Acoustophoretic Contactless Transport and Handling of Matter in Air

TECHNICAL FIELD

The invention relates to an acoustophoretic contactless transport and handling of matter in air and is especially related to an acoustic manipulation apparatus to trap, fix, transport, move, deform, bend or rotate objects comprising a host fluid as acoustic medium and the object(s) to be moved, wherein a plurality of acoustic wave oscillators is arranged in at least one line in a predetermined distance from an essentially flat plate wherein the wave oscillators are connected to a control unit adapted to generate control signals for the wave oscillators to generate a gradient force by superposing one over another the gradient force fields generated by the acoustic waves produced by the wave oscillators.

PRIOR ART

Contactless transport and handling of matter is of fundamental importance to the study of many physical phenomena (references 1, 2, 3 and 4) and biochemical processes (reference 5). Among the possible mechanisms of contactless handling of matter are electrostatic, magnetic, optical (references 6, 7,8 and 9) or acoustic levitation (references (10, 11). Only the latter is, however, both contact-free and material independent, also without requiring laborious sample preparation. Drawbacks of the existing methods have to date limited the utility of acoustic levitation (references 12, 13 and 14). Its full exploitation requires fundamental advances in material transport with high controllability and movement resolution, long transport length, versatility and multi dimensionality.

US 6,216,538 discloses an ultrasonic manipulation apparatus with a plurality of ultrasonic wave oscillators arranged in two dimensions to trap, fix or move particles to an optional position in a liquid solution or perform cell fusion by using a gradient force obtained by superposing one over another the gradient force fields generated by ultrasonic waves produced by a plurality of ultrasonic wave oscillators. The ultrasonic wave oscillators, functioning independently of one another, can emit ultrasonic waves with optional intensities and phases, and by using an external force produced by superposed gradient force fields generated by ultrasonic waves, particles are handled within the fluid. The movement is obtained by phase shift between the different actuators.

SUMMARY OF THE INVENTION

A novel acoustophoretic concept is presented, enabling the continuous planar transport and processing of an unlimited number of acoustically levitated droplets and particles over a wide range of volumes (0.1-10 μΐ) in air. The concept is based on the ability to spatially and temporally modulate the acoustic node regions in the acoustic field, enabling the reversible transition from material trapping to. Representative experiments with droplets or particles, illustrating contactless coalescence, mixing, encapsulation and DNA transfection, amply underpin the capabilities of the method. Additionally, the levitation and handling of extremely elongated objects with characteristic length much larger than the acoustic wavelength was demonstrated through their transport and rotation.

More than a century after the pioneering work of Lord Rayleigh on acoustic radiation pressure (reference 15), a substantial advancement is made toward harvesting the significant benefits of acoustic levitation.

Based on the prior art it is an object of the present invention to provide the possibility for easier acoustic levitation handling of objects and especially of matter in air as a fluid. Matter in this sense comprises solid objects as well as liquid droplets, cells and material having a defined boundary in view of the surrounding acoustic host medium.

According to the invention the control unit is adapted to maintain a constant acoustic potential magnitude during transition between two transducers, which is an important requirement for stable levitation of liquids. In acoustic levitation, an ultrasonic standing wave is established between an emitting surface and a reflector (reference 10). The radiation pressure, a non-linear property of the acoustic field, originates the levitation potential (the sum of the acoustic potential (reference 16) and the gravitational potential, Supplementary Note 1). It varies non- monotonically between emitting surface and reflector; in its minima (nodes) small amounts of matter can be levitated and trapped, if the acoustic force can overcome the gravitational force. Pressure sensors can be provided on the opposite side of the reflector plate for each wave oscillator. These sensors are then connected to the control unit to control the essentially constant acoustic potential emitted by each corresponding wave oscillator. This creates a closed loop feedback circuit. This can be achieved, inter alia, when the amplitudes of the sinusoidal inputs of adjacent wave oscillators are adjusted in a parabolic or cubic manner between a predetermined minimum and a predetermined maximum value over the travel time needed for the object to travel the distance between the centres of the two adjacent wave oscillators. Both alternative choices have advantages. Changing the excitation function from parabolic to cubic also affects the translation pattern of the object. While a parabolic function offers a more linear acoustic force variation during movement, a cubic function compensates both the effects of nonlinearity and the horizontal gap between the wave oscillators.

The control unit can be adapted to provide drive signals over several adjacent wave oscillators in two adjacent rows to move an object with a high aspect ratio as e.g. 5: 1 to 10:1 or more extending over several of the wave oscillators in one of the rows for a movement transversal to the longitudinal axis of the object from one row to another. The example within the specification is a tooth pick with a diameter of 2 mm and a length of 80 mm, thus having an aspect ratio of 40:1.

The control unit can also be adapted to provide drive signals over several adjacent wave oscillators to move an object with a high aspect ratio extending over several of the wave oscillators in one of the rows for a rotation of the object around a central wave oscillator in a plane parallel to the outer surfaces of the reflector. This allows also bending of an object as a wire extending over several wave oscillators, adding a new functionality.

The essentially flat plate can be a passive reflector plate or also comprise actuators. The passive reflector plate can have a rigid surface or a deformable surface adapted to be deformed by the acoustic radiation pressure.

When the reflector plate is deformable, then it comprises a rigid back casing providing a reservoir which is filled by a deformable material providing the outer surface towards the emitters. The deformable material and back casing can be covered by a membrane. The deformable material can be glycerine and the membrane can be a PP membrane.

Said reflector can be a rigid plate and the reflector can be mounted at the top or at the bottom of the chamber (with the wave oscillators on the opposite side). If the term "chamber" used in this specification, this relates either to an open room between the reflector plate and the transducers but without any side surfaces and especially holes as an injection system and gaps between transducers fixed in space. In case that the fluid is not a gas or air but a liquid there might be side surfaces enclosing the fluid. In order to achieve an improved handling of objects to be lifted and especially to lift heavier devices, it is an option to use a reflector based on the morphing of an acoustically soft -reflector surface. The soft-reflector is able to focus the reflected sound waves emanating from a line assembly of discrete emitters, i.e. the wave oscillators. By exploiting both the low reaction forces and low relaxation time of a liquid (e.g. glycerin) and enhancing the surface tension by the use of a thin membrane of plastic compound, the soft structure is able to morph and adapt its shape at the needed location. The generated acoustic radiation pressure magnitude was able to support heavy objects during acoustic node motion, rendered through spatiotemporal modulation of the acoustic field. This was a direct result of the mobility of the reflector surface acoustically generated indentation, continuously focusing the reflected acoustic waves during transport. With such interplay of emitters and reflecting soft-structure, a 5 mm steel sphere (0.5 grams) was contactlessly transported in air solely by acoustophoresis.

US 6,216,538 provides an ultrasound manipulation apparatus, since the frequencies used are higher than 20 kHz for a particle in a liquid. Although some experiments shown here were done with an excitation at 24.3 kHz, also lower frequencies can be used. BRIEF DESCRIPTION OF THE DRAWINGS

Preferred embodiments of the invention are described in the following with reference to the drawings, which are for the purpose of illustrating the present preferred embodiments of the invention and not for the purpose of limiting the same. The drawings show:

Fig. 1 shows a schematic of a contactless multi-drop manipulator according to an embodiment of the invention and its excitation mechanism;

Fig. 2 shows a sequence in time of a controlled approach of two droplets in air using the manipulator according to Fig. 1 with A.) The levitation potential inside a five- LPT device by varying the driving voltage of the LPTs; B.) The experimental results of the horizontal position of the two coalesced water droplets of 0.84 mm in diameter for four traveling velocities along with the numerical predictions; C), The experimental movement velocity of one of the two approaching water droplets:; and D.) The analytical and experimental values of total acceleration of the droplet near collision, with respect to the center to-center droplet distance r; Fig. 3 shows a series of representative experiments with droplets or particles using a manipulator according to the present acoustophoretic concept for: A.) Stable water droplet coalescence; B.) Explosive atomization after water droplet coalescence; C.) Tetradecane droplets bouncing and subsequently coalescing; D.) Polystyrene particle collision with tetradecane droplet; E.) Collision of a porous particle (instant coffee) and a water droplet; F.) Mixing experiment of fluorescein droplet and a droplet of physiological solution;

Fig. 4 shows a contactless transport of an elongated object as a toothpick, wherein a controlled rotation is shown in A.) as a top view and B.) in a side view and in C.) a controlled translation in top view is shown;

Fig. 5 shows a variation of maximum |Utot| with respect to FI/λ;

Fig. 6 shows the pattern of Utot at the middle plane for the five-LPT configuration platform;

Fig. 7 shows the variation of Utot and the related horizontal and vertical forces along the lines crossing at the potential minimum shown in Fig. 6;

Fig. 8 shows the maximum particle velocity vrms for T = 1.6, V0 = 1 m/s and different values of FI/λ;. v _rmS;m ax exhibits similar behavior as |Utot„max| shown in Fig. 5;

Fig. 9 shows the analytical and experimental values of acceleration of water and tetradecane droplets of different radii near collision under acoustophoretic handling as a function of their center-to-center distance r;

Fig. 10 shows the effects of the excitation function Aj(t) and H on the transport and mixing patterns of objects;

Fig. 1 1 shows the effects of the reflector height on droplets translation and mixing for the

0.6mm/s case;

Fig. 12 shows a similar view to Fig. 1 and 2 A for the manipulator and the effect on a droplet;

Fig. 13 shows a schematic view similar to the image of Fig. 4;

Fig. 14 shows in A. a schematic view of the principle of a reflector according to a further embodiment of the invention in comparison to a reflector according to Fig. 1 in

B. and the function of the flexible reflector in C;

Fig. 15 shows the transport of a heavy object using the reflector according to Fig. 14; and Fig. 16 shows a schematic of a further contactless multi-drop manipulator according to an embodiment of the invention and its excitation mechanism using feedback information.

DESCRIPTION OF PREFERRED EMBODIMENTS

In acoustic levitation, a standing wave is established between an emitting surface and a reflector (reference 10). The radiation pressure, a non- linear property of the acoustic field, engenders the levitation potential (the sum of the acoustic potential (16) and the gravitational potential, Supplementary Note 1). This varies non-monotonically between emitting surface and reflector. If strong enough to overcome the gravitational force, small amounts of matter can be levitated and trapped in its minima (nodes). An acoustic potential node can correspond to an acoustic pressure node or antinode, depending on the density and compressibility of the levitated sample ( ¾ and /¾) and of the surrounding medium (/¾ and ¾,). Note to this end, that in the overwhelming majority of envisioned applications in air, p _s >po and /¼ < ¾ ( SI text, Section 1 ). Embodiments of the manipulator device are described by reference to the drawings. Fig. 1 shows a schematic of the contactless multi-drop manipulator and its excitation mechanism. The levitation nodes can be shifted with high accuracy, controllability and adjustable speed of motion of the order of mm/s through the spatial and temporal control of the emission of acoustic waves, when using a sequence of LPT's, i.e. a sequence of Langevin piezoelectric transducers. The amplitude resolution of the driving signal A;(t) determines the movement resolution of the object. An 8-bit digital signal (256 levels) was employed for controlling the amplitude and with d = 16 mm, the theoretical movement step size is calculated to be 1 6* 1 0-3/256 ~ 62 um. In fact, due to the nonlinearity of the LPTs and node translation process, the actual positioning resolution is lower than this value; the minimum step size at the gap between the two LPTs for the case shown in Fig. 2B was found to be around 400 um. In the illustrated scenario, droplets are introduced to the system at three locations. They move and mix and the final sample is delivered to the output. The introduction of droplets into the system can be achieved with either a manual micropipette or an automatized syringe pump and glass capillary. See Supplementary Note 7 for more details on droplet injection. As Fig. 1 shows a schematic of a contactless multi-drop manipulator according to an embodiment of the invention, the reflector 30 is shows being in a height 65 of a value H above an array of actuator plates 10. Here parts of a 5 times 5 array of actuator plates 10 are shown. Beneath the actuator plates 10 are the actuator drives 20 generating the necessary excitation. The plates and drives form ultrasonic wave oscillators. The oscillators are functioning one independently form another and are adapted to emit ultrasonic waves with an intensities to levitate particles above them. Through applying drive signals to adjacent oscillators a gradient force field is obtained moving the particles in a specific predetermined direction. Particles can be liquid or solid particles in air in the chamber or solid particles in a liquid in the chamber.

The actuator plates 10 are provided with a gap 61 of in between so that the length "actuator plus gap" is equal to the distance 60 with the value d. In the embodiment of Fig. 1 the actuators 10 are presented below the reflector plate 30. The reflector 30 is a rigid plate, e.g. a steel plate or a metal plate or a plastic plate. The actuators are Langevin piezoelectric transducers driven by a control unit, wherein the reference numeral 50 designates the box showing the output of a driving signal 51 and 52 for two adjacent actuators 21 and 22. The frequency of the actuators is high enough to obtain the levitation effect. A droplet 42, the second droplet, is provided over the first actuator 21. Then the amplitude of the excitation is changed over time as shown in box 50, i.e. the excitation of actuator 21 is reduced and the excitation of the second adjacent actuator 22 is raised, which means that over the time IT the droplet 41 moves along arrow 28 in direction of the first mixing result 45, when at the same time the first droplet 41 is displaced toward the middle actuator. Then the combined result droplet 45 is displaced perpendicularly in direction of arrow 29 to become the final result 46 when enjoined by a third droplet 43.

Beside the provision of a rectangular array, e.g. with five times five actuators, it is also possible to provide a different lay out of actuators.

The reflector 30 can comprise one or more small holes, either opposite to specific transducers 20 or between adjacent transducers 21 , 22 to allow injection of objects, e.g. droplets, between the reflector plate 30 and the transducers 20. In case of a deformable reflector as explained below, hollow sleeves can be provided at such a place going through and providing through holes through the reflector.

Fig. 2 shows the procedure for a controlled approach of two droplets in air. The apparatus in Fig. 2A is based on the lay-out of the apparatus of Fig. 1 , here shown in one line of actuators 10 facing a reflector 30. In Fig. 2a the levitation potential inside a five-LPT device is varyied through the driving voltage 110 of the LPTs (the levitation nodes are shown as dark on the scale 120 on the right hand side. The levitation potential is higher at places 121 and lower at places 122. The small ellipses illustrate the experimental droplet positions 41 and 42. From top to bottom of Fig. 2 A the evolution over two time bases T is shown. At the beginning the amplitude is an high amplitude 1 13 under the exterior actuators 10; in the next step a medium, e.g. 50% maximum voltage 112 is applied on adjacent actuators and then the voltage is moving "inwards", leaving the exterior actuators 10 without excitation voltage 111.

Fig. 2B shows the experimental results of the horizontal position of the two coalesced water droplets 41 and 42 of 0.84 mm in diameter for four traveling velocities (0,6 mm/s, 1.1 mm/s. 2.2 mm/s and 4.9 mm/s along with the numerical predictions shown with the position of model dropletsl41 and 142, moving along the x-axis of in total 70 mm between the exterior actuators 10, wherein at a specific point in time the droplets 145 are moving quite suddenly from above one actuator 10 to the adjacent actuator 10 and finally find together at 1.5T by the move of both particles/droplets 141/142 together.. The oscillations of the droplets 41, 42 or 141 , 142 in the model during translation are due to the very low damping effect of the surrounding fluid (air). The faster movement of the droplets 41, 42 and 141, 142 at 0.5T where two adjacent LPTs 10 are excited with the same amplitude is attributed to the presence of two slightly separated nodes at the top of LPTs 10 and transition of the droplet from one node to another. Utilizing a cubic function for Aj(t) showed less variation in the levitation potential magnitude as it partly compensates the LPT's nonlinearity (Supplementary Note 5).

Fig. 2C shows the experimental movement velocity 150 of one of the two approaching water droplets: The secondary forces (and consequently the droplet velocity ' and acceleration x") increase when (R _sl + R _s2 )/r increases, wherein R _s x is the diameter of the droplet X and r is the distance between the two droplets; and approaches its maximum

6 4

which is equal to unity, in accordance with the R _s Ix dependency of the secondary force (Eq. 1) (the velocity is shown against the distance between the droplets.

Fig. 2D shows the analytical (Eq. 1) and experimental values of total acceleration x" of the droplet near collision, with respect to the centerto-center droplet distance r (Vo = 2.6 ms-1, Η λ = 0.496). The dotted line marks the primary acceleration, due to the acoustic potential field. The experimental uncertainty in the estimation of Vnn _S is reflected in the error bars in the analytical data.

Fig. 3 A shows series of representative experiments with droplets 41, 42 or particles using the present acoustophoretic concept. When two flying droplets 41 and 42 collide, they may undergo different regimes of coalescence, bouncing and separation (see reference 20). Fig. 3A shows a stable water droplet coalescence (We = 0.42). Fig. 3B shows an explosive atomization after water droplet coalescence. Fig. 3c shows two tetradecane droplets 41, 42 bouncing (We = 0.875) and subsequently coalescing (We = 0.25). Fig. 3D shows polystyrene particle collision with tetradecane droplet (We = 0.66). Fig.3E shows the collision of a porous particle (instant coffee) and a water droplet (We = 0.24). The bottom images show an instant coffee particle before and after the mixing-evaporation process. Fig. 3G shows the schematic of the contactless DNA transfection process and the transfected cells with blurred edges. The transfection agent TA was premixed with the DNA solution. The chamber temperature was 36±2°C and relative humidity was close to saturation. Fig. 3F shows a mixing experiment of fluorescein droplet on the left, with logarithmic acid dissociation constant of pK _a = 6.4 and pH = 3 (the acidity suppresses the fluorescence of the fluorescein) and a droplet of physiological solution with pH = 12 on the right. When the two droplets 41, 42 mix, the pH becomes neutral which maximizes the fluorescent emission. Fig. 4 shows the contactless transport of an elongated object 240 (a toothpick with L= 8cm ~ 6λ, Η~λ). Fig. 4A, 4B and 4C shows a controlled rotation around an axis perpendicular to the plane of reflector 30 and in line with the main axis of LPT actuators 20. Fig. 4A is a top view, Fig. 4B shows a side view. Fig 4C a top view on connection with a controlled translation of the toothpick 240. In principle, there is no limit on the length of the object that can be handled, i.e. the aspect ratio can be from 5: 1 to 10: 1 or 50: 1 or more.

Between the time 0T and 2.0T the toothpick rotates in Fig. 4A by around 90 degree in clockwise direction. The apparatus here comprises a five times five array of actuators 10 wherein the 4 corner actuators are left out.

Fig. 5 shows the variation of maximum |Utot| with respect to FI/λ. As can be see the relative maximum amount of |Utot| can be reached at a height of 53,5 % of HA, which means, a little bit more than 50% of the wave length is an ideal distance between the actuator plates 10 and the reflector plate 30. The droplets will then be in the middle of the distance between the actuator 10 and the reflector 30. Of course, it will be possible to find further stable levitation points, when the distance is be chosen to be around HA, when the height of the distance is the double of the distance of Fig. 1. If the distance is tripled and is 1,5 HA,, then three stable levitation points can be found at 0,25 HA; 0,75 HA and 1,25 HA.

Fig. 6 shows the pattern of Utot at the middle plane for the five-LPT configuration platform of Fig. 1 (HA = 0.496, Vexp = 2.6 ms ^"1 , time = 1.6T). The white dot 340 represents the location of the minimum potential Utot.min.

Fig. 7 shows the variation of IJ tot (left side VStot.v for vertical and right side U tot, h for horizontal) and the related horizontal (FA) and vertical (Fv) forces along the lines crossing at the potential minimum shown in Fig. 6.

Fig. 8 shows the maximum particle velocity v _rms for T = 1.6, Vo = 1 m s and different values of . FI/λ. Vrms.max exhibits similar behavior as shown in Fig. 5. Fig. 9 shows the analytical (Eq. 1 of the main manuscript) and experimental values of acceleration of water and tetradecane droplets of different radii near collision under acoustophoretic handling as a function of their center-to-center distance r. The dotted lines represent the values of the primary acceleration x" _p . Experimental values of Vo and FI/λ used in these plots are: a) 2.6m/s, 0.496 b) 3.0m/s, 0.496 c) 2.8m s, 0.489 d) 2.6m/s, 0.489.

Fig. 10 shows the effects of the excitation function Aj(t) and H on the transport and mixing patterns of objects. The excitation function, i.e. the variation of the amplitude of specific adjacent nodes as shown in box 50 in Fig. 1 , is provided as parabolic and cubic for two different FI/λ values. The explanation in view of Fig. 2B can also be applied here.

Fig. 11 shows the effects of the reflector height on droplets translation and mixing for the 0.6mm/s case. The dark gray movement curve 146 and the light gray movement curve are shown 147 in the same diagram for the parabolic and cubic excitation function A;(t). The dark grey curve is related to Η/λ = 0.489, the light grey curve is related to Η/λ = 0.507. The movement at YU = 0.507, e.g. curve in light grey, is in overall smoother, but characterized by stronger oscillations.

The amplitude of the wave oscillators is shown in the drawing to be between Zero and the maximum value of the generator. However; these values can be chosen to be between a predetermined minimum value (0 or 1/10 maximum generator value) and a predetermined maximum value. Said maximum value is usually chosen to generate an acoustic pressure to allow the safe movement of the object in question. Fig. 12 shows a similar view to Fig. 1 and 2A for the manipulator and the effect on a droplet 41. Fig. 12 shows the potential lines around the middle actuator 10; allowing a droplet 41 to be maintained at that place. It can be seen that the difference in potential is rather small between adjacent actuators 10 but very different in the direction between reflector plate 30 and the actuators 10.

Fig. 13 finally shows a schematic view similar to the image of Fig. 4, wherein an elongated object with an aspect ratio of more than 5: 1, here more than 10: 1, and which is far longer than one actuator 10, here it is almost five times longer, a length of more than 3 times the actuator 10 and up to ten times are not a problem; is rotated around an axis in direction between the reflector 30 and the actuator plates 10.

Fig. 14 shows a schematic view of a reflector 30 according to a further embodiment of the invention and Fig. 15 shows the transport of a heavy object 440 over time using the reflector according to Fig. 14.

Fig. 14A shows a line-focused acoustic levitator in a front view. The radiation pressure acts on the emitter 210, reflector 30 and levitated sample 40. The reflector 30 can be a rigid or a morphing reflector. The structure of Fig. 14A is that of a morphing reflector, but it is shown without showing a morphing action. Fig. 14(b) shows a rigid configuration of a line-focused levitator in a front view, along with the acoustic pressure ρη™ and velocity Vnns distributions; wherein the height reference H _re f is taken between the surface of the reflector (which is also the outer surface of the chamber) and the deepest indentation of the emitter 210. Fig. 14C below Fig, 14B shows a deformable reflector 30 morphing under the radiation pressure effect, enhancing the acoustic field. The Vo is the same of the rigid case, and the acoustic pressure and velocity increases by a factor 2 by the sole morphing of the soft reflector. By vibration of the emitter, an intense acoustic field can be created, strong enough to levitate an object under terrestrial gravity conditions. The acoustic pressure exerts a force to all parts of the device exposed to the acoustic field: emitter, reflector and sample (Fig. la). The emitter vibrates sinusoidally at the driving frequency f with a velocity amplitude Vo. To achieve the highest forces, the emitter 210 is placed at a resonance distance H ~ λ/2, where λ is the acoustic wavelength, to establish a standing wave with a single vertical acoustic node. If soft enough it is possible to have the reflector deform under the effect of the radiation pressure. The levitator configuration has a reflector 30 deforming to a typical concave shape due to the acoustic field itself. As a result of deformation, the acoustic field is increased in magnitude compared to the flat configuration, and a higher force is applied by the radiation pressure on the deformable surface. The geometry self-adapts again until a final equilibrium is found. A curvatures of 1 to 2 λ requires a deformation of the present soft self-focusing structure in the mm range for an operating frequency of 25 kHz.

The reflector comprises a hard back plate 31 onto which a deformable material 32 is applied, preferably but not mandatorily covered by a membrane 33. The deformable material 32 can be a hydrogel (with the problem of alteration over time). Use of glycerine as material with a PP membrane achieved a long standing result. The polypropylene membrane had a thickness of 7.5 um. The liquid tank was a 135x100x7mm Poly(methyl methacrylate) (PMMA) container. This length and width minimized the effect of the edges of the acoustic field on the levitation sites and provided sufficient travel length for transport. The emitters are Langevin piezo transducers (LPTs) used as acoustic sources. The driving voltage is varied within time T between two adjacent LPT (Al and A2) being the wave oscillators 21 and 22 with a maximum value of Ao (120 Volts). This modulation allows the smooth motion of the acoustic node during a period T, time needed to move the acoustic node between two adjacent emitters 21 to 22. This is in line with the procedure shown and explained in connection with control unit 50 in Fig. 1 and Fig. 2A. Here the three points in time during the parabolic or cubic maximum amplitude change are shown with the value Ao times 0, 0.75 and 1. The sphere size of the metal ball 440 here is 5 mm in diameter and travels between two neighboring emitters 21 to 22. The dimple or indentation 35 on the morphing reflector travels along with the acoustic field and the sample 440. For this experiment, a PDMS 33 membrane was used.

The acoustophoretic method is based on the spatiotemporal modulation of the acoustic levitation potential within the acoustic chamber, here a controlled contactless transport of a steel spheres 440 of 5 mm of diameter (density ps= 7.9 kg cm3, total mass = 0.5 g) along a 16 mm path solely by acoustophoretic forces. The acoustically induced dimple 35 moves along with the sample and the acoustic node. In a further experiment, a 2 mm steel sphere (total mass = 32 mg) was moved along a path of several cm.

An enhancement of the levitation forces takes place: the dimple 35 produced on the reflector surface by the radiation pressure has a focusing effect on the field, increasing the force acting on a particle introduced inside of the levitator (higher levitation forces and horizontal stability). The acoustic force magnitude is enhanced up to 120% compared to the rigid flat surface case (reflector of E = 1.02 kPa). This behavior is not monotonic. To this end, if a moderate deformation enhances the field, an excessive deformation reduces it.

The resonant height shift Hr shows also a non-monotonic behaviour: by decreasing the elastic modulus of the reflector a higher deformation is obtained until a minimum height of H = 0.54 λ for E = 1.02 kPa is reached. For the softest reflector with the PDMS membrane the resonance height increases again until H = 0.55 λ. The considered distance H is a reference height measured in the undeformed, initial configuration H _ref , while the real distance in the final configuration is higher, H _rea i. As a consequence, the more the reflector is deformable, the sooner the resonance height is reached. In this case, a softer reflector corresponds to an increase of the real resonant height. This behavior is typical in acoustic levitators: strong emitter/reflector curvatures are usually characterized by higher resonance heights than the plane wave ideal case of H = 0.5 λ. On the other hand, if the deformation spreads over a large area of the deformable reflector, as for the PDMS membrane reflector, its curvature radius increases, requiring a lower reflector height (approaching the plane reflector case).

The acoustic levitation and handling concept presented here provides full control of the acoustic field through the ability of space and time modulation of the acoustic node regions. The concept is realized with the help of a discretized planar resonator platform and a single flat reflector placed at a uniform distance H. Each discrete resonator element is a Langevin piezoelectric transducer (LPT) excited by a sinusoidal voltage at ultrasound frequencies (Fig. 1). The LPT's can be specially-designed and optimized. A novel excitation mechanism enables controllable and smooth propulsion of the levitation potential nodes from one or a group of LPTs to the next. To exemplify this mechanism, the amplitudes of the sinusoidal inputs A _\ (i) and _^ 4 ₂ ( of the two adjacent LPTs are adjusted over the travel period T (time needed for the object to travel the distance d between the centers of two adjacent LPTs) in a parabolic manner as shown in Fig. 1. As a result, a nearly constant acoustic force magnitude during movement is obtained, due to the proportionality of the acoustic force to the square of the driving voltage amplitude (see Methods section). The present set-up can acoustophoretically perform a multi-step process, where two water droplets are introduced, transported from opposite directions, mixed, transported in the orthogonal direction to be mixed with a third droplet, and finally collected.

The physical principle behind the spatial and temporal node modulation is shown in Figure 2A. The transport and mixing of two droplets in a device consisting of a 1 -D array of five LPTs is numerically analyzed using a validated 3-D finite element model (See Methods). The model calculates the levitation potential inside the system as a function of the vibrational velocity of the emitting surface VQ.

Figure 2B shows the experimental results of the horizontal position of the two approaching droplets with four traveling velocities (0.6, 1.1 , 2.2, and 4.9 mm/s) along with the numerical predictions. Before node merging, the velocity of the droplets equals that of the nodes. After node merging, the droplets they carry with approach one another with a primary acceleration, x" _p in the range 0.1-1 ms ^"2 (Fig. 2D), due to the primary scattering field described by the acoustic potential. These acceleration values are in agreement with the model, with the horizontal force being one order of magnitude lower than the vertical force (see Supplementary Note 3). When two droplets come in close proximity (Fig. 2C), the secondary acoustic force starts to dominate, inducing an additional acceleration, x" _s of the order of 1-10 ms ^"2 (the total acceleration can be calculated as X" = X"P + X" ). The theoretical derivation of such a secondary acoustic force induced between two closely placed spheres in an oscillating flow dates back to more than a century ago (reference 17). The present work allows the approach of two objects in a contactless and controllable manner and provides a unique platform to actually observe and investigate this physical phenomenon. To this end, it constitutes the first experimental quantitative confirmation of the secondary acoustic force. Assuming that the density of the spheres p _s is much larger than the density of their environment pO (as in the case of a liquid droplet levitated in air), the attraction force on either sphere F _r when the angle between the direction of wave propagation and the axis connecting two spheres is Θ = 90° (our configuration) is calculated according to reference 17 as,

where r is the center-to-center distance of spheres, R _s i, are the radii of the two spheres, and Vrm _S is the root mean square acoustic velocity of the surrounding fluid which here cannot be measured directly. Supplementary Note 4 explains the numerical model employed to estimate Vrms at the levitation node, where the mixing takes place.

Figure 2D shows the analytical (Eq. 1) and experimental values of x" for two water droplets of R ₅ = 0.84 mm which agree very well. The agreement is also excellent for droplets of different densities (water, p _s = 1 gem ^"3 and tetradecane, ps = 0.76 gem ^"3 ) and radii, spanning over a wide range of acceleration (x " = 0.4÷20 ms ^" , Supplementary Note

4). One distinctive advantage of the present acoustophoretic method is that it features an almost constant acoustic potential magnitude during the node transition between two transducers, which is an important requirement for stable levitation of liquids (reference 18). In fact, not only does the acoustic force have to be strong enough to overcome the gravitational force, it also has to be below the threshold of atomization of the droplet in the acoustic field. Indeed, when the acoustic force is stronger than the interfacial force, the droplet atomizes explosively. The ratio of acoustic to surface forces for a levitated droplet scales with R _s and is described by the acoustic Bond number (reference 19), B _a = 2v rmsPoRs σ, where σ is the surface tension of the liquid. The maximum Rs that can be levitated depends on the critical acoustic Bond number B _a , _cr which was determined experimentally to be between 2.5 to 3.6. The definition of B _a , _cr implies that when V _rms increases, Rs has to decrease. For a driving frequency of 24 kHz, the theoretical upper size limit for water and hydrocarbons is around 2.7 mm and 1.6 mm in radius, respectively. Approaching the upper limit of the static levitated droplet, our method enables transport and mixing of two droplets with large size ratio.

Owing to the above-mentioned feature and the inherent independence of the acoustic force from special material properties (magnetic optical or electrical), a rich palette of combinations of liquid-liquid, liquid-solid and solid-solid transport and interaction is possible.

Fig. 3A to 3C show the different behavior observed during mixing of two water droplets, and two tetradecane droplets. For head on merging of droplets, the different regimes of coalescence, bouncing and separation depend on the Weber number, We = 2R _s u ps/σ, where u is the relative impact velocity (reference 20). The two water droplets coalesce at We = 0.42 (Fig. 3a). Shown in Fig. 3B are two droplets, for which prior to mixing, the low value of B _a (1.85±0.47) prevents atomization. However, after merging due to the larger size of the mixed droplet, B _a increases above critical (2.33±0.59) yielding explosive atomization. Figure 3c shows that two tetradecane droplets first bounce off (We = 0.875), then the acoustic force pushes them back together (double-bouncing) and they coalesce at the second encounter due to the lower impact velocity (We = 0.25).

Figures 3D and 3E show representative solid-liquid interaction scenarios. When a solid polystyrene particle (R _s = 0.5 mm, p _s = 1 gem ^"3 ) and a high surface tension liquid (water) collide, they do not merge. On the other hand, particle encapsulation is observed if a low surface tension liquid such as tetradecane is employed (Fig. 3D). When dealing with a porous or soluble solid particle, two typical configurations are considered. First, if the particle is large enough, it acts as a sponge absorbing the liquid. With evaporation rate of 0.0036 mmV ¹ for water (reference 21), the droplet volume reduction due to evaporation (1.1% over 10 sec) does not play a significant role. Alternatively, small porous particles (instant coffee granule) dissolve in the water droplet (Fig. 3E). If the droplet solution is kept in the device and the water is allowed to completely evaporate, a bowl-shaped particle is formed. The behavior of stationary evaporating droplets containing diluted particles has only recently been studied (reference 22), and the findings are qualitatively comparable to those shown in Fig. 3E.

Biomedical and biochemical processes are among the major areas that could benefit from the presented contactless handling mechanism. Therefore, the biocompatibility of the present, purely acoustic, transport and mixing process was tested by performing contactless DNA transfection, in a temperature and humidity controlled environment (See Supplementary Note 8 for more details). Fig. 3F shows the schematic of the contactless DNA transfection and the transfected cells with blurred edges. Demonstrating similar efficiency and viability as the standard process, our contactless transport method is shown to be biocompatible and suitable for DNA transfection. The occurrence of a photochemical 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 extends the capability of the present concept beyond the spherical or near spherical particle and droplet transport and enables the generation and smooth motion of elongated nodes and similar objects they carry within the chamber. Therefore, an extremely elongated object 240 with a characteristic length L much larger than λ can be also levitated, propelled, transported, and rotated in a controllable manner, going beyond the typical limit of 7 2 for the maximum size of the acoustically levitated samples (Fig. 4). It is worth noting that, to the best of our knowledge, no previously reported acoustic levitation devices, including near field acoustic levitators (reference 23), have been shown to even simply levitate elongated objects of the kind shown in Fig. 4.

The presented device and concept paves the way for new classes of processes, ranging from substrate-free biological and chemical reactions to novel containerless materials processing methods by acoustophoretically transporting and mixing droplets and particles. A wide range of microgravity experiments can now be performed in a convenient, contact free manner in a laboratory environment, and the contactless material handling can be extended to hazardous, chemical or radioactive samples. Fig. 16 shows a schematic of a further contactless multi-drop manipulator according to an embodiment of the invention and its excitation mechanism using feedback information. Pressure sensors 70 are placed on the surface of reflector 30 opposite to the transducers 20. One pressure sensor 70 is positioned opposite from each piezoelectric transducer 20. The sensors 70 are connected to the control unit and are adapted to measure the effect from the field either directly through a hole in the reflector or indirectly through the vibrations the acoustic pressure field induces on the reflector. The forces acting on the sample are the result of the oscillating acoustic pressure field, which is confined inside the acoustic levitator device. Changes in the acoustic pressure field are reflected as changes on the forces the sample experience. This fact enables to translate matter inside the acoustic levitator. During the translation phase, the smooth movement of the sample requires almost constant amplitude of the force acting on the direction of the translation. The design comprises an array of piezoelectric or magnetorestrictive transducers, which emit the acoustic pressure field. It is possible to provide predetermined excitation functions to ensure this constant field. Here, to improve the function of the device and to have a constant force amplitude, the pressure emitted by each transducer 20 is regulated through a feedback loop.

The knowledge of the distribution of the acoustic pressure field can be exploited so as to improve the smoothness of the transport of the samples. Since the measurement of the pressure field in the whole domain between the reflector and the piezoelectric transducers is impossible, the pressure field has to be reconstructed using a limited number of point wise pressure measurements. The best candidate position to acquire these pressure measurements is close to the reflecting surface, as the sensor will not interfere neither with the field itself or the moving sample. A 2D array of pressure sensors 70 is incorporated to the reflector 30, one opposite from each piezoelectric transducer and their signals are provided to the control unit. The reconstruction of the pressure field can be accomplished using the measurements from the sensors along with the knowledge of the actuation level of each transducer.

METHODS SUMMARY

Experimental setup. In the optimized design, the emitting surface of LPTs had dimensions of 15mm l5mm. The working frequency was f = 24.3 kHz corresponding to a wavelength in air of λ = 14.2 mm (See Supplementary Note 6). The amplitude of the excitation voltage was adjusted using an in-house designed microcontroller-based potentiometer and a Lab VIEW program, and was amplified to the desired value using an amplifier (ECLER, DPA-4000T) as shown in Fig. 1 (See Supplementary Note 5). VQ was measured using a laser vibrometer Polytec CLV-2534. Small holes of diameter 1.2 mm in the Plexiglas reflector allowed droplet injection.

Acceleration measurement. The experimental values of velocity and acceleration of two approaching droplets were obtained by processing the images acquired by a high-speed camera (Phantom V9.1). Image processing was performed using the open source package Image J 1.46a.

Acoustic field simulation. The package Simulia Abaqus (6.9) was used to calculate the levitation potential for different vibration amplitudes of the LPTs and the sample position was estimated by determining the levitation potential minima. The model was validated against the experimental values of force acting on a sphere inside an axi-symmetric levitator (Supplementary Note 1,2). At = 24.3 kHz, the characteristic time of the acoustic wave is f ^A = 41 s. Considering that the acoustic force requires between 50 to 100 periods to reach its steady state value, the acoustic potential is valid for object movement in the ms range (reference 24). The quasi-static model suffices, since the characteristic time of the acoustic force (20CH-400 us) is several orders of magnitude smaller than that of the sample movement (T _MIN = 3 s).

SUPPLEMENTARY INFORMATION

Supplementary Note 1 : The Acoustic and gravitational potentials

A time-averaged acoustic potential Ό was introduced by Gorkov (reference 16),

(SI) where p _rms and v _rms are the root mean square of the acoustic pressure and the particle velocity, respectively, p ₀ is the density of the fluid, c is the speed of sound of the acoustic medium, and is the radius of the levitated rigid spherical particle. Its convenient non- dimensional form is:

(S2) where Vo is the oscillation velocity of the transducer VQ = 1 ms ^" in the current simulations). One of the assumptions of the Gorkov theory is that the particle size is much smaller than the wavelength of the acoustic field λ (practically, Rs/λ < 0.1). The levitation force acting on a small sphere can be predicted by:

When dealing with droplets, the gravitational potential influences their position, since the acoustic force should be just enough for levitation (markedly overshooting gravity would cause the atomization of the droplet). The gravitational potential can be described as:

(S4) where z is the vertical coordinate in the direction of gravitation, g = 9.81 ms-2 is the gravitational acceleration, and p _s is the density of the levitated object. The non- dimensional gravitational potential reads:

where V _exp is the velocity amplitude of the emitter in the experiments. Similarly, the total force acting on the particle can be calculated as:

(S6) tJ _to i is the levitation potential and is the sum of the acoustic and gravitational potentials. The nondimensional force is given by: ~ _ d(u ₊ u _g ) _d u _t

(S7)

Supplementary Note 2: FEM acoustic model

The momentum equation for small scale motion of a compressible, adiabatic and inviscid fluid is:

Vp _a +p(x) u = ®,

(S8) where p _a is the excess pressure in the fluid and is the fluid acceleration. The constitutive behavior of the fluid is assumed to be inviscid, linear, and compressible, therefore, we can write: p _a = -K _f Vu,

(S9) where Kf is the bulk modulus of the fluid. We assume that all the variables of interest oscillate harmonically at an angular freqi ω ( ζ = β' ⁶ * ).

Using the harmonic time-derivative relations we obtain:

(S10)

The combination of the spatial derivatives of Eq. (S9) with Eq. (S10) yields:

(Sl l)

Due to symmetry, only half of the domain was modeled. The radiating plate and the reflector were implemented as rigid shells accounting for acoustic-structural coupling. On the radiating plate, the displacement boundary condition was applied. Infinite elements were used at the outer boundary of the acoustic medium. An additional acoustic medium volume was added to the model to avoid the influence of the non-reflecting boundary on the core of the levitator. Supplementary Note 3: The primary acoustic force

To allow planar movement of levitated samples, a flat reflector is used in our acoustophoretic handling device, generating lower levitation power compared to spherical and cylindrical reflectors (references 25 and 26). On the other hand, an acoustic levitator with a flat reflector is less sensitive to changes in height (H) than one with a curved reflector, which results in a smoother acoustic field inside the levitator chamber. It is worth noting that the characteristic dimension of the presented acoustic manipulator is of the order of 0.1 m (~7λ), while the acoustic resonances are sensitive to a 20 μηι (-0.0014λ) change in H. Fig. 5 shows the variation of the maximum \U _t0 with respect to Η/λ at transition time of 1.6J(Fig. 2).

The primary acoustic force acts vertically, counteracting the gravitational force, and horizontally, transporting and stabilizing the sample. We used the FEM model to calculate U _tot for the five-LPT platform configuration (Η/λ = 0.496, V _exp = 2.6 ms ^"1 , time = 1.6J). The model was validated against the experimental values of the force acting on a sphere inside an axi-symmetric levitator (reference 24 and 27). Fig. 6 shows a typical pattern of U _lot at the middle plane. The horizontal and vertical variations of U _tot and the related forces along the lines crossing at the potential minimum (Fig. 6) are shown in Fig. 7. The horizontal force is more than one order of magnitude lower than the vertical one (which overcomes the gravitational force), corresponding to the maximum primary acceleration of around O.lg ~ 1 ms ^"2 .

Supplementary Note 4: The secondary acoustic force

In deriving Eq. (1) of the main manuscript, it has been assumed that r, R _s i, and R _S 2 are small compared to the ultrasonic wavelength λ. Knowledge of v _rms at the pressure node where the coalescence takes place, is needed in order to obtain the force from Eq. (1) of the main manuscript. Since this parameter cannot be measured directly, we used the validated FEM model to estimate it. V ₀ and H can be measured experimentally. Fig. 8 shows the estimated maximum v _rms for V ₀ = 1 ms ^"1 at different values οΐΗ/λ at the time of collision of two spheres (T= 1.6, Fig. 2b).

Fig. 9 shows the analytical and experimental values of acceleration of water and tetradecane droplets of different radii near collision in an acoustic field with respect to their center-to-center distance r. The values of v _rms used for different experimental values of Vo and HA, in Fig. 9 are given in Table SI.

Table S 1 : Estimated v _rms values

Supplementary Note 5: Effects of the excitation function A\(t) andH

As already mentioned, especially when dealing with liquids, a constant magnitude of the acoustic potential during node transition is necessary in the levitator chamber. Once the geometry is fixed, the acoustic potential depends mainly on H, Vo, and A t). Fig. 10 depicts the horizontal positions of the two coalesced water droplets for two values of HIX and parabolic and cubic curves of A t). The figure also shows the reproducibility of droplet movement under the tested conditions. By increasing HIX from 0.489 to 0.507, closer to the resonance {HIX = 0.535, Fig. 5), Vo can be reduced. The transport behavior is similar to the case of HIX = 0.489, noting that at 0.5Tthe node translation is smoother and the oscillations of the levitated sample are larger, especially at merging (1.67). The difference is highlighted in Fig. 1 1, where the 0.6 mm/s case is shown. According to equations (S1)-(S3), the acoustic force is proportional to the second power of the acoustic pressure p and acoustic velocity v. These acoustic quantities are linearly dependent on the emitter velocity VQ. This relationship is also used in equation (S2) to normalize the acoustic potential (Vo ² ). In our assumption, the driving voltage A is proportional to the emitter velocity Vo . Accounting for the relations A oc V ₀ ∞ p _rms and U oc p _RN yields, U∞A ² (SI 2)

In the simplest form of transition, an acoustic node moves over two closely placed LTPs, LPT-1 and LTP-2. If LPT- 1 is emitting and LPT-2 is not emitting, the acoustic node is placed according to LPT-1. Vice versa, the node is placed according to LPT-2, when LPT- 1 is not emitting. When both these LTPs are emitting a continuous, smooth movement of the node requires the use of appropriate excitation functions A _\ (t) and ₂ (/). Assuming that the maximum magnitude of the acoustic potential node within the acoustophoretic levitator \ U _m in\ is given by the sum of the acoustic potential generated by the single LPTs \ Ui _min \ and \ U2min\, the acoustic potential during the transition can be written as:

In particular when dealing with (sensitive, due to possible atomization) liquid samples, \U _min \ should be constant during the entire transition. By combining equation (SI 2 and SI 3) such a constrain can be written as: tfmin l = COnSt∞ (t) + \A ₂ (t) (S 14) A solution satisfying the constraint of equation (S14) is A _x {t) = A _Q cos(t/T - ) and ^( = sin(i/ - f) , with 0≤ t < \T . In our configuration, the LPTs are aligned with a gap in between of around 1 mm. During the transition, at 0.5 T, the acoustic node will travel over this gap, where the acoustic potential is unavoidably slightly reduced. To compensate for this reduction without markedly deviating from the desired constant value of the potential minimum (equation (SI 2)), an overshoot for the potential can be obtained by using the parabolic (quadratic) excitation functions A _x t) - A^{\ - {t/T) ² ) and

A^i) = A ₀ (l - (t/T - Ϊ) ² ) . The results of both trigonometric and excitation parabolic functions, along with their normalized combination as in (SI 4), are presented in the Figure. The choice of the parabolic excitation functions facilitates the passage over the LPT-gap, without imposing a large variation in the minimum potential value (ideally constant), which would endanger the transport of (sensitive) liquid samples.

The Figure shows further the variation of [/-minimum inside the five LTP platform configuration during transport, for four different excitation functions. The linear emission shows an undesirably large decrease of the acoustic force magnitude of more than 50% at times 0.5 T and 1.5 T. The behaviors of the trigonometric and quadratic emissions are similar to one another (as also discussed above). Here it can be further appreciated how the decrease in the magnitude of the potential of the trigonometric emission at 0.5 T and 1.5 J is compensated with the quadratic emission, with a small overshoot around times 0.25 T, 0.75 T, 1.25 J and 1.75 T. A cubic emission results in very large (undesirable) overshoot (approximately 80%) at 1.7 T. Edge effects influence the potential at 0 and T, corresponding to x = 0.6 λ and x = 4.8 λ (Fig. 2). In fact, the absence of an LPT surface at the ends of the device (before the first and after the fifth LPT) results in a reduction of the acoustic potential at these locations.

Regarding x(i) (the horizontal coordinate of the nodes as function of time), it is related to the reflector-emitter height H, or, more generally, to the geometrical parameters of the acoustic chamber (4). Increasing the height H yields a smoother, practically linear motion.

Supplementary Note 6: Design optimization

An LPT is composed of a back metal mass, a front metal mass and a set of piezoelectric elements in between, clamped by a bolt. An envelope of parameters affects the performance of the LPT including, size, thickness and number of piezoceramic disks, material, and dimensions of backing and matching metal pieces, shape of the emitter and the reflector, assembling torque, and input voltage. Hence, a number of factors should be considered in the design of LPTs: a) sufficient acoustic force is needed to levitate waterlike density objects; b) the requirements of a 2D motion and modularity impose the use of a flat reflector, therefore, the enhancement of the acoustic field through concave or cylindrical reflectors is not an option; c) in order to have precise movement control, the characteristic dimension of the radiating plate should be comparable with λ, and d) targeting a 2D array of LPTs and a smooth field transition between the transducers points towards a square or hexagonal geometry. In conclusion, we adopted L PTs with a square radiating plate able to work at ultrasonic frequency (f= 24.3 kHz). In fact, when driven at their resonance frequency, the LPTs are able to provide a high Vo needed to properly couple the ultrasound to the medium (reference 28). However, when driven at high power, the LPTs show strong nonlinearity, temperature and time dependent resonance frequency and a sharp resonance peak. These issues are more serious when dealing with several transducers, since a difference of less than 0.1% in the resonance frequency can prevent the transport mechanism from proper functioning (reference 29). We attempted to minimize the resonance frequency dissimilarity by performing a fastening torque adjustment process during the assembly of the LPTs.

To facilitate the acoustophoresis of matter in air, two key points are addressed here: the piezoelectric transducer is driven close to its resonance frequencies and b) the supplied current is precisely regulated to each of them. The movement of high density samples in air requires a high radiation pressure that can only be achieved close to the resonance frequency of the piezoelectric transducer. Here, the driving frequency for all transducers is preferably common, originating from the signal generator. On the other hand, manufacturing limitations, aging phenomena and non-linearities makes it impossible to construct multiple transducers with their resonance in an adequate enough narrow band that enables the use of a preselected operation frequency. The problem can be addressed by a control system that continuously monitors the differences between the current and the best working frequency region of each transducer and decides on changing or not the operating frequency. Moreover, precise movement of the samples from one point to the other is possible by altering the vibration amplitude of the different transducers. The vibration amplitude is directly proportional to the amplitude of the transducer current. Thus, the ability to accurately define the current provided to the transducer further facilitates the transport of the samples in the acoustic chamber. To regulate the current, a closed loop controlled system can be employed. Measuring the current of each transducer is of importance for the control tasks. The current controller needs direct information of the current amplitude so as to act appropriately. Moreover, the phase difference between the measured current and the known voltage signal produced by the signal generator indicates how far each transducer operates from its resonance frequency. This fact motivates the incorporation of a current sensor in each piezoelectric transducer installed in the levitation device. The actuation mechanism involves two quantities the controller is able to act upon: the frequency of the signal generator, common among the difference transducers, and the amplitude of the voltage signal provided to each transducer. Two separate control loops works in parallel: one to find the best working frequency for the all transducers and the second to regulate the current to each transducer. The controller involved in the first loop is unique for the system and is referred as the "frequency controller", while the second has as many instances as piezoelectric transducers and is referred as the "current controller".

For the implementation of the previously described control concept, a variable frequency oscillator is needed. This oscillator can be implemented as an analog voltage controlled oscillator (VCO) or by a microcontroller using the direct digital synthesis algorithm. The output signal is distributed among the different channels feeding the different piezoelectric elements. A voltage controlled amplifier (VCA) and a high voltage power amplifier are introduced in each channel, before each piezoelectric transducer. Using the VCA, we are able to regulate the voltage amplitude to the specific channel. A current sensor measures the current fed to each transducer. Since we are only interested in the amplitude and the phase difference of the current, signal processing is necessary before provide these information to the controllers. This function can be mapped to a microcontroller or a digital signal processor (DSP). The frequency controller and the current controller functions can be realized by a dedicated module (personal computer (PC), separate microcontroller) or by one of previously mentioned microcontrollers. Note that the control system has multiple characteristics times. The algorithms to produce the oscillating signal and to process the current measurements have the fastest execution requirement. To accomplish satisfactory precision the refresh and sampling rates have to be at least one order of magnitude faster than the driving frequency of the transducers (that is the signal produced by the signal generator). On the other hand, the changes in the transducer vibration do not affect the acoustic field immediately, having a characteristic time of about 50— 100 times the period of the acoustic waves. This fact poses the maximum of the refresh frequency of the controllers, being one to two orders of magnitude lower that the driving frequency of the transducers.

Manipulation of object in a 2D plane requires an array of transducers 10. So as to avoid providing each transducer 10 with a channel, the following technique can be employed. The number of channels can be kept to three and each transducer is multiplexed to all channels using relays. At any given time each transducer will be connected to either one or none of the three channels. For moving samples, there are four possible states that a transducer is probable to have: ramping up, ramping down, having constant maximum power or be turned off. The first three states will be implemented by the three channels. The turn off state can be implemented if the transducer stays disconnected from all channels. This technique allows theoretically to manipulate an arbitrary number of transducers and move samples between them only using three channels. Only one limitation applies on this design: the movement of different particles has to be done either simultaneously or movement of one particle has to start after the movement of the previous particle has finished. The extended system should contain one more controlling module, referred as the "supervision controller". This controller has to main tasks: a) to decide which piezoelectric transducer should be connected to each channel and b) to produce the setpoints for the current and the frequency controller.

As can be seen from the above explanation, wave oscillators can be used having an actuator with a sufficient V ₀ . The experiments were conducted with piezoelectric devices. However, it is clear that magneto strictive transducers can be used as well or other acoustic transducers delivering the necessary and constant acoustic potential.

Supplementary Note 7: Injection

Droplet injection into the acoustic manipulator was easily achieved using a Teflon micropipette with inner diameter of 275 μηι. The acoustic force acts as a body force on the droplet at the outlet of the micropipette. When the sum of the body forces (gravitational and acoustic forces) overcomes the capillary force, the droplet is detached. The capillary force acting on a droplet at the outlet of a pipette of radius R _c is F _c = lnR^. If gravity is the only body force acting on a water droplet, by simply equating the surface tension force to the gravitational force at the point of detachment, the radius of the detached droplet can be found to be R _s = 1.18 mm, corresponding to a volume of 6.9 μΐ. Since R _c is much smaller that the capillary length of water, 3.8 mm, no correction to this calculation is needed (reference 30). The presence of the additional acoustic body force can reduce the droplet size at detachment (for example, in Fig. 9a, R _s , _m in = 0.63 mm, volume = 1.05 μΐ). For hydrocarbons with smaller surface tension, R _s , _min decreases further. The lower limit is set by the critical acoustic Bond number: if the acoustic field is too strong, atomization occurs before droplet detachment.

Supplementary Note 8: DNA Transfection

The transfection of nucleic acids into a cell is a widely used method to induce the expression of a gene of interest by a target cell (when DNA is transfected) or alternatively to down regulate the synthesis of specific proteins (when a small interfering siRNA is transfected). The number of potential application is enormous and mostly depends on the type of target cells and on the vector used to bypass the cellular membrane. The established methods for transfection (Liposomemediated, non-liposomal agents, electroporation, and microinjection) require many steps involving contact with the container walls, cell starvation or two cell passages before plating the transfected cells on the final specimen, and the involvement of critical steps which have to be performed manually by trained personnel. Our contactless handling concept enables the undertaking of most of the required steps in a contact-free and automated manner thus dramatically reducing the amount of reagents required (and thus the related costs) and time of this process.

To demonstrate the potential of our contactless acoustic manipulation concept, HeLa cells were transfected in our device by mixing a drop of cells (at a concentration of 3000 cells/μΐ) in fully supplemented medium with serum (DMEM, Sigma) and a drop of a stock solution containing the transfection reagent (XtremeGENE HP, Roche, 3 μΐ) and a DNA plasmid (1 μg) encoding for enhanced GFP in 50 μΐ (100 μΐ) serum free medium. The two drops fused by levitation were of 2.5 μΐ each. In general, the technique can also be applied to the study of incremental transfections, in which several DNA plasmids can be introduced in the same cells or in a multiple of cells line. The temperature of the chamber was maintained at 36±2°C, while the relative humidity was close to saturation. A humid environment is necessary to slow down evaporation. The process was fully viable; the cells were mixed with the DNA solution in our contactless manipulation platform (requiring a few seconds for merging and remaining thereafter 1 to 5 minutes in steady levitation position) and were subsequently plated into a 96 well plate containing 50 μΐ of fully supplemented medium. After 18 hours of incubation, GFP-positive cells were clearly detected showing high levels of expression. The transfection efficiency of the levitation protocol was comparable to the standard protocol conducted in micro-wells, while the amount of reagents used was reduced by 50-75%. REFERENCES

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BEZUGSZEICHENLISTE actuator plate 52 second actuator signal central actuator 60 horizontal distance d actuator row 61 horizontal gap

actuator row 65 vertical gap H

actuator row 70 pressure sensor

transducer 110 voltage amplitude transducer one 111 no voltage

transducer two 112 ½ max voltage

first movement direction 113 maximum voltage second movement direction 120 levitation potential reflector plate 121 high levitation potential rigid back plate 122 low levitation potential glycerin 141 model first droplet membrane 142 model second droplet deformation 145 move between actuators droplet 146 movement curve Η/λ=0.489 first droplet 147 movement curve Η/λ=0.507 second droplet 150 droplet velocity

third droplet 210 emitter

first mixing result 240 toothpick

second mixing result (output) 340 minimum potential point control unit output 440 heavy object

first actuator signal