Acoustophoretic contactless transport and handlingof matter in airDaniele Foresti, Majid Nabavi, Mirko Klingauf, Aldo Ferrari, and Dimos Poulikakos1

Department of Mechanical and Process Engineering, Laboratory of Thermodynamics in Emerging Technologies, Eidgenössische Technische Hochschule Zürich,CH-8092 Zurich, Switzerland

Edited by William R. Schowalter, Princeton University, Princeton, NJ, and approved June 8, 2013 (received for review January 30, 2013)

Levitation and controlled motion of matter in air have a wealth ofpotential applications ranging from materials processing to bio-chemistry and pharmaceuticals. We present a unique acoustopho-retic concept for the contactless transport and handling of matterin air. Spatiotemporal modulation of the levitation acoustic fieldallows continuous planar transport and processing of multipleobjects, from near-spherical (volume of 0.1–10 μL) to wire-like,without being limited by the acoustic wavelength. The indepen-dence of the handling principle from special material properties(magnetic, optical, or electrical) is illustrated with a wide palette ofapplication experiments, such as contactless droplet coalescence andmixing, solid–liquid encapsulation, absorption, dissolution, andDNA transfection. More than a century after the pioneering workof Lord Rayleigh on acoustic radiation pressure, a path-breakingconcept is proposed to harvest the significant benefits of acousticlevitation in air.

acoustics | fluid | ultrasounds | manipulation | microfluidics

Contactless transport and handling of matter are of funda-mental importance to the study of many physical phenomena

(1, 2) and biochemical processes (3). Typical state-of-the-artmethods of contactless handling of matter are based on electro-magnetic (4–6) principles and have interesting capabilities but alsoclear limitations in terms of particle size (micrometer range) and/or inherent requirements of special material properties.Acoustic levitation (7–11) is both contact-free and material-

independent, also without requiring laborious sample preparation.Although significant progress has been made in the handlingof microsized particles suspended in a liquid (12, 13), wherebuoyancy forces are almost entirely responsible for the levitation,various drawbacks in the state of the art of acoustic levitation haveprohibited the realization of controlled and reliable transport ofmatter in air, thereby limiting the remarkable potential and utilityof acoustic levitation (14–16). Its full exploitation requires funda-mental advances leading to material transport with high control-lability and movement resolution, long transport length, versatility,and multidimensionality.Here, we present a unique acoustophoretic concept, enabling

the continuous planar transport and processing of multiple acous-tically levitated droplets and particles in air. This is a significantadvance in the area of contactless handling in air, making it a viablecomplementary methodology to existing advanced approaches ina liquid environment (17, 18), one that has its own unique features,expanding the horizon of possible applications. The concept isbased on the ability to modulate the acoustic node regions in theacoustic field spatially and temporally, enabling the reversibletransition from material trapping to transport. Additionally,the levitation and handling of extremely elongated objects witha characteristic length much longer than the acoustic wavelengthis demonstrated through their transport and rotation.

Results and DiscussionIn acoustic levitation, a standing wave is established between anemitting surface and a reflector (9, 11, 19). The radiation pres-sure, a nonlinear property of the acoustic field, engenders the

levitation potential [the sum of the acoustic potential (20) andthe gravitational potential; SI Text, section 1]. This varies non-monotonically between the emitting surface and reflector. If it isstrong enough to overcome the gravitational force, small amountsof matter can be levitated and trapped in its minima (nodes). Anacoustic potential node can correspond to an acoustic pressurenode or antinode, depending on the density and compressibilityof the levitated sample (ρs and βs) and of the surrounding me-dium [ρ0 and β0 (21)]. To this end, note that ρs > ρ0 and βs < β0in the overwhelming majority of envisioned applications in air(SI Text, section 1).The acoustic levitation and handling concept is realized with

the help of a discretized planar resonator platform and a singleflat reflector placed at a uniform distance H. Each discrete res-onator element is a specially designed and optimized Langevinpiezoelectric transducer (LPT) excited by a single sinusoidalsignal voltage of ultrasound frequency f (Fig. 1 and Methods). Anewly developed excitation mechanism allows controllable andsmooth propulsion of the levitation potential nodes from one LPTor a group of LPTs to the next. In this mechanism, the amplitudesof the sinusoidal inputs A1(t) and A2(t) of the two adjacent LPTsare varied over the travel period T (time needed for the object totravel the distance d between the centers of two adjacent LPTs)in a parabolic manner, as shown in Fig. 1. As a result, a nearlyconstant acoustic force magnitude during movement is obtaineddue to the proportionality of the acoustic force to the square ofthe driving voltage amplitude (Methods). Movie S1 demonstratesthe capability of the present mechanism to perform a multistepplanar process in air acoustophoretically, where two water drop-lets are introduced, transported from opposite directions, mixed,transported in the orthogonal direction to be mixed with a thirddroplet, and finally collected. We are not aware of any other methodor technology able to perform such multidroplet transport andhandling in a gaseous environment.The physical principle behind the demonstrated controlled

acoustophoretic transport of matter lies in the spatiotemporalmodulation of the levitation acoustic field, shown in Fig. 2A andMovie S2. The transport and mixing of two droplets in a deviceconsisting of a 1D array of five LPTs are numerically analyzedusing a validated 3D finite element model (Methods). The modelcalculates the levitation potential inside the system as a functionof the vibrational velocity of the emitting surface V0. Fig. 2Bshows the experimental results of the horizontal position of thetwo approaching droplets with four traveling velocities (0.6, 1.1,2.2, and 4.9 mm/s), along with the numerical predictions. Notethat air has a very low damping effect and oscillation of thesamples is present. However, the droplets are stably kept at the

Author contributions: D.F. and D.P. designed research; D.F. performed research; D.F.,M.K., and A.F. contributed new reagents/analytic tools; D.F., M.N., and D.P. analyzeddata; and D.F., M.N., and D.P. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. E-mail: dpoulikakos@ethz.ch.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1301860110/-/DCSupplemental.

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middle of a node for a wide range of transport velocities. Fabrica-tion tolerances are challenging for acoustic resonances (Methods),but future purely technical improvements in platform fabricationwill certainly help reduce such fluctuations, which, although pos-sibly presenting a problem to individual sample analysis (22), arenot expected to affect sample advancing and processing seriously.Before node merging, the velocity of the droplets equals that

of the nodes. After node merging, the droplets approach oneanother with a primary acceleration, €xp in the range of 0.1–1 m/s2

(Fig. 2D), due to the primary scattering field described by theacoustic potential. These acceleration values are in agreementwith the model, with the horizontal force being one order ofmagnitude lower than the vertical force (SI Text, section 3, andFigs. S1–S3). When two droplets come into close proximity (Fig.2C), the collision velocity increases sharply, with an additionalacceleration €xs of the order of 1–10 m/s2, which cannot be solelyexplained with the primary acoustic field. Understanding of theunderlying physics is critical to realize acoustophoretic mergingof droplets.A secondary acoustic field originating from the scattering of

the primary waves on the two levitated objects significantly con-tributes to the collision dynamics (the total acceleration is calcu-lated as €x=€xp +€xs). The theoretical derivation of such a secondaryforce for the simple case of two closely placed spheres in anoscillating flow dates back to more than a century ago (23). Thepresent work provides a unique platform to observe and inves-tigate this physical phenomenon. To this end, the present resultsconstitute experimental quantitative confirmation of such secondaryacoustic force (SI Text, section 4). Assuming that the density of thespheres ρs is much larger than that of ρ0 (as in the case of a liquiddroplet levitated in air), the attraction force on either sphere Fr,when the angle between the direction of wave propagation and

the axis connecting two spheres is θ = 90° (our configuration), iscalculated as (23):

Fr = -3πρ0R3s1 R

3s2 v

2rms=r

4; [1]

where r is the center-to-center distance of spheres; Rs1 and Rs2are the radii of the two spheres; and vrms is the rms acousticvelocity of the surrounding fluid, which cannot be measured di-rectly here. SI Text, section 4 explains the numerical model usedto estimate vrms at the levitation nodes, where the mixing takesplace (Fig. S4). Fig. 2D shows the analytical and experimentalvalues of €x for two water droplets of Rs = 0.84 mm, which agreevery well. The agreement is also excellent for droplets of differ-ent densities (ρs = 1 g/cm3 for water and ρs = 0.76 g/cm3 fortetradecane) and radii, spanning over a wide range of acceleration(€x = 0.4–20 m/s2; SI Text, section 4, Fig. S5 A–D, and Table S1).The presented features of local control in space, time, and

magnitude of the acoustic forces and the wide range of possi-bilities of matter that can be simultaneously handled provide arich palette of combinations of liquid–liquid, liquid–solid, andsolid–solid transport and interaction.One distinctive advancement of the present acoustophoretic

method is that it features an almost constant acoustic potentialmagnitude during the node transition between two transducers,which is an important requirement for stable levitation of liquids(24). In fact, not only does the acoustic force have to be strongenough to overcome the gravitational force, but it has to be belowthe threshold of atomization of the droplet in the acoustic field.Indeed, when the acoustic force is stronger than the interfacialforce, the droplet atomizes explosively. The ratio of acousticforces to surface forces for a levitated droplet scales with Rs andis described by the acoustic Bond number (25), Ba = 2v2rmsρ0Rs/σ,where σ is the surface tension of the liquid. The maximum Rs thatcan be levitated depends on the critical acoustic Bond numberBa,cr, which was determined experimentally to be between 2.5and 3.6 (25). The definition of the Ba,cr implies that when thevrms increases, the Rs has to decrease strongly. For a drivingfrequency of 24 kHz, the theoretical upper size limit for waterand hydrocarbons is around 2.7 mm and 1.6 mm in radius,respectively (24). Approaching the upper limit of the static lev-itated droplet, our method allows transport and mixing of twodroplets with a large size ratio.Fig. 3 A–C shows the different behaviors observed during mixing

of two water droplets and two tetradecane droplets. For head-onmerging of droplets, the different regimes of coalescence, bounc-ing, and separation depend on theWeber number,We= 2Rsu

2ρs/σ,where u is the relative impact velocity (26). The two waterdroplets coalesce at We = 0.42 (Fig. 3A and Movie S3). Shown inFig. 3B are two droplets for which, before merging, the low valueof Ba (1.85 ± 0.47) prevents atomization. However, after merg-ing, due to the larger size of the resulting combined droplet, Baincreases above the critical point (2.33 ± 0.59), yielding explo-sive atomization (Movie S4). In Movie S5, explosive atomizationoccurs at the very beginning of the merging process (Ba = 2.03 ±0.72 and Ba = 1.93 ± 0.68). The slow motion of this movie cap-tures visually the effect of the secondary acoustic force discussedearlier, causing significant deformation of the droplet just beforemerging. Fig. 3C shows that two tetradecane droplets first bounceoff (We = 0.875), the acoustic force then brings them back to-gether (double bouncing), and they coalesce at the second en-counter due to the lower impact velocity (We = 0.25; Movie S6).The above-mentioned material independence of acoustic lev-

itation allows an unprecedented flexibility in the handling andinteractions of solid and liquid entities. Fig. 3 D and E showsrepresentative solid–liquid interaction scenarios. When a solidpolystyrene particle (Rs = 0.5 mm, ρs = 1 g/cm3) and a liquid(water) with a high surface tension collide, they do not merge

Fig. 1. Schematic of the contactless multidrop manipulator and its excita-tion mechanism. In the illustrative example, droplets are introduced into thesystem at three locations (inlets 1, 2, and 3) in a five-one-two LPT levitator.Their numbers correspond to the number of LPTs in a certain row. All rowsare on the same plane, parallel to the reflector plane. The droplets move andmix, and the final sample is delivered to the outlet. The introduction ofdroplets into the system can be achieved either manually with a micropi-pette or with an automatized syringe pump and a glass capillary (Methods).The reflector height H is adjusted with a linear micrometer stage.

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(Movie S7). On the other hand, particle encapsulation is ob-served if a low surface tension liquid, such as tetradecane, is used(Fig. 3D and Movie S8). The delicate nature of the acousto-phoretic forces is advantageous when dealing with fragile mate-rials, such as crystals and porous media. In this respect, two typicalconfigurations of porous particle contactless transport and in-teraction with a liquid drop are considered. First, if the particle islarge enough, it acts as a sponge, absorbing the liquid (Movie S9).With an evaporation rate of 0.0036 mm2/s for water (27), thedroplet volume reduction due to evaporation (1.1% over 10 s)does not play a significant role. Alternatively, small porous par-ticles (e.g., instant coffee granule) dissolve in the water droplet(Fig. 3E and Movie S10). If the droplet solution is kept in thedevice and the water is allowed to evaporate completely, a bowl-shaped particle is formed. The behavior of stationary evaporatingdroplets containing diluted particles has only recently been studied(28), and the findings are qualitatively comparable to those shownin Fig. 3E.The inherent substrate-independent and contamination-free

characteristics of the presented concept can be beneficial to majorareas of biomedical and biochemical processes. Therefore, its bio-compatibility was tested by performing contactless DNA trans-fection in a temperature- and humidity-controlled environment(Methods). Fig. 3F shows the schematic of the contactless DNAtransfection and the transfected cells with blurred edges. Dem-onstrating similar efficiency and viability as the standard process,our contactless transport method is shown to be biocompatibleand suitable for DNA transfection. The occurrence of a photo-chemical switch in a contactless manner is shown in Fig. 3G,where a fluorescein solution with pH 3 and a physiological solution

with pH 12 are mixed. The resulting solution becomes neutral,which maximizes the fluorescent emission.The spatial and temporal modulation of the acoustic nodes of

the present method allows the levitation and transport functionsof such nodes to be manifested in collaborative manner, whereinseveral nodes act as a group and can even merge to form a singleelongated node and carry out a task. This extends the capabilityof the present concept beyond the handling of spherical or near-spherical particle and droplet transport and to the controlledmotion of very elongated, wire-like objects. As a result, an ex-tremely elongated object with a characteristic length L muchlarger than λ can be levitated, propelled, transported, and ro-tated in a controllable manner, going beyond the widely acceptedlimit (9, 11, 14, 15, 27) of λ/2 for the maximum size of an acous-tically levitated sample (Fig. 4 and Movie S11). It is worth notingthat, to the best of our knowledge, no previously reported acousticlevitation devices, including near-field acoustic levitators (29),have even been shown to levitate elongated objects of the kindshown in Fig. 4.

ConclusionsThe presented concept paves the way for new classes of processes,ranging from substrate-free biological and chemical reactions tonovel containerless materials processing methods, by acous-tophoretically transporting and mixing droplets and particles.Matter can now be manipulated at atmospheric conditions bycounteracting the effect of the gravitational force, without re-quiring a microgravity environment to remove its presence, andthe contactless material handling can be extended to hazardous,chemical, or radioactive samples. Because the occurrence of a

Fig. 2. Controlled approach of two droplets in air. (A) Levitation potential inside a five-LPT device by varying the driving voltage of the LPTs (the levitationnodes are shown in blue). The small ellipses illustrate the experimental droplet positions. For clarity, only the emitting surfaces of the LPTs are shown. (B)Experimental results for the horizontal position of two acoustophoretically transported and eventually coalesced water droplets 0.84 mm in diameter for fourtraveling velocities, along with the numerical predictions (Figs. S6–S8). The oscillations of the droplets during translation are due to the very low damping effectof the surroundingfluid (air). (C) Experimentalmovement velocity ( _x) of one of the two approachingwater droplets. (D) Analytical and experimental values of totalacceleration (€x) of the droplets near collision, with respect to the center-to-center droplet distance r (V0 = 2.6 m/s, H/λ = 0.496). The dotted line marks the primaryacceleration €xp due to the acoustic potential field. The experimental uncertainty in the estimation of vrms is reflected in the error bars of the analytical data.

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phase change in the samples is not expected to affect their handlingby the acoustophoretic force, related exothermal and endothermalreactions do not limit the field of applications of the presentedconcept. Magnetic, electrostatic, diamagnetic, and optical forcescan be coupled with the acoustophoretic handling to enhanceeven further the stability and the degrees of freedom of themanipulation.

MethodsExperimental Setup. An LPT is composed of a back brass mass, a front alu-minum mass, and a set of piezoelectric elements between the two, clampedby a bolt (SI Text, section 6, and Fig. S9).

In the optimized design, the emitting surface of LPTs had dimensions of15 mm × 15 mm. The working frequency was f = 24.3 kHz, corresponding toa wavelength in air of λ = 14.2 mm. The amplitude of the excitation voltagewas adjusted using an in-house-designed microcontroller-based potenti-ometer and a LabVIEW program (National Instruments), and it was amplifiedto the desired value with an amplifier (DPA-4000T; ECLER), as shown in Fig. 1.The amplitude resolution of the driving signal Ai(t) determines the move-ment resolution of the object. We used an eight-bit digital signal (256 levels)

for controlling the amplitude, and with d = 16 mm, the theoretical move-ment step size is calculated to be 16 × 10−3/256 ≈ 62 μm. Due to the non-linearity of the LPTs and the node translation process, the actual positioningresolution is lower than this value; the minimum step size at the gap be-tween the two LPTs for the case shown in Fig. 2B was found to be around400 μm. The V0 was measured using a laser vibrometer Polytec CLV-2534.Small holes with a diameter of 1.2 mm in the Plexiglas reflector alloweddroplet injection.

The Numerical Model. The Simulia Abaqus (6.9) package was used to calculatethe levitation potential for different vibration amplitudes of the LPTs, and thesample position was estimated by determining the levitation potentialminima. A 3D finite element model was implemented to solve the linearacoustic equations in the frequency domain (SI Text, section 2). The linearacoustic pressure and particle velocity are sufficient to determine the radi-ation force (nonlinear) based on the levitation potential approach (SI Text,section 1). Due to symmetry, only half of the domain was modeled. Theradiating plate and the reflector were implemented as rigid shells, ac-counting for acoustic-structural coupling. On the radiating plate, the dis-placement boundary condition was applied. Infinite elements were used at theouter boundary of the acoustic medium. An additional acoustic medium

Fig. 3. Series of representative experiments with droplets or particles using the present acoustophoretic concept. (A) Stable water droplet coalescence (We =0.42). (B) Explosive atomization after water droplet coalescence. (C) Tetradecane droplets bouncing (We = 0.875) and subsequently coalescing (We = 0.25). (D)Polystyrene particle collision with tetradecane droplet (We = 0.66). (E) Collision of a porous particle (instant coffee) and a water droplet (We = 0.24). Thecolored image at the bottom shows an instant coffee particle before and after the mixing/evaporation process. (F) Schematic of the contactless DNAtransfection process and micrographs of the transfected cells with blurred edges. The transfection agent (TA) was premixed with the DNA solution. (G) Mixingexperiment of fluorescein droplet (Left), with a logarithmic acid dissociation constant of pKa = 6.4 and pH 3, and of a droplet of physiological solution with pH12 (Right). (Scale bars: B–E, 1 mm.)

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volume was added to the model to avoid the influence of the nonreflectingboundary on the core of the levitator. The model was validated against theexperimental values of force acting on a sphere inside an axisymmetricallevitator (30). The implemented quasistatic model suffices for our analysis.The characteristic time scale of the acoustophoretic forces is related to thecharacteristic time of the radiation pressure τrad . The radiation pressureacting on a sphere in a standing wave becomes fully established after a pe-riod of τrad =N · τwave, with N being the number of acoustic wave cyclesneeded to reach steady state and τwave = f−1 = 41 μs being the wave period.N was determined numerically to be between 50 and 100 (30, 31). Thecharacteristic time of a sample transported at an average linear speed _x isdefined as τmov = λ= _x , and for our case, λ∼d → τmov ∼ T . When using theacoustic potential for the dynamic analysis, we assume τmov � τrad . In ourexperiments, the highest linear transport speed of 4.9 mm/s corresponds toτmovmin = Tmin = 3 s, which is much larger than τrad = 400 μs, justifying ourassumptions.

Droplet Input Method. In the feasibility studies carried out in this paper,droplet input into the acoustic manipulator was easily achieved using a Teflonmicropipette with an outer radius Rc = 150 μm (Movie S1). The acoustic forceacts on the droplet at the outlet of the micropipette and scales with itsvolume Rs

3, as the gravitational force (SI Text, section 1). When the sum ofthe two forces (gravitational and acoustic) overcomes the capillary force, thedroplet is detached. The capillary force acting on a droplet at the outlet ofa pipette of radius Rc is Fc = 2πRcσ. If gravity is the only force acting on awater droplet, by simply equating the surface tension force to the gravita-tional force at the point of detachment, the radius of the detached droplet isdetermined to be Rs = 1.18 mm, corresponding to a volume of 6.9 μL. Be-cause Rc is much smaller than the capillary length of water, 3.8 mm, no cor-rection to this calculation is needed (32). The presence of the additionalacoustic force can reduce the droplet size at detachment (e.g., in Fig. S5A,Rs,min = 0.63 mm, volume = 1.05 μL). For hydrocarbons with a smaller

surface tension, Rs,min decreases further. The lower limit is set by the criticalacoustic Bond number: if the acoustic field is too strong, atomization occursbefore droplet detachment.

DNA Transfection. HeLa cells were transfected in our device by mixing a dropof cells (at a concentration of 3,000 cells per microliter) in fully supplementedmediumwith serum (DMEM; Sigma) and a drop of a stock solution containingthe transfection reagent (3 μL of XtremeGENE HP; Roche) and a DNAplasmid (1 μg) encoding for enhanced GFP in 50 μL (100 μL) of serum-freemedium. The two drops fused by levitation were each 2.5 μL in volume.In general, the technique can also be applied to the study of incrementaltransfections, in which several DNA plasmids can be introduced in the samecells or in a multiple of the cell line. The temperature of the chamber wasmaintained at 36 ± 2 °C, and the relative humidity was close to saturation.A humid environment is necessary to slow down evaporation. The pro-cess was fully viable; the cells were mixed with the DNA solution in ourcontactless manipulation platform (requiring a few seconds for mergingand remaining for 1–5 min in a steady levitation position) and were sub-sequently plated into a 96-well plate containing 50 μL of fully supplementedmedium. After 18 h of incubation, GFP-positive cells were clearly detectedshowing high levels of expression. The transfection efficiency of the levita-tion protocol was comparable to that of the standard protocol con-ducted in microwells, whereas the amount of reagents used was reducedby 50–75%.

ACKNOWLEDGMENTS. We thank the Swiss National Science Founda-tion (Grant 144397) for financial support. We also thank Paolo D’Aleo[Eidgenössische Technische Hochschule (ETH) Zürich] for support with electroniccontrols, Bruno Kramer (ETH Zürich) for the manufacturing of parts of theexperimental device, and Dr. Manish Tiwari (Laboratory of Thermodynamicsin Emerging Technologies, ETH Zürich) for helpful discussions.

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