Attoliter-level droplet-ordered arrays based on acoustic nano-scissors

Abstract

In the field of nano-fluidics, the generation and manipulation of minuscule droplets with volumes ranging from attoliters (aL) to femtoliters (fL) represents a crucial frontier. Such ultrasmall droplets exhibit immense potential in single-molecule detection, targeted drug delivery, and fundamental research into nanoscale biochemical processes, owing to their unique physicochemical properties, such as low Reynolds number flow and interface-dominated mass transport. Furthermore, ordered liquid-patterned arrays hold promise for applications in optically tunable nano-lenses. However, generation and manipulation of attoliter-scale droplets have long posed significant challenges, particularly for open-interface operations like dispensing, merging, splitting, and patterning into arrays. This study introduces acoustic nano-scissors generated by lateral modes of high-frequency bulk acoustic waves. The induced acoustofluidic effect in thin liquid films forms shear forces between the adjacent wave peaks and wave valleys, thereby successfully cutting the liquid into attoliter-scale droplets at an open interface. This approach could produce droplets with volumes more than three orders of magnitude smaller than those from existing acoustic solutions. Furthermore, the acoustic nano-scissors could generate ordered attoliter droplet arrays with specific patterns, with fast droplet splitting and merging controlled by switching on and off the device. This work provides a novel and flexible solution for various applications requiring attoliter droplet arrays on open interfaces.

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Introduction

Droplets with the attoliter (aL) to femtoliter (fL) volume range have garnered significant attention due to their unique properties and potential applications.^1,2 On the one hand, they exhibit distinct characteristics compared with conventional bulk liquids, making them valuable for fundamental research. For instance, their extremely high surface-area-to-volume ratio profoundly influences phenomena such as reaction kinetics and heat transfer. Interactions with the environment or interfaces become more pronounced, thereby affecting reaction rates, evaporation, and other surface-dependent processes.³ On the other hand, droplets of this scale enable the processing and analysis of exceedingly small sample volumes, significantly enhancing detection limits and sensitivity, as exemplified in single-molecule enzyme-linked immunosorbent assays (ELISA).^4,5 Furthermore, droplet arrays composed of these ultrasmall droplets can be utilized to dispense samples into a multitude of minute reaction vessels, thereby facilitating massively parallel and high-throughput analysis.³ Moreover, by controlling the size and arrangement of these droplets, structures with specific optical properties can be created in practices such as the fabrication of nano-lens arrays for photonic manipulation⁶ and other applications.

However, generating and manipulating droplets within the attoliter to femtoliter volume range presents significant challenges. Typically, in enclosed interfaces, droplet generation based on nanochannel conduits is the most common solution in microfluidics,⁷ which is achieved through the mutual extrusion or shearing of two immiscible liquids.^8,9 Nevertheless, within nanochannels, surface tension and capillary forces become the dominant factors influencing droplet formation and movement. This makes the flow and manipulation of liquids within nanochannels exceptionally difficult, readily leading to issues such as high flow resistance and clogging.¹⁰ To address such problems, interface modification¹¹ and active field-assisted fabrication¹² are commonly employed. For instance, James Friend et al.¹³ utilized 40 MHz-range surface acoustic waves (SAWs) to manipulate 200 fL droplets within a nanochannel. By creating localized widened regions along the channel to act as traps, they successfully achieved the propulsion, splitting, mixing, and merging of individual 200 fL droplets.

On the other hand, generating femtoliter to attoliter droplets on open platforms overcomes the flow limitations of traditional enclosed microchannels and offers advantages such as independent addressability and the construction of droplet arrays. Existing open-platform droplet generation techniques typically involve creating pre-defined structures on a surface or printing droplets onto an open surface. Examples include photolithography, inkjet printing,^14,15 condensation-driven nucleation,¹⁶ depositing droplets on pre-patterned substrates,¹⁷ or utilizing solvent exchange for nanodroplet growth.¹⁸ Generally, these methods necessitate the preparation of pre-set surface structures. For instance, Bao et al.⁶ fabricated arrayed, ordered femtoliter-scale droplets on smooth, hydrophobically pre-patterned microdomain arrays on a hydrophilic substrate.

High-frequency acoustic waves have shown great potential to flexibly manipulate liquids on open platforms with no pre-defined structures. SAWs generate acoustic streaming within droplets at the Rayleigh angle,¹⁹ thereby inducing droplet transport, splitting, and delivery operations.²⁰ In the realm of droplet generation, SAW-based atomization and jetting techniques are well-established for producing picoliter and even femtoliter-scale droplets by inducing capillary instability in the source liquid.²¹ However, when it comes to the manipulation of discrete, independent droplets on an open interface, this capability has long been limited to the much larger microliter to nanoliter range.²² For example, James Friend et al.²³ employed SAWs to act on microliter-scale droplets and initiated weak rotational flow within the droplets, successfully splitting a single droplet into two droplets. However, the controlled formation of micrometer-sized attoliter droplet arrays on open interfaces using acoustic waves has remained a significant challenge to date.²⁴

To address the mentioned challenge, this work adopts acoustic nano-scissors (ANS) that utilize ultrahigh-frequency bulk acoustic waves and coupled acoustofluidic effects, enabling the cutting of liquid films to controlled attoliter-scale droplet arrays on surfaces. Bulk acoustic wave resonators excite strong lateral modes acting on the liquid film, which creates an effect we term ‘acoustic nano-scissors’ with nano-cutting capabilities. Droplet formation and fusion can be achieved by switching the device on and off, enabling the generation of specific shape droplet arrays on open surface systems.

Results and discussion

Principle and design

The ultrahigh-frequency bulk acoustic wave (BAW) resonator primarily comprises a resonant layer and a Bragg reflector layer. The resonant layer generates acoustic resonance via the piezoelectric effect, while the Bragg reflector suppresses downward acoustic wave leakage through a multilayer structure composed of materials with varying acoustic impedances. For the specific manufacturing process and structure of the device refer to the SI. A symmetric design enhances the excitation of lateral bulk acoustic wave modes within the resonator. Based on this lateral mode, we designed acoustic nano-scissors with nanoscale cutting capabilities (Fig. 1). As shown in Fig. 1(a), liquid thin films spread on the surface of the acoustic nano-scissors are segmented into attoliter-scale droplets under resonant operation, and the droplets can form different array types according to various symmetric designs of the device. Under the lateral mode, when the resonator couples the periodic oscillations of acoustic wave peaks and troughs into the liquid, strong volumetric forces at the wave peaks cause protrusions to form on the liquid surface, as shown in Fig. 1(b). Two adjacent wave peaks act as nanoscale scissors, enabling precise liquid segmentation.

Fig. 1 Conceptual diagram of the working principle of acoustic nano-scissors: (a) schematic diagram showing the acoustic resonator structure of the acoustic nano-scissors and the effect of device switching on liquids. (b) Cross-sectional diagram of the acoustic nano-scissors cutting liquids. N represents the normal direction of the liquid surface, P_s represents the pressure induced by surface tension, the blue sinusoidal curve represents high-frequency acoustic waves, and the arrows indicate the propagation direction of bulk acoustic waves.

The piezoelectric aluminum nitride thin film used in the resonant layer simultaneously excites longitudinal and transverse waves under high-frequency electric voltage stimulation. These two waves superimpose in space to form Lamb waves, resulting in energy distribution in both thickness and in-plane directions (Fig. 2(a)). Owing to the differing acoustic velocities of the longitudinal and transverse waves within the material, wave dispersion occurs, causing Lamb waves to exhibit distinct vibrational modes at different frequencies.^25,26 These include the symmetric mode (S₁) and antisymmetric mode (A₀), among others. The surface vibration distribution can be determined by solving the Rayleigh–Lamb equation. Given a plate thickness of h, and by applying the stress-free boundary conditions at the surfaces along with the wave-propagation characteristics into the elastic constitutive equations, the Lamb wave equation can be derived:²⁷

Fig. 2 Working principle of the lateral mode in bulk acoustic wave resonators. (a) Cross-sectional view showing laterally transmitting Lamb waves formed by the superposition of transverse and longitudinal waves. (b) Top-view showing the propagation and reflection paths of laterally transmitting Lamb waves under different boundary conditions. (c) Surface stress distribution diagram of a circular resonant device. The colors in the legend represent stress magnitude.

In the equations, k denotes the acoustic wave number, representing the number of acoustic wave cycles per unit length in the corresponding direction. The terms k_l and k_s refer to the wave number components of the longitudinal and transverse acoustic waves, respectively. h indicates the thickness of the thin film or plate medium. c_l and c_n represent the longitudinal and transverse wave velocities of the material, respectively, and ω is the angular frequency. The ±1 exponent in eqn (1) selects between two distinct families of modes: an exponent of +1 defines the symmetric Lamb modes (S₀, S₁, etc.), where particle displacement is symmetric about the plate's central plane. Conversely, an exponent of −1 defines the antisymmetric modes (A₀, A₁, etc.), which exhibit a bending motion. Using our device's film thickness of h = 1.1 μm, we solve these equations to generate a set of dispersion curves. These curves plot frequency versus lateral wave number, mapping all possible Lamb wave modes for the structure. The primary objective of the acoustic nano-scissors is to generate a stable, periodic pattern of wave peaks and valleys on the device surface. To achieve this, we selected the symmetric Lamb wave mode (exponent = +1). Analysing the dispersion curves allows us to purposefully excite a specific lateral mode. This choice is fundamental to the device's function, as the resulting mode dictates the physical spacing and distribution of the wave peaks.

On the other hand, lateral boundaries play a critical role in device design. Acoustic waves undergo reflection at the lateral boundaries of the device, and if the incident and reflected waves satisfy specific resonance conditions, specific resonance modes can be established. As illustrated in Fig. 2(b), when the device boundary is triangular, laterally propagating acoustic waves tend to concentrate and reflect within the acute angles, resulting in continuous frequency resonances. For quadrilateral boundaries, acoustic Lamb waves more readily form resonances between the parallel sides. In contrast, pentagonal shapes lack both acute angles and parallel sides, and thus rarely support the formation of lateral mode resonances. In the case of circular boundaries, the complete geometric symmetry facilitates the formation of resonances across the entire plane, leading to stronger lateral modes and making circular geometries more suitable for the nano-scissors structure. Furthermore, the spacing and distribution between adjacent wave peaks and valleys can be calculated via finite element simulations. The simulated vibration pattern is shown in Fig. 2(c), where acoustic wavefronts undergo phase accumulation due to periodic reflections at the boundaries during radial propagation. At this point, the device surface exhibits alternately distributed wave peaks and valleys, with spatial periodicity determined by the wave number of the lateral mode. The operating frequency of the device used in this study is 2560 MHz. The compact acoustic field structure generated by lateral mode excitation is key to overcoming the spatial resolution limitations of conventional SAW technology. When the frequency is 2560 MHz, the width of the trough is approximately 2 μm, which limits the diameter of the droplet formed. When the peak-to-valley spacing of lateral acoustic waves is compressed to the micrometer scale, the region affected by the acoustic pressure can be confined to micrometer scale dimensions. This allows the volumetric force to produce sufficient pressure gradients on this short distance, effectively overcoming capillary forces and viscous resistance to form nanodrops. Consequently, this provides the technical foundation for achieving precise control functionalities of the ANS in open systems.

Experimental

Liquid cutting by nano-scissors

When the acoustic nano-scissors (ANS) act on liquids within a certain viscosity range, the liquid spreads into thin films. The liquid used here is light liquid paraffin, which at 20 °C has a density of approximately 0.83–0.86 g mL⁻¹, a dynamic viscosity of around 50 mPa s, and a speed of sound of 1440 m s⁻¹. As illustrated in the conceptual diagrams in Fig. 3(a) and (b), the liquid film is initially relatively thick, but gradually thins under sustained acoustic wave excitation. Specifically, the film thickness can be reduced to the sub-micrometer scale,²⁸ and ultimately, micrometer-scale droplets are formed under the action of the nano-scissors. The formation process based on the acoustic nano-scissors mechanism proceeds as follows: at the initial time point (0 ms), the liquid is uniformly distributed on the device surface, forming a relatively thick liquid film referred to as the bulk liquid (BL). Upon activation of the acoustic nano-scissors, the upper oil film is rapidly displaced, and the liquid film begins to exhibit pronounced flow behavior under acoustic excitation, forming a steep leading edge. This transitional stage is defined as the intermediate film (IF), which subsequently evolves into an ultrathin film (UF). Due to the lateral vibration mode generated on the device surface, local velocity changes occur at the liquid film front edge, thereby triggering the fingering instability mode of the liquid film.²⁹ As shown in Fig. 3(c), at 23 ms, continued acoustic excitation causes the liquid film flow to become unstable, compressing localized regions into a “platform-like” IF. This platform-like region subsequently migrates outward along the film and develops into an UF. Meanwhile, the lateral-mode bulk acoustic wave resonator produces a periodic distribution of pressure nodes and antinodes. At the antinodes, the liquid experiences an upward acoustic radiation force, causing the surface to rise and form capillary ridges—sharp protrusions of the liquid. In the ultrathin film regions, concentric ring-like structures can be observed. At 46 ms, driven by surface tension, the liquid film ruptures at the antinodes, resulting in the formation of micrometer-scale droplets.

Fig. 3 Schematic diagrams and experimental images of attoliter droplet formation driven by acoustic nano-scissors. (a) Top-view and (b) side-view schematics showing different thickness regions of liquid thin films formed under acoustic nano-scissors excitation. TE represents the top electrode and BE represents the bottom electrode. (c) Experimental images at 0 ms, 23 ms, and 46 ms under 100 mW power.

The film thinning and rupture process is governed by a three-stage acoustic streaming mechanism,²⁸ with transitions dictated by the ratio of film height H to acoustic wave length λ and viscous penetration depth γ. Initially, in the thick film regime (H ≫ λ, where λ ≈ 560 nm), Eckart streaming, driven by a bulk force from acoustic energy absorption, causes rapid fluid displacement. As the film thins to the sub-micron level (H ∼ λ), the mechanism transitions to Rayleigh streaming, characterized by a stable convective drift that forms the intermediate film (IF). Finally, when the thickness approaches or falls below the viscous penetration depth (H ≥ γ, where ≈ 100 nm and μ, ρ, ω are the dynamic viscosity and density of the fluid and the angular frequency of the sound waves, respectively), boundary-layer-dominated Schlichting streaming becomes predominant. This flow, featuring periodic counter-rotating vortices, organizes the fluid into aggregation and depletion zones, completing the thinning and sculpting the film morphology for subsequent droplet formation. The sequence of these transitions is controlled by the geometric ratios (H/λ and H/γ) and is thus critically dependent on the operating frequency that defines λ and γ. While the applied power (100 mW in this work) does not control the transition sequence, it must be sufficient to overcome viscous and capillary resistance, influencing the thinning rate. Droplet generation is ultimately triggered when the localized shear stress induced by the acoustic field overcomes the capillary resistance, effectively “cutting” the liquid.

At open interfaces, droplet merging and splitting using acoustic nano-scissors represent a crucial process. When a small amount of the liquid film is present on the device surface, acoustic wave energy is directly transferred to the liquid, enabling controlled droplet merging and splitting. As shown in Video S2, upon device activation, acoustic energy from the bulk acoustic wave resonator couples into the fluid, leading to the formation of acoustic nano-scissors that segment the liquid film on the surface into discrete microdroplets. When the device is deactivated, the volumetric forces induced by acoustic waves vanish, and the liquid reverts to its original state under the influence of viscous and capillary forces. In the acoustic streaming model, these volumetric forces, f, arise from the momentum flux generated by the attenuation of acoustic waves, and are expressed as:^30,31

f = −ρ₀〈(v₁·∇)v₁ + v₁(∇·v₁)〉 (3)

where v₁ represents the acoustic wave velocity distribution entering the fluid. The S₁ mode vibration excited on the upper surface of the device is oriented perpendicular to the transducer surface. The direction of the volumetric forces near the fluid–air interface aligns with the direction of acoustic wave propagation. In the numerical model, an air layer is defined above the liquid, and a two-phase flow model is constructed. Based on the Navier–Stokes (N–S) equations, the following governing equations are derived:ρ₀, v₀, p₀, μ, and μ_B represent the density, velocity, pressure, dynamic viscosity, and bulk viscosity of the liquid, respectively; r_s and n denote the position coordinates and the unit normal vector of the liquid surface, respectively. Volumetric forces deform the liquid thin film, while gravity and surface tension partially constrain these forces, resulting in a regular pattern of surface deformation. Using COMSOL software simulation, we obtained the simulation results shown in Fig. 4(a). To simplify the calculation, a 2D model is used here to simulate an arbitrary circular cross-section of the 3D system through the origin, accurately capturing the radial physical process of the interaction between the device and the droplet above it. Specific modeling parameters and steps are also included in the SI. After device activation, the liquid thin film is divided into multiple peaks and valleys due to volumetric forces, ultimately splitting into droplets. As shown in Fig. 4(b), the elongated annular droplets originally formed by acoustic nano-scissors undergo further geometric amplification under surface tension. This ultimately leads to the Rayleigh–Plateau instability in liquid columns with aspect ratios exceeding the critical value, generating smaller-scale discrete droplets. Through optical characterization and droplet size statistics, these secondary splitting droplets exhibit diameter distributions ranging from 500 nm to 3 μm, with approximately 20% of droplets falling within the 0.5–1 μm range (Fig. 4(c)). Although the global size distribution of droplets spans a broad range of 0.5–3 μm, local regions demonstrate significant size clustering. Experimental observations reveal that droplet populations formed within specific breakup radii exhibit similarity, with droplets of 1.5–3 μm diameter and 0.5–1 μm diameter clustering at different spatial radii, presenting a distribution where smaller radii correspond to larger diameters. Because the acoustic wave amplitude generated by the circular resonator varies with the radius, the acoustic energy intensity differs at various radial positions. Regions with higher acoustic energy can aggregate more liquid into the capillary protrusions, forming annular liquid columns with larger initial cross-sectional volumes and diameters. Consequently, the size of the droplets generated from the final breakup exhibits this spatial dependence. This splitting characteristic enables the system to generate and collect droplets of specific particle sizes through parameter control, providing droplet size diversity. Taking 500 nm droplets as an example, when approximated as hemispheres, their volume is approximately 37 attoliters. Compared with SAW technology and electrowetting-on-dielectric (EWOD) approaches, the acoustic nano-scissors technology reduces the droplet volume by more than three orders of magnitude. This efficient preparation capability for micrometer droplets provides a new technical pathway for precision applications such as nano-drug carrier preparation in microfluidic chips.

Fig. 4 (a) Simulation diagram of droplet formation, showing the state of the liquid film on the device surface before and after device activation, where red represents the liquid phase and blue represents the air phase. (b) Bright-field microscopy images of droplet formation after device activation. (c) Droplet size distribution statistics.

Conclusions

To address the physical limitations of traditional acoustic methods in the generation of minute droplets, this work proposes a novel acoustic shearing mechanism based on bulk acoustic wave resonators. By generating micrometer-scale wave peaks and valleys on the device surface through high-frequency acoustic excitation, ultra-high volumetric force gradient fields are induced at the solid–liquid interface, triggering liquid film shearing effects and achieving, for the first time, acoustically controlled preparation of attoliter droplets with diameters on the order of hundreds of nanometers. This droplet manipulation is achieved without the need for enclosed microfluidic channels, making the approach particularly advantageous for open-system operations involving biological samples. This technology breaks through the lower limit of fluid size control by acoustic waves and overcomes the bottleneck of traditional acoustofluidics, which struggle to generate sub-femtoliter (fL) droplets due to limitations imposed by acoustic wavelengths and their operating mechanisms.

Author contributions

Wei: data curation (lead); methodology (lead); writing – original draft (lead) and review & editing (equal). Zhaoxun Wang: investigation (lead); supervision (lead). Yiming Liu: investigation (equal). Xinyuan He: investigation (equal). Bingnan Wang: resources (equal). Yaping Wang: resources (equal). Menglun Zhang: writing – review & editing (lead). Xuexin Duan: conceptualization (lead).

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information: the SI also includes specific device simulation and fabrication steps, as well as videos of droplet formation. See DOI: https://doi.org/10.1039/d5lc00807g.

Acknowledgements

Quanning Li, Xuejiao Chen, Bohua Liu, and Chongling Sun are acknowledged for their help with device fabrication.

Notes and references

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