Droplet trapping and fast acoustic release in a multi-height device with steady-state flow

Richard W. Rambach a, Kevin Linder a, Michael Heymann b and Thomas Franke *ac
aSoft Matter and Biological Physics Group, Universität Augsburg, Universitätsstr. 1, D-86159 Augsburg, Germany
bDepartment of Cellular and Molecular Biophysics, Max Planck Institute of Biochemistry, Am Klopferspitz 18, D-82152 Martinsried, Germany
cDivision of Biomedical Engineering, School of Engineering, University of Glasgow, Oakfield Avenue, G12 8LT Glasgow, UK. E-mail: Thomas.Franke@glasgow.ac.uk

Received 7th April 2017 , Accepted 2nd August 2017

First published on 2nd August 2017


We demonstrate a novel multilayer polydimethylsiloxane (PDMS) device for selective storage and release of single emulsion droplets. Drops are captured in a microchannel cavity and can be released on-demand through a triggered surface acoustic wave pulse. The surface acoustic wave (SAW) is excited by a tapered interdigital transducer (TIDT) deposited on a piezoelectric lithium niobate (LiNbO3) substrate and inverts the pressure difference across the cavity trap to push a drop out of the trap and back into the main flow channel. Droplet capture and release does not require a flow rate change, flow interruption, flow inversion or valve action and can be achieved in as fast as 20 ms. This allows both on-demand droplet capture for analysis and monitoring over arbitrary time scales, and continuous device operation with a high droplet rate of 620 drops per s. We hence decouple long-term droplet interrogation from other operations on the chip. This will ease integration with other microfluidic droplet operations and functional components.


1. Introduction

Interdigital transducers (IDTs) on piezoelectric substrates are used to excite travelling surface acoustic waves (SAW). SAWs are common in everyday commodities, such as wireless networks, navigation systems and as smart phone high-quality filters. They are also used as vibration-sensors,1 gas-sensors,2 bio-sensors,3,4 and in total analysis systems5 or lab-on-a-chip platforms.6–10 In microfluidics, the interaction of SAWs with fluids has become an especially powerful and well recognized method, with a broad spectrum of applications from simple fluid handling to sophisticated diagnostics and drug delivery.8,9,11–19 SAWs are widely used, for example to deflect and sort particles20–22 and droplets,23–27 to pump28–32 and to atomize19,33–37 fluids, or to detect droplets.38 Accordingly, SAW technology is rapidly expanding into new scientific and commercial applications in biomedicine, diagnostics and analytical chemistry.19,34,39–42

In particular, SAW fluid management has enabled drop manipulation on chip in a surpassing and robust way, both at high speed and high precision with ultra-fast processing times and versatile applicability. In digital microfluidics,43 droplets on a surface are acoustically moved,44–46 mixed,8,47–50 or fused and split51 on chip. In high-throughput emulsion droplet microfluidics, SAWs enable on demand encapsulation,52 sizing,53–56 merging,57 splitting,58 storing59 and sorting60–62 of droplets at kHz rates.63

An as of yet missing functionality is controlled trapping of single droplets, which is of great interest for mixing and diluting of smallest volumes and also to monitor reaction dynamics in droplets.64–66 Such drop trapping is critical for selective and controllable encapsulation,67 cell analysis68–71 and OBOC (one-bead-one-compound library) combinatorial searches.72,73

Transient trapping can be realized with traditional microfluidic methods, but often these are complex and contain numerous valves to control flow in different channels, or reverse flow direction to release trapped drops after capture.43,66,74–77 Both, valve action or flow rate tweaks in such setups interfere with other operations on the chip and hence are difficult to integrate as an independent module.

Ideally, single droplet capture and release can be performed in a system operating at constant flow. This would help to isolate and probe individual droplets from a continuous droplet stream for example for quality control, to monitor drop reactions, or to obtain other information from the droplets. This is especially challenging with fast moving droplets. For example, droplets produced and traveling along a channel at 1 kHz rates typically pass a detection window within <1 ms and it is not possible to analyse and measure the relevant information of an object over such a short time. For example when a low intensity fluorescence level of the sample requires integration of the signal for a longer period. A system, which captures single droplet and enables observation over a longer time before unloading the trap and reinjection into the constant flow, overcomes this problem.

Here, we demonstrate the capture and release of single droplets at constant flow conditions. In contrast to already published approaches with drop flow and operation rates of about 1–3 per second,78–81 we use a microfluidic trap with a three-height PDMS design and accomplish very fast (below 20 ms) selection and release of drops by the actuation of a SAW in a densely populated microchannel (average distance between subsequent droplets is below 150 μm) with a droplet flow rate of about 620 drops per s and a droplet operation rate of 50 drops per s. Since droplet selection and release does not require a change in flow rate of the main channel the device does not interfere with other flow dependent components and features implemented on a more complex chip and can be integrated as an independent module.

2. Results

2.1. SAW-drop trap design

The setup consists of a piezoelectric substrate (lithium niobate; LiNbO3) with the deposited IDT (with working frequencies of 160–170 MHz) on top to excite SAWs into a multilayer PDMS microchannel placed above. The PDMS device is aligned onto the piezoelectric substrate in such a way, that the SAW travels into the coupling channel. The position can be adjusted by fine-tuning the applied frequency of the IDT. The PDMS wall between IDT and microchannel has a fixed width of 100 μm. We use a channel layout that is composed of five different regions moulded into three heights as shown in Fig. 1. Each part of the trap has a specific function: 1.) the drop well itself is 40 × 50 μm large and 45 μm high so that trapped droplets can adopt a spherical shape that is not deformed by the walls. 2.) Capillary valve restrictions capture droplets. 3.) An inner short bypass (30 μm height) allows droplets to pass around the well and lowers the pressure difference across the well. 4.) An outer long bypass (30 μm high) further reduces the pressure difference across the trap and helps to isolate the trap from flow rate fluctuations 5.) a coupling channel connects the droplet well with the IDT to funnel SAWs into the droplet well. Emulsion droplets are produced in a T-junction upstream of the trap76,82–84
image file: c7lc00378a-f1.tif
Fig. 1 Multi-height drop trap with SAW-actuated drop release. Microscope image of trap during operation (A) and schematic layout with detailed view of the drop well (B). All channels are 30 μm high and 30 μm wide, except 1.) the drop well (green, 45 μm high, 50 × 40 μm length × width) and the 2.) restrictions (red) for drop capture (15 μm high, 8 μm wide). The 3.) inner (dark blue) and 4.) outer (light blue) bypass channels route droplets around the well. There are two bypass channels, instead of a single one, to decrease the pressure gradient across the drop well and the restrictions. A SAW is excited with the TIDT (not shown) to propagate into the 5.) coupling channel (yellow) to release captured droplets. The complete trap design in DWG format (Autodesk 2016) is included as ESI.

2.2. Droplet capture

2.2.1. Working mechanism. The trap is designed such that droplets are routed into an empty trap quickly, or around via bypass channels when it is already loaded (Fig. 1). Droplets are passively captured through capillary valve action.76 In brief, every oil–water interface has a finite surface tension, which as a function of geometric constraints yields a Laplace pressure that can be determined by the Young–Laplace equation as
 
image file: c7lc00378a-t1.tif(1)
with R1 and R2 as the main radii of curvature and γ being the surface tension of the interface. To minimize its energy, a droplet interface has to minimize its surface, which is equivalent to maximizing its main radii of curvature at constant volume. Conversely, a low curvature interface in a wide channel has a lower Laplace pressure then a high curvature interface in a narrow channel segment. Therefore, a droplet entering from the 30 μm high bypass channel into the 45 μm high well is quickly pulled in to assume a lower curvature shape. The same surface tension however prevents penetration of the narrower 8 μm wide and 15 μm high restrictions (the curvatures of the droplet would have to decrease from about 40 μm and 45 μm to 8 and 15 μm, quadruplicating the Young–Laplace pressure). Instead flow is routed through the bypass channels. As a result, no droplets can enter the coupling channel.

We tailor the hydrodynamic resistance of the empty well and downstream capillary valve restrictions to be slightly lower than the resistance of the bypass channels. By incorporating multiple parallel valves, we reduce the overall hydrodynamic resistance of the valve section without compromising its Laplace pressure. The shorter inner bypass has a lower hydrodynamic resistance than the longer outer bypass, so that droplets enter the inner bypass first. As the number of droplets in the inner bypass increases, so does the hydrodynamic resistance and hence subsequent droplets enter the outer bypass. Combining these two bypasses, instead of a single one, helped to further reduce the pressure change across the droplet well to increase operational robustness. If the pressure drop across the well were to exceed the Laplace pressure of the droplet in the restrictions, the droplet would be squeezed through the restrictions into the coupling channel.

2.2.2. Characterization. To validate trapping performance and robustness, we compare different drop sizes and flow rates. Droplets that are too small to be deformed in the main channel (Fig. 2A) cannot reduce their overall surface tension by rounding up after entering the trap. Also, such small droplets do not block the continuous phase as much as larger droplets, so the pressure gradient over a droplet is smaller. Accordingly, small droplets do not enter the well and define a lower limit, smaller than the channel width of 30 μm, for the drop size that can be captured. If droplets are too large to completely enter the well, a section of the droplet will protrude into the bypass. In our design such droplets are quickly pulled out of the well and into the downstream inner bypass channel (Fig. 2B). Large droplets are often split at the junction, resulting in undesired polydiserpsity.85 The ideal droplet size (Fig. 2C), is hence larger than the channel width and smaller than the volume of the drop well. Such droplets block the continuous phase and the flow rates are high enough to ensure a sufficient pressure in the system for droplet capture. In another failure mode, droplets that are too small or droplets that have a too low surface tension (i.e. high surfactant concentration) to be pinned in the capillary valve can be pushed through the restrictions into the coupling channel.
image file: c7lc00378a-f2.tif
Fig. 2 Droplet capture as a function on drop size. Depending on the size of the droplets the trapping behaviour changes. (A) Droplets with a diameter smaller than the channel width do not sufficiently increase the pressure across the trap and droplets do not enter the trap. Here droplets were formed in a standard T-junction geometry with flow rates of 600 μl h−1 for the continuous phase and 100 μl h−1 for the dispersed phase.76,82–84 (B) Very large droplets (produced with flowrates of 300 μl h−1 for both continuous and dispersive phase) split at the first junction between inner and outer bypass, as previously reported by Stone et al.85 this results in an increased polydispersity of the droplets and effectively set an upper limit for the drop size. Additionally, droplets larger than the well, are dragged by the flow into the inner bypass and do not enter the well completely. (C) Ideally, droplets are larger than the channel width. For this size and high enough flow rates (300 μl h−1 for continuous and 100 μl h−1 for the dispersive phase), the pressure in the system is ideal. All experiments were performed with surfactant concentrations of 0.05% (wt%).

2.3. Acoustic droplet release

2.3.1. Working mechanism. Captured droplets can be released with a short SAW pulse (Fig. 3). The excited SAW propagates on the piezoelectric substrate and into the coupling channel. There it couples into the fluid, causing a pressure increase. This acoustic pressure then pushes the droplet out of the drop well into the inner bypass channel. A subsequent droplet can then enter the drop well, to be released again by another SAW pulse.
image file: c7lc00378a-f3.tif
Fig. 3 Acoustic droplet release. In the initial state (A) the droplet (highlighted by blue overlay) is trapped. Upon excitation of a SAW, it propagates on the substrate towards the microchannel and into the coupling channel (B). Couples of the SAW into the fluid induces a pressure, forcing the droplet to move (B) and to leave the trap (C). The ejected droplet travels downstream along the small bypass channel. A subsequent droplet (red) refills the trap (C + D). The pulse of the SAW is 20 ms short and has a period of 2 s, with a power of 398 mW. A movie showing the complete acoustic droplet release and subsequent droplet capture is included as ESI.
2.3.2. Characterization. The threshold power needed to push a droplet out of the well depends on the pulse length and on the position of the acoustic sound path. We adjust the position of the SAW actuation and determined the threshold value for the power (at constant pulse length of 350 ms) for drop release (Fig. 4). We obtain the lowest threshold power, when the SAW is centered on the coupling channel. If the SAW propagates the coupling channel with a slight off-set, a higher acoustic power is needed to release the drop. The effective aperture A of the sound beam can be estimated by the aperture A0 of the IDT, the number of fingerpairs N, the minimum and maximum working frequencies fmin and fmax and the applied frequency f:78,86
 
image file: c7lc00378a-t2.tif(2)

image file: c7lc00378a-f4.tif
Fig. 4 Position and required power for pushing a droplet out of the trap. The minimum power for drop release strongly depends on SAW position. For reference, we highlight the coupling channel with a corresponding red overlay. We define zero X position to be the center of the coupling channel and find the power minimum to precisely be at this position. With higher distance to the coupling channel, the power needed for pushing a droplet out of the trap increases. In the graph, we only plot data of x-positions where we could push out drops (−110 μm < x < 65 μm). Out of that region, we could not release the drops even for much higher input power levels. The left channel wall is broadened by about 8 μm, as the second layer was not perfectly aligned to the first layer in the production step for this experiment. Error bars indicate the maximum errors given by the power steps of 0.1 dBm. We derive SAW position from the IDT operating frequency.87 A pulse length of 350 ms and a pulse period of 2 s were chosen to minimize crosstalk between subsequent pulses and potential heating effects and where kept constant throughout the experiment.

For the used frequencies of 160–170 MHz we determine an effective aperture to 135–140 μm. This rough estimate is in good agreement with the experimental determined width of 180 μm where drop release could be achieved, as shown in Fig. 4.

The pulse length for a SAW centered on the coupling channel is inversely proportional to the SAW power applied (Fig. 5). A critical value of the power has to be overcome to release a droplet from the trap. We determined this minimum SAW input power to be 251 mW with a pulse length of 10 ms. The minimum threshold pulse length is about ∼2 ms for input powers exceeding 1260 mW. The total energy E necessary for pushing a droplet out of the well is approximately constant and was determined to be E = 2292 ± 94 μJ from a hyperbolic fit to the critical pulse-length–power spectrum (Fig. 5).


image file: c7lc00378a-f5.tif
Fig. 5 Power and pulse length needed for drop ejection. With increasing applied power, PSAW, the threshold pulse length, l, for pushing a droplet out of the well decreases nonlinearly. The minimum input power for releasing a droplet was experimentally determined to be 251 mW (red dotted line). Below this critical power no droplet could be pushed out of the well. The total energy E of a single pulse needed is constant (E = PSAW·l) as can be seen by the hyperbolic fit of l against SAW power PSAW (l = E/PSAW with E = 2292 ± 94 μJ). The pulse length was increased in 1 ms steps and the error indicate half of this step value. The SAW was excited with a pulse period of 2 s. The measurement points reflect that droplets completely leave the trap well in three subsequent experiments. Droplets never split into daughter drops nor fuse with other drops.

3. Discussion

Trapping of droplets can be analyzed through the different pressures and hydrodynamic resistances in the system. The drop well with the small restrictions connecting to the coupling channel have in sum a smaller resistance than the bypass channels. Thus, a single droplet preferentially enters the trap instead of propagating through inner or outer bypass. As the inner bypass has a smaller resistance than the outer longer bypass, droplets populate the inner bypass first. With increasing numbers of droplets traveling in the inner bypass, the pressure drop along this microchannel increases,88–90 and subsequent droplets move through the outer bypass. We found that having two bypass channels is very useful to ensure robust trap operation. The combination of two bypass channels, decreases the applied pressure difference across the trapped droplet enough to reliably prevent droplets from being pushed through the small restrictions, as had been observed during initial experiments with single bypass trap geometries.

A similar system has been used to split drops into daughter drops for controlled pipetting.80 They estimated the pressure drop of the hydrodynamic resistances to estimate the pipetted drop volume. Similarly, we estimate here the pressure drop form the channel geometry.

The hydrodynamic resistances HRectangular for rectangular (width, w and height, h) and HSquared for squared (width w = h) microchannels with length, L can be calculated in a fluid with the dynamic viscosity, η by:91,92

 
image file: c7lc00378a-t3.tif(3)
 
image file: c7lc00378a-t4.tif(4)

For the inner and outer bypass, the resistance is hence approximately 15.1 × 1012 Pa s m−3 and 29.8 × 1012 Pa s m−3 respectively. The resistance through the drop well back to the small bypass (including the four parallel and the additional sideward oriented restriction) has a combined resistance of approximately 1.3 × 1012 Pa s m−3. The pressure gradient Δp for the whole system can be determined for a given flow of Q = 400 μl h−1 and the hydrodynamic resistances as:

 
Δp = H·Q(5)

With no droplets in the microfluidic system and accordingly the hydrodynamic resistance consisting only of the three parallel resistors of the trap, the inner, and the outer bypass, the pressure gradient is equal to about Δp = 130 Pa. Assuming that a loaded drop well is fully blocking flow, the overall hydrodynamic resistance is only set by both bypass channels and the pressure gradient increases to 1.1 kPa. The same trap layout without the outer bypass in turn almost doubles the pressure gradient across the drop well to about 1.7 kPa. This simple estimation illustrates that the additional bypass helps to reduce the applied pressure on the drop significantly and makes the trap more robust.

For acoustic droplet removal, the pressure gradient across the trap needs to be overcome. The excited SAW propagates into the coupling channel, where it couples into the fluid. The viscous attenuation of the SAW in the fluid bulk along the sound propagation path causes acoustic streaming, the Eckart streaming. This streaming pushes the fluid away from the IDT44,93–95 and can be described as an effective pressure on the drop. The effect was investigated in more detail by Schmid and colleagues recently and has been shown to be the dominant effect to cause deflection of drops.53,54,60 It can also be used to collect particles in a far away from the IDT in a vortex96 similarly to particle collection in standing surface acoustic waves devices.22,97,98 The long coupling channel ensures that most of the acoustic energy of the SAW is absorbed in the fluid. Using an identical IDT geometry,54 the induced pressure gradient ΔpSAW, required for releasing a drop from the trap, can be estimated from the applied power PSAW in a linear model:

 
ΔpSAW = ε·PSAW(6)

The linear coefficient ε was determined to be in the range of 6–13 kPa W−1.54 Using this estimate, the power necessary for droplet removal is expected to fall into the range of 183–85 mW. The energy required to push a droplet out of the trap had to be larger than 250 mW, which is slightly higher than the estimate. One reason is the damping of the 100 μm thick PDMS wall between IDT and microchannel which can be estimated by:60,99–101

 
P/P0 = eαx = ex/l(7)
P0 and P is the power before and after damping, respectively, α the absorption coefficient and l the attenuation length:
 
image file: c7lc00378a-t5.tif(8)
ρ and ν are the densities and velocities of PDMS and LiNbO3, respectively.102–104 For the frequencies of 160 to 170 MHz used in the experiments (and λ = νLiNbO3/f), the damping is given by roughly 22%. Considering this damping effect the real needed power is 195 mW, which is even closer to the estimation above. More detailed studies of SAW damping in PDMS and in fluids be found elsewhere.60,98,102

Another reason is the fact that the fluid absorbs not the complete energy of the sound wave, as the coupling channel has only a length of about 200 μm, which is of the order of the absorption length in the oil of 270–290 μm (for frequencies of 170–160 MHz). We have chosen this length, so that the distance along which the SAW is absorbed by the fluid is long enough, but the device is still capable of being integrated into a microfluidic device. Analogue to the damping by the PDMS (see eqn (7)), the energy absorption by the oil can be calculated (density for the oil of 1614 kg m−3 taken from the manufacturer datasheet and speed of sound from ref. 105) to be about 60% (for frequencies of 160–170 MHz).

The deviation between experimental value and reference estimation suggests that the actual resistance in the whole system is slightly higher than estimated, which can be explained from the small resistance increase that arise from droplets propagating in microchannels.88–90 However, taking this effect into account, our experiments are in very good agreement with the model, showing that a threshold of about 250 mW input power is needed for ejecting a droplet out of the trap.

The system can be operated at different flow rates, but increasing the flow rates (at constant drop size and flow ratio) will result in higher pressure gradients in the system, thus the required energy for releasing a droplet will increase as well. There is a limit (depending on e.g. pulse length) for the input power as high levels of SAW power are known to produce heat in the fluid, may generate bubbles or even lead to cracks in the chip. Another concern is that with higher pressures droplets may squeeze through a restriction, thus the geometry of the microchannel would need to be adapted to higher flow regimes, e.g. by including more shunts to reduce the pressure drop across the trap. However, it is possible to run the system with higher flow rates and droplet rates of a few kHz. Here, we have chosen 100 and 300 μl h−1 to show the system working with different input powers and pulse lengths, as well as to avoid any possible heating effects and squeezing of droplets through a restriction.

4. Conclusions

We demonstrated a microfluidic droplet trap that loads spontaneously and that can be unloaded by a short actuation (2 ms) of a surface acoustic wave. The trap is operated in situ in the presence of a continuously running droplet stream (with a rate of 620 drops per s) without changing or adjusting flow rates in the system, or actuating valves. Drops can be selected on-demand from an emulsion of continuously flowing droplets and single drops can be incubated for a desired duration of time. For example, to enable measurements on drops for extended times such as for high sensitive fluorescence measurements that are impossible on fast flowing drops and that require longer exposure times or investigation of the life cycle of encapsulated malaria cells106 in red blood cells while having a constant but variable flow for modifying the environment. Furthermore, reactions can be observed while changing the environment like the reaction of encapsulated bacteria depending on different drugs flowing by. Besides the possibility to analyse content of droplets over long periods of time, our system enables monitoring droplets shortly after production directly on chip, which is important if the reactants inside the droplets react very fast or if an external off-chip analysis is not possible. This includes applications where the effect of reactants of single cells in drops is probed by gradually changing the reactant concentration, for example the effect of an antibiotic on bacteria. Encapsulated single cell, cell to cell interactions or chemical reactions can be another possible utilization.

Moreover, the system also allows fast and robust loading of drops in a few milliseconds, which we expect to be beneficial when assaying larger population of drops at single drop resolution. It enables “rare event detection” in a running system, like finding and analyzing an encapsulated cell in one of a few hundred running droplets in a short time. Quality checks of random sample during a running process are also possible, which could be used to probe the crystallization in droplets directly after the production.107 In the future, the setup may be further improved by multiplexing and integrating a larger number of droplet traps onto a single IDT to increase throughput.

5. Experimental setup and methods

For exciting the SAW a tapered IDT (aperture 500 μm, wavelength 23 to 24.3 μm, 60 finger-pairs) was produced by electron deposition of 100 nm aluminium an with adhesive primer (TI-Primer from Microresist technology GmbH) on a 17.5 mm × 17.5 mm 128° y-cut LiNbO3 substrate. This tapered IDT (with a frequency range of 160–169 MHz) was connected to a frequency generator (SML-01 by Rhode & Schwarz) and an amplifier (ZHL-1-2W, Mini-Circuits). The chip was mounted on a microscope (CKX41 microscope, Olympus Germany). The four layer PDMS microchannel is placed on top of the chip and connected to two syringe pumps (PHD2000, Harvard Apparatus). The continuous phase consists of oil (3M Novec 7500 Engineered Fluid) with 0.3 to 0.5 wt% (and 2 wt% for Fig. 3) fluorinated surfactant (ammonium carboxylate of DuPont Krytox 157). The dispersed phase is MilliQ-filtered water stained with 2 mg ml−1 Brillant Blau purchased from Roth. The multi-height PDMS microchannel is fabricated by soft lithography.108 The first 15 μm layer negative photoresist (SU8 from Microchem) is spin-coated, baked, exposed and baked on a Si substrate. Then the next layer of 15 μm is produced the same way. After spin-coating, pre-baking, exposure and post exposure baking the third layer, the whole structure is developed (MR-Dev 600, micro resist technology GmbH). The mold is used to fabricate the three layer PDMS microchannel, which is bonded with an O2-plasma onto a structured thin (∼8–10 μm) spin coated PDMS foil.21,22 A high-speed camera (Fastcam 1024 PCI, Photron) is used to capture pictures and movies that were analyzed with the Fiji software package.109–111 Flow rates were set to 300 μl h−1 for the continuous phase and 100 μl h−1 for the dispersed phase in all experiments, except for the different drop size analysis as specified in (Fig. 2). The produced droplets have an average volume of about 45 pl.

Acknowledgements

R. W. R. and T. F. acknowledge support by the “Bayerisches Staatsministerium für Umwelt und Verbraucherschutz”, German Academic Exchange Service (DAAD) and the Center for NanoScience (CeNS). T. F. thanks the DFG for financial support. R. W. R and T. F. thank Lothar Schmid, Viktor Skowronek and Achim Wixforth for helpful discussions and support. R. W. R. thanks Llyod Ung for very helpful ideas and discussions.

References

  1. A. P. Gnadinger, MATEC Web Conf., 2015, 24, 2002 CrossRef.
  2. R. Arsat, M. Breedon, M. Shafiei, P. G. Spizziri, S. Gilje, R. B. Kaner, K. Kalantar-zadeh and W. Wlodarski, Chem. Phys. Lett., 2009, 467, 344–347 CrossRef CAS.
  3. X. Liu, J.-Y. Wang, X.-B. Mao, Y. Ning and G.-J. Zhang, Anal. Chem., 2015, 87, 9352–9359 CrossRef CAS PubMed.
  4. S. U. Senveli, Z. Ao, S. Rawal, R. H. Datar, R. J. Cote and O. Tigli, Lab Chip, 2016, 16, 163–171 RSC.
  5. D. E. W. Patabadige, S. Jia, J. Sibbitts, J. Sadeghi, K. Sellens and C. T. Culbertson, Anal. Chem., 2016, 88, 320–338 CrossRef CAS PubMed.
  6. J. P. Lafleur, A. Jönsson, S. Senkbeil and J. P. Kutter, Biosens. Bioelectron., 2016, 76, 213–233 CrossRef CAS PubMed.
  7. T. Franke and A. Wixforth, ChemPhysChem, 2008, 9, 2140–2156 CrossRef CAS PubMed.
  8. A. Wixforth, 2009 IEEE Int. Freq. Control Symp. Jt. with 22nd Eur. Freq. Time Forum, 2009, pp. 778–783 Search PubMed.
  9. J. K. Luo, Y. Q. Fu, Y. Li, X. Y. Du, A. J. Flewitt, A. J. Walton and W. I. Milne, J. Micromech. Microeng., 2009, 19, 54001 CrossRef.
  10. L. Derzsi, T. S. Kaminski and P. Garstecki, Lab Chip, 2016, 16, 893–901 RSC.
  11. G. Destgeer and H. J. Sung, Lab Chip, 2015, 15, 2722–2738 RSC.
  12. T. Dung Luong and N. Trung Nguyen, Micro Nanosyst., 2010, 2, 217–225 CrossRef.
  13. L. Y. Yeo and J. R. Friend, Annu. Rev. Fluid Mech., 2014, 46, 379–406 CrossRef.
  14. X. Ding, P. Li, S.-C. S. Lin, Z. S. Stratton, N. Nama, F. Guo, D. Slotcavage, X. Mao, J. Shi, F. Costanzo and T. J. Huang, Lab Chip, 2013, 13, 3626–3649 RSC.
  15. T. Laurell and A. Lenshof, Microscale Acoustofluidics, Royal Society of Chemistry, Cambridge, 2014 Search PubMed.
  16. T. M. Gronewold, Anal. Chim. Acta, 2007, 603, 119–128 CrossRef CAS PubMed.
  17. J. Reboud, Y. Bourquin, R. Wilson, G. S. Pall, M. Jiwaji, A. R. Pitt, A. Graham, A. P. Waters and J. M. Cooper, Proc. Natl. Acad. Sci. U. S. A., 2012, 109, 15162–15167 CrossRef CAS PubMed.
  18. L. Y. Yeo, H.-C. Chang, P. P. Y. Chan and J. R. Friend, Small, 2011, 7, 12–48 CrossRef CAS PubMed.
  19. A. Rajapaksa, A. Qi, L. Y. Yeo, R. Coppel and J. R. Friend, Lab Chip, 2014, 14, 1858–1865 RSC.
  20. V. Skowronek, R. W. Rambach, L. Schmid, K. Haase and T. Franke, Anal. Chem., 2013, 85, 9955–9959 CrossRef CAS PubMed.
  21. V. Skowronek, R. W. Rambach and T. Franke, Microfluid. Nanofluid., 2015, 19, 335–341 CrossRef CAS.
  22. R. W. Rambach, V. Skowronek and T. Franke, RSC Adv., 2014, 4, 60534–60542 RSC.
  23. S. Li, X. Ding, F. Guo, Y. Chen, M. I. Lapsley, S.-C. S. Lin, L. Wang, J. P. McCoy, C. E. Cameron and T. J. Huang, Anal. Chem., 2013, 85, 5468–5474 CrossRef CAS PubMed.
  24. T. Laurell, F. Petersson and A. Nilsson, Chem. Soc. Rev., 2007, 36, 492–506 RSC.
  25. T. Franke, A. R. Abate, D. A. Weitz and A. Wixforth, Lab Chip, 2009, 9, 2625–2627 RSC.
  26. T. Franke, S. Braunmüller, L. Schmid, A. Wixforth and D. A. Weitz, Lab Chip, 2010, 10, 789 RSC.
  27. J. Nam, H. Lim, C. Kim, J. Yoon Kang and S. Shin, Biomicrofluidics, 2012, 6, 24120–2412010 CrossRef PubMed.
  28. S. Girardo, M. Cecchini, F. Beltram, R. Cingolani and D. Pisignano, Lab Chip, 2008, 8, 1557–1563 RSC.
  29. Y. Q. Fu, X. Y. Du, J. K. Luo, A. J. Flewitt, W. I. Milne, D. S. Lee, N. M. Park, S. Maeng, S. H. Kim, Y. J. Choi and J. Park, in 2007 IEEE Sensors, IEEE, 2007, pp. 478–483 Search PubMed.
  30. X. Y. Du, M. E. Swanwick, Y. Q. Fu, J. K. Luo, J. Flewitt, D. S. Lee, S. Maeng and W. I. Milne, J. Micromech. Microeng., 2009, 19, 35016 CrossRef.
  31. M. B. Dentry, J. R. Friend and L. Y. Yeo, Lab Chip, 2014, 14, 750–758 RSC.
  32. R. J. Shilton, M. Travagliati, F. Beltram and M. Cecchini, Appl. Phys. Lett., 2014, 105, 74106 CrossRef.
  33. D. J. Collins, O. Manor, A. Winkler, H. Schmidt, J. R. Friend and L. Y. Yeo, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2012, 86, 56312 CrossRef PubMed.
  34. A. Qi, J. R. Friend, L. Y. Yeo, D. A. V. Morton, M. P. McIntosh and L. Spiccia, Lab Chip, 2009, 9, 2184 RSC.
  35. S. R. Heron, R. Wilson, S. A. Shaffer, D. R. Goodlett and J. M. Cooper, Anal. Chem., 2010, 82, 3985–3989 CrossRef CAS PubMed.
  36. J. Reboud, R. Wilson, Y. Zhang, M. H. Ismail, Y. Bourquin and J. M. Cooper, Lab Chip, 2012, 12, 1268 RSC.
  37. T. Vuong, A. Qi, M. Muradoglu, B. H.-P. Cheong, O. W. Liew, C. X. Ang, J. Fu, L. Yeo, J. Friend and T. W. Ng, Soft Matter, 2013, 9, 3631 RSC.
  38. T.-T. Wu and I.-H. Chang, J. Appl. Phys., 2005, 98, 24903 CrossRef.
  39. Y. Bourquin, A. Syed, J. Reboud, L. C. Ranford-Cartwright, M. P. Barrett and J. M. Cooper, Angew. Chem., Int. Ed., 2014, 53, 5587–5590 CrossRef CAS PubMed.
  40. J. Reboud, Y. Bourquin, R. Wilson, G. S. Pall, M. Jiwaji, A. R. Pitt, A. Graham, A. P. Waters and J. M. Cooper, Proc. Natl. Acad. Sci. U. S. A., 2012, 109, 15162–15167 CrossRef CAS PubMed.
  41. N. Sivanantha, C. Ma, D. J. Collins, M. Sesen, J. Brenker, R. L. Coppel, A. Neild and T. Alan, Appl. Phys. Lett., 2014, 105, 103704 CrossRef.
  42. K. Länge, B. E. Rapp and M. Rapp, Anal. Bioanal. Chem., 2008, 391, 1509–1519 CrossRef PubMed.
  43. P. M. Korczyk, L. Derzsi, S. Jakieła and P. Garstecki, Lab Chip, 2013, 13, 4096–4102 RSC.
  44. A. Wixforth, C. Strobl, C. Gauer, A. Toegl, J. Scriba and Z. V. Guttenberg, Anal. Bioanal. Chem., 2004, 379, 982–991 CrossRef CAS PubMed.
  45. Y. Bourquin, J. Reboud, R. Wilson and J. M. Cooper, Lab Chip, 2010, 10, 1898 RSC.
  46. A. Wixforth, J. Assoc. Lab. Autom., 2006, 11, 399–405 CrossRef CAS.
  47. T. Frommelt, D. Gogel, M. Kostur, P. Talkner, P. Hänggi and A. Wixforth, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 2008, 55, 2298–2305 CrossRef PubMed.
  48. R. Shilton, M. K. Tan, L. Y. Yeo and J. R. Friend, J. Appl. Phys., 2008, 104, 14910 CrossRef.
  49. A. M. Gracioso Martins, N. R. Glass, S. Harrison, A. R. Rezk, N. A. Porter, P. D. Carpenter, J. Du Plessis, J. R. Friend and L. Y. Yeo, Anal. Chem., 2014, 86, 10812–10819 CrossRef CAS PubMed.
  50. K. Sritharan, C. J. Strobl, M. F. Schneider, A. Wixforth and Z. Guttenberg, Appl. Phys. Lett., 2006, 88, 54102 CrossRef.
  51. S. Collignon, J. Friend and L. Yeo, Lab Chip, 2015, 15, 1942–1951 RSC.
  52. D. J. Collins, T. Alan, K. Helmerson and A. Neild, Lab Chip, 2013, 13, 3225–3231 RSC.
  53. L. Schmid and T. Franke, Lab Chip, 2013, 13, 1691–1694 RSC.
  54. L. Schmid and T. Franke, Appl. Phys. Lett., 2014, 104, 133501 CrossRef.
  55. F. Dutka, A. S. Opalski and P. Garstecki, Lab Chip, 2016, 16, 2044–2049 RSC.
  56. V. van Steijn, P. M. Korczyk, L. Derzsi, A. R. Abate, D. A. Weitz and P. Garstecki, Biomicrofluidics, 2013, 7, 24108 CrossRef PubMed.
  57. M. Sesen, T. Alan and A. Neild, Lab Chip, 2014, 14, 3325–3333 RSC.
  58. M. Sesen, T. Alan and A. Neild, Lab Chip, 2015, 15, 3030–3038 RSC.
  59. B. Ahn, K. Lee, H. Lee, R. Panchapakesan, L. Xu, J. Xu and K. W. Oh, Lab Chip, 2011, 11, 3915 RSC.
  60. L. Schmid, D. A. Weitz and T. Franke, Lab Chip, 2014, 14, 3710–3718 RSC.
  61. D. J. Collins, T. Alan and A. Neild, Appl. Phys. Lett., 2014, 105, 33509 Search PubMed.
  62. D. J. Collins, A. Neild and Y. Ai, Lab Chip, 2016, 16, 471–479 RSC.
  63. M. T. Guo, A. Rotem, J. A. Heyman and D. A. Weitz, Lab Chip, 2012, 12, 2146 RSC.
  64. J. Shim, G. Cristobal, D. R. Link, T. Thorsen, Y. Jia, K. Piattelli and S. Fraden, J. Am. Chem. Soc., 2007, 129, 8825–8835 CrossRef CAS PubMed.
  65. W. Shi, J. Qin, N. Ye and B. Lin, Lab Chip, 2008, 8, 1432–1435 RSC.
  66. A. Huebner, D. Bratton, G. Whyte, M. Yang, A. J. DeMello, C. Abell and F. Hollfelder, Lab Chip, 2009, 9, 692–698 RSC.
  67. M. He, J. S. Edgar, G. D. M. Jeffries, R. M. Lorenz, J. P. Shelby and D. T. Chiu, Anal. Chem., 2005, 77, 1539–1544 CrossRef CAS PubMed.
  68. M. Yang, C.-W. Li and J. Yang, Anal. Chem., 2002, 74, 3991–4001 CrossRef CAS PubMed.
  69. A. R. Wheeler, W. R. Throndset, R. J. Whelan, A. M. Leach, R. N. Zare, Y. H. Liao, K. Farrell, I. D. Manger and A. Daridon, Anal. Chem., 2003, 75, 3581–3586 CrossRef CAS PubMed.
  70. D. Di Carlo, N. Aghdam and L. P. Lee, Anal. Chem., 2006, 78, 4925–4930 CrossRef CAS PubMed.
  71. C. Kim, J. H. Bang, Y. E. Kim, J. H. Lee and J. Y. Kang, Sens. Actuators, B, 2012, 166–167, 859–869 CrossRef CAS.
  72. W.-H. Tan and S. Takeuchi, Proc. Natl. Acad. Sci. U. S. A., 2007, 104, 1146–1151 CrossRef CAS PubMed.
  73. R. D. Sochol, B. P. Casavant, M. E. Dueck, L. P. Lee and L. Lin, J. Micromech. Microeng., 2011, 21, 54019 CrossRef.
  74. C. Dammann and S. Köster, Lab Chip, 2014, 14, 2681–2687 RSC.
  75. H. Nuss, C. Chevallard, P. Guenoun and F. Malloggi, Lab Chip, 2012, 12, 5257–5261 RSC.
  76. H. Boukellal, S. Selimović, Y. Jia, G. Cristobal and S. Fraden, Lab Chip, 2009, 9, 331–338 RSC.
  77. T. Yeo, S. J. Tan, C. L. Lim, D. P. X. Lau, Y. W. Chua, S. S. Krisna, G. Iyer, G. S. Tan, T. K. H. Lim, D. S. W. Tan, W.-T. Lim and C. T. Lim, Sci. Rep., 2016, 6, 22076 CrossRef CAS PubMed.
  78. J. H. Jung, G. Destgeer, J. Park, H. Ahmed, K. Park and H. J. Sung, Anal. Chem., 2017, 89, 2211–2215 CrossRef CAS PubMed.
  79. W. Wang, C. Yang, Y. Liu and C. M. Li, Lab Chip, 2010, 10, 559 RSC.
  80. M. Sesen, C. Devendran, S. Malikides, T. Alan and A. Neild, Lab Chip, 2017, 17, 438–447 RSC.
  81. W. Wang, C. Yang and C. M. Li, Lab Chip, 2009, 9, 1504 RSC.
  82. P. Garstecki, M. J. Fuerstman, H. A. Stone and G. M. Whitesides, Lab Chip, 2006, 6, 437–446 RSC.
  83. G. F. Christopher, N. N. Noharuddin, J. A. Taylor and S. L. Anna, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2008, 78, 36317 CrossRef PubMed.
  84. M. De Menech, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2006, 73, 31505 CrossRef PubMed.
  85. D. R. Link, S. L. Anna, D. A. Weitz and H. A. Stone, Phys. Rev. Lett., 2004, 92, 54503 CrossRef CAS PubMed.
  86. H. Yatsuda, K. Noguchi and K. Yamanouchi, Jpn. J. Appl. Phys., 2000, 39, 3041–3044 CrossRef CAS.
  87. R. W. Rambach, J. Taiber, C. M. L. Scheck, C. Meyer, J. Reboud, J. M. Cooper and T. Franke, Sci. Rep., 2016, 6, 21980 CrossRef CAS PubMed.
  88. M. J. Fuerstman, A. Lai, M. E. Thurlow, S. S. Shevkoplyas, H. A. Stone and G. M. Whitesides, Lab Chip, 2007, 7, 1479–1489 RSC.
  89. C. N. Baroud, F. Gallaire and R. Dangla, Lab Chip, 2010, 10, 2032–2045 RSC.
  90. V. Labrot, M. Schindler, P. Guillot, A. Colin and M. Joanicot, Biomicrofluidics, 2009, 3, 12804 CrossRef PubMed.
  91. H. Bruus, Theoretical Microfluidics, Oxford University Press, New York, 2007 Search PubMed.
  92. P. Tabeling, Introduction to Microfluidics, Oxford University Press, Oxford, NewYork, 2005 Search PubMed.
  93. M. Wiklund, R. Green and M. Ohlin, Lab Chip, 2012, 12, 2438–2451 RSC.
  94. J. Friend and L. Y. Yeo, Rev. Mod. Phys., 2011, 83, 647–704 CrossRef.
  95. C. Eckart, Phys. Rev., 1948, 73, 68–76 CrossRef.
  96. T. Franke, S. Braunmüller, T. Frommelt and A. Wixforth, Proc. SPIE, 2009, 7365, 73650O-73650O-9 CrossRef.
  97. J. Shi, D. Ahmed, X. Mao, S.-C. S. Lin, A. Lawit and T. J. Huang, Lab Chip, 2009, 9, 2890–2895 RSC.
  98. S. M. Langelier, Y. Yeo and J. Friend, Lab Chip, 2012, 2970–2976 RSC.
  99. P. W. Mason and R. N. Thurston, Physical Acoustics, Principles and Methods, Academic Press, New York, London, 1970, vol. 3 Search PubMed.
  100. L. Schmid, A. Wixforth, D. A. Weitz and T. Franke, Microfluid. Nanofluid., 2011, 12, 229–235 CrossRef.
  101. M. B. Dentry, L. Y. Yeo and J. R. Friend, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2014, 89, 13203 CrossRef PubMed.
  102. I. Leibacher, S. Schatzer and J. Dual, Lab Chip, 2014, 14, 463–470 RSC.
  103. G. Kovacs, M. Anhorn, H. E. Engan, G. Visintini and C. C. W. Ruppel, in IEEE Symposium on Ultrasonics, IEEE, 1990, pp. 435–438 Search PubMed.
  104. I. Takanaga and J. Kushibiki, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 2002, 49, 893–904 CrossRef.
  105. N. Muñoz-Rujas, A. Srhiyer, E. A. Montero and F. Aguilar, in Nineteenth Symposium on Thermophysical Properties, At Boulder, Colorado, USA, 2015 Search PubMed.
  106. F. E. G. Cox, Parasites Vectors, 2010, 3, 5 CrossRef PubMed.
  107. B. Zheng, L. S. Roach and R. F. Ismagilov, J. Am. Chem. Soc., 2003, 125, 11170–11171 CrossRef CAS PubMed.
  108. M. Heymann, S. Fraden and D. Kim, J. Microelectromech. Syst., 2014, 23, 424–427 CrossRef.
  109. J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak and A. Cardona, Nat. Methods, 2012, 9, 676–682 CrossRef CAS PubMed.
  110. J. Schindelin, C. T. Rueden, M. C. Hiner and K. W. Eliceiri, Mol. Reprod. Dev., 2015, 82, 518–529 CrossRef CAS PubMed.
  111. C. A. Schneider, W. S. Rasband and K. W. Eliceiri, Nat. Methods, 2012, 9, 671–675 CrossRef CAS PubMed.

Footnote

Electronic supplementary information (ESI) available: Complete trap design in DWG format (Autodesk 2016); movie of the acoustic droplet release. See DOI: 10.1039/c7lc00378a

This journal is © The Royal Society of Chemistry 2017