Steegmans, A. Warmerdam, K. G. P. H. Schroën, and R. M. Boom, “Dynamic interfacial tension measurements with microfluidic Y-junctions,” Langmuir 25(17), 9751–9758 (2009). [CrossRef] [PubMed]

46.

T. Thorsen, R. W. Roberts, F. H. Arnold, and S. R. Quake, “Dynamic pattern formation in a vesicle-generating microfluidic device,” Phys. Rev. Lett. 86(18), 4163–4166 (2001). [CrossRef] [PubMed]

47.

K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Trapping and rotating nanoparticles using a plasmonic nano-tweezer with an integrated heat sink,” Nat Commun 2, 469 (2011). [CrossRef] [PubMed]

48.

K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Scannable plasmonic trapping using a gold stripe,” Nano Lett. 10(9), 3506–3511 (2010). [CrossRef] [PubMed]

49.

K. Wang, E. Schonbrun, and K. B. Crozier, “Propulsion of gold nanoparticles with surface plasmon polaritons: Evidence of enhanced optical force from near-field coupling between gold particle and gold film,” Nano Lett. 9(7), 2623–2629 (2009). [CrossRef] [PubMed]

50.

H. W. Hou, Q. S. Li, G. Y. H. Lee, A. P. Kumar, C. N. Ong, and C. T. Lim, “Deformability study of breast cancer cells using microfluidics,” Biomed. Microdevices 11(3), 557–564 (2009). [CrossRef] [PubMed]

51.

E. Schonbrun, R. Piestun, P. Jordan, J. Cooper, K. D. Wulff, J. Courtial, and M. Padgett, “3D interferometric optical tweezers using a single spatial light modulator,” Opt. Express 13(10), 3777–3786 (2005). [CrossRef] [PubMed]

52.

E. Schonbrun, C. Rinzler, and K. B. Crozier, “Microfabricated water immersion zone plate optical tweezer,” Appl. Phys. Lett. 92(7), 071112 (2008). [CrossRef]

53.

E. Schonbrun, A. R. Abate, P. E. Steinvurzel, D. A. Weitz, and K. B. Crozier, “High-throughput fluorescence detection using an integrated zone-plate array,” Lab Chip 10(7), 852–856 (2010). [CrossRef] [PubMed]

OCIS Codes
(350.4855) Other areas of optics : Optical tweezers or optical manipulation
(120.5475) Instrumentation, measurement, and metrology : Pressure measurement

ToC Category:
Optical Trapping and Manipulation

History
Original Manuscript: August 21, 2012
Revised Manuscript: September 21, 2012
Manuscript Accepted: September 22, 2012
Published: October 11, 2012

Citation
Yuhang Jin, Antony Orth, Ethan Schonbrun, and Kenneth B. Crozier, "Measuring the pressures across microfluidic droplets with an optical tweezer," Opt. Express 20, 24450-24464 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-22-24450


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  41. ThorLabs model OTKG/M.
  42. M. J. Fuerstman, A. Lai, M. E. Thurlow, S. S. Shevkoplyas, H. A. Stone, and G. M. Whitesides, “The pressure drop along rectangular microchannels containing bubbles,” Lab Chip7(11), 1479–1489 (2007). [CrossRef] [PubMed]
  43. W. P. Wong and K. Halvorsen, “The effect of integration time on fluctuation measurements: calibrating an optical trap in the presence of motion blur,” Opt. Express14(25), 12517–12531 (2006). [CrossRef] [PubMed]
  44. A. R. Abate, J. Thiele, M. Weinhart, and D. A. Weitz, “Patterning microfluidic device wettability using flow confinement,” Lab Chip10(14), 1774–1776 (2010). [CrossRef] [PubMed]
  45. M. L. J. Steegmans, A. Warmerdam, K. G. P. H. Schroën, and R. M. Boom, “Dynamic interfacial tension measurements with microfluidic Y-junctions,” Langmuir25(17), 9751–9758 (2009). [CrossRef] [PubMed]
  46. T. Thorsen, R. W. Roberts, F. H. Arnold, and S. R. Quake, “Dynamic pattern formation in a vesicle-generating microfluidic device,” Phys. Rev. Lett.86(18), 4163–4166 (2001). [CrossRef] [PubMed]
  47. K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Trapping and rotating nanoparticles using a plasmonic nano-tweezer with an integrated heat sink,” Nat Commun2, 469 (2011). [CrossRef] [PubMed]
  48. K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Scannable plasmonic trapping using a gold stripe,” Nano Lett.10(9), 3506–3511 (2010). [CrossRef] [PubMed]
  49. K. Wang, E. Schonbrun, and K. B. Crozier, “Propulsion of gold nanoparticles with surface plasmon polaritons: Evidence of enhanced optical force from near-field coupling between gold particle and gold film,” Nano Lett.9(7), 2623–2629 (2009). [CrossRef] [PubMed]
  50. H. W. Hou, Q. S. Li, G. Y. H. Lee, A. P. Kumar, C. N. Ong, and C. T. Lim, “Deformability study of breast cancer cells using microfluidics,” Biomed. Microdevices11(3), 557–564 (2009). [CrossRef] [PubMed]
  51. E. Schonbrun, R. Piestun, P. Jordan, J. Cooper, K. D. Wulff, J. Courtial, and M. Padgett, “3D interferometric optical tweezers using a single spatial light modulator,” Opt. Express13(10), 3777–3786 (2005). [CrossRef] [PubMed]
  52. E. Schonbrun, C. Rinzler, and K. B. Crozier, “Microfabricated water immersion zone plate optical tweezer,” Appl. Phys. Lett.92(7), 071112 (2008). [CrossRef]
  53. E. Schonbrun, A. R. Abate, P. E. Steinvurzel, D. A. Weitz, and K. B. Crozier, “High-throughput fluorescence detection using an integrated zone-plate array,” Lab Chip10(7), 852–856 (2010). [CrossRef] [PubMed]

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