Flexural wave-based soft attractor walls for trapping microparticles and cells

Acoustic manipulation of microparticles and cells, called acoustophoresis, inside microfluidic systems has significant potential in biomedical applications. In particular, using acoustic radiation force to push microscopic objects toward the wall surfaces has an important role in enhancing immunoassays, particle sensors, and recently microrobotics. In this paper, we report a flexural-wave based acoustofluidic system for trapping micron-sized particles and cells at the soft wall boundaries. By exciting a standard microscope glass slide (1 mm thick) at its resonance frequencies <200 kHz, we show the wall-trapping action in sub-millimeter-size rectangular and circular cross-sectional channels. For such low-frequency excitation, the acoustic wavelength can range from 10–150 times the microchannel width, enabling a wide design space for choosing the channel width and position on the substrate. Using the system-level acousto-structural simulations, we confirm the acoustophoretic motion of particles near the walls, which is governed by the competing acoustic radiation and streaming forces. Finally, we investigate the performance of the wall-trapping acoustofluidic setup in attracting the motile cells, such as Chlamydomonas reinhardtii microalgae, toward the soft boundaries. Furthermore, the rotation of microalgae at the sidewalls and trap-escape events under pulsed ultrasound are demonstrated. The flexural-wave driven acoustofluidic system described here provides a biocompatible, versatile, and label-free approach to attract particles and cells toward the soft walls.


Supplementary Note 1
In Figure S1, we characterized the locations of PDMS channel and PZT/brass plate on a glass plate of 75 mm length. The diameter of PZT/brass plate is 20 mm, which is almost proportional with the wavelength of higher flexural modes of the glass plate (λ = 2L/n). We placed the PZT/brass plate a length of its radius away from the end of glass plate. Further, the distance between PZT/brass plate and the center of PDMS channel is determined as the length of PZT/brass plate diameter. This configuration transfers the most of the PZT energy to the channel through the glass plate, where the PZT/brass plate and the PDMS microchannel are aligned by the distance proportional with the wavelength of higher flexural modes of the glass plate.
In Figure S3, we performed the modal analyses of a glass plate and the whole system by using the 2D and 3D modelling. The various flexural modes of a glass plate are examined and we found that the resonance frequencies ( f M1 , f M2 , f M3 ) are almost the same for the 2D and 3D models as shown in Figure S3a and S3c. In Figure S3b and S3d, it is also shown that the resonance frequencies of the whole system are approximately equal for both 2D and 3D model. In numerical calculations, we used the simplified 2D modelling, where the complexity of the 3D modelling is high.
In Figure S4, we implemented the simplified 2D modelling by defining the flexural waves as the displacement condition on a glass substrate instead of analyzing the whole 2D system shown in Figure S3d. In the 2D numerical model, The displacement condition is defined as the sinusoidal function (A 1 cos(k 1 x), A 2 sin(k 2 x)) for two cases, where the wavenumbers (k = ω/c) are calcualated for the corresponding flexural mode from the dispersion curves shown in Figure S10. As the wavelength of flexural wave at low frequency is considerably larger than the width of microchannel, the pressure nodes can be located at the outside of the microchannel. In the first case shown in Figure S4a, the pressure nodes are placed at the PDMS cover by cos displacement profile, where the pressure antinode is alinged at the center of the microchannel. This configuration leads the wall trapping. For the second case shown in Figure S4b, the pressure node is placed at the the center of the microchannel by sin displacement profile. As expected, the particles move towards the center of channel in the second configuration. Figure S10 shows the wave velocity as a function of frequency in a 1 mm thick glass plate, where we calculated the dispersion curves for the Lamb waves propagating in a plate by using the GUIGUW (Graphical User Interface for Guided Ultrasonic Waves) software 1 . Flexural waves are dispersive whereas longitudinal waves are not where f < 1 MHz. For the operating frequencies 50 kHz < f < 200 kHz, the wavelengths of flexural waves are calculated as 6.6 mm < λ < 13.8 mm.
It is important to note that the 2D numerical models presented in Figures S11 and S12 are the exactly same models used for the calculation of particle trajectories presented in Figures 3 and 5, respectively. Figures S11a and S12a show the displacement profiles for the top and bottom channel walls of the rectangular microchannel and the top and bottom semicircle channel walls of the circular microchannel, respectively. In both cases, the cosine displacement profile is applied on the bottom PDMS layer with 105 kHz for the rectangular channnel and 87 kHz for the circular channnel. Further, Figures S11b and S12b show the acoustic fields inside the rectangular and circular microchannels. In our numerical analysis, we get the first order acoustic fields (p 1 , v v v 1 1 1 ) to calculate the radiation force (F F F rad ) and second order acoustic field (v v v 2 2 2 ) to calculate the drag force(F F F drag ). Further, Figures S11c and S12c show the v v v 2 2 2 inside the channels close to the bottom wall, where the boundary streaming rolls are not observed within the calculated boundary layer thickness. In our configuration, we actuate the bottom channel wall vertically from where the streaming is driven. The velocity decays to zero at the wall due to the no-slip boundary condition. In contrast to hard wall configurations 2 , we used lossy soft material (PDMS) in our design which minimizes the velocity gradients near the walls by allowing the first-order velocity to have a slip-velocity. This behavior was also observed in the study defined the PDMS channel walls as lossy boundary conditions 3 .

PDMS
Glass ߪ • n = −p n