Acoustophoretic contactless transport and handling of matter in air

Abstract

Levitation and controlled motion of matter in air have a wealth of potential applications ranging from materials processing to biochemistry and pharmaceuticals. We present a unique acoustophoretic concept for the contactless transport and handling of matter in air. Spatiotemporal modulation of the levitation acoustic field allows continuous planar transport and processing of multiple objects, from near-spherical (volume of 0.1–10 μL) to wire-like, without being limited by the acoustic wavelength. The independence of the handling principle from special material properties (magnetic, optical, or electrical) is illustrated with a wide palette of application experiments, such as contactless droplet coalescence and mixing, solid–liquid encapsulation, absorption, dissolution, and DNA transfection. More than a century after the pioneering work of Lord Rayleigh on acoustic radiation pressure, a path-breaking concept is proposed to harvest the significant benefits of acoustic levitation in air.

Contactless transport and handling of matter are of fundamental importance to the study of many physical phenomena (1, 2) and biochemical processes (3). Typical state-of-the-art methods of contactless handling of matter are based on electromagnetic (4–6) principles and have interesting capabilities but also clear 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 handling of microsized particles suspended in a liquid (12, 13), where buoyancy forces are almost entirely responsible for the levitation, various drawbacks in the state of the art of acoustic levitation have prohibited the realization of controlled and reliable transport of matter in air, thereby limiting the remarkable potential and utility of acoustic levitation (14–16). Its full exploitation requires fundamental advances leading to material transport with high controllability 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 acoustically levitated droplets and particles in air. This is a significant advance in the area of contactless handling in air, making it a viable complementary methodology to existing advanced approaches in a liquid environment (17, 18), one that has its own unique features, expanding the horizon of possible applications. The concept is based on the ability to modulate the acoustic node regions in the acoustic field spatially and temporally, enabling the reversible transition from material trapping to transport. Additionally, the levitation and handling of extremely elongated objects with a characteristic length much longer than the acoustic wavelength is demonstrated through their transport and rotation.

Results and Discussion

In acoustic levitation, a standing wave is established between an emitting surface and a reflector (9, 11, 19). The radiation pressure, a nonlinear property of the acoustic field, engenders the levitation potential [the sum of the acoustic potential (20) and the gravitational potential; SI Text, section 1]. This varies nonmonotonically between the emitting surface and reflector. If it is 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 (ρ_s and β_s) and of the surrounding medium [ρ₀ and β₀ (21)]. To this end, note that ρ_s > ρ₀ and β_s < β₀ in 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 single flat reflector placed at a uniform distance H. Each discrete resonator element is a specially designed and optimized Langevin piezoelectric transducer (LPT) excited by a single sinusoidal signal voltage of ultrasound frequency f (Fig. 1 and Methods). A newly developed excitation mechanism allows controllable and smooth propulsion of the levitation potential nodes from one LPT or a group of LPTs to the next. In this mechanism, the amplitudes of the sinusoidal inputs A₁(t) and A₂(t) of the two adjacent LPTs are varied 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 (Methods). Movie S1 demonstrates the capability of the present mechanism to perform a multistep planar process in air acoustophoretically, 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. We are not aware of any other method or technology able to perform such multidroplet transport and handling in a gaseous environment.

Fig. 1.

Schematic of the contactless multidrop manipulator and its excitation mechanism. In the illustrative example, droplets are introduced into the system 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 rows are on the same plane, parallel to the reflector plane. The droplets move and mix, and the final sample is delivered to the outlet. The introduction of droplets into the system can be achieved either manually with a micropipette or with an automatized syringe pump and a glass capillary (Methods). The reflector height H is adjusted with a linear micrometer stage.

The physical principle behind the demonstrated controlled acoustophoretic transport of matter lies in the spatiotemporal modulation of the levitation acoustic field, shown in Fig. 2A and Movie S2. The transport and mixing of two droplets in a device consisting of a 1D array of five LPTs are numerically analyzed using a validated 3D finite element model (Methods). The model calculates the levitation potential inside the system as a function of the vibrational velocity of the emitting surface V₀. Fig. 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. Note that air has a very low damping effect and oscillation of the samples is present. However, the droplets are stably kept at the middle of a node for a wide range of transport velocities. Fabrication tolerances are challenging for acoustic resonances (Methods), but future purely technical improvements in platform fabrication will certainly help reduce such fluctuations, which, although possibly presenting a problem to individual sample analysis (22), are not expected to affect sample advancing and processing seriously.

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 levitation nodes 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 four traveling velocities, along with the numerical predictions (Figs. S6–S8). The oscillations of the droplets during translation are due to the very low damping effect of the surrounding fluid (air). (C) Experimental movement velocity () of one of the two approaching water droplets. (D) Analytical and experimental values of total acceleration () 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 primary acceleration due to the acoustic potential field. The experimental uncertainty in the estimation of v_rms is reflected in the error bars of the analytical data.

Before node merging, the velocity of the droplets equals that of the nodes. After node merging, the droplets approach one another with a primary acceleration, in the range of 0.1–1 m/s² (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 (SI Text, section 3, and Figs. S1–S3). When two droplets come into close proximity (Fig. 2C), the collision velocity increases sharply, with an additional acceleration of the order of 1–10 m/s², which cannot be solely explained with the primary acoustic field. Understanding of the underlying physics is critical to realize acoustophoretic merging of droplets.

A secondary acoustic field originating from the scattering of the primary waves on the two levitated objects significantly contributes to the collision dynamics (the total acceleration is calculated as ). The theoretical derivation of such a secondary force for the simple case of two closely placed spheres in an oscillating flow dates back to more than a century ago (23). The present work provides a unique platform to observe and investigate this physical phenomenon. To this end, the present results constitute experimental quantitative confirmation of such secondary acoustic force (SI Text, section 4). Assuming that the density of the spheres ρ_s is much larger than that of ρ₀ (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 as (23):

where r is the center-to-center distance of spheres; R_s1 and R_s2 are the radii of the two spheres; and v_rms is the rms acoustic velocity of the surrounding fluid, which cannot be measured directly here. SI Text, section 4 explains the numerical model used to estimate v_rms at the levitation nodes, where the mixing takes place (Fig. S4). Fig. 2D shows the analytical and experimental values of for two water droplets of R_s = 0.84 mm, which agree very well. The agreement is also excellent for droplets of different densities (ρ_s = 1 g/cm³ for water and ρ_s = 0.76 g/cm³ for tetradecane) and radii, spanning over a wide range of acceleration ( = 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 possibilities of matter that can be simultaneously handled provide a rich palette of combinations of liquid–liquid, liquid–solid, and solid–solid transport and interaction.

One distinctive advancement 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 (24). In fact, not only does the acoustic force have to be strong enough to overcome the gravitational force, but it 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 forces to surface forces for a levitated droplet scales with R_s and is described by the acoustic Bond number (25), B_a = 2v²_rmsρ₀R_s/σ, where σ is the surface tension of the liquid. The maximum R_s that can be levitated depends on the critical acoustic Bond number B_a,cr, which was determined experimentally to be between 2.5 and 3.6 (25). The definition of the B_a,cr implies that when the v_rms increases, the R_s has to decrease strongly. 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 (24). Approaching the upper limit of the static levitated droplet, our method allows transport and mixing of two droplets 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-on merging of droplets, the different regimes of coalescence, bouncing, and separation depend on the Weber number, We = 2R_su²ρ_s/σ, where u is the relative impact velocity (26). The two water droplets coalesce at We = 0.42 (Fig. 3A and Movie S3). Shown in Fig. 3B are two droplets for which, before merging, the low value of B_a (1.85 ± 0.47) prevents atomization. However, after merging, due to the larger size of the resulting combined droplet, B_a increases above the critical point (2.33 ± 0.59), yielding explosive atomization (Movie S4). In Movie S5, explosive atomization occurs at the very beginning of the merging process (B_a = 2.03 ± 0.72 and B_a = 1.93 ± 0.68). The slow motion of this movie captures visually the effect of the secondary acoustic force discussed earlier, causing significant deformation of the droplet just before merging. Fig. 3C shows that two tetradecane droplets first bounce off (We = 0.875), the acoustic force then brings them back together (double bouncing), and they coalesce at the second encounter due to the lower impact velocity (We = 0.25; Movie S6).

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). The colored image at the bottom shows an instant coffee particle before and after the mixing/evaporation process. (F) Schematic of the contactless DNA transfection process and micrographs of the transfected cells with blurred edges. The transfection agent (TA) was premixed with the DNA solution. (G) Mixing experiment of fluorescein droplet (Left), with a logarithmic acid dissociation constant of pK_a = 6.4 and pH 3, and of a droplet of physiological solution with pH 12 (Right). (Scale bars: B–E, 1 mm.)

The above-mentioned material independence of acoustic levitation allows an unprecedented flexibility in the handling and interactions of solid and liquid entities. Fig. 3 D and E shows representative solid–liquid interaction scenarios. When a solid polystyrene particle (R_s = 0.5 mm, ρ_s = 1 g/cm³) and a liquid (water) with a high surface tension collide, they do not merge (Movie S7). On the other hand, particle encapsulation is observed if a low surface tension liquid, such as tetradecane, is used (Fig. 3D and Movie S8). The delicate nature of the acoustophoretic forces is advantageous when dealing with fragile materials, such as crystals and porous media. In this respect, two typical configurations of porous particle contactless transport and interaction with a liquid drop are considered. First, if the particle is large enough, it acts as a sponge, absorbing the liquid (Movie S9). With an evaporation rate of 0.0036 mm²/s for water (27), the droplet volume reduction due to evaporation (1.1% over 10 s) does not play a significant role. Alternatively, small porous particles (e.g., instant coffee granule) dissolve in the water droplet (Fig. 3E and Movie S10). If the droplet solution is kept in the device and the water is allowed to evaporate completely, a bowl-shaped particle is formed. The behavior of stationary evaporating droplets containing diluted particles has only recently been studied (28), and the findings are qualitatively comparable to those shown in Fig. 3E.

The inherent substrate-independent and contamination-free characteristics of the presented concept can be beneficial to major areas of biomedical and biochemical processes. Therefore, its biocompatibility was tested by performing contactless DNA transfection in a temperature- and humidity-controlled environment (Methods). 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 of the present method allows the levitation and transport functions of such nodes to be manifested in collaborative manner, wherein several nodes act as a group and can even merge to form a single elongated node and carry out a task. This extends the capability of the present concept beyond the handling of spherical or near-spherical particle and droplet transport and to the controlled motion of very elongated, wire-like objects. As a result, an extremely elongated object with a characteristic length L much larger than λ can be levitated, propelled, transported, and rotated in a controllable manner, going beyond the widely accepted limit (9, 11, 14, 15, 27) of λ/2 for the maximum size of an acoustically levitated sample (Fig. 4 and Movie S11). It is worth noting that, to the best of our knowledge, no previously reported acoustic levitation devices, including near-field acoustic levitators (29), have even been shown to levitate elongated objects of the kind shown in Fig. 4.

Fig. 4.

Contactless transport of an elongated object (a toothpick with L= 8 cm ≈ 6λ, H ≈ λ). Controlled rotation: top view (A) and side view (B). (C) Controlled translation: top view. In principle, there is no limit to the length of the object that can be handled.

Conclusions

The presented 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. Matter can now be manipulated at atmospheric conditions by counteracting the effect of the gravitational force, without requiring a microgravity environment to remove its presence, and the contactless material handling can be extended to hazardous, chemical, or radioactive samples. Because the occurrence of a phase change in the samples is not expected to affect their handling by the acoustophoretic force, related exothermal and endothermal reactions do not limit the field of applications of the presented concept. Magnetic, electrostatic, diamagnetic, and optical forces can be coupled with the acoustophoretic handling to enhance even further the stability and the degrees of freedom of the manipulation.

Methods

Experimental Setup.

An LPT is composed of a back brass mass, a front aluminum mass, and a set of piezoelectric elements between the two, clamped by a bolt (SI Text, section 6, and Fig. S9).

In the optimized design, the emitting surface of LPTs had dimensions of 15 mm × 15 mm. The working frequency was f = 24.3 kHz, corresponding to a wavelength in air of λ = 14.2 mm. The amplitude of the excitation voltage was adjusted using an in-house-designed microcontroller-based potentiometer and a LabVIEW program (National Instruments), and it was amplified to the desired value with an amplifier (DPA-4000T; ECLER), as shown in Fig. 1. The amplitude resolution of the driving signal A_i(t) determines the movement resolution of the object. We used an eight-bit digital signal (256 levels) for controlling the amplitude, and with d = 16 mm, the theoretical movement step size is calculated to be 16 × 10⁻³/256 ≈ 62 μm. Due to the nonlinearity of the LPTs and the 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 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 allowed droplet injection.

The Numerical Model.

The Simulia Abaqus (6.9) package 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. A 3D finite element model was implemented to solve the linear acoustic equations in the frequency domain (SI Text, section 2). The linear acoustic pressure and particle velocity are sufficient to determine the radiation force (nonlinear) based on the levitation potential approach (SI Text, section 1). 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 nonreflecting boundary on the core of the levitator. The model was validated against the experimental values of force acting on a sphere inside an axisymmetrical levitator (30). The implemented quasistatic model suffices for our analysis. The characteristic time scale of the acoustophoretic forces is related to the characteristic time of the radiation pressure . The radiation pressure acting on a sphere in a standing wave becomes fully established after a period of , with being the number of acoustic wave cycles needed to reach steady state and being the wave period. was determined numerically to be between 50 and 100 (30, 31). The characteristic time of a sample transported at an average linear speed is defined as , and for our case, λ∼d → . When using the acoustic potential for the dynamic analysis, we assume . In our experiments, the highest linear transport speed of 4.9 mm/s corresponds to , which is much larger than , justifying our assumptions.

Droplet Input Method.

In the feasibility studies carried out in this paper, droplet input into the acoustic manipulator was easily achieved using a Teflon micropipette with an outer radius R_c = 150 µm (Movie S1). The acoustic force acts on the droplet at the outlet of the micropipette and scales with its volume R_s³, as the gravitational force (SI Text, section 1). When the sum of the two forces (gravitational and acoustic) 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 = 2πR_cσ. If gravity is the only 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 is determined to be R_s = 1.18 mm, corresponding to a volume of 6.9 μL. Because R_c is much smaller than the capillary length of water, 3.8 mm, no correction to this calculation is needed (32). The presence of the additional acoustic force can reduce the droplet size at detachment (e.g., in Fig. S5A, R_s,min = 0.63 mm, volume = 1.05 μL). For hydrocarbons with a 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.

DNA Transfection.

HeLa cells were transfected in our device by mixing a drop of cells (at a concentration of 3,000 cells per microliter) in fully supplemented medium with serum (DMEM; Sigma) and a drop of a stock solution containing the transfection reagent (3 μL of XtremeGENE HP; Roche) and a DNA plasmid (1 μg) encoding for enhanced GFP in 50 μL (100 μL) of serum-free medium. 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 incremental transfections, in which several DNA plasmids can be introduced in the same cells or in a multiple of the cell line. The temperature of the chamber was maintained at 36 ± 2 °C, and 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 for 1–5 min in a steady levitation position) and were subsequently plated into a 96-well plate containing 50 μL of fully supplemented medium. After 18 h of incubation, GFP-positive cells were clearly detected showing high levels of expression. The transfection efficiency of the levitation protocol was comparable to that of the standard protocol conducted in microwells, whereas the amount of reagents used was reduced by 50–75%.