Lab on a Chip

PAPER

Cite this: Lab Chip, 2016, 16, 3024

Received 19th November 2015,Accepted 12th January 2016

DOI: 10.1039/c5lc01420d

www.rsc.org/loc

Onset of particle trapping and release via acousticbubbles

Yun Chen,a Zecong Fang,b Brett Merritt,b Dillon Strack,a Jie Xu*c and Sungyon Lee*a

Trapping and sorting of micro-sized objects is one important application of lab on a chip devices, with the

use of acoustic bubbles emerging as an effective, non-contact method. Acoustically actuated bubbles are

known to exert a secondary radiation force (FSR) on micro-particles and stabilize them on the bubble sur-

face, when this radiation force exceeds the external hydrodynamic forces that act to keep the particles in

motion. While the theoretical expression of FSR has been derived by Nyborg decades ago, no direct experi-

mental validation of this force has been performed, and the relationship between FSR and the bubble's abil-

ity to trap particles in a given lab on a chip device remains largely empirical. In order to quantify the con-

nection between the bubble oscillation and the resultant FSR, we experimentally measure the amplitude of

bubble oscillations that give rise to FSR and observe the trapping and release of a single microsphere in the

presence of the mean flow at the corresponding acoustic parameters using an acoustofluidic device. By

combining well-developed theories that connect bubble oscillations to the acoustic actuation, we derive

the expression for the critical input voltage that leads to particle release into the flow, in good agreement

with the experiments.

1. Introduction

In the past two decades, microfluidics technology has becomean emerging field that allows precise control of fluid behaviorat the microscale level.1,2 Based on microfluidics technology,functional units, such as pumps, valves, sensors, and actua-tors, can be miniaturized and integrated into a small micro-fluidic chip to form a lab on a chip system,3,4 which is nowfinding numerous applications in chemistry,5 biology,6–8 med-icine,9,10 biotechnology,11 food science12 and environmentalengineering.13 One of the most important functions in lab ona chip applications is the manipulation of micro-sized ob-jects, including reagents, particles, cells, and microorganisms.Various methods have been developed for manipulation in amicrofluidic environment. These methods often harness in-teractions between fluids and multi-physics phenomena, suchas the electric field,14–19 magnetic field,20–23 electromagneticfield,24–26 temperature field27,28 and centrifugal forcefield.29,30 In recent years, acoustics has also started to attractattention as an alternative source that can be utilized for ma-nipulation of micro-objects in microfluidics, and a new termacoustofluidics has gained popularity in the research

community.31,32 Compared with other actuation techniques,acoustic methods offer many advantages, such as versatility,compactness, a non-contact feature and relatively simple op-eration. However, the interactions between fluids and anacoustic field can be quite complex. Fig. 1 briefly summarizes

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aDepartment of Mechanical Engineering, Texas A & M University, College Station,

TX 77840, USA. E-mail: sungyon.lee@tamu.edubDepartment of Mechanical Engineering, Washington State University, Vancouver,

WA 98686, USAc Department of Mechanical and Industrial Engineering, University of Illinois,

Chicago, IL 60607, USA. E-mail: jiexu@uic.edu

Fig. 1 Diagram showing different interactions between acousticactuation and fluid flows. The microbubble oscillation caused by anacoustic field is in the secondary interaction category. The oscillatingbubble can impact the objects in the nearby field generatingmicrostreaming flows and secondary radiation forces, FSR. In thisstudy, we focus on the effect of the FSR.

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the possible acoustic effects that may arise when acousticsand fluids encounter at the microscale level.

Two types of interactions have been explored in the past.One is to directly use the interactions between the objectsand acoustic waves, which include the surface waves33,34 orbulk standing waves.35,36 The other is to harness the second-ary acoustic effects in the vicinity of the solid structures in-cluding microchambers37 and sharp edges,38 or most often,microbubbles.39,40 In particular, microbubbles oscillating inan acoustic field can be categorized into inertial or non-inertial types depending on the oscillation magnitude. Iner-tial bubble oscillation, or inertial cavitation, is very violent,unstable, and transient, resulting in liquid jetting in the caseof the asymmetrical bubble collapse, or energy emitting viashock waves or light.41 This particular mode of acoustic bub-bles has been widely used in medical ultrasonics.42–45 Non-inertial microbubble oscillation is much gentler with variousstable oscillation modes that may be observed in the form ofinterfacial waves.46,47 Non-inertial microbubbles may influ-ence the surrounding objects by generating microstreamingflows,48–50 or by exerting a secondary radiation force, FSR.

51,52

Most bubble-based lab on a chip systems to date utilizenon-inertial microbubbles, due to the fact that non-inertialmicrobubbles are more stable and can be easily controlledboth spatially and temporally in a microfluidic environment.For example, the secondary radiation force from an oscillat-ing bubble can be used to trap micro-objects, while the posi-tion of the bubble itself can be controlled by using an electro-wetting technique53 or simply attaching the bubble to atraverse rod.54 If an array of bubbles is fixed inside a micro-channel and acoustically actuated, a trapping zone will formnear the oscillating bubbles, which can be used to enrich,sort and manipulate C. elegans in a flow.55 Moreover, if ex-cited with maximized microstreaming flows, spatially ar-ranged bubbles in a microchannel can be used as fixatedtransporters.56–59 Other notable applications involving acous-tic bubbles include enhanced mixing,60 pumping flow in amicrochannel,61,62 switching particle pathlines,63 switchingflow optical properties,64 assembling and driving micro-rotors,65 generating chemical gradients66 and propellingobjects.67,68

Although applications of acoustic bubbles in lab on a chipsystems have witnessed tremendous progress recently, theoperating conditions of the experiments are largely deter-mined empirically in most applications mentioned above,and there exists a lack of theoretical guidance for designingdevices. Indeed, it has been shown that even for a simplestraight 1D channel, the actual outcome of the acoustic actu-ation is difficult to predict using theoretical or numericalmethods.69 Therefore, for any given device, initial experimen-tal validation is important for any further theoretical ormodeling efforts. One particular area of acoustofluidics withthe latest theoretical development is microstreamingflows,57,70–75 as both the microstreaming flow field and its ef-fect on micro-sized objects have been resolved analytically intwo-dimensional and quasi-three dimensional geometries.

On the contrary, while the theoretical expression of FSR hasbeen developed by Nyborg76 and Doinikov,77 it has not beenexperimentally verified or implemented to directly quantifythe bubble's ability to trap a given micro-object in micro-fluidic devices. For instance, Xu et al.55 and Neild et al.78

demonstrated trapping of microworms and microspheres, re-spectively, via acoustically actuated bubbles that exert sec-ondary radiation forces. However, no measurement of bubbleoscillations has been made to connect the amplitude of bub-ble oscillations to the FSR, then to the ability of the bubblesto trap particles. The authors also reported the critical volt-ages at a given frequency that lead to particle trapping but of-fered no quantitative analysis that connects the critical acous-tic parameters to the FSR.

In order to address this current lack of quantitative analy-sis of the FSR, we hereby present the combined experimentaland theoretical studies on particle trapping and release viaan acoustic bubble in a simple 1D microfluidic channel. Thiswill serve as an important first step towards more compre-hensive future studies. Experimentally, we quantify the bub-ble's ability to stabilize a particle in two ways: first, by mea-suring the critical acoustic input at which a pre-loadedparticle is released into the flow (Exp A); secondly, by measur-ing the critical acoustic voltage and frequency at which a par-ticle is directed towards the bubble and is stabilized (Exp B).The corresponding amplitudes of bubble oscillations thatgive rise to the FSR are also measured. Furthermore, to isolatethe effects of the FSR from all other forces acting on the parti-cle, we keep the flow rate inside the channel constant to en-sure that the relative effects of the microstreaming flows maybe neglected in our study. In addition, we combine the well-developed theories that connect bubble oscillations yieldingFSR to the acoustic actuation to theoretically derive the criti-cal voltage.

Following the experimental method and image processingin section 2, the experimental results are reported in section3.1, consisting of the bubble oscillation magnitudes and thecorresponding behavior of the microsphere at given voltagesand frequencies. Sections 3.2 and 3.3 include the theoreticalanalysis to calculate the critical input voltage that leads tothe particle release into the mean flow, in reasonable agree-ment with the experiments. The summary and future direc-tions are given in section 4.

2. Methods and materials2.1. Experimental setup

The experimental apparatus used in this study includes atransparent microfluidic chip, a piezoelectric transducer, andan aluminum block base, as shown in Fig. 2(a). The micro-fluidic channel (depth 2.79 mm × height 1.35 mm × length14.01 mm) has been micro-milled out of PMMA and is sealedwith PDMS and plastic sheets, with two flat needles (Lab Ex-press Management) used as an inlet and an outlet. The chan-nel also consists of a cylindrical cavity with a diameter of 254μm which is treated with a superhydrophobic coating (Rain-X)

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to serve as a pre-defined site of bubble formation and stabili-zation.79 An additional cylindrical cavity is drilled from theside to incorporate a miniature screw to actively control thebubble volume and is sealed by ultrasound gel (Aquasonic100, Parker Laboratories), as shown in Fig. 2(c).

In our experiment setup, an air bubble forms automati-cally inside the cavity and remains stable when the solutionwith polystyrene microspheres (25–30 μm radius, ThermoFisher Scientific) is introduced into the main channelthrough a syringe pump at a constant flow rate of 4 mLmin−1 (NE-1000, New Era Pump Systems). Following the bub-ble formation, the screw is actively adjusted to achieve thedesired bubble radius, typically in the range of 140–160 μm.We use a piezoelectric transducer (20 mm × 2 mm)sandwiched between the PMMA chip and an aluminum blockto excite the channel periodically using a function generator(DG1022, Rigol Technologies) and an amplifier (7602 M,Krohn-Hite). The driving frequency, f, ranges from 20 kHz to36 kHz with an increment of 1 kHz, while the driving voltage,V, is varied from 10 V to 190 V at each frequency.

Two sets of experiments are conducted to quantify thethreshold acoustic parameters for particle trapping and re-lease, as depicted in Fig. 3(a) and (b). In the first set (Exp A),we observe particles that have been stabilized onto the bub-ble surface at a high voltage being released into the externalflow as the voltage is decreased. The critical voltage, Vc , atwhich the particles are released is recorded for a given fre-quency, f. In the second set (Exp B), we measure the criticalvoltage, Vc, at which an acoustic bubble is able to trap parti-cles originally in motion for varying f. Image sequences ofthe particle release and trapping processes in Exp A and ExpB are shown in Fig. 3(d) and (e), respectively. The experi-ments are recorded using a high-speed camera (PhantomMiro M310, Vision Research) from the side of the micro-channel. For each experiment at a given V and f, the interac-tion between the bubble and particle is captured at 1000 fps(240 × 320 pixels) to produce the images in Fig. 3(d) and (e),

while the bubble oscillations are recorded at 120 171 fps(128 × 128 pixels) with the resultant images shown inFig. 4(a) and (b).

2.2. Data analysis

To measure the bubble oscillation amplitude, we use aMATLAB Canny function to detect the edge of the oscillatingbubble as shown in Fig. 4(a). Once the coordinates of thebubble edge has been determined, the least squares errormethod is used to find a circle that best fits the edge(Fig. 4(b)). Fig. 4(c) shows one example of the oscillation dis-placement at 21 kHz and 190 V as a function of the framenumber calculated using the instantaneous bubble radius,RIJt), minus the equilibrium bubble radius Rb = 152.5 μm over100 frames. The bubble amplitude is subsequently calculatedby averaging over the local maxima of |RIJt) − Rb|. The consis-tency and periodicity of the displacement in Fig. 4(c) demon-strate the effectiveness of our data analysis method.

3. Results3.1. Experimental data

The dimensionless amplitude, ξ, of the bubble oscillation(scaled by the bubble radius, Rb) is extracted from the singlebubble oscillation videos of Exp B and is plotted as a func-tion of f for a given V in Fig. 5(a). The plot shows that the os-cillation amplitude generally increases with V but variesnonlinearly with f. We divide the plot into four different re-gimes depending on the behavior of ξ as a function of

Fig. 2 (a) A perspective view of the device: the piezoelectrictransducer is sandwiched between the transparent PMMA chip and analuminum block. (b) A side view of the chip: the microchannel is milledon top of the chip. DI water is injected from the inlet and the sphericalbubble is constrained on the bottom of the channel. (c) A miniaturescrew is used to control the bubble volume. (d) Once the piezoelectrictransducer is excited, the bubble starts oscillating and generates asecondary radiation force to trap particles.

Fig. 3 (a) In Exp A, the particle is first trapped on the surface of thebubble. The critical voltage, Vc, at which the particles are released isrecorded as the voltage is decreased for a given frequency, f. (b) In ExpB, we measure the critical voltage, Vc, at which an acoustic bubble isable to trap particles originally in motion for varying f. (c) Here Rb andRp are the radii of the bubble and particle, respectively, while d is thecenter-to-center distance between the particle and bubble. Imagesdepicting particle trajectories are included in (d) and (e), respectively.

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voltage, which is explained in more detail in section 3.3. Inparticular, the acoustic bubble exhibits a resonant behavioraround f = 21 kHz and 35 kHz, which matches the device res-onance shown in Fig. 5(b). The bubble resonant behavior ap-pears to intensify with V at f = 35 kHz, as the bubble switchesfrom volumetric to shape oscillations for V greater than 30 V.In this study, we will only focus on the effect of volumetricoscillations on the particles and neglect the data range for V> 30 V at 35 kHz.

The particle and bubble interaction data are summarizedin the f–V phase diagram in Fig. 6(a): the triangular markersindicate the critical voltages for a given f at which the parti-cles are released from the bubble (Exp A), while the dotsmark the frequencies and voltages at which the particles aretrapped and remain on the bubble surface (Exp B). While thethreshold release voltages are consistently lower than theminimum trapping voltages, they follow the same generaltrend for varying f. In addition, no particle trapping and sub-sequent release are observed between 22 kHz and 25 kHz, aswell as at 30 kHz for both experimental sets.

The phase diagram is overlaid with the gray scale map of ξfrom Exp B, to show the correlation between the oscillationamplitudes and the bubble's ability to trap particles. We ob-serve that the dot markers (trapped particle) tend to appear

in the regime where the oscillation amplitude is higher than0.2%. The critical bubble amplitudes, ξc, at the onset of parti-cle releasing or trapping are plotted as a function of f inFig. 6(b). Except for f = 35 kHz, most values of ξc fall in therange between 0.2 and 0.8%.

3.2. Critical secondary radiation force

The qualitative physical mechanism (from acoustic actuationto bubble oscillation) behind particle trapping via an acousticbubble is summarized in the flow chart in Fig. 7 (top row). Inorder to derive the critical input voltage, Vc, that leads to par-ticle trapping for a given f, each stage of the flow chart is con-sidered quantitatively by employing the following three steps(Fig. 7 bottom row): first, a force balance between the attrac-tive secondary radiation force and the net hydrodynamicforce on the particle to derive the critical bubble oscillation,ξc; second, a linearized Rayleigh–Plesset equation to solve forthe critical pressure, P′c, needed to generate ξc; finally, a re-duced Helmholtz equation to relate P′c to the critical appliedvoltage, Vc, to address the current lack of direct pressuremeasurement inside the microchannel. The details of each

Fig. 4 (a) The edge of the bubble is first detected using the MatlabCanny function. (b) The least squares error method is used to find acircle that best fits the edge. (c) The plot shows the displacement of anoscillation bubble versus frame number at 21 kHz and 190 V calculatedusing a fitted circle.

Fig. 5 (a) Dimensionless bubble amplitude ξ as a function offrequency f at various voltages. The plot shows that the magnitude ofthe oscillation amplitude generally increases with V but variesnonlinearly with f. We divide the plot into 4 different regimesdepending on the behavior of the amplitude as a function of voltage.(b) Device vibration amplitude, lref, as a function of frequency at 3 V.The plot shows two peaks at 21 kHz and 35 kHz. (c) The snapshot ofthe oscillating bubble excited at 35 kHz shows that the bubbleswitches from volumetric to shape oscillations for V greater than 30 V.

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quantitative analysis are included in sections 3.2 & 3.3, culmi-nating in the plot of Vc at a given f (Fig. 9(b)) in good agree-ment with the experimental data.

The secondary radiation force, FSR, refers to the near-fieldattractive or repulsive force between the bubble and an objectdue to the pressure waves generated by the oscillating bub-ble.40 The initial theoretical development of the secondary ra-diation force was made by Nyborg76 who derived the follow-ing expression for the FSR,

(1)

where ρl and ρp are the liquid and particle densities, respec-tively; Rp corresponds to the particle radius, and d is thecenter-to-center distance between the bubble and particle; ω= 2πf is the radian frequency. Doinikov77,80–82 extended thework of Nyborg to derive a more general expression for theFSR, which reduces to eqn (1) in the limit of Rp/d ≪ 1. In ourcurrent experiments, Rp/d ∼ 0.1, so that the expression byNyborg is valid. Here, the primary acoustic radiation forcegenerated by the vibrating microchannel itself is neglected,as the wavelength of the acoustic pressure in our case (∼60

Fig. 6 (a) Phase diagram of the experimental results from Exp A and B.The triangular markers represent the voltages at which the particlesare released, while the dot markers correspond to particle trapping.The gray scale map gives the magnitude of the oscillation amplitude ξ

of the bubble from Exp B. (b) Critical oscillation amplitude, ξc, as afunction of frequency, f, with the empirical fit to Exp A as a dashedline.

Fig. 7 Flow chart of the working mechanism and correspondingtheory for particle trapping. Upon the piezoelectric actuation, thebubble oscillates in response to acoustic pressure waves, and, in turn,generates a secondary radiation force, FSR. The bottom row includesthe mathematical models that inform each physical process.

Fig. 8 (a) Images showing the particle location at the onset of release(Exp A) and trapping (Exp B). The top row confirms that the particlesare consistently released from the bubble stagnation point, while thebottom row images indicate the particle location upon trapping varieswith the frequency. (b) Schematic of a particle located at the bubblestagnation point. The secondary radiation force, FSR, must balance thehydrodynamic force, FD, that tends to pull the particle off the bubblesurface. (c) Critical secondary radiation force, FSRc, as a function offrequency f. The values for the FSR for Exp A appear constant,corresponding to the consistent release location. The zoom-in plotshows the values from 20 kHz to 30 kHz. In contrast, the values of theFSRc for Exp B show dependency on f.

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mm) is much greater than the channel height (1.35 mm) andyields no spatial pressure gradient.83

To isolate the effects of the FSR from all other forces actingon the particle, the flow rate is fixed at 4 mL min−1, so thatthe mean channel velocity, ue, is an order of magnitudegreater than the characteristic microstreaming velocity,73 us =ξ2Rbω. As the effects of the microstreaming flows can beneglected in our current setup,84,85 with ue/us ∼ OIJ101) , thehydrodynamic effects on the particle are independent of theinput voltage and frequency and only vary as a function ofthe particle's location with respect to the bubble. Further-more, as shown in Fig. 8(a), the release location of the parti-cle is observed to match the stagnation point of the bubblefor all frequencies, ensuring that the net hydrodynamic forceon the particle, FD, must be constant for Exp A, while the par-ticle trapping location in Exp B varies between experimentalruns. Therefore, for the sake of simplicity, all the theoreticalconsideration from hereon will be limited to Exp A.

Based on the simple force balance depicted in Fig. 8(b), inthe critical moment of particle release from the stagnation

point, FD must balance the threshold secondary radiationforce, FSRc, needed to hold the particle on the bubble (i.e., ifFSR < FSRc, the particle is released from the bubble). By plug-ging in the experimental values of ξc in eqn (1), the FSRc iscalculated and plotted in Fig. 8(c) to reveal that the FSRc is in-deed constant for Exp A (triangle), as FSRc = FD = constant.On the other hand, FD can be estimated by considering amodified Stokes drag on a sphere (i.e., micro-particle)experiencing a local straining flow near the stagnation pointof another spherical obstacle (i.e., bubble). Valid in the limitof Rp/Rb ≪ 1, Goren and O'Neill86 derived the expression forthis modified drag as

(2)

where U∞ is the external flow velocity at infinity, and μ is theliquid viscosity; f0 is the correction factor that varies with theparticle distance from the obstacle. While this expression hasbeen derived for a solid obstacle that satisfies a no-slipboundary condition on the surface, it is reasonable to assumethat the same functional relationship will hold for a bubbleas an obstacle but with a different value of f0.

Finally, by balancing the FSRc (eqn (1)) with the FD (eqn(2)), we can derive an expression for ξc upon particle release,

(3)

where the value of the correction factor, f0, is found by empir-ically fitting eqn (3) to the data in Fig. 6(b). This allows us toquantify how the threshold bubble oscillation must dependon the different physical parameters of the system, in partic-ular, the driving frequency, f.

3.3. Threshold acoustic parameter

For isotropic, volumetric bubble oscillations, the relationshipbetween the resultant oscillation amplitude and the drivingpressure is given by the Rayleigh–Plesset equation,87,88

(4)

where R is the instantaneous bubble radius as a function oftime and the overhead dot refers to differentiation with re-spect to time. Here, pg and p correspond to the internal andexternal driving pressures of the bubble, respectively, while σ

is the surface tension of the water/air interface. Since thebubble oscillation amplitude in our experiments is less than1%, we may linearize the Rayleigh–Plesset equation by as-suming R = R0 + R′ and p = p0 + p′, where R′ and p′ are thesmall perturbations of the bubble radius and driving pres-sure (i.e., R′/R0 ≪ 1 and p′/p0 ≪ 1). The solution to the linear-ized Rayleigh–Plesset equation yields a linear relationship be-tween p′ and R′:

Fig. 9 (a) Dimensionless pressure p′/(ρlf2hlref) as a function of voltage

V/Vref. The pressure increases in an approximately linear fashion inregime I, II and IV at different rates, K, while the pressure increasesnonlinearly in regime III. (b) The dashed curve corresponds to thetheoretical result, Vc (eqn (11)), based on the empirical values of K.

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p′ = R′/G, (5)

where

(6)

and

(7)

with γ = 1.4 as the gas constant. Here we define the Reynoldsnumber, Reb = ρlRbIJRbω)/μ, the capillary number, Cab =μ(Rbω)/σ, and the Weber number, Web = ρlIJωRb)

2Rb/σ, specificto the acoustic bubble, respectively. Since R′c = ξcRb, eqn (5)allows us to solve for the critical driving pressure, p′c = R′c/G.

The pressure field generated by the acoustic actuation ofthe device can be solved based on the Helmholtz equation,89

∇2p′ + k2p′ = 0, (8)

where the wave number k is given by k ∼ ω/ca, and ca is thespeed of sound in water. In the case of one-dimensionalpropagation of pressure waves, the solution to the Helmholtzequation is given by

(9)

where l is the device vibration amplitude. For simplicity, thedevice amplitude is assumed to increase linearly with V, or l= KlrefV/Vref, where lref is the reference device amplitude at 3 Vshown in Fig. 5(b), and K is the fitting parameter whose valuedepends on the voltage regime. Since kx ≪ 1 and kh ≪ 1, weuse the Taylor expansion to further simplify p′ to

(10)

where h is the channel half-height.Finally, combining eqn (3), (5) and (10) leads to the ex-

pression for the critical voltage that leads to particle releaseat a given frequency:

(11)

where

J( f ) = KGlrefWeb f. (12)

Each term in JIJ f ) is a function of the excitation frequency,f; here we define an alternate Reynolds number with respect

to the micro-channel as Reh = ρlU∞h/μ. This theoretical func-tion of the critical voltage must depend on the experimentalparameters (i.e., the particle and bubble radii). For instance,Vc is shown to decrease with increasing channel height, h.The quantification of Vc for particle release and trapping viaan acoustic bubble will allow the optimization of lab on achip operating conditions to trap or sort micro-sized objects.

The value of the fitting parameter, K, that relates the de-vice amplitude to the bubble amplitude, or the driving pres-sure, can be extracted by calculating the pressure, p′, basedon eqn (5) for varying V. The corresponding dimensionlessplot is shown in Fig. 9(a), which clearly exhibits four differentvoltage regimes for varying f. In regimes I, II, and IV, thepressure increases in an approximately linear fashion withthe voltage at different rates, or K, while the pressure variesnonlinearly with the voltage in regime III. By plugging in theempirical values of K into eqn (11), we plot the critical voltageVc for varying f (dashed line) on the experimental phase dia-gram in Fig. 9(b), in particularly good agreement with Exp A.Notably, our current theoretical results can be easily extendedto other acoustic devices by simply updating the reference de-vice vibration amplitude lref and K in eqn (12) to match theparticular experimental setup.

4. Conclusions

In summary, we have hereby quantified the secondary radia-tion force, FSR, of an acoustic bubble used to trap micro-objects in lab on a chip systems, by combining experimentsand reduced modeling. Experimentally, we measure the mini-mum input voltage at a given f needed for a single acousticbubble to generate sufficient FSR to trap and stabilize amicrosphere entrained in a flow. This critical voltage is exper-imentally tested in two ways: by recording the maximum volt-age at which an already attached particle is released from thebubble (Exp A) and the minimum voltage at which a particleentrained in a flow is first trapped by the oscillating bubble(Exp B), as summarized in a phase diagram. For all experi-ments, the flow rate of water containing particle suspensionsis kept constant and sufficiently high so that the effects ofmicrostreaming flows can be neglected in our current study.In addition to measuring the onset behavior, the amplitudeof bubble oscillation is also measured at the correspondingvoltages and frequencies to verify the relationship betweenthe oscillation amplitude and the FSR, as given by Nyborg.76

In parallel with the experiments, we combine well-developed theories to derive an expression for the critical in-put voltage that leads to the particle release into the externalflow. By balancing the hydrodynamic force on a sphere neara stagnation point86 with FSR, a functional relationship be-tween the threshold bubble oscillation and experimental pa-rameters, such as the particle size and driving frequency, isderived. Then, linearized Rayleigh–Plesset and Helmholtzequations are employed to connect this threshold bubble am-plitude to the driving pressure, then to the applied voltage.Aided by empirical parameters to determine the vibration

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amplitude of the channel, the resultant expression for thecritical voltage, Vc, is an explicit function of the driving fre-quency, f, and is in good quantitative agreement with thedata from Exp A. While the final result, VcIJ f ), has been testedfor our particular experimental setup, its theoretical approachand results should be valid for a wide range of acoustic de-vices and can easily accommodate them by adjusting the de-vice vibration amplitude.

Overall, our work here takes an initial step to quantita-tively analyze the secondary radiation force of an acousticbubble for particle trapping and release in a flow. Therefore,this work paves the way towards future design of next-generation acoustic-based lab on a chip devices for more ver-satile applications. Future work includes developing a bettermathematical model for the hydrodynamic forces on the par-ticle near the oscillating bubble surface. On the experimentalside, performing the analogous experiments with a widerange of particle and bubble sizes and measuring the pres-sure field based on PIV (Particle Image Velocimetry)90 willhelp validate our current model. Furthermore, extending thiswork to include multiple bubbles, microstreaming effects, ornon-spherical objects is also of great practical interest for labon a chip applications.

Acknowledgements

This research has been supported by a DARPA Young FacultyAward through grant N66001-11-1-4127. YC and SL thank Dr.Sascha Hilgenfeldt (UIUC) for fruitful discussions and Dr.Tony Yu for help with image processing. The authors wouldalso like to acknowledge Dr. Feng Zhao (WSUV) for resonantfrequency measurements and Darius Saadat-Moghaddam forhis help with experiments. BM thanks the support from theWSUV ENCS Undergraduate Summer Research Program.

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