Particle distributions in Lamb wave based acoustofluidics

Particle separation is a crucial research area, and in cell biology,¹ biomedicine,² and chemistry,³ particles (microspheres, cells, protein molecules, etc.) must be separated from samples for disease diagnosis⁴ and other clinical applications. In recent years, various techniques have emerged for manipulating particles either macroscopically or microscopically,^5,6 such as immunomagnetic cell separation,⁷ fluorescence-activated cell sorting,⁸ and density gradient centrifugation.⁹ These methods have shown great practicability and potential for particle separation, but they are relatively complex and time-consuming. Compared to conventional particle separation platforms, microfluidic^10,11 platforms have the advantages of material savings and cost reduction and are suitable for developing miniaturized equipment. Therefore, it is very important to design microfluidic particle separation platforms, and in recent years several methods based on fluid mechanics,¹² acoustics,^13–15 electricity,¹⁶ and optics¹⁷ have shown their potential in practical applications.

Most hydrodynamic methods require customized design of the microfluidic structure. For example, designing a microchannel as an expansion–contraction structure¹⁸ allows fluid inertia¹⁹ to be used to generate microvortices for particle capture. To achieve higher efficiency, various types of microstructures are used, such as pillar-type,²⁰ weir-type, and cross-flow²¹ microfiltration structures. However, although these structures can increase the throughput of the system, they can also lead to a lack of flexibility and clogging problems. In comparison, common active separation methods based on for example electrophoresis, dielectrophoresis,²² optics,²³ or surface acoustic waves²⁴ are more flexible and accurate, and with good biocompatibility,^25,26 acoustic manipulation has become a microscale manipulation technique of great interest at this stage.²⁷ The emergence of acoustic resonators based on MEMS technology has also made them important for miniaturized devices.

Typically, acoustic particle manipulation uses interdigitated transducers²⁸ placed on either side of a microchannel to generate a standing surface acoustic wave;^29,30 the pressure field causes the particles in the microchannel to move toward the pressure nodes, and the different force magnitudes cause different particle trajectories. By using this method, Guldiken et al. achieved particle separation in microchannels.³¹ Also, there are methods based on acoustic streaming that can capture particles or cells by generating high-speed acoustic vortices.³² The vortices generated by acoustic streaming can be quickly and easily adjusted by varying the power and frequency. Furthermore, the phenomenon of particles or cells being subject to intricate acoustic radiation forces within a sound field has always been a subject of extensive scholarly investigation.^33,34 In acoustic methods, the particle trajectories in the fluid are determined by the competition between two relatively important forces, i.e., the acoustic radiation force and the drag force,¹³ and by utilizing the relationship between these two forces, larger particles can be captured selectively in a continuous fluid.³⁵ 

Higher resonant frequency indicates stronger acoustic streaming, which is determined by the shorter acoustic decay length at the solid–liquid interface.³⁶ In recent work, we proposed an acoustofluidic method based on a Lamb wave resonator (LWR) to achieve an orbital distribution of particles in an acoustic vortex,³⁷ and we demonstrated the use of LWR-induced acoustic streaming in a microfluidic channel for particle trapping, enrichment, and liquid manipulations for point-of-care applications.³⁸ 

Because Lamb waves combine the features of bulk acoustic waves and surface acoustic waves, the resulting acoustic streaming in the LWR occurs in multiple planes. However, the drag force is controlled dynamically by the applied power, so it could also be used for particle separation. Herein, we investigate the flow behaviors of particles of different sizes in LWR-induced acoustic streaming, and we propose using the resulting particle distribution pattern as a means of particle separation. We find that the LWR resonant frequency and the particle diameter determine the dominant forces on the particles. In a mixed solution with two types of particles, when the dominant forces are different (i.e., the acoustic radiation force is dominant for one particle type and the fluid drag force is dominant for the other particle type), the larger particles are pushed to the inner part of the vortex while the smaller particles appear in the outer region of the vortex. When the acoustic radiation force is dominant for both particle types, the particles show a centrifugal-like³⁹ effect in the vortex, i.e., the smaller particles are inside the vortex and the larger particles are at the edge of the vortex. Leveraging the distinct acoustic field distribution of the LWR, the microsphere assemblies will exhibit disparate distribution patterns within the shared acoustic field when subjected to multiple forces. This investigation of particle behavior within acoustic vortices has significant implications for manipulating and separating particles via acoustic streaming.

All reagents were purchased unpurified from commercial suppliers. Monodisperse fluorescent microspheres (polystyrene microspheres, ∼10 mg/ml) with diameters of 1 μm and 2 μm were obtained from Aladdin Industrial Corporation (Shanghai, China). Monodisperse fluorescent microspheres (polystyrene microspheres, ∼10 mg/ml) with diameters of 5 μm and 10 μm were supplied by Baseline Chromatographic Technology Development Centre (Tianjin, China). SU-8 2025 photoresist was purchased from Suzhou Research Materials Microtech Corporation (Suzhou, China). Polydimethylsiloxane (PDMS, Sylgard 184) was purchased from Dow Chemical Corporation (USA).

The LWRs used in this study were fabricated using a conventional MEMS process. The substrate was a silicon wafer that had been cleaned with piranha solution (a mixture of concentrated sulfuric acid and 30% hydrogen peroxide). A cavity was etched on the substrate using reactive ion etching and then filled with phosphosilicate glass (PSG) via chemical vapor deposition, with any excess removed by chemical mechanical polishing; the PSG inside the cavity was a sacrificial layer. Next, a molybdenum film (200 nm) was deposited on the sacrificial layer by magnetron sputtering as the bottom electrode, followed by an aluminum nitride layer (1.5 µm) and a molybdenum film (200 nm, top electrode) by magnetron sputtering. Because the deposited aluminum nitride layer covered the sacrificial layer, the former was etched by potassium hydroxide wet etching and plasma etching to expose the latter for subsequent processing. Finally, a gold film was deposited via physical vapor deposition and then partially removed by lift-off to act as the electrical interconnection. For the fabricated sacrificial layer, diluted hydrofluoric acid was used to etch and release the resonant cavity to form the overhang structure.

The microchannel was fabricated using rapid prototyping and UV photolithography. Specifically, an SU-8 2025 photoresist mold was formed using photomasking and then cured to create the desired PDMS structures. The PDMS microchannel was then punched precisely to serve as an inlet and outlet for fluids.

Applying an AC signal to a fork-finger electrode induces the propagation of Lamb waves toward the perpendicular electrode and their subsequent leakage into the liquid at the boundary, leading to the generation of acoustic streaming. Because Lamb waves are a combination of bulk and surface acoustic waves, the resulting acoustic streaming in the LWR occurs in multiple planes, and this poses challenges for resolving the 3D acoustic vortex in a coordinate system and is suboptimal for comprehensive experimental observation. However, by adjusting the height of the microchannel, the acoustic vortex is limited in the vertical direction and can be considered as existing in the horizontal plane.

Numerical simulations of the 3D geometry of the fluid streamlines near the LWR were carried out using a multi-field finite-element analysis tool (COMSOL Multiphysics ver. 5.6). The simulation parameters included the flow path width W, the flow path height H, the through-flow velocity v, and the power P; we set W = 400 µm, P = 45 mW, v = 1 µl/min, and simulated the fluid streamlines for H = 160 µm, 80 µm, and 40 µm. The simulation framework incorporated four distinct COMSOL Multiphysics modules, i.e., Solid Mechanics, Electrostatics, Pressure Acoustics (Frequency Domain), and Laminar Flow. In the Solid Mechanics module, the solution domains were the electrodes and piezoelectric layer; the upper and lower electrodes were given linear elasticity characterized by metallic molybdenum material properties and assumed to be isotropic, and the inverse piezoelectric effect was applied to the piezoelectric layer. In the Electrostatics module, the only solution domain was the piezoelectric layer, endowed with the piezoelectric effect; the junctions connecting the electrodes and piezoelectric layer were defined as terminals (or grounding points), with terminals and grounding points arranged in an alternating pattern. In the Pressure Acoustics (Frequency Domain) module, the solution domain was the entire fluid domain. Similarly, the entire fluid domain was set as the solution domain in the Laminar Flow module, with appropriate inlet and outlet positions selected. Study 1 in the COMSOL investigated the interfaces between the Solid Mechanics and Electrostatics modules in the frequency domain, with stress, displacement, and related data at resonant frequencies calculated for subsequent analysis, and Study 2 involved steady-state analysis at the interface of the Laminar Flow module. The values of the independent variables were adjusted, and the solutions obtained in Study 2 were used as the values of the non-solving variables. The initial values of the solving variables were dictated by the physical field. Studies 2 and 3 used the MUMPS linear solver for solution derivation, and the ultimate outcomes encompassed the strain distribution in the LWR and the flow field distribution in the fluid domain.

For H = 160 µm [Fig. 1(a)], it is clear from the simulated streamline diagram that the streamlines are distributed along the z axis, and the overall distribution of streamlines within the vortices is relatively chaotic. For H = 80 µm [Fig. 1(b)], the streamline density decreases significantly and the streamlines are clear within the vortices, which can be considered as being essentially vortices in the xy plane. For H = 40 µm [Fig. 1(c)], the streamlines are sparse and there are none in the z direction within the vortices. Based on the simulation results, H = 80 µm was found to be suitable: the vortices are compressed into being flat, but the effect of the acoustic streaming on particle capture is not limited. Figure 1(d) shows an experimental result, where the microfluidic channel is marked by red lines, and green fluorescent microspheres were added to the liquid to visualize the microvortices. The left vortex can be seen clearly in the figure and agrees perfectly with the simulation results; the right vortex is not visible because not enough microspheres entered because of the trapping effect of the LWR on the microspheres.

The x axis is parallel to the direction of the LWR electrode, and the y axis is perpendicular to the electrode (as shown in Fig. 3). The acoustic radiation force in this coordinate system is further decomposed, where f_x and f_y are the x and y components of the acoustic radiation force on the particle at this point. In Fig. 3, the x component of the acoustic radiation force pushes the particle toward the center of the vortex, while the y component of the force accelerates the particle along the direction of fluid flow.

Based on the above discussion, we propose the following particle distribution patterns in the LWR acoustic streaming. The particle diameter of 0.9 µm is calculated as the critical condition: for particles with d ≤ 0.9 µm, the fluid drag force dominates and they are captured in the entire vortex; for particles with d > 0.9 µm, the acoustic radiation force dominates and pushes them toward the center of the vortex, keeping them in the inner position as shown by pattern A in Fig. 2. When two types of particles with particle size larger than the critical value are within the liquid simultaneously, the acoustic radiation force is dominant for both types. As mentioned above, the particles always start from the center of the LWR edge. When θ > 45°, the y component of the acoustic radiation force becomes dominant and accelerates the particle in the y direction; because F_A ∝ R³, the larger particle obtain larger y-axis acceleration and thus enter the orbit of the outer part of the vortex, whereas the small particles are in the inner part of the vortex, as shown by pattern B in Fig. 2.

The following experiments were conducted under conditions in which the motions of two types of particles were governed by the fluid drag force and the acoustic radiation force, respectively. Recognizing that the acoustic vortex generated in the liquid by the LWR operating at a resonant frequency of 370 MHz exhibits limited efficacy in capturing nanoparticles, the experiments used two types of polystyrene microspheres with distinct particle diameters. The first type was green fluorescent polystyrene microspheres with a particle diameter of 764.7 ± 68.8 nm as measured by a Zetasizer Nano ZS90 (Malvern Instruments). These microspheres are close to the critical condition, implying that the fluid drag force dominates their trajectories. The second type was red fluorescent polystyrene microspheres with a particle diameter of 5 µm, surpassing the critical value. It can be inferred that the acoustic radiation force governs their trajectories. According to the theoretical principle that the dominant forces differ, one can anticipate that upon mixing the two particle types in the microfluidic system, the red and green fluorescent microspheres will reside in the inner and outer parts of the vortex, respectively, under the influence of the LWR.

The LWR generates symmetrically distributed acoustic vortices at the four corners in a liquid environment; however, too many vortices are not ideal for experimental observation, so only two vortices on one side were selected for observation. To suppress the generation of vortices on the other side, one side of the LWR was placed close to the edge of the microchannel as shown in Fig. 3, and thus only one pair of symmetrical vortices on the same side existed in the microchannel. At the beginning of an experiment, the fluorescent microspheres were pumped into the microchannel at a stable rate of 1 µl/min from the right side via a syringe pump. After confirming the absence of air bubbles in the microchannel, the LWR was excited at 50 mW, and under its action the two types of fluorescent microspheres swirled rapidly into the vortex near the inlet side. After capturing a certain number of microspheres, Fig. 5 shows clearly that the inner zone of the vortex was red and the outer zone was green, which is consistent with the results of the theoretical analysis.

However, when both particle motions were dominated by the acoustic radiation force, the experimental result was totally different. Again, two types of fluorescent polystyrene microspheres were used: green ones with a diameter of 2 µm and red ones with a diameter of 5 µm, both exceeding the critical value. Consequently, the trajectories of both microsphere types are influenced predominantly by the acoustic radiation force. Given that the acoustic radiation force exhibits a cubic relationship with the particle radius, it grows exponentially with increasing particle size. The theoretical analysis predicts that the larger particles will experience greater acceleration in the y direction, leading them to reside in the outer region of the vortex.

Solutions containing the 2-µm and 5-µm fluorescent microspheres were pumped uniformly into the microchannel from the right side at a rate of 1 µl/min using a syringe pump. Under an excitation of 50 mW, the LWR captured both microspheres in a vortex. After capturing sufficiently many microspheres, Fig. 6(a) shows clearly that the inner region of the vortex was green and the outer region was red, which is consistent with the theoretical analysis. Also, COMSOL Multiphysics (ver. 5.6) was used to simulate the particle trajectories, with the Particle Tracing for Fluid Flow module added to the previous simulation to simulate the trajectories of particles of different sizes. Figure 6(b) shows the simulation results, where the red particle is approximately twice the size of the black particle. The simulation reveals that the larger particle is situated farther from the vortex center than is the smaller particle, aligning with the experimental findings presented in Fig. 6(a). Also, unlike the results in Fig. 5, the microspheres in Fig. 6(a) do not fill the whole vortex and are closer to the vortex center. This can be explained by the effect of the x component of the acoustic radiation force, which pushes the particles toward the vortex center along the x direction.

Presented herein was an analysis of the forces acting on particles within an LWR acoustic vortex, revealing two distinct particle distribution patterns. The combination of radiation force and drag force resulting from acoustic streaming was used to manipulate particles. At a specific frequency (370 MHz), the acoustic radiation force influenced the motion of larger particles, guiding them toward the inner zone of the vortex. The acoustic streaming propelled smaller particles toward the periphery because of the stronger influence of the drag force on smaller particles. When the acoustic radiation force was dominant for both types of particles in the liquid, they exhibited a centrifugal-like motion within the vortex, with the larger particles directed toward the periphery region while the smaller particles accumulated in the center of the vortex. The experimental results show that acoustic actuation techniques based on LWRs can be used in microfluidic systems to separate microspheres and even cells.

The authors gratefully acknowledge the financial support of the National Natural Science Foundation of China (Grant No. 62174119), the 111 Project (Grant No. B07014), and the Foundation for Talent Scientists of Nanchang Institute for Microtechnology of Tianjin University. Thanks go to Wenlan Guo, Chen Sun, Bohua Liu, and Chongling Sun for their help with device fabrication.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Chuanchao Zhang received a B.S. degree in 2020 from Tianjin University in China, where he is currently working toward an M.S. degree in instrument science and technology. His research interests are in acoustofluidics and its applications.

Xian Chen is an assistant researcher at the National Institute of Metrology. She received a Ph.D. degree in instrument science and technology from Tianjin University. Her research interests are in acoustofluidic manipulation and biochemical detection.

Wei Wei received an M.S. degree in 2022 from Tianjin University, where he is currently working toward a Ph.D. degree. His research interests are in MEMS devices and acoustofluidics, especially for the manipulation of nanoparticles and bio-nanoparticles.

Xuejiao Chen received a B.S. degree from Hebei University of Technology in China. Currently, she is an engineer in the School of Precision Instrument and Optoelectronics Engineering at Tianjin University. Her research interests are in MEMS processes.

Li Quanning is an experimentalist and engineer in the School of Precision Instruments and Optoelectronics Engineering and the State Key Laboratory of Precision Measuring Technology and Instruments at Tianjin University. He is primarily involved in laboratory operation and administration for micro- and nano-electromechanics and semiconductors, as well as the development of associated equipment.

Xuexin Duan is a professor at Tianjin University. He received a Ph.D. degree from the University of Twente in the Netherlands. After postdoctoral studies at Yale University, he moved to Tianjin University. His research interests are in MEMS/NEMS devices, microsystems, and microfluidics and their interfaces with chemistry, biology, medicine, and environmental science.