Microfluidic particle manipulation

Abstract

The present invention relates to the use of acoustic waves for the manipulation and sorting of particles and cells. In an embodiment, there is provided a microfluidic device for manipulating a particle in a fluid suspension, the device comprising: (a) a substrate; (b) a channel defined in the substrate, the channel having an inlet for receiving the fluid suspension and an outlet for discharging the fluid suspension; and (c) an acoustic source configured to deliver a travelling surface acoustic wave transverse the flow of the fluid suspension in the channel, wherein the acoustic source is an interdigital transducer (IDT), the IDT comprises a plurality of concentric circular arcs having a tapered end directed at the channel, and the tapered end has an aperture of between 4 m and 150 m. In an alternative embodiment, the device comprises a second channel disposed intermediate the first channel and the acoustic source wherein the first and second channels are connected by a pumping channel.

Claims

1. A microfluidic device for manipulating a particle in a fluid suspension, the device comprising: (a) a substrate; (b) a first channel defined in the substrate, the first channel having an inlet for receiving the fluid suspension and an outlet for discharging the fluid suspension; and (c) an acoustic source configured to generate and deliver a single travelling surface acoustic wave transverse the flow of the fluid suspension in the channel and configured to propagate into the solution confined within the channel, wherein the acoustic source is a single interdigital transducer (IDT), and the IDT comprises a plurality of concentric arcs having a tapered end directed at the channel, and the tapered end has an aperture of between 4 m and 150 m.

2. The device according to claim 1, wherein the aperture is 56 m.

3. The device according to claim 1, further comprising a second channel defined in the substrate, the second channel having an inlet for receiving a fluid and an outlet for discharging the fluid, the second channel is disposed intermediate the first channel and the acoustic source, wherein the first and second channels are disposed alongside each other and the direction of flow of fluids in the first and second channels are in the same direction, the first and second channels are connected in fluid communication by a pumping channel disposed between the first and second channels, the pumping channel connecting the first and second channels is disposed intermediate the inlets and outlets of both the first and second channels, and the acoustic source is disposed adjacent the second channel to generate and deliver the travelling surface acoustic wave transverse the flow of the fluid from the second channel to the first channel through the pumping channel, the flow of the fluid from the pumping channel to the first channel manipulates the particle in the fluid suspension in the first channel.

4. The device according to claim 3, wherein each of the first and second channels has a width of about 120 m and a height of about 25 m.

5. The device according to claim 4, wherein the width of the second channel adjacent the acoustic source is narrower than the width of the second channel at the inlet and outlet.

6. The device according to claim 5, wherein the width of the second channel adjacent the acoustic source is about 20 m.

7. The device according to claim 3, wherein the pumping channel has a width of about 20 m and a length of about 170 m.

8. The device according to claim 3, wherein the inlet of each of the first and second channel is in fluid communication with a pump.

9. The device according to claim 1, wherein the substrate is a piezoelectric substrate selected from the group consisting of: lithium niobate, lithium tantalite, and lanthanum gallium silicate.

10. The device according to claim 1, wherein the surface acoustic wave has an average frequency of between 100 MHz and 1000 MHz.

11. The device according to claim 1, wherein the first channel comprises a plurality of outlet channels.

12. A method for manipulating a particle in a fluid suspension, the method comprising: (a) introducing the fluid suspension along a first channel; and (b) using an acoustic source to generate a highly focused travelling surface acoustic wave transverse the flow of the fluid suspension in the first channel to manipulate the particle travelling in the first channel, wherein the acoustic source is an interdigital transducer (IDT), the IDT comprises a plurality of concentric arcs having a tapered end directed at the channel, and the tapered end has an aperture of between 4 m and 150 m.

13. The method according to claim 12, wherein the aperture is 56 m.

14. The method according to claim 12, further comprising: (a) introducing a fluid along a second channel, the second channel disposed alongside the first channel, the fluids in both channel travelling in the same direction, the second channel intermediate the first channel and the acoustic source; (b) connecting in fluid communication the second channel to the first channel with a pumping channel, the pumping channel disposed between the first and second channels, and intermediate the inlets and outlets of both the first and second channels, wherein the acoustic source is disposed adjacent the second channel on the opposing side of the first channel to generate and deliver the travelling surface acoustic wave transverse the flow of the fluid in the second channel and to pump the fluid from the second channel to the first channel through the pumping channel, and manipulating the particle in the fluid suspension in the first channel with the flow of the fluid from the pumping channel.

15. The method according to claim 14, wherein width of the second channel adjacent the acoustic source is narrower than the width of the second channel at the inlet and outlet, thereby constricting the flow of the fluid in the second channel adjacent the acoustic source.

16. The method according to claim 15, wherein the width of the second channel adjacent the acoustic source is about 20 m.

17. The method according to claim 14, wherein the pumping channel has a width of about 20 m and a length of about 170 m.

18. The method according to claim 14, wherein the inlet of each of the first and second channel is in fluid communication with a pump for pumping fluid through the channels.

19. The method according to claim 14 , wherein the surface acoustic wave has an average frequency of between 100 MHz and 1000 MHz.

20. An interdigital transducer comprising a plurality of concentric circular arcs having a tapered end, wherein the tapered end has an aperture of between 4 m and 150 m and wherein the interdigital transducer is configured to generate a travelling the surface acoustic wave placed adjacent a microfluidic channel to deliver the wave transverse the flow of the fluid suspension in the channel.

Description

(1) In order that the present invention may be fully understood and readily put into practical effect, there shall now be described by way of non-limitative examples only preferred embodiments of the present invention, the description being with reference to the accompanying illustrative figures.

(2) In the Figures:

(3) FIG. 1: Schematic illustration of the device design. (a) Sheath flow is used to hydrodynamically focus the sample prior to the focused interdigital transducers (FIDTs), which generate the focused surface acoustic wave (SAW) that translates selected particles. (b) Highly focused SAW is used to sort at the single-particle level, where the width of the focused SAW is on the order of 10's of m.

(4) FIG. 2: Focused SAW and device design. The SAW beam is concentrated using a FIDT structure that results in maximum surface displacements in a defined region 300 m from the patterned FIDT features. The fluid channel is bonded directly to the FIDT structure, where the maximum-displacement region is centred on the channel location. The highly focused nature of the SAW results in large and localized substrate velocities for a given applied power. Scale bar represents 100 m.

(5) FIG. 3: Demonstration of particle sorting using pulsed SAW. (a,b) Individual 3 m particles in a 1 l/min flow, bounded by a focusing 8 l/min sheath flow, are displaced using a 300 s, 30 mW pulsed focused SAW at 5 ms intervals, which couples into the fluid within an 25 m wide beam. (c,d) While the geometry in (a,b) is optimized for sorting using minimal powers and displacements, particles can be translated substantial distances over several wavelengths using travelling SAW. Flow rates of 0.5 and 3 l/min are used for the particle, buffer flow inlets with SAW pulsed at 100 mW for 1 ms at 10 ms intervals. (a,c) show individual images captured at 10,000 and 5,000 frames per second, respectively, whereas (b,d) show the overlay of 200 frames to demonstrate overall particle trajectories. Images taken from videos. All scale bars represent 50 m.

(6) FIG. 4: Particle velocities in the sorting region. (a) The measured velocity magnitudes of tracked particles not subject to SAW roughly double in the flow constriction region, where the channel width is halved from 80 m. Inset shows the velocity distributions just prior to (red), in the middle of (green) and after (blue) the flow constriction region, where the variation in velocity magnitudes is a result of the non-uniform (parabolic) flow velocity profile in the z-direction. (b) Velocity magnitudes of tracked particles sorted by the focused SAW. Particles are translated laterally within the beam of the tightly focused SAW, approximately 25 m wide, where particles are translated at approximately 0.15 m/s using 300 s, 30 mW pulses.

(7) FIG. 5: Particle translation behaviour. (a) The percentage of particles translated using a continuously applied SAW is a function of the applied power, here with a total combined flow rate of 6 l/min. Error bars represent one S.D. from 5 measurements of equal numbers of randomly selected particles (min. 20 selected). Scale bars are 20 m. (b) The number of particles ejected per pulse is a function of the pulse length for a given particle concentration, here 0.7% v/v, with the average number per pulse defined by Eq. 2. (c) The 1 m particles are shown travelling through the unsorted outlet meander. Scale bar 400 m. (d) High frequency affords the sorting of particle sizes not otherwise accessible using travelling waves as per Eq. 1, here demonstrating the selective translation and sorting of 2 m particles (blue) from 1 m (green) particles at 4 l/min with continuously applied 26 mW SAW. Scale bar is 50 m.

(8) FIG. 6: Acoustic streaming in a confined chamber. In these images, 1 m particles in a static flow condition are subject to a time-averaged flow induced by a body force in the direction of acoustic propagation in two different channel heights (30 m and 20 m). Increased acoustic forcing relative to acoustic-induced flow results in greater particle capture in trapping locations on either side of the acoustic beam, where particles are subject to the acoustic gradient force for longer periods in the channel with the smaller height. Scale bar is 100 m.

(9) FIG. 7: Acoustic streaming in flow conditions. As the acoustic intensity is increased in a continuous flow (0.5 l/min in a 160 m channel) at (a) 10 mW, (b) 15 mW, (c) 25 mW, (d) 40 mW, in a solution containing 1 m (green) and 2 m (orange) particles, the influence of acoustic streaming induced flow relative to particle forces becoming apparent. Here the dominant particle force changes from direct acoustic radiation force (seen shifting the 2 m particles in (a)) to fluid drag (in (d)), where particles are bound in streamlines according to the superposition of the incident and acoustic streaming flow fields. Scale bar is 100 m.

(10) FIG. 8: Micropumping generated by acoustic streaming. In addition to the force exerted on suspended objects, the acoustic field can result in bulk fluid motion due to the force imparted within the fluid itself in the propagation direction, as well as due to acoustic cavitation. (a) In the steady-state, fluid flows through two microchannels with a pumping channel in-between, with a SAW used to pump fluid through this channel. (b) Blue dye is used here in the lower channel fluid to visualize the fluids originating from different channels. (c) With the application of a 10 m wavelength (same design as in FIG. 2) 0.5 ms pulse SAW at 100 mW, fluid from the lower (dye-filled) channel is rapidly pumped into the upper one. (d) The pumped fluid remains in the upper channel and co-flows with the fluid there. Note the visualization of the parabolic flow profile with the rapidly translated dyed fluid body. Both top and bottom flows are 2 l/min. Scale bar is 100 m.

(11) FIG. 9: Acoustic micropumping for particle translation. Only the upper channel from FIG. 8 is shown here. (a) A suspended 7 m diameter polystyrene microparticle (circled, dotted line) continues with the lateral flow in the upper channel (same design as in FIG. 8). (b,c,d) With the application of a 5 ms SAW pulse at 50 mW (longer here than in FIG. 8 to better visualize particle motion), the particle is translated in the pumping direction within the fluid volume in which it is suspended. Subsequent particles that are not translated in this manner (dual particles in (d)) continue unperturbed in the direction of fluid flow. Both top and bottom flows are 2 l/min. Scale bar is 100 m.

(12) In this work we use highly focused travelling SAW to obviate sorting region width limitations in order to generate large and rapid displacements for robust sorting. This localized SAW is produced using a 10 m wavelength focused IDT (FIDT) structure that generates a beam 25 m wide at the narrowest point, sufficient to sort discrete particles using sub-ms SAW pulses without pre-ordering. The device concept is demonstrated in FIG. 1, where FIG. 1b demonstrates the single-particle level sorting that is achievable with a tightly focused translating force field. Furthermore, because of the high-frequency nature of the device generating these highly focused fields, particles as small as 2 m can be translated and separated.

(13) We also demonstrate the utility of this focused SAW device for streaming-based fluidic micropumping and the use of this pumping effect for particle translation. These effects are seen in FIGS. 8 and 9, where the application of short duration SAW (millisecond order) results in fluid pumping between co-flowing channels, and where suspended microparticle trajectories can be individually altered within a few milliseconds in fluid streamlines. This will be described in detail below. Both methodologies have potential use in a wide variety of applications, including the on-demand dilution of particle/cell mixtures and selective cell sorting, as an alternative to the deflection of airborne droplets in FACS.

1. SYSTEM PRINCIPLES AND DESIGN

(14) With reference to FIG. 1, the device 10 has at least one channel 15 defined in a substrate 20. The channel has an inlet 25 for receiving a fluid suspension, where the fluid suspension contains the particles to be manipulated or sorted, and an outlet 30 for discharging the fluid suspension. In various embodiments, there may be a plurality of outlets 30n for providing channels for directing the sorted particles 50 to its respective or corresponding channels/receptacles.

(15) The device 10 further comprises an acoustic source 35 for generating and delivering a travelling surface acoustic wave transverse the flow of the fluid suspension in the channel (see direction of arrow A). The acoustic source 35 is disposed near, at or adjacent the exterior wall of the channel. The wave generated by the acoustic source 35 manipulates the particles present in the channel when it travels along the channel from the inlet to the outlet. In particular, the particles 50 get manipulated when they travel past the acoustic source 35.

(16) In an embodiment, the acoustic source 35 is an interdigital transducer (IDT) which comprises a plurality of concentric arcs 40 having a tapered end. The tapered end 45 is directed toward or at the channel. The tapered end 45 has an aperture of between 4 m and 150 m. In an embodiment, that aperture (or opening) has a width of about 56 m.

(17) The mechanisms underlying the translation of particles subject to a travelling acoustic wave force have been the subject of substantial theoretical work, where several expressions have been analytically been derived to estimate the directional force they experience..sup.60-62 In the limiting case where a particle is significantly smaller than the wavelength in the fluid, but not so small that viscous interfacial effects become important, such that the particle radius R>>, where is the viscous penetration depth given by =(2/).sup.1/2 and , are the fluid density and viscosity and =2f, the formulation from King is sufficient to describe particle motion. The travelling wave force is given by.sup.61,63

(18) $\begin{array}{cc}F=64{\left(\frac{}{c}\right)}^4{R}^6{v}_0^2\frac{1+\frac{2}{9}\left(1-{\left(/{}_p\right)}^2\right)}{{\left(2+/{}_p\right)}^2}& \left(1\right)\end{array}$
where c is the speed of sound in the fluid, .sub.p is the particle density and v.sub.0 is the displacement velocity in the fluid, with v.sub.0v.sub.SAW. Principally, larger frequencies result in substantially larger forces due to the F.sup.4 scaling. For objects approaching or exceeding the acoustic wavelength (RA), however, the imparted force scales in a highly nonlinear way, albeit at a substantially larger magnitude than in the R>> regime.sup.39,64. The 386 MHz frequency employed here, where the resonant SAW frequency is given by f=c, corresponding to substrate wavelengths around 10 m (with c4000 m/s) and fluid ones around 3 m (with c1500 m/s), is thus capable of generating large forces efficiently on particles on the scale of the fluid wavelength to counteract the fact that standing waves typically generate larger force magnitudes for a given fluid displacement velocity..sup.60,63 For polystyrene particles in water, the particle radius should exceed approx. 1.4.sub.f/2, where .sub.f is the fluid wavelength.sup.64,65, corresponding to a minimum diameter of 1.6 m for .sub.SAW=10 m above which the acoustic radiation force magnitudes are substantially larger, and thus much more effectively applied, than for particle diameters below this critical value (in which Equation 1 could reasonably be applied).

(19) The direction of this force has a vertical as well as horizontal component, with the acoustic wave propagating at the Rayleigh angle, where .sub.R=sin.sup.1(c.sub.l/c.sub.s) is this quantity with respect to the orthogonal. In the system described here, with c.sub.s=3964 m/s and c.sub.l=1484 m/s, .sub.R22. While the majority of the energy is thus directed vertically.sup.57, rather than in the horizontal direction, in practice this vertical displacement also serves to aid the horizontal displacement when the force is applied laterally to a continuous flow, whereby the vertical component of the force pushes particles into the slower moving flow near the channel boundaries and thus allowing them to be exposed to the field and thus translated horizontally over a longer period of time.

(20) The propagation of an acoustic field through a fluid medium will also result in a body force within the fluid that is imparted due to a momentum flux gradient, ultimately arising from the attenuation of the acoustic displacement along the propagation direction.sup.66. The outcome of this force is termed acoustic streaming, where bulk fluid motion occurs along the axis of maximum acoustic amplitude, and can result in recirculatory motion elsewhere. The magnitude of the acoustic body force is related by the attenuation coefficient of the fluid, where the body force can be expressed as.sup.67

(21) $F_B=v_0^{-2x_i}$
where is the attenuation coefficient of the fluid media, is the fluid density, v.sub.0 is the initial (unperturbed) acoustic velocity magnitude, and x.sub.i is the direction along which the wave propagates. The attenuation coefficient scales with .sup.2, where higher frequencies (with =2f) result in larger body forces that occur closer to the acoustic source. Also important for acoustic systems utilizing a SAW wavemode is the characteristic attenuation length along the substrate, approximately .sup.1=12.sub.SAW in the case of the common water/lithium niobate fluid/substrate combination.sup.68. In microfluidic systems the frequency and channel dimensions can be chosen such that the attenuation length scale is on the order of that of the channel lengths or less to optimize the transfer of energy from the substrate to fluid motion. The time-averaged effect of this acoustic body force can result in hydrostatic pressure differentials for microfluidic pumping.sup.55 We utilize these two effects, direct acoustic force on suspended microparticles with a focused travelling wave and acoustic micropumping, to selectively translate individual particles in a continuous flow. While the travelling wave force has been used to perform continuous size-based separation.sup.69, here we demonstrate a highly focused system that is amenable to highly selective translation using an acoustic beam with a width on the order of individual cells. Additionally, while the physics of the acoustic streaming phenomena is well understood, we use it for the first time to demonstrate particle translation, where rapid micropumping of minute fluid volumes between co-flowing channels can selectively translate individual suspended objects in a continuous flow. At higher power levels, a focused acoustic beam can also induce rapid cavitation, further enhancing the micropumping effect.

(22) In FIG. 2 we show the most highly focused SAW transducer yet demonstrated for microfluidic applications, resulting in efficiently generated substrate displacements concentrated in a target area. FIG. 2 shows the device that is bonded to a series of PDMS channels for selective continuous particle sorting due to acoustic forces acting on individual particles.

(23) In FIGS. 8 and 9, we also show an alternative embodiment of the present invention, i.e. using this device 10 to rapidly pump fluid from one channel into another.

(24) The embodiment presented in FIGS. 8 and 9 is similar to the embodiment presented in FIG. 1, i.e. the device 10 has a channel 15 and an acoustic source 35 for manipulating particles 50 travelling in the channel 15.

(25) In this alternatively embodiment, there is a second channel 55 disposed alongside the first channel 15. Similarly, the second channel 55 has an inlet 60 for receiving a fluid and an outlet 65 for discharging the fluid. The direction of the fluid travelling in both the first 15 and second 55 channels are in the same direction. As seen in FIG. 8, the second channel 55 is disposed between the first channel 15 and the acoustic source 35. The two channels 15 and 55 are in fluid communication with each other via a pump channel 70 disposed between them. The pump channel 70 is disposed intermediate the inlets and outlets of the two channels 15 and 55. The pump channel 70 connects both first 15 and second 55 channels. At this location of the pump channel 70, the acoustic source 35 is disposed adjacent the second channel 55 to generate and deliver the travelling surface acoustic wave transverse the flow of the fluid from the second channel 55 to the first channel 15 through the pumping channel 70. This flow of fluid from the pumping channel 70 to the first channel 15 causes the manipulation of the particles in the first channel 15. In an embodiment, the portion of the second channel 55, where the pumping channel 70 branches out into the first channel 15, adjacent the acoustic source 35 is constricted 80. In other words, the width of the second channel 55 adjacent the acoustic source 55 is narrower than the width of the second channel 55 at the inlet 60 and outlet 65. In an embodiment, the width of the second channel 55 that is connected to the pumping channel 70 adjacent the acoustic source is about 20 m.

(26) In various embodiments, each of the first 15 and second 55 channels has a width of about 120 m and a height of about 25 m. The pumping channel 70 may have a width of about 20 m and a length of about 170 m.

(27) In various embodiments, the inlets of the first 15 and second 55 channels may be connected in fluid communication to reservoirs or containers for containing and storing the respective fluids. In addition, the inlets 25 and 60 of each of the first 15 and second 55 channel is in fluid communication with a pump for pumping the fluids through the channels.

(28) When a short (millisecond-order) SAW pulse is triggered a burst of fluid is pumped in the direction of SAW propagation from the channel closer to the SAW source to one more distal. The focused beam is advantageous as it allows the use of more confined, higher pressure drop pumping channels, which permit the more stable maintenance of continuous flow in a dual-flow configuration and the minimization of recirculatory backflow that can occur in wider channels.sup.70 (see FIG. 6).

2. METHODS

(29) In operation, the method of carrying particle manipulation by the device 10 of the present invention follows this general concept:

(30) (a) introducing the fluid suspension along the first channel 15; and

(31) (b) using an acoustic source 35 to generate a highly focused travelling surface acoustic wave transverse the flow of the fluid suspension in the first channel 15 to manipulate the particle 50 travelling in the first channel 15.

(32) The manipulated particles 50 are then sorted out in respective plurality of outlets 30n.

(33) The microfluidic particle manipulation device, or sorting system, is comprised of a series of FIDTs patterned on a piezoelectric 128 Y-cut lithium niobate (LN, LiNbO.sub.3) substrate. The FIDTs are comprised of a 200 nm thick conductive Al layer on top of 7 nm thick Cr layer, which serves as an adhesion layer between the LN and Al. IDTs are patterned in concentric circle segments with a geometric focal point 160 m from the IDT finger-pair, comprising 36 finger-pairs in total with an aperture of 56 m at the proximal end up to 210 m at the distal end, subtending an angle of 26. The physically realized focusing region does not occur at the geometric one, however, with the maximum displacement and highest degree of focusing occurring 300 m from the last finger-pair, as noted in FIG. 2a. Due to the nature of wave propagation in an anisotropic material such as LN, the focusing point is effectively stretched in the crystallographic x-direction, the orientation with a minimum power flow angle and maximum propagation velocity,.sup.71 where this effective displacement of the focal point from the geometric one is consistent with previous observations..sup.72 The entire device is coated with 300 nm SiO.sub.2 using plasma enhanced chemical vapour deposition to prevent corrosion and improve bonding. FIG. 2b shows the completed device, composed of a microfluidic channel bonded directly to the assembled SAW device using plasma activation (PDC 32G, Harrick Plasma, USA).

(34) The device is actuated using A/C pulses generated by a signal generator (APSIN3000HC, Anapico, Switzerland) and amplified by a power amplifier (Model 1100, Empower, USA). Imaging is performed using a high-speed camera (Fastcam Mini UX100, Photron Limited, Japan) on an inverted microscope. Elimination of birefringence effect that would otherwise result in a double-image in an optically anisotropic material is performed by mounting the completed device on a separate piece of double-sided LN in the opposite crystallographic orientation to that of the device. Particle trajectories were recorded using DMV software, a MATLAB-based software package that offers a suite of detection algorithms and parameters to track droplets and particles..sup.73

(35) Though PDMS has minimal effect on the resonant frequency of the device,.sup.56 it strongly attenuates SAW displacement at the substrate interface, where the attenuation length is inversely proportional to the wavelength,.sup.74 and is thus an important consideration for the high frequencies used here. The PDMS-attenuating region is minimized by enclosing the SAW transducer in an air-filled chamber, with only a 20 m wide PDMS wall separating this region from the liquid filled channel.

(36) In the case of particle translation due to the acoustic force imparted on the particles directly (FIGS. 2-5), a flow constriction serves to further minimize the distance the SAW is subjected to any attenuating interface prior to particle interaction and also to reduce the chance that multiple particles will be translated simultaneously by stretching the flow locally. As noted in FIG. 1a, the device has only two independent inlets and outlets, where both sheath and outlet.sub.2 channel flows are hydrostatically balanced though the use of equidistant channel lengths upstream and downstream. The channel, fabricated using PDMS (10:1 elastomer/curing agent ratio) soft lithography on an SU-8 mould, has a height of 20 m. To perform sorting, particle-free buffer flow and a particle solution containing 3 m particles are injected in the sheath and sample inlets, respectively, using separate syringe pumps (NE-1000, New Era Pump Systems, Inc., NY, USA and Legato 111, KD Scientific, MA, USA). The sorting designs used have two independent outlets, outlet.sub.1 and outlet.sub.2. When a particle is in the path of the focused SAW at sufficient amplitude, it is translated from the sample stream into fluid flow that exits via outlet.sub.2, as opposed to unsorted particles that exit via outlet.sub.1.

(37) In the case of particle translation due to micropumping, FIGS. 8 and 9 show a further embodiment of the present invention, i.e. the channel configuration used for particle translation. The method involved introducing a fluid along a second channel 55, the second channel 55 disposed alongside the first channel 15, the fluids in both channel travelling in the same direction, the second channel 55 intermediate the first channel 15 and the acoustic source 35; (b) connecting in fluid communication the second channel 55 to the first channel 15 with a pumping channel 70, the pumping channel 70 disposed between the first 15 and second 55 channels, and intermediate the inlets and outlets of both the first 15 and second 55 channels, wherein the acoustic source 35 is disposed adjacent the second channel 55 on the opposing side of the first channel 15 to generate and deliver the travelling surface acoustic wave transverse the flow of the fluid in the second channel 55 and to pump the fluid from the second channel 55 to the first channel 15 through the pumping channel 70, and manipulating the particle in the fluid suspension in the first channel with the flow of the fluid from the pumping channel.

(38) It can be seen that the upper first channel 15 contains a continuous fluid flow with suspended particles 50, where fluid from a co-flowing lower second channel 55 is injected with the application of a ms-order SAW to translate particles suspended within the upper first channel 15 by displacing the fluid in which the particles 50 are suspended in the fluid pumping/propagation direction. Both continuous flows are generated from separate syringe pumps (NE-1000, New Era Pump Systems, Inc., NY, USA and Legato 111, KD Scientific, MA, USA). Importantly, this pumping-based translation method is insensitive to the properties of the suspended object, as opposed to the case of a direct acoustic force on the particle which will be a function of its mechanical properties. This acoustic pumping effect is enhanced and isolated in a system where the pumping channel is on the order of the attenuation length in the substrate or larger. In the realization shown in FIGS. 8 and 9, the fluid flow first 15 and second 55 channels are 120 m wide each and 25 m high. The lower flow second channel 55 contains a constriction 80 (to a 20 m channel width) on either side of the focused SAW to prevent the formation of acoustic vortices, and where the 20 m wide, 170 m long pumping channel 70 has a width on the order of the focused SAW beam width to maximize the unidirectionality of pumping within this channel. The total propagation distance of the SAW at the substrate/water interface is thus the sum of the constricted 20 m wide channel 80 through which the lower channel fluid continuously flows and the 170 m pumping channel 70, yielding 190 m in total, approx. 1.5 times the acoustic attenuation length for a 10 m SAW. These channel dimensions can be scaled appropriately for a given acoustic wavelength and beam dimensions.

3. RESULTS AND DISCUSSION

(39) Particle sorting can be accomplished over a minimal sorting width using focused SAW, where the beam width is minimized by using a small wavelength (10 m), small aperture (56 m at minimum) FIDT structure that results in a highly localized maximum displacement region. Further, displacements are maximized in utilizing travelling SAW, as opposed to standing SAW; at this wavelength a standing wave would yield a theoretical maximum displacement of 2.5 m, as opposed to much larger translations possible with a travelling wave for a given wavelength, though the force magnitude is maximized in the near field due to the attenuation at the substrate/fluid interface with an attenuation length (at which the substrate velocity decays to 1/e) of approximately 12.sub.SAW..sup.55 We demonstrate both of these characteristics, where individual 3 m particles are displaced with the application of a SAW. Pulses with periods t.sub.p1 ms are utilized, similar to the pulse lengths in other work,.sup.36,37,46,47 as minimizing the SAW exposure time in a continuous flow reduces the chance of unintended sorting events (false-positives). FIG. 3 shows that the highly focused beam, with an aperture of 25 m, is compatible with different device geometries, here using a flow focusing geometry (FIG. 3a,b) and a H-filter arrangement (FIG. 3c,d), where FIG. 3b,d show the trajectories of sorted and unsorted particles as a continuous particle stream passes through a pulsed SAW.

(40) The fact that substantial displacements, 50 m in FIG. 3d, can be generated using short SAW pulses at low powers (100 mW) further reflects the advantages of a focusing aperture and a high-frequency (386 MHz) SAW that generates larger travelling wave forces as per Eq. 1, and 3 m particles can be deterministically displaced more rapidly and at lower power levels than demonstrated elsewhere..sup.42 Partially displaced particles that do not exit via outlet2 are those subject to a sub-threshold acoustic force at the edge of the focused beam, outside the sorting region.

(41) The power required is minimized by limiting the lateral displacement needed for sorting, hence the geometry in FIG. 3a requires lower powers for sorting at equivalent flow rates due to the 40 m wide flow restriction region in the centre of the channel, half the 80 m width immediately upstream and downstream. The effect of this flow restriction is reflected in the velocities of particles tracked through this region. FIG. 4a shows the velocity magnitudes of unsorted particles in the focused sorting region (those exiting through outlet1) where the average velocity magnitude doubles. Though flow focusing aligns the particles in the y-direction, a parabolic flow profile (resulting from the no-slip boundary condition at the fluid/channel interface) yields a range of particle velocities in the z-direction. The dotted lines in this figure show the particle velocity magnitudes of tracked particles, where the inset in FIG. 4a shows a histogram of these velocities. If the acoustic force acted solely in the direction of SAW propagation, this range of velocities would necessitate substantially higher powers to deterministically translate all particles, especially the fastest moving ones. As the .sub.R that results from a LN/H.sub.2O interface is directed principally in the direction normal to the surface, however, the velocity disparities are quickly eliminated, where particles are first pushed against the channel roof before being translated laterally. This is demonstrated in FIG. 4b, where despite a range of particle velocities prior to sorting, the maximum velocity magnitudes are equalized around approximately 15 cm/s with an applied power of 30 mW. Importantly, this feature of acoustic coupling also results in power-efficient translation, where the slower flow at the channel interface results in longer exposure times to the acoustic beam, resulting in equivalent lateral translation velocities for same-sized particles. The maximum translation velocities, effectively comprised of sole translation in the lateral direction, occurs within the 25 m wide sorting region. At the cessation of the SAW pulse, particles continue with the flow in the sorted outlet at a relatively uniform and low velocity, reflecting the low flow velocity at the fluid/channel interface.

(42) The percentage of sorted particles can be directly attributed to both the power and length of the applied pulses; while characterizing the effects of these parameters is important for understanding the powers and pulse times required for sorting, modifying these parameters can also be used to perform selective fractionation. FIG. 5a shows the effect of increasing applied power on the percentage of particles sorted, as measured at the outlets (particle solution contains 1 m tracer particles that are not sorted, whose path through the system is shown in FIG. 5c), where the quick transition from no sorting to near-complete sorting occurs due to the aforementioned velocity equalization with acoustic forcing at .sub.R. Sorting percentage is measured by the number of particles counted (min. 102 total) in outlet.sub.1 and outlet.sub.2 at different power levels (0-10 mW) from an input of 3 m particles subject to a constantly applied SAW. The quantity of particles dispensed can be more deterministically defined, however, by changing the pulse length. FIG. 5b demonstrates that the number of particles sorted per SAW pulse is a linear function of the pulse length, where any number of particles in the sorting volume Vs when a SAW pulse is generated are translated; additional particles arriving in this region in the continuous flow while a SAW is generated will also be sorted. The slope of this line is a function of the particle concentration C, here 0.07% vol/vol, with the average number of dispensed particles given by

(43) $\begin{array}{cc}N={\mathrm{CV}}_s\left(1+\frac{t_p{v}_f}{w}\right)& \left(2\right)\end{array}$
where t.sub.p is the pulse time, w is the sorting region width and v.sub.f is the average flow velocity in the sorting region, provided the pulse lengths are at least as long as the time it takes for a particle to translate a sufficient distance to be sorted (t.sub.pO(100 s)).

(44) An important consequence of using high frequencies is that substantially larger forces can be generated for equivalently sized particles subject to a travelling wave, as noted by the scaling in Eq. 1. This is demonstrated in FIG. 5d, where fluorescent 2 m particles are separated from a solution with 1 m particles in a continuous flow. This is the smallest size yet shown to be displaced using a travelling SAW, where recent work demonstrated the translation of particles as small as 3.2 m using a 200 MHz field..sup.42 As SAW is readily capable of generating fields up to the GHz scale, this points the way to using travelling wave forces to potentially manipulate even smaller objects.

(45) Not yet addressed is the potential for acoustic streaming to affect the flow profile in the vicinity of the focused acoustic beam. Acoustic streaming is a phenomena caused by the attenuation of the acoustic displacement amplitude as it passes through a dispersive media, including water, resulting in momentum transfer in the direction of acoustic propagation.sup.55 This phenomenon can be used to drive fluid flow for pumping or mixing.sup.72 or particle concentration, as demonstrated in FIG. 6. Here 1 m particles are concentrated in the closed fluid streamlines in the vicinity (on either side) of the acoustic beam. This phenomenon can be understood in the context of the acoustic radiation force, where the acoustic force gradient prevents particles from passing through the region of maximum beam intensity.sup.75, resulting in these particles being shifted into tighter streamlines with every pass through the focusing region. The magnitude of the acoustic force relative to the flow induced by acoustic streaming can also be altered, with viscous-shear induced drag (caused by the no-slip channel boundary conditions at the channel interfaces) resulting in an inverse relationship between flow velocity and channel height. This greater proportion of acoustic radiation force over fluid drag results in more complete particle capture in the case of smaller channel heights.

(46) FIG. 7 shows the effect of increasing acoustic streaming on the trajectory of particles through an acoustic beam. FIG. 7a demonstrates the flow regime necessary for particle sorting, where the acoustic force results in particle displacement (here displacing 2 m particles in combined 2+1 m particle solution) without substantive disturbance to the flow profile. At higher applied powers in the same flow, acoustic streaming contributes more to the local velocity profile, leading to a transitional regime (FIG. 7d) where particles are displaced both according to the direct acoustic force, but also with the fluid streamlines in the vicinity of the acoustic beam. This opens the possibility for not only particle sorting, but also particle capture and concentration in a continuous flowchanging the ratio between the flow velocities induced by acoustic streaming and those from the continuous input flow shifts the regime from one where the acoustic particle force is dominant to one where fluid drag determines particle behaviour. Acoustic streaming, however, does not substantively affect the flow profile in high flow conditions, whose flow velocities exceed those induced by the travelling wave acoustic forces necessary to induce particle displacement (of >2 m particles).

(47) The body forces that give rise to acoustic streaming can also give rise to acoustic pumping effects, with a time-averaged hydrostatic pressure differential at either end of a channel in which a SAW is present resulting in fluid translation. Moreover, acoustic cavitation can occur at high displacement amplitudes, enhancing the fluid translation effect. In FIG. 8 we demonstrate the use of a focused pulsed SAW to perform micropumping between two co-flowing fluid bodies. FIG. 8a shows the pumping concept, where fluid pumped from the lower channel displaced fluid streamlines in the upper one. A body of fluid (on the order of nanolitres or less) which would usually continue through the flow constriction in the lower channel (FIG. 8b) is pumped in the direction of SAW propagation into the upper channel with the application of this SAW pulse (FIG. 8b,c). FIG. 9 shows the effect of this pumping on suspended microparticles, where (if appropriately located relative to the pumping outlet) they are translated with the fluid in which they are suspended (circled particle in FIG. 9), likewise in the direction of SAW propagation. Combined with an appropriate upstream particle/cell detection apparatus, this method points the way toward the selective and robust sorting of suspended micro and sub-micron objects regardless of their physical properties.

4. CONCLUSIONS

(48) SAW has rightly been applied to a wide number of microfluidic applications, where their ability to generate substantial and biocompatible forces on particles, cells and droplets is an essential feature. Further, because these forces can be generated and applied locally, it is straightforward to integrate compartmentalized SAW systems with other microfluidic processes. Microfluidic high-speed sorting is one such application where SAW is ideally suited, where sufficient forces can be generated on cells using sub-ms pulses to translate them. Minimizing the width of the sorting region is essential to deterministic translation, where minimum-width standing wave transducers and limited PDMS posts have been previously demonstrated. For robust and reliable sorting in a variety of sample concentrations the sorting region should be comparable to the size of cells being processed.

(49) In this work we have demonstrated the use of highly localized acoustic fields generated by focused SAW for single-particle level displacement, where deterministic sorting is made possible using a focused beam with a width of only 25 m. As the minimum beam width is by necessity on the scale of the wavelength or larger, this is realized using a high-frequency, 386 MHz, 10 m wavelength set of FIDTs. Using pulses on the scale of 100's of s, sorting rates between 1-10 kHz can theoretically be achieved. Further, because objects with diameters down to 2 m can be translated on-demand using this frequency, varying pulse lengths can also be used to create time-varying particle concentrations. While this demonstration does not include a sensing apparatus, the integration of such an optical detection system is relatively straightforward in optically transparent materials such as LN/PDMS, or where detection based on impedance is possible through the integration of suitable electrodes..sup.76 With such integration, highly focused SAW is ideally suited to deterministic sorting and microfluidic manipulation, potentially with specimens down to the scale of bacteria. Furthermore, proper control of the applied power on the FIDTs and the flow rate of the continuous input flow can also incorporate the acoustic streaming in the vicinity of the focused acoustic beam for particle capture and concentration in a continuous flow.

(50) We have also demonstrated a device principle that is capable of similar sorting potential, though is able to accomplish this without respect to the mechanical properties or dimensions of the sorted objects. This device utilizes the newly demonstrated principle of acoustic micropumping, where the body force produced in a fluid body by a propagating acoustic wave results in an enhanced hydrostatic pressure differential when the acoustic beam is confined in a channel with similar dimensions to the beam width. The resulting fluid pumping can be used to selectively translate particles in a continuous flow in an analogous manner to that using the acoustic force on the particles directly; particles in the vicinity of the pumping channel outlet can be displaced within the fluid they are suspended in with the application of a pulsed SAW, which rapidly pumps fluid between co-flowing channels. Both of these methodologies have the potential to enhance single particle level sorting.

(51) Advantageously, particle manipulation in such a device and system of the present invention can occur resulting from either (or both) embodiments where the force imparted on the particle or particle surfaces to translate particles with respect to the surrounding fluid media, or resulting from displacement of the fluid in which the particle is suspended.

(52) Whilst there has been described in the foregoing description preferred embodiments of the present invention, it will be understood by those skilled in the technology concerned that many variations or modifications in details of design or construction may be made without departing from the present invention.

References

(53) 1 Barteneva, N. S., Ketman, K., Fasler-Kan, E., Potashnikova, D. & Vorobjev, I. A. Cell sorting in cancer researchDiminishing degree of cell heterogeneity. Biochimica et Biophysica Acta (BBA)Reviews on Cancer 1836, 105-122 (2013). 2 Qi, W. et al. Sorting and identification of side population cells in the human cervical cancer cell line HeLa. Cancer Cell Int 14, 3 (2014). 3 Garner, D. L., Evans, K. M. & Seidel, G. E. in Spermatogenesis 279-295 (Springer, 2013). 4 Wang, B. L. et al. Microfluidic high-throughput culturing of single cells for selection based on extracellular metabolite production or consumption. Nat. Biotechnol. 32, 473-478 (2014). 5 Fung, E. et al. High-throughput screening of small molecules identifies hepcidin antagonists. Mol. Pharmacol. 83, 681-690 (2013). 6 Lab on a Chip Proc Natl Acad Sci USA Ultrasonics, F., and Frequency Control, IEEE Transactions on Journal of Micromechanics and Microengineering Segers, Tim & Versluis, M. Acoustic bubble sorting for ultrasound contrast agent enrichment. Lab Chip 14, 1705-1714 (2014). 7 Xia, Y. et al. in Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS), 2015 Transducers-2015 18th International Conference on. 1814-1817 (IEEE). 8 Alix-Panabires, C. & Pantel, K. Technologies for detection of circulating tumor cells: facts and vision. Lab Chip 14, 57-62 (2014). 9 Antfolk, M., Magnusson, C., Augustsson, P., Lilja, H. & Laurell, T. Acoustofluidic, label-free separation and simultaneous concentration of rare tumor cells from white blood cells. Anal. Chem. (2015). 10 Collins, D. J., Alan, T. & Neild, A. Particle separation using virtual deterministic lateral displacement (vDLD). Lab Chip 14, 1595-1603 (2014). 11 Kim, H., Lee, S., Lee, J.-h. & Kim, J. Integration of a microfluidic chip with a size-based cell bandpass filter for reliable isolation of single cells. Lab Chip (2015). 12 Ai, Y., Sanders, C. K. & Marrone, B. L. Separation of Escherichia coli bacteria from peripheral blood mononuclear cells using standing surface acoustic waves. Anal. Chem. 85, 9126-9134 (2013). 13 Zborowski, M. & Chalmers, J. J. Rare cell separation and analysis by magnetic sorting. Anal. Chem. 83, 8050-8056 (2011). 14 Hejazian, M., Li, W. & Nguyen, N.-T. Lab on a chip for continuous-flow magnetic cell separation. Lab Chip 15, 959-970 (2015). 15 Robert, D. et al. Cell sorting by endocytotic capacity in a microfluidic magnetophoresis device. Lab Chip 11, 1902-1910 (2011). 16 Laurell, T., Petersson, F. & Nilsson, A. Chip integrated strategies for acoustic separation and manipulation of cells and particles. Chem. Soc. Rev. 36, 492-506 (2007). 17 Nam, J., Lim, H., Kim, C., Kang, J. Y. & Shin, S. Density-dependent separation of encapsulated cells in a microfluidic channel by using a standing surface acoustic wave. Biomicrofluidics 6, 024120 (2012). 18 Schor, A. & Buie, C. in Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS), 2015 Transducers-2015 18th International Conference on. 1617-1620 (IEEE). 19 McFaul, S. M., Lin, B. K. & Ma, H. Cell separation based on size and deformability using microfluidic funnel ratchets. Lab Chip 12, 2369-2376 (2012). 20 Wu, T.-H. et al. Pulsed laser triggered high speed microfluidic fluorescence activated cell sorter. Lab Chip 12, 1378-1383 (2012). 21 Shaker, M., Colella, L., Caselli, F., Bisegna, P. & Renaud, P. An impedance-based flow microcytometer for single cell morphology discrimination. Lab Chip 14, 2548-2555 (2014). 22 Song, H. et al. A microfluidic impedance flow cytometer for identification of differentiation state of stem cells. Lab Chip 13, 2300-2310 (2013). 23 Bonner, W., Hulett, H., Sweet, R. & Herzenberg, L. Fluorescence activated cell sorting. Rev. Sci. Instrum. 43, 404-409 (1972). 24 Guo, M. T., Rotem, A., Heyman, J. A. & Weitz, D. A. Droplet microfluidics for high-throughput biological assays. Lab Chip 12, 2146-2155 (2012). 25 Collins, D. J., Neild, A., deMello, A., Liu, A.-Q. & Ai, Y. The Poisson distribution and beyond: methods for microfluidic droplet production and single cell encapsulation. Lab on a Chip 15, 3439-3459 (2015). 26 Chen, Y. et al. Pulsed laser activated cell sorting with three dimensional sheathless inertial focusing. small 10, 1746-1751 (2014). 27 Nan, L., Jiang, Z. & Wei, X. Emerging microfluidic devices for cell lysis: a review. Lab Chip 14, 1060-1073 (2014). 28 Wiklund, M. Acoustofluidics 12: Biocompatibility and cell viability in microfluidic acoustic resonators. Lab Chip 12, 2018-2028 (2012). 29 Hammarstrm, B. et al. Non-contact acoustic cell trapping in disposable glass capillaries. Lab Chip 10, 2251-2257 (2010). 30 Wiklund, M. et al. Ultrasound-induced cell-cell interaction studies in a multi-well microplate. Micromachines 5, 27-49 (2014). 31 Sivanantha, N. et al. Characterization of adhesive properties of red blood cells using surface acoustic wave induced flows for rapid diagnostics. Applied Physics Letters 105, 103704 (2014). 32 Ding, X. et al. On-chip manipulation of single microparticles, cells, and organisms using surface acoustic waves. Proc. Natl. Acad. Sci. U.S.A. 109, 11105-11109 (2012). 33 Leibacher, I., Hahn, P. & Dual, J. Acoustophoretic cell and particle trapping on microfluidic sharp edges. Microfluidics and Nanofluidics, 1-11 (2015). 34 Yeo, L. Y. & Friend, J. R. Surface acoustic wave microfluidics. Annu. Rev. Fluid Mech. 46, 379-406 (2014). 35 Jakobsson, O., Grenvall, C., Nordin, M., Evander, M. & Laurell, T. Acoustic actuated fluorescence activated sorting of microparticles. Lab Chip 14, 1943-1950 (2014). 36 Nawaz, A. A. et al. Acoustofluidic Fluorescence Activated Cell Sorter. Anal. Chem. 87, 12051-12058 (2015). 37 Ren, L. et al. A high-throughput acoustic cell sorter. Lab Chip 15, 3870-3879 (2015). 38 Ding, X. et al. Standing surface acoustic wave (SSAW) based multichannel cell sorting. Lab Chip 12, 4228-4231 (2012). 39 Destgeer, G. et al. Microchannel Anechoic Corner for Size-Selective Separation and Medium Exchange via Traveling Surface Acoustic Waves. Anal. Chem. 87, 4627-4632 (2015). 40 Collins, D. J. et al. Atomization off thin water films generated by high-frequency substrate wave vibrations. Phys. Rev. E 86, 056312 (2012). 41 Destgeer, G. et al. Adjustable, rapidly switching microfluidic gradient generation using focused travelling surface acoustic waves. Appl. Phys. Lett. 104, 023506 (2014). 42 Destgeer, G., Ha, B. H., Jung, J. H. & Sung, H. J. Submicron separation of microspheres via travelling surface acoustic waves. Lab Chip 14, 4665-4672 (2014). 43 Bourquin, Y. & Cooper, J. M. Swimming Using Surface Acoustic Waves. PloS one 8, e42686 (2013). 44 Behrens, J. et al. Microscale anechoic architecture: acoustic diffusers for ultra low power microparticle separation via traveling surface acoustic waves. Lab Chip 15, 43-46 (2015). 45 Shilton, R. J., Travagliati, M., Beltram, F. & Cecchini, M. Nanoliterdroplet acoustic streaming via ultra high frequency surface acoustic waves. Adv. Mater. 26, 4941-4946 (2014). 46 Franke, T., Braunmliller, S., Schmid, L., Wixforth, A. & Weitz, D. Surface acoustic wave actuated cell sorting (SAWACS). Lab Chip 10, 789-794 (2010). 47 Schmid, L., Weitz, D. A. & Franke, T. Sorting drops and cells with acoustics: acoustic microfluidic fluorescence-activated cell sorter. Lab Chip 14, 3710-3718 (2014). 48 Skowronek, V., Rambach, R. W., Schmid, L., Haase, K. & Franke, T. Particle deflection in a poly (dimethylsiloxane) microchannel using a propagating surface acoustic wave: size and frequency dependence. Analytical chemistry 85, 9955-9959 (2013). 49 Bourquin, Y., Wilson, R., Zhang, Y., Reboud, J. & Cooper, J. M. Phononic crystals for shaping fluids. Adv. Mater. 23, 1458-1462 (2011). 50 Cooper, J. Use of phononic materials in microfluidic & lab-on-a-chip manipulations. J. Acoust. Soc. Am. 131, 3303-3303 (2012). 51 Reboud, J. et al. Shaping acoustic fields as a toolset for microfluidic manipulations in diagnostic technologies. Proc. Natl. Acad. Sci. U.S.A. 109, 15162-15167 (2012). 52 Reboud, J. et al. Nebulisation on a disposable array structured with phononic lattices. Lab Chip 12, 1268-1273 (2012). 53 Salehi-Reyhani, A. et al. Chemical-Free Lysis and Fractionation of Cells by Use of Surface Acoustic Waves for Sensitive Protein Assays. Anal. Chem. 87, 2161-2169 (2015). 54 Witte, C., Reboud, J., Wilson, R., Cooper, J. & Neale, S. Microfluidic resonant cavities enable acoustophoresis on a disposable superstrate. Lab Chip 14, 4277-4283 (2014). 55 Dentry, M. B., Friend, J. R. & Yeo, L. Y. Continuous flow actuation between external reservoirs in small-scale devices driven by surface acoustic waves. Lab Chip 14, 750-758 (2014). 56 Collins, D. J., Alan, T., Helmerson, K. & Neild, A. Surface acoustic waves for on-demand production of picoliter droplets and particle encapsulation. Lab Chip 13, 3225-3231 (2013). 57 Collins, D. J., Alan, T. & Neild, A. The particle valve: On-demand particle trapping, filtering, and release from a microfabricated polydimethylsiloxane membrane using surface acoustic waves. Appl. Phys. Lett. 105, 033509 (2014). 58 Ai, Y. & Marrone, B. L. Droplet translocation by focused surface acoustic waves. Microfluid. Nanofluid. 13, 715-722 (2012). 59 Sesen, M., Alan, T. & Neild, A. Microfluidic on-demand droplet merging using surface acoustic waves. Lab Chip (2014). 60 Settnes, M. & Bruus, H. Forces acting on a small particle in an acoustical field in a viscous fluid. Phys. Rev. E 85, 016327 (2012). 61 King, L. V. in Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. 212-240 (The Royal Society). 62 Hasegawa, T. & Yosioka, K. AcousticRadiation Force on a Solid Elastic Sphere. J. Acoust. Soc. Am. 46, 1139-1143 (1969). 63 Qi, Q. & Brereton, G. J. Mechanisms of removal of micron-sized particles by high-frequency ultrasonic waves. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42, 619-629 (1995). 64 Ma, Z., Collins, D. J. & Ai, Y. A detachable acoustofluidic system for particle separation via a travelling surface acoustic wave. Anal. Chem. 88, 5316-5323 (2016). 65 Skowronek, V., Rambach, R. W., Schmid, L., Haase, K. & Franke, T. Particle deflection in a poly(dimethylsiloxane) microchannel using a propagating surface acoustic wave: size and frequency dependence. Anal. Chem. 85, 9955-9959, doi:10.1021/ac402607p (2013). 66 Dentry, M. B., Yeo, L. Y. & Friend, J. R. Frequency effects on the scale and behavior of acoustic streaming. Phys. Rev. E 89, 013203 (2014). 67 Nyborg, W. L. Acoustic streaming due to attenuated plane waves. J. Acoust. Soc. Am. 25, 68-75 (1953). 68 Collins, D. J., Neild, A. & Ai, Y. Highly focused high-frequency travelling surface acoustic waves (SAW) for rapid single-particle sorting. Lab Chip 16, 471-479 (2016). 69 Destgeer, G., Lee, K. H., Jung, J. H., Alazzam, A. & Sung, H. J. Continuous separation of particles in a PDMS microfluidic channel via travelling surface acoustic waves (TSAW). Lab Chip 13, 4210-4216 (2013). 70 Collins, D. J., Ma, Z. & Ai, Y. Highly Localized Acoustic Streaming and Size-Selective Submicrometer Particle Concentration Using High Frequency Microscale Focused Acoustic Fields. Anal. Chem. 88, 5513-5522 (2016). 71 Holm, A., Stirzer, Q., Xu, Y. & Weigel, R. Investigation of surface acoustic waves on LiNbO 3, quartz, and LiTaO 3 by laser probing. Microelectron. Eng. 31, 123-127 (1996). 72 Shilton, R., Tan, M. K., Yeo, L. Y. & Friend, J. R. Particle concentration and mixing in microdrops driven by focused surface acoustic waves. J. Appl. Phys. 104, 014910 (2008). 73 Basu, A. S. Droplet morphometry and velocimetry (DMV): a video processing software for time-resolved, label-free tracking of droplet parameters. Lab Chip 13, 1892-1901 (2013). 74 Langelier, S. M., Yeo, L. Y. & Friend, J. UV epoxy bonding for enhanced SAW transmission and microscale acoustofluidic integration. Lab Chip 12, 2970-2976 (2012). 75 Gor'Kov, L. in Soviet Physics Doklady. 773. 76 Schoendube, J., Wright, D., Zengerle, R. & Koltay, P. Single-cell printing based on impedance detection. Biomicrofluidics 9, 014117 (2015).