Dynamically reprogrammable acoustofluidic metasurface for subwavelength particle manipulation and assembly

Abstract

A dynamically reprogrammable acoustofluidic metasurface includes an array of resonators in which each of the array of resonators are spaced from the other resonators and further includes one or more excitation sources positioned proximate the array of resonators. The excitation source(s) generate an acoustic wavefield that interacts with the array of resonators to reconfigurably displace the array of resonators and in which at least some of the array of resonators are acoustically coupled to one another via a fluid. Related systems, in which the metasurface is positioned in a fluid or fluid channel, and related methods of capturing and / or enriching particles using the metasurface are also provided. The radiation force generated by the standing acoustic wavefield can manipulate microscale particles in real time with precision and reversibility, in both static and flowing conditions.

Description

DYNAMICALLY REPROGRAMMABLE ACOUSTOFLUIDIC METASURFACE FOR SUBWAVELENGTH PARTICLE MANIPULATION AND ASSEMBLYCROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of U.S. Provisional Patent Application No. 63 / 572,808 entitled "Dynamically Reprogrammable Acoustofluidic Metasurface for Subwavelength Particle Manipulation and Assembly" filed April 1, 2024, the contents of which are incorporated by reference herein in its entirety for all purposes.STATEMENT OF FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] Not applicable.TECHNICAL FIELD

[0003] This disclosure relates to the metasurfaces which are dynamically reprogrammable using, for example, acoustofluidics.BACKGROUND

[0004] Microscale particle manipulation plays a pivotal role in scientific and technological domains such as materials science, physics, and the life sciences. These advancements are primarily driven by the growing need for precise control over particles, including biological cells, microparticles, nanoparticles and colloids, to enable a wide array of applications such as lab-on- a-chip devices, biosensing platforms, and studies of fundamental particle dynamics.Acoustofluidics use ultrasonic waves to manipulate microscale biological particles in a gentle, non-contact, and label-free manner. However, the radiation forces required for manipulation increase as the size of particles reduces, necessitating the use of expensive high-frequency transducers and sophisticated electronics for handling nanoscale particles.SUMMARY

[0005] To overcome the limitations associated with small particle size, unconventional approaches employing phononic crystals and metamaterials can be used manipulate particles at scales much smaller than the acoustic wavelength. However, state-of-the-art systems rely on rigid metasurfaces or phononic crystals that can only trap and localize particles at fixed locations based on the surface geometry and are not dynamically tunable. Accordingly, any change in trapping location would require the fabrication of a completely new surface geometry.

[0006] Disclosed herein, the deficiencies of static, non-re-configurable surfaces are overcome by the development of a dynamically tunable acoustic metasurface based on an array of oscillating membranes. The disclosed platform allows for dynamic real-time adjustments without requiring repeated structural modifications, thus offering broad utility and advancement in various domains.

[0007] A dynamically reconfigurable acoustofluidic metasurface (which may be referenced using the acronym "DReAM" for Dynamically REconfigurable Acoustofluidic Metasurface) is disclosed herein for microscale trapping and manipulation in liquid environments. This planar metasurface supports multiple subwavelength acoustic wavefields, each with distinct spatial distributions. These distributions can be reconfigured in real-time by tuning the frequency and phase of a far-field acoustic source. DReAM can include a two-dimensional array of periodically arranged silicon micromachined membrane resonators. When an acoustic wave from the far field propagates across the surface, this propagation initiates the formation of evanescent standing waves (ESW) in the near-field above DReAM through the acoustic coupling of the resonator elements or membranes. These reconfigurable standing wavefields generate strong acoustophoretic radiation forces capable of collectively trapping and patterning thousands of microscale particles at subwavelength resolution. The spatial distribution of the wavefield over DReAM is actively controllable to achieve the translation of individual particles and the formation and rotation of monolayer colloidal crystals.

[0008] Furthermore, DReAM can be seamlessly integrated with a laser-cut microfluidic channel (and fluid channels more generally, regardless of how the channel is fabricated) and off-the-shelf piezoelectric transducers to capture, enrich, and concentrate micro and nanoscale particles such as cells, large extracellular vesicles and exosomes in flow with high throughput. As one example, the device or system could potentially be used to isolate biomarkers such as circulating tumor cells, large extracellular vesicles and exosomes from body fluids such as blood. The biomarkers can then be further analyzed downstream for early disease detection.

[0009] The device could also be used to further enrich or concentrate a diluted sample containing biomarkers. The acoustic field can be used to capture and release particles over the surface on demand and can be integrated in microfluidic systems.

[0010] DReAM can employ a capacitive micromachined ultrasonic transducer (cMUT) array as the metasurface. cMUTs have previously been used for medical imaging, therapy, and a handful of microfluidic applications. However, this is the first instance of using it as a metamaterial for particle capture and manipulation as best understood. The ability to dynamically reconfigure the wavefield above the cMUT array provides greater flexibility compared to state of the art metasurface-based microfluidic devices. The subwavelength nature of the wavefield also allows capture of small particles using off-the-shelf excitation transducers.

[0011] According to one aspect and most generally, a dynamically reprogrammable acoustofluidic metasurface is disclosed. The dynamically reprogrammable acoustofluidic metasurface includes an array of resonators in which each resonator of the array of resonators are spaced from the other resonators and further includes one or more excitation sources positioned proximate the array of resonators. The excitation source(s) generate an acoustic wavefield that interacts with the array of resonators to reconfigurably displace the array of resonators via acoustofluidic interaction therewith and in which at least some of the array of resonators are acoustically coupled to one another.

[0012] In some forms, each resonator in of the array of resonators may have a respective deformable membrane. However, it is certainly well-contemplated that deformable membranes are not the only structures that could serve as resonators and so any possible resonator structure is contemplated as being used more generally. When the resonator is a deformable membrane, the dynamically reprogrammable acoustofluidic metasurface may include a substrate having supports thereon, upon which supports the respective deformable membranes may be supported. It is contemplated that, in various forms, the device might be fabricated such that the supports have the substate material between the supports, that there are spaced gaps between the supports with no material in them, or that the support might be shared or continuous such that a single support could support edges of two adjacent membranes. Putting trenches between the membranes (i.e., the space between the supports) and changing the trench shape and geometry - or eliminating it by filling it in - will change the crosstalk and hence will change the trapping and coupling behavior. A vacuum gap may exist between the substrate and the deformable membranes. However, there are certainlystructures contemplated in which no vacuum gap will be present and there could be other structures with an air or gas gap. In one particular form, the substrate may be fabricated from silicon and the respective deformable membranes may be fabricated from silicon nitride. The substrate may support one or more substrate electrodes thereon and each of the respective deformable membrane may support a respective membrane electrode thereon. It is contemplated the electrodes might be used to measure deflection of the membranes under the conditions of applied waves and / or, under some potential variations, could even potential be used as a mechanism for deflecting the membrane itself alone or in combination with the acoustofluidic with the one or more excitation sources. An electrical membrane actuator may be connected to the one or more substrate electrodes and the respective membrane electrodes and the electrical membrane actuator may be operable to excite the array of resonators (in whole or in combination with any other excitation sources such as acoustic sources or waveform generators). In consideration of the membranes and in at least some forms, it is contemplated that the respective deformable membranes may be a 100 nm to a 10 pm thick layer. Membrane materials are not limited to silicon nitride and can include other materials such as silicon, SiCh and even metals such as but not limited to aluminum. Membranes can be formed by depositing thin layers as well as other techniques such as bonding two wafers together and then removing the handle layer of the top wafer. In at least one particular form, the deformable membranes may be a 1.5 pm thick layer of silicon nitride (SialX ). Such a layer may be formed using deposition techniques such as those described below in which a thin layer that will constitute the membrane is deposited over another layer that will ultimately be etched away to leave just the suspended membrane and any structural supports for the membrane. However, more generally, the resonators do not need to be silicon-based. For examples, the device and the membranes could also be plastic or polymeric in nature. All that is needed is that the resonators are in an array or periodic form. Indeed, the resonators can be just bubbles even made of air.

[0013] In some forms, the array of resonators can be a two-dimensional array. The array of resonators might be at least ten by ten resonators large; however, larger arrays and arrays of higher resolution are also contemplated, provided that the membranes are deflectable. It is also contemplated that arrays as small as two by one (or one by two) could be workable oreven two by two. It is also contemplated that, in some forms, the array might be three- dimensional with multiple layers of membranes on top of each other dampening each other.

[0014] In some forms, the array of resonators may be capable of supporting subwavelength evanescent waves, including at least some modes in the 50 kHz - 500 MHz frequency range.However, a wider range is certainly contemplated as working; for example, cMUTs can operate at 50mHz and piezoelectrics can operate at a much higher range.

[0015] In some forms, the one or more excitation sources may be piezoelectric transducers. However, the excitation source may be any external stimuli that is acoustic, magnetic, or optic that triggers the resonators to produce the underlying coupling of the resonators.

[0016] According to another aspect, a system for capturing particles from a flow of the fluid flow is disclosed. The system includes a channel having an inlet for receiving the fluid and an outlet for outputting the fluid and the dynamically reprogrammable acoustofluidic metasurface (as described above and under the various variations to that metasurface described herein and throughout the disclosure) in which the metasurface is positioned in the channel between the inlet and the outlet.

[0017] In some forms and for the sake of clarity, the fluid flow comprises a liquid as the fluid introducing the particles over the metasurface.

[0018] According to still yet another aspect, a method of capturing and / or enriching particles in a fluid using the dynamically reprogrammable acoustofluidic metasurface (as described above and under the various variations to that metasurface described herein and throughout the disclosure) is also disclosed. According to this method, the fluid containing the particles is introduced over the dynamically reprogrammable acoustofluidic metasurface. At least some of the respective resonators of the array of resonators are displaced. This displacement results in at least one of trapping or manipulating particles from the fluid on the dynamically reprogrammable acoustofluidic metasurface while the at least some of the resonators of the array of resonators are displaced.

[0019] In some forms of the method, displacing at least some of the resonators of the array of resonators may involve generating an acoustic wavefield that interacts with the array of resonators to reconfigurably displace the array of resonators via acoustic interaction with the resonators. The generating of the acoustic wavefield may be produced by one or moreexcitation sources positioned proximate the array of resonators. The array of resonators thereby can generate a standing wave that interacts with the particles in the fluid to lead to at least one of trapping or manipulating particles from the fluid on the dynamically reprogrammable acoustofluidic metasurface.

[0020] In some forms of the method, the dynamically reprogrammable acoustofluidic metasurface may be received in a channel and introducing the fluid containing the particles over the dynamically reprogrammable acoustofluidic metasurface may involve flowing the fluid through the channel and over the dynamically reprogrammable acoustofluidic metasurface.

[0021] In some forms of the method, the particles may be label-free.

[0022] In some forms of the method, displacing at least some of the resonators of the array of resonators may result in generation of an acoustophoretic radiation force on the particles in a vicinity of the dynamically reprogrammable acoustofluidic metasurface to draw the particles toward the dynamically reprogrammable acoustofluidic metasurface.

[0023] According to yet another aspect, a method of operating the dynamically reprogrammable acoustofluidic metasurface in a collapsed mode is disclosed in which the resonators are deformable membranes that are collapsed. A central portion of at least one of the deformable membranes is caused to collapse (in a way that could but does not necessarily require contacting the substrate). This creates multiple vibrating regions on either side of the central portion of the deformable membrane(s) and alters the periodicity of the array of resonators. For example, if the membrane is a square, then there may be four vibrating regions created. As another example, in the case of a circular membrane, the vibrating region may resemble a cylinder with a cylindrical hole in it. The selected geometry and shape of the membrane can, in any event, change the collapse mode and periodicity.

[0024] In some forms, the method can further involve displacing the deformable membrane(s) that are collapsed to provide the multiple vibrating regions by generating an acoustic wavefield that interacts with the multiple vibrating regions of the deformable membranes that are collapsed. This can result in the reconfigurable displacement of the multiple vibrating regions of the deformable membranes that are collapsed via acoustic interaction therewith.

[0025] In one form, the collapse may be achieved by applying a voltage across electrodes supported by the deformable membrane or membranes and a substrate in order to cause the collapse of the central portion. In another form, the collapse of the central portion may be achieved by a pressure of air on the deformable membrane. Other forms of collapsing are also contemplated as long as they result in taking one vibrating surface of a respective membrane and turning it into multiple vibrating surfaces.

[0026] In some forms, operating in the collapsed mode may result in multiple periodicities between the multiple vibrating regions as compared to operating in a non-collapsed mode. The multiple periodicities may be dependent upon a shape or geometry of the membrane and the thickness of the membranes (or other characteristics of the membrane that impact membrane response).

[0027] In some forms, there may be one or more pillars beneath the membranes and the interaction of the pillars with the membranes may introduce additional periodicities in the collapsed mode of operation.

[0028] In some forms, the membranes may be of variable thickness such that the membranes are thicker at the central portion and thinner at an outer periphery to facilitate collapse or to change resonance modes.

[0029] According to yet another aspect, a method of operating the dynamically reprogrammable acoustofluidic metasurface in a collapsed mode is disclosed in which the resonators are deformable membranes that are circular. A central portion of at least one of the deformable membranes is collapsed, thereby creating a vibrating region extending around the central portion of the at least one of the deformable membranes and altering the periodicity of the array of resonators. In this geometry, the collapse can potentially create a frustoconical vibrating surface on the membrane and / or a frusto-toroidial surface.

[0030] These and still other advantages of the invention will be apparent from the detailed description and drawings. What follows is merely a description of some preferred embodiments of the present invention. To assess the full scope of the invention, the claims should be looked to as these preferred embodiments are not intended to be the only embodiments within the scope of the claims.BRIEF DESCRIPTION OF THE FIGURES

[0031] FIGS. 1A through IE illustrate the DReAM platform supporting reconfigurable evanescent standing acoustic waves for microscale particle manipulation. FIG. 1A is a schematic of the membrane-based metasurface in which an incoming acoustic wave can excite subwavelength standing waves above DReAM. FIG. IB illustrates that each individual resonator on the metasurface includes of a deformable, vacuum-sealed membrane that vibrates when excited by an acoustic wave. FIG. 1C illustrates how all the membranes on the metasurface are acoustically coupled to each other via the surrounding fluid and how this results in the generation of evanescent surface waves above DReAM when excited by an acoustic wave from the far-field. FIG. ID and IE show how the standing waves supported by DReAM generate acoustic radiation forces can be used to trap and manipulate microscale particles at a subwavelength resolution as colloidal clusters are formed with 5 pm fluorescent polystyrene beads on the surface of the membranes when excited by a 1 MHz acoustic wave [scale bars, 100 pm in FIG. ID],

[0032] FIGS. 2A through 21 illustrate the simulation and characterization of DReAM. FIG. 2A shows the simulated displacement response of the center membrane which reveals the presence of multiple resonances or array modes. FIG. 2B illustrates simulated displacement, pressure, velocity, and Gor'kov potential fields at 1.48 MHz in which arrows overlaid on the Gor'kov potential field display the direction of the resultant acoustic radiation force on particles with a positive acoustic contrast factor (although it is difficult to see, these arrows point downward toward the metasurface membrane). FIG. 2C illustrates that the acoustic pressure in the Z-direction reduces exponentially with distance from the metasurface due to the evanescent nature of the standing wavefield. FIG. 2D depicts that non-zero forces are observed only in the region above DReAM, emphasizing the local nature of the array modes. FIG. 2E is an image of a microfabricated 10x10 DReAM array, in the top panel, in which a closer look at the surface, in the bottom panel, shows the periodically spaced membrane resonators [scale bars, 100 pm], FIG. 2F is a schematic of the setup used to characterize DReAM in which the array is excited electrically and a laser vibrometer is used to measure membrane displacement. FIG. 2G provides a Fourier transform of the displacement response of a single membrane on DReAM and reveals multiple array resonance modes and a stopband above 2.1 MHz. FIG. 2H shows thetime domain response and FIG. 21 shows the frequency-time transform of the resulting excitation indicating the early arrival of low frequency components, subsequently followed by the slower high frequency components, confirming the dispersive nature of DReAM.

[0033] FIGS. 3A through 3D illustrate the trapping, reconfigurable patterning, and manipulation of microparticles using DReAM. FIG. 3A shows the creation of subwavelength wavefields with distinct spatial distributions using different source configurations and emission frequencies [scale bar, 100 pm] in the top row and shows 10 pm fluorescent polystyrene beads aligning in response to the shape of the excited array mode on the metasurface [scale bar, 100 pm] in the bottom row. FIG. 3B depicts the reversible translation of a single 10 pm polystyrene bead within a single membrane of DReAM over time [scale bar, 20 pm], FIG. 3C illustrates multiple particles being captured on a single membrane to form closely packed colloidal clusters [scale bar, 20 pm], FIG. 3D demonstrates that clusters can be rotated on demand by modulating the frequency and amplitude of the acoustic source [scale bar, 20 pm],

[0034] FIGS. 4A through 4M illustrate particle enrichment in a fluidic channel with DReAM. FIG. 4A schematically illustrates the effect of the different forces acting on particles in flow over the metasurface when the acoustics are off and on. FIG. 4B are photographs of a fluidic platform integrating a DReAM surface and two piezoelectric acoustic sources [scale bar, 5 mm], with the acoustic sources being spaced from the metasurface in the left panel and being moved closer to the metasurface in the right panel. FIG. 4C shows particles flowing over DReAM getting trapped and enriched on its surface when the acoustic source is turned on (bottom panel) as opposed to being turned off (top panel) [scale bar, 100 pm], FIG. 4D depicts particles captured by a 10x10 array and 20x20 array and demonstrates the larger arrays can be used to capture a greater number of particles without the need to modify the channel dimensions or the frequency of the acoustic source [scale bar, 100 pm], FIGS. 4E through 4H provide characterization of the effect of different system parameters such as capture duration in FIG. 4E, driving frequency in FIG. 4F, particle concentration in FIG. 4G, and flow rate on the total capture area in FIG. 4H. FIG. 41 provides a comparison of the capture area as a function of particle size [scale bar, 100 pm]. FIG. 4J illustrates the enrichment of white blood cells (WBCs) at different concentrations [scale bar, 200 pm], FIG. 4K is a bar graph illustrating the effect of acoustic enrichment on a solution containing 5000 cells / ml, measured at three time points(n-3). FIG. 4L illustrates the enrichment of SK-MEL-28 cell line from a solution containing 25,000 cells / ml on a 20x20 array [scale bar, 200 urn], FIG. 4M shows the viability of the acoustically trapped cells after release (n— 3) in which the viability before and after perfusion was compared for significant differences using a student's t-test (one-sided) [scale bar, 100 pm],

[0035] FIG. 5 illustrates, in a top panel, resonators of a metasurface in which a deformable membrane of the resonators are operated in a collapsed mode (which in some forms may be done by applying a large voltage across the electrodes on the membrane and substrate, by applying a pressure to the membrane, or by the weight of the membranes not being sufficiently supported) to create multiple vibrating sections of the membrane on either side of the collapsed central section. In the bottom panel of FIG. 5, an uncollapsed mode of operation is shown for the sake of comparison.DETAILED DESCRIPTION

[0036] As initially discussed above, particle trapping and manipulation at microscale and nanoscale dimensions has become pivotal in numerous scientific and technological domains, spanning from particle physics to biomedicine. These advancements are primarily driven by the growing need for precise control over particles, including biological cells, microparticles, nanoparticles and colloids, to enable a wide array of applications such as lab-on-a-chip devices, biosensing platforms, and studies of fundamental particle dynamics. To achieve efficient and versatile manipulation at these small length scales, several techniques have been developed, including optical tweezers, dielectrophoresis, magnetic traps, and acoustofluidics. Among these methods, acoustofluidics has garnered significant attention due to its non-contact and label-free nature, biocompatibility, and capacity to manipulate particles over larger volumes.

[0037] Acoustofluidics harnesses the mechanical forces induced by acoustic waves within fluidic environments to manipulate particles and fluids. Acoustofluidic systems typically employ Surface Acoustic Wave (SAW) or Bulk Acoustic Wave (BAW) devices to achieve efficient and precise control over particles. This control is achieved using acoustic radiation force and acoustic streaming. While the radiation force offers precision and control, the magnitude of force generated is inversely proportional to both the dimensions of the fluidic channel and the wavelength of the acoustic source. This inverse relationship necessitates using expensive highfrequency transducers and sophisticated electronic systems to achieve micron-level resolution when manipulating particles. For example, the acoustic radiation force acting on particles decreases with size, thus requiring the use of high frequency (>20 MHz) sound waves and expensive electronics for effective particle trapping and manipulation. Recent advances in additive manufacturing have given rise to innovative approaches that address these challenges, including subwavelength approaches, phononic crystals and acoustic holograms. Metasurfaces including a periodic arrangement of holes, pillars, and other rigid subwavelength structures have demonstrated remarkable capability to trap and manipulate particles at length scales that are significantly smaller than the operating wavelength of the acoustic waves.

[0038] However, many of these approaches are restricted to the generation of acoustic wavefields with a fixed spatial distribution determined by the geometry of the trapping surface or hologram. Modifying the wavefield typically involves altering the geometry or employing complex actuation waveforms. For example, the spatial reconfiguration of these fields may require the use of phased array transducers or sophisticated interdigital transducers (IDTs). A platform that allows for dynamic real-time adjustments without requiring repeated structural modifications would offer broad utility and advancement in various domains and is much needed, but without that need having been yet satisfied.

[0039] To address these challenges, an innovative metasurface-based acoustofluidic platform is proposed that can be dynamically reconfigured to trap and manipulate particles at subwavelength scales.

[0040] The core of the approach lies in the innovative utilization of a passive two- dimensional acoustic metasurface to generate reprogrammable subwavelength acoustic fields. In contrast to traditional acoustofluidic systems that rely on the interference of opposing waves or the reflection of waves from a boundary, this system and metasurface can take advantage of the dynamic interactions between acoustically coupled oscillating structures to generate reprogrammable subwavelength acoustic fields. Understanding the fundamentals around the interactions of particles with contrasting physical properties with these evanescent fields, opens new avenues in applications requiring the dexterous capture and manipulation of a single particle or collection of particles. There is a pressing demand for microfluidic systems capable of effectively manipulating small-scale biological particles, including extracellularvesicles, exosomes, RNA, DNA and viruses. Addressing these challenges, the sub-wavelength approach utilizing a metasurface represents an elegant solution which may render obsolete the reliance on high frequency IDTs or expensive driving electronics typical in traditional acoustofluidic systems.

[0041] This approach represents a new paradigm in particle tunable fluidic metasurfaces and its applications in particle manipulation and can employ capacitive micromachined ultrasonic transducers (cMUTs) in a new way. It should be appreciated that, while cMUTs are described herein as the resonator, that any resonator structure could potentially be employed to similar results.

[0042] cMUTs are resonator arrays including periodically-spaced, electrostatically actuated membranes. cMUT arrays can be used to transmit and receive ultrasonic waves and are widely used in medical imaging applications due to their large bandwidth and high sensitivity. cMUTs have also been used in microfluidics for applications such as particle manipulation, mixing and sensing, primarily due to their small form factor and the ease of electronics integration. Traditionally, however, cMUTs in microfluidics have been deployed as active ultrasound sources, serving as alternatives to traditional piezoelectric transducers. In this context, they have still relied on the presence of hard reflectors or IDTs to generate the standing waves essential for particle trapping and manipulation. For example, the cMUT devices have been electrically driven to generate a propagating wave that reflects of a hard wall to create standing waves in an enclosed channel. Particles are trapped at the pressure nodes in a manner like conventional BAW devices. Similarly, the energy from such propagating wave has used to displace the liquid at the liquid-air interface in order to move the floating particles. In these cases, the cMUT elements are electrically actuated to generate a pressure wave to manipulate the particles. Operating the cMUTs in this regime makes them inherit the fundamental limitations associated with conventional acoustofluidic systems such as requiring higher frequencies and smaller channel dimensions as the particle size reduces.

[0043] Notably, the intrinsically periodic structure of cMUT arrays results in acoustic coupling between neighboring membrane elements through the surrounding fluid, leading to the formation of evanescent waves at the fluid-structure interface. This phenomenon is called acoustic 'cross-talk' and is undesirable in ultrasound imaging applications as it leads to areduction in image quality. Closer analysis of this phenomena has revealed that cMUT arrays demonstrate dispersive behavior in a narrow frequency band (similar to locally-resonant metamaterials), and can support subwavelength acoustic modes having phase velocities that are slower than the speed of sound in water (cPhase < cwater)- This unique property of cMUT arrays has been exploited to demonstrate high sensitivity mass detection in fluid, subwavelength focusing and ultrasonic imaging, but most of the research using such arrays has been focused on wave control and manipulation and not on the interaction of these evanescent waves with microparticles in fluid that will be discussed herein.

[0044] This disclosure proposed that cMUT arrays can be used as passive and reconfigurable acoustic metasurfaces for microfluidic isolation and manipulation. Traditionally, cMUTs have been employed as active ultrasound sources for particle manipulation, relying on hard reflectors or IDTs to generate standing waves. In contrast, the proposed approach treats cMUTs as a locally-resonant metasurface, allowing for the generation of subwavelength evanescent wavefields on its surface. This enables the cMUT array to support multiple subwavelength modes that can be selectively excited from a far-field acoustic source, leading to potential advancements in particle trapping and reconfigurable manipulation in microfluidic environments at subwavelength scales.

[0045] For example, consider a ID array of 'n' periodically spaced resonating membranes, where each resonating membrane is described by a lumped stiffness (K) and a lumped mass (M) value. The effect of the surrounding fluid is considered in the form of a mutual radiation impedance Zr(a> ) . The force balance equation solved for the membrane displacement {it} in the frequency domain is given by,[[ / C] + io>[Zr(o>)] — a>2[M] ]{%(&))} = {P(a>)}Where P is the forcing per surface area. The mutual radiation impedance can be calculated by the Green's function for a baffled point source in a semi-infinite fluidand Cf are the density and speed of sound in the fluid respectively, S is the surface area of the resonating membrane, rmnis the distance between any two membranes m and n, aeff is the effective radius of a small piston and k is the angular wavenumber.

[0046] The homogenous solution to this system of equations can be solved by setting the forcing to zero. The quadratic eigenvalue problem is then linearized and solved by using a Taylor's expansion in a narrow frequency range as the radiation impedance is a function of a>2. Doing so gives us n eigenvalueswith each eigenvalue having an associated eigenvector {Xn}. Each eigenvalue and eigenvector pair represent the frequency and mode shape of the ntharray mode. A system with loss will have complex eigenvalues and in such a case the solution can be written asIf (i)n— dn+ ibnAnd the quality factor of each mode is given by,Each set of eigenvalues and corresponding eigenvectors represent the array's resonance frequencies and the associated mode shapes. Typically, modes with the lowest quality factors are found to possess modal wavelengths exceeding the sound wavelength in water, classifying them as highly radiative or 'leaky' modes. In contrast, modes with higher quality factors are less radiative. As their wavelength shortens below that of sound in water, the wave speed on the array surface drops below the speed of sound in the fluid, resulting in the energy being confined to the array surface as evanescent waves. This disclosure proposes to use these subwavelength evanescent waves to manipulate particles. As these modes are poor radiators, it is correspondingly difficult to excite from the far-field at normal incidence. However, a modespecific excitation with the appropriate frequency and phase can be used to excite them efficiently.

[0047] The ability to modify the spatial distribution of the standing wavefield in a simple and real-time manner allows for the efficient capture and manipulation of particles with high throughput for broad applications in fields including but not restricted to biomedicine and chemistry. This contrasts sharply to conventional acoustofluidic techniques that rely on sophisticated phased array transducers, multiple pairs of IDTs or expensive function generators to synthesize complex waveforms that can create reconfigurable fields. Additionally, the fields supported by the metasurface are subwavelength in nature which allows (1) manipulation of particles with resolution beyond the diffraction limit, and (2) generation of larger acoustophoretic forces on small particles without having to use high frequency transducers. As detailed elsewhere herein, the radiation force acting on particles reduces with size and increases with frequency. Utilizing subwavelength fields allows the generation of large pressure gradients which result in greater acoustophoretic forces, without needing sophisticated high frequency transducers. In fact, the use of compliant membranes as unit resonators in the proposed metasurface allows the exploitation of its dispersive properties in the low MHz frequency range whereas more traditional acoustofluidic metasurfaces that use rigid inclusions or stiff plates, typically operate at higher frequencies. As such, we are able to use low-cost ceramic piezoelectric transducers that are available off-the-shelf to make this platform cost-effective and accessible.

[0048] It is also worth noting that while the cMUT array has been chosen as the passive metasurface in this disclosure, the acoustic-structure interaction mediating the generation of these reconfigurable fields can potentially be realized on other structures consisting of periodic subwavelength compliant resonators.

[0049] In this disclosure, and with reference being had to FIGS. 1A through IE, an exemplary dynamically reconfigurable acoustofluidic metasurface (referred to as "DReAM") is disclosed for microscale trapping and manipulation in liquid environments. This planar metasurface supports multiple subwavelength acoustic wavefields, each with distinct spatial distributions.

[0050] As depicted in FIG. 1A, which depicts a schematic of DReAM in which an incoming acoustic wave excites a subwavelength standing wave above DReAM, these distributions can be reconfigured in real-time by tuning the frequency and phase of a far-field acoustic source(which may also be referred to herein more generally as an "excitation source" and which source may be singular or multiple). As can be seen from FIG. 1A, DReAM includes a two- dimensional array of periodically arranged silicon micromachined membrane resonators which are shown in array form in FIG. 1A in a top perspective environmental view and in which one of the resonators is individually schematically illustrated in FIG. IB in a side view. In the detail of one of the resonators in FIG. IB, a silicon substrate has supports extending outwardly therefrom, across which a deformable membrane is extended. There is a vacuum gap between the silicon substrate and the deformable membrane, and each of the silicon substrate and deformable membrane can support a respective electrode thereon.

[0051] Incoming acoustic wave(s) - which are schematically depicted as three sources in FIG. IB, but which could readily be multiple sources coming in from any number of excitation sources at various locations and directions as will be clear from the description that follows - can excite and vibrate the deformable membrane. As best shown in FIG. 1C, when an acoustic wave from the far field propagates across the surface of DReAM, the acoustic wave initiates the formation of evanescent standing waves (ESW) in the near-field above DReAM through the acoustic coupling of the resonator elements. Adjacent individual resonators in the array can thus be considered acoustic coupled with one another under activated conditions via the surrounding fluid.

[0052] FIGS. ID and IE show how the standing waves interacting with DReAM generate acoustic radiation forces can be used to trap and manipulate microscale particles at a subwavelength resolution as colloidal clusters are formed with 5 pm fluorescent polystyrene beads on the surface of the membranes when excited by a 1 MHz acoustic wave. The reconfigurable standing wavefields generate strong acoustophoretic radiation forces capable of collectively trapping and patterning thousands of microscale particles at subwavelength resolution as demonstrated in FIG. ID in which the left panel of FIG. ID shows the acoustics off and in which the right panel of FIG. ID depict acoustic on. The spatial distribution of the wavefield over DReAM can be actively controlled to achieve the translation of individual particles and the formation and rotation of monolayer colloidal crystals as schematically depicted in FIG. IE, and which will be experimentally verified below in the discussion of FIGS. 3B through 3D.

[0053] Furthermore, and with reference being had back to FIG. 1A and forward reference to FIG. 4B, DReAM can be seamlessly integrated with a laser-cut microfluidic channel and off-the- shelf piezoelectric transducers (as the one or more excitation sources, waveform generators, or acoustic sources) to capture and enrich microscale particles in flow with high throughput. The applicability is not necessarily so limited however, and DReAM could be more generally useable in any channel in flow through conditions, either involving continuous or periodic or controlled flow. Similarly, such metasurfaces could be employable in non-flow through conditions as well.

[0054] The development of this tunable metasurface opens a new paradigm for precise and versatile particle manipulation at subwavelength scales, without the need for high frequency IDTs, complex waveform generators, or expensive driving electronics.Simulations

[0055] To design DReAM, finite element simulations were employed to design and investigate DREAM's dynamic behavior and characteristics.

[0056] A 2D-computational model featured an array of ten periodically spaced vibrating membranes submerged in water and excited by an acoustic source. This model treats the 2D metasurface as a line array consisting of evenly spaced thin plates clamped at both ends in an inviscid fluid half-space. A normal velocity is prescribed at the right domain boundary to simulate an acoustic excitation.

[0057] FIG. 2A displays the out-of-plane displacement of the fifth membrane as a function of frequency. The presence of multiple peaks indicates the excitation of distinct array resonance modes due to acoustic coupling between the membranes and frequency domain analysis of this system reveals the existence of 'n' array modes at distinct excitation frequencies, where 'n' is the number of individual resonating units comprising the array. Notably, some of these peaks with large quality factors (Q>100) correspond to evanescent subwavelength array modes. These near-field modes have a phase velocity lower than the speed of sound in the surrounding fluid and consequently have shorter wavelengths than the corresponding propagating waves.

[0058] To gain a deeper understanding of the surface dynamics when one of these high-Q modes was excited (fi-1.48 MHz), the membrane displacement, acoustic pressure, particle velocity, and Gor'kov potential fields for fi=1.48 MHz was analyzed as shown in FIG. 2B. Thesubwavelength nature of the excited mode becomes apparent as alternate membranes exhibit a 180-degree out of-phase displacement. This displacement corresponds to a standing wave with a wavelength of 150 pm when excited by a far-field acoustic source of approximately 1 mm wavelength. The pressure and velocity fields generated by this standing wave are highly localized at the array surface and at the center of each membrane. As one moves away from the surface or approaches the rigid boundary support between adjacent membranes, both pressure and velocity rapidly decrease.

[0059] Notably, these subwavelength evanescent modes have a greater spatial pressure variation which in turn leads to larger acoustophoretic radiation forces, that isPrad = ~^UradWhere Uradis the scalar radiation potential and Fradis the spatial gradient of Urad. / j and f2are the monopole and dipole scattering coefficient of the particle respectively, K0is the compressibility and pQis the density. Different array modes having distinct spatial distributions can be selectively excited by selecting the appropriate far-field excitation frequency.

[0060] The acoustophoretic radiation force acting on particles in the surrounding fluid was calculated based on the Gor'kov potential field. Notably, particles with a positive contrast factor experience a force directed toward the membrane's center, coinciding with a pressure antinode. This contrasts with conventional standing-wave-based acoustofluidic systems where the radiation force typically points toward pressure nodes. The complex acoustic impedance in the near field of the vibrating surface demonstrates phenomena not typically observed in traditional SAW and BAW acoustofluidic systems. Conversely, particles with a negative contrast factor experience a force directed away from the membranes. The evanescent nature of the wavefield is evident in FIG. 2C, in which the acoustic pressure diminishes exponentially within a wavelength's distance from the surface. Consequently, the vertical component of the radiation force is maximum at z = 0 and rapidly reduces with increasing distance from the surface. FID. 2D illustrates the X and Z components of the radiation force along the surface (z = 0), emphasizing that the nonzero force is localized around the resonating membranes (in which the X component is the top line including a repeating local maximum, small step, and localminimum repeated, and the Z component is the bottom line including the greatest local minimums with periodic jumps back to a near zero radiation force).

[0061] The array's response was investigated at two other resonance frequencies, f2- 1.15 MHz and f3= 1 MHz. The wavelength of the standing wave and the strength of the resulting force field was found to strongly depend on the specific mode that is excited. For instance, the high-Q factor mode at f2generates greater forces compared to the low-Q factor dissipative mode at f3because of a tenfold greater pressure at the array surface. However, by comparing the two high-Q modes, it was found that although the mode at f2generates a higher surface pressure, the mode at fi produces a comparable force as its shorter wavelength enables larger pressure and velocity gradients.

[0062] The commercial finite element software COMSOL Multiphysics 6.1 (Burlington, MA, USA) was used for numerical simulations. The pressure acoustics module was used to compute the pressure and velocity fields in the fluid domain. The solid mechanics module was used to compute the membrane displacements. The coupling between the fluid and solid domains were facilitated by the acoustic-structure interaction module. The Gor'kov potential field and the acoustic radiation force field were derived through the postprocessing of the simulated pressure and velocity fields. The motion of particles due to the resultant radiation force was visualized using the particle tracing for fluid flow module.

[0063] These simulations collectively demonstrate that a surface consisting of periodically spaced resonating membranes can support multiple standing wave modes, each of which can be dynamically realized by applying the appropriate far-field acoustic excitation. Moreover, these standing waves result in radiation forces that could potentially be harnessed for particle trapping and manipulation.Validation by Fabrication

[0064] To experimentally validate the simulation results, and as shown in the image of FIG. 2E, a DReAM array was fabricated in which there was a 10x10 grid of periodically arranged resonating silicon nitride (Si3N4) membranes on a 500 pm silicon (Si) substrate. The silicon nitride membranes were fabricated using a sacrificial release process on a silicon substrate. Each square membrane has an edge of 70 pm (for a 70 pm x 70 pm measurement with 5 pm spacing between each membrane) and a thickness of 1.5 pm and was created by a sacrificialrelease process which is now described. A 100 nm layer of chromium (Cr) is deposited and patterned on the silicon wafer providing the substrate to form the bottom electrode. This is followed by the deposition of a 400 nm thick layer of sputtered copper (Cu), that defines the thickness of the vacuum gap. The Si3N4membrane is then deposited in two steps. First, a 700 nm thick layer of Si3N4is deposited via Plasma Enhanced Chemical Vapor Deposition (PECVD). Etch holes are patterned and the sacrificial copper layer is then released via wet etching to realize a free-standing membrane. Another 800 nm film of PECVD Si3N4is subsequently deposited under vacuum conditions to seal the etch holes and to increase the thickness of the membrane to its final value of 1.5 pm. Finally, a 100 nm layer of aluminum (Al) is deposited and patterned on top of the membranes to define the top electrode. The individual arrays are then obtained after dicing the wafer using a wafer saw. The fabricated array was electrically characterized using an impedance analyzer (Agilent E4990A produced by Keysight, Santa Rosa, CA). The electrode pair could be used to actuate the array and the resonance frequency of the membranes in air was measured to be 4.39 MHz at a bias of 40V.

[0065] It should be appreciated that the resonators do not need to be silicon-based. For example, the device and the membranes could also be plastic or polymeric in nature. All that is needed is that the resonators are in an array or periodic form. Indeed, the resonators can be just bubbles even made of air or other fluids (including potentially air-liquid and liquid-liquid interfaces) or empty shells or thin films. It should also be appreciated that as described above, if the resonator is a membrane, a wide range of thicknesses for the membrane could be employed extending into the nanoscale (e.g., down to approximately 100 nm). Any materials or thicknesses could be suitable as long as they exhibit the coupling behavior.

[0066] The vibrational response of the fabricated DReAM was characterized by providing an electrical impulse excitation to the array and measuring membrane velocity using a laser doppler vibrometer as depicted in FIG. 2F. More specifically, the vibrational characteristics of the metasurface was characterized by mounting the array on a printed circuit board (PCB) and then immersing it in a dish filled with deionized water. Care was taken to ensure that the dish is large enough to avoid overlapping reflections from the walls of the container. The two electrodes of DReAM were connected to a signal generator (Agilent 33500B produced by Keysight, Santa Rosa, CA) and a 100 ns, 10V pulse was provided to excite the array. In suchcapacity, it is contemplated that the signal generator could serve as a "excitation source." The membrane displacement was measured using a Polytec OFV-5000 / 534 Laser Doppler Vibrometer (Polytec, Inc. of Irvine, CA) and the output signal was acquired using a Picoscope 5000 series oscilloscope (Pico Technology of Tyler, TX). The raw rata was then averaged over 512 cycles and was processed using MATLAB (Mathworks, MA USA). Signal arrival times over the array as a function of frequency was obtained by performing a smoothened Pseudo Wigner- Ville distribution (SWVD) transform in MATLAB. The frequency response as shown in FIG. 2G reveals multiple resonant peaks between 0.5 - 2 MHz, each corresponding to an array resonance mode, followed by a sharp dip beyond 2.1 MHz, indicating a stopband.

[0067] Acoustic characterization was then performed by placing a 3.4 MHz piezoelectric disc transducer (STEMiNC SMD12T06R412WL, Steiner & Martins, Inc. of Davenport FL) at 10 mm from the center of the array, at 8 different equidistant location around DReAM. A two- cycle 1.5 MHz sine wave burst was programmed in the signal generator and was fed to the piezoelectric transducer through an RF power amplifier (E&l 1020L, Electronics & Innovation, Ltd. of Rochester, NY). The angle of actuation was intentionally chosen to be close to 90 degrees to efficiently excite the subwavelength modes on the array. To obtain the Green's function, the temporal response of all 100 membranes on the array were recorded for each transducer location. To create the displacement maps of the various standing wave modes arising from different acoustic source configurations, the recorded signals for the source locations of interest were first added, after which a Fourier transform of the resultant signal was obtained. The amplitude and phase of each membrane was then plotted on a surface map for the frequency of interest to obtain the spatial distribution of the mode.

[0068] With specific reference to FIG. 2H, a gaussian acoustic pulse was generated from a piezoelectric disc transducer placed adjacent to DReAM (position 1), and the array response to this acoustic excitation was measured. As depicted in FIG. 2H, the time-domain response shows an initial short pulse at approximately 10 ps corresponding to the broadband bulk pressure wave propagating over the array, followed by the delayed arrival of a longer, dispersive wave packet after 20 ps. A frequency-time transform, as shown in FIG. 21, reveals that low-frequency components in this second packet precede higher frequency waves, demonstrating the dispersive nature of DReAM, where the wave speed is a function offrequency. The slower phase velocity of higher-frequency components results in shorter spatial wavelengths that are confined to the array's surface as evanescent waves. The plot of FIG. 21 also shows the bandgap beyond 2.1 MHz as expected from the response in FIG. 2G.

[0069] It should be appreciated that the positions and angling of any excitation source or sources, be it a piezoelectric, or some different excitation source, can be varied from the positions and angles depicted so long as the coupling is achieved.

[0070] There are multiple configurations that can be used in 3D space to excite the metasurface array modes. It is not limited to the 8 positions described. The excitation could more broadly also be achieved using other actuation techniques that generate a mechanical force. Also, the shape of the pulse is not limited to gaussian and can also be arbitrary signals.

[0071] Moreover, it will be appreciated that, while a piezoelectric is described herein as the excitation source, any external stimuli that is acoustic, magnetic, thermal, or optic (or any applied energy source including gradients thereof) that triggers the resonators may be suitable to produce the underlying coupling of the resonators.

[0072] These experimental results highlight the unique capabilities of the fabricated DReAM array, including its ability to support multiple subwavelength standing wavefields.Dynamically Reconfigurable Patterning at Subwavelength Scales

[0073] Effectively and instantly exciting various DReAM array modes from a distance involves accurate selection of frequency and source emission patterns. Mapping the impact of different emission patterns and frequencies on the array's performance enables determination of optimal target conditions for exciting specific modes. To determine the complete set of Green's functions that connect surface displacement to emissions from each source, a gaussian pulse was generated from the piezoelectric transducer at eight different locations around the DReAM array. The displacement of all 100 membranes was recorded for each source location and this linear superposition to be utilized to recreate the displacement over DReAM for any emission pattern and frequency.

[0074] With reference being had to FIG. 3A, the predicted displacement field over the entire array for four distinct driving conditions is presented in the top row. By altering the frequency and phase of the emission source, subwavelength standing wave modes can be excited over the DReAM array, each with a different field strength and spatial distribution. Thisflexibility extends beyond the four modes depicted in the figure, as the array modes being orthogonal allows superposing any number of modes to create a new mode. Iterative timereversal techniques can also be employed to generate highly localized or focused fields. This remarkable versatility offers the potential to create virtually any field distribution, provided possession of the prior knowledge of the Green's function for different external emission locations as well as emissions generated by individual membranes of the array.

[0075] To visualize the impact of the standing wavefield over DReAM on microscale particles, 10 pm fluorescent polystyrene beads were introduced over the metasurface. As anticipated by the simulations, beads above the DReAM array were drawn towards the center of the membranes due to the radiation force and aligned themselves at the pressure antinodes as depicted in FIG. 3A, bottom row. The discrepancy observed between the projected field distribution in the top row of FIG. 3A, and the actual bead patterns in the bottom row of FIG. 3A can be ascribed to minor deviations in the positioning of the source transducers during the experiments. Beads outside the area above the DReAM array did not experience this force and remained unaffected. This means that thousands of beads can be collectively manipulated and reconfigurably patterned by adjusting the emission source's frequency and phase. The distance between consecutive antinodes where the beads are trapped is not dependent on the source wavelength but is instead determined by the pitch between the resonating membranes. In contrast to acoustofluidic techniques that require the Fourier synthesis of complex signals or the use of high-frequency IDTs, DReAM supports multiple evanescent standing wave modes, enabling efficient trapping and reconfigurable positioning of particles with subwavelength resolution.

[0076] Radiation forces generated by DReAM can also be used for precise manipulation of individual beads via translation and rotation.

[0077] By changing the emission frequency, the spatial pattern of the standing wave can be modified, allowing the movement of a single trapped particle (here a 10 pm polystyrene bead within a single membrane) to a new location on the surface as depicted in FIG. 3B. Reverting to the original emission frequency returns the particle to its initial position. The position of three adjacent beads were tracked over multiple translation cycles, and it was established that particles can be positioned within a membrane with high precision and repeatability.

[0078] Using DReAM, two-dimensional (2D) colloidal crystal monolayers can also be formed from the beads trapped on the membrane as depicted in FIG. 3C. The combination of in-plane primary radiation force due to the standing wave and the secondary radiation force between particles resulting from scattering creates closely packed colloidal crystals that can also be rotated by adjusting the driving frequency as depicted in FIG. 3D. Modification of the spatial wavefield allows for the application of an off-center force that rotates the crystal. The rotational speed depends on the wavefield's strength and can be adjusted proportionally by varying the amplitude of the applied acoustic excitation. In essence, the ability to generate and reconfigure standing wavefields on demand enables the trapping and manipulation of particles at both an individual and collective scale. This versatility makes DReAM a valuable tool for a wide range of applications, whether they require intricate particle control or the efficient trapping of particles and colloids.Microparticle Trapping and Enrichment Under Flow

[0079] Moving beyond the confines of static fluid environments, DReAM is exceptionally effective for trapping and enriching particles in microfluidic channels. In such use case however, and with reference being made to FIG. 4A (which illustrates the force differences acting on particles with acoustics on and off), in the presence of an external acoustic field, the acoustophoretic radiation force exerted on the particle should overcome the drag force due to the flowing fluid.

[0080] As depicted in the photograph of FIG. 4B, an exemplary planar DReAM array was mounted on the surface of a laser-cut microfluidic channel and two piezoelectric transducers were placed on either side of the channel to act as the acoustic emission source. A microfluidic chip was fabricated by mounting the DReAM array inside a laser-cut cavity in a 3.5 mm thick cast acrylic substrate (McMaster Carr of Cleveland, OH); however, it is certainly contemplated that different thicknesses might have been employed. The array is mounted such that the top of the metasurface is flush with the surface of the substrate. A channel with a length of 40 mm and an average width of 2.5 mm is then cut in a 150 pm thick double-sided tape (Adhesives Research Inc. of Glen Rock, PA) to define the microfluidic channel. One end of the cut tape is stuck to a 1.5 mm thick cast acrylic sheet and this assembly is then mounted over the base substrate and metasurface to create the DReAM platform. Inlet and outlet holes are laser-cuton the top cover and tubing is inserted and held in place using hot glue. Two 3.4 MHz piezoelectric transducers are mounted on either side of the channel to provide the acoustic emission source. To couple the acoustic emissions from the source to the fluidic channel, the entire assembly is lowered into a dish filled with deionized water. The output voltage from the signal generator was set at 60 mV.

[0081] Solutions containing different concentrations of 10 pm fluorescent beads were flown through the channel. However, before loading any samples, a 0.01% Titron-X (Sigma Aldrich of St. Louis, MO) solution was flown through the platform for two minutes to coat the microfluidic chamber. A stock solution of 10 pm fluorescent polystyrene beads (Spherotech Inc. of Lake Forest, IL), with an initial concentration of 1.819 x 107 beads per milliliter (beads / mL), was divided into four separate tubes, each containing 2 milliliters (mL). The stock solution was diluted using a 0.01% Triton-X solution in DI water, resulting in final concentrations of 1:50, 1:100, 1:500, and 1:1000 in each respective tube. A Bartels micropump and pump controller were used to control the duration and rate of flow in the microfluidic channel. The capture duration was 60s and the flowrate was 200 pL / min unless mentioned otherwise. 10 pm, 6 pm and 2 pm polystyrene beads diluted at a ratio of 1:50 were used for the experiments comparing the particle capture area for different bead sizes.

[0082] Demonstrating the capturing and enrichment of the particles in flow over conditions, particles travelling over the DReAM array were trapped on the membranes when the acoustics were turned on as depicted in FIG. 4C, which depicts capture with acoustics off in the top panel and with acoustic on in the bottom panel. Over time, more particles were trapped at various sites on the array until the surface was saturated. The enriched particles could then be released by turning off the acoustic source.

[0083] With reference being had to FIG. 4D, in which a smaller 10x10 array is illustrated in the top panel and a larger 20 x 20 array is illustrated in the lower panel, a higher trapping throughput can be realized by increasing the active area of the DReAM array. For the same emission frequency, drive amplitude and source location, the effective capture area is increased by four times in the case of a 20 x 20 array when compared to the 10 x 10 array. This ability to localize radiation forces based on geometry opens the possibility to trap particles at specific locations within an acoustic field without the need for sophisticated sound manipulationtechniques or array beamforming. This also demonstrates that larger arrays can be used to capture a greater number of particles without the need to modify the channel dimensions or the frequency of the acoustic source.

[0084] Parameters were systematically varied in a series of experiments to gain an understanding of their effects on particle capture by DReAM. The input voltage to the emission source was set to the minimum value at which particle capture was observed.

[0085] As illustrated in FIG. 4E, the polystyrene beads were then circulated through the channel for 5 minutes at a flow rate of 200 pL / min and the total capture area was evaluated. It was found that the number of captured particles sharply increased during the first 60 - 100 seconds of capture. After 100 seconds, the capture rate reduced, and the curve flattened because the individual membranes of the array became saturated with beads. New particles that arrive at this time either fail to get trapped or replace previously trapped beads by displacing them from their trapped locations.

[0086] The choice of the excited array mode also plays a meaningful part in determining the trapping efficiency of the surface. FIG. 4F illustrates that the mode excited at 1.6 MHz was able to capture 50% more particles than the 1.41 MHz mode for the same time and input voltage. This mode-dependent efficiency can be influenced by the number of trapping points generated by the particular mode as well as the strength of the radiation force field.

[0087] With reference being had to FIG. 4G, DReAM's efficiency was also tested for different concentrations of bead solutions, and it was found that the number of particles captured is proportional to the solution's concentration. Remarkably, DReAM exhibited efficient particle capture at concentrations as low as 1:1000, suggesting its potential for gentle, label-free particle enrichment in diluted solutions. As illustrated in FIG. 4H, this enrichment was achieved at flow rates greater than 100 pL / min, which demonstrated that the system could sustain a high throughput. A drop-off was observed in the capture area above 200 pL / min, as the drag force on the particles overcame the trapping force generated by DReAM. However, note that the strength of the radiation force field can be increased by providing greater power to the emission transducers.

[0088] With reference to FIG. 41, when the effect of particle size on DReAM's trapping efficiency was evaluated, it was found that, under the same operating conditions, the numbersof 10 pm and 6 pm particles trapped on the surface were comparable. The influence of the viscous drag force, however, becomes increasingly dominant as the particle size reduces, rendering the trapping of particles smaller than 2 pm very challenging.

[0089] Building on the platform's ability to trap microscale particles, the capability to enrich biological material from low concentration solutions was demonstrated. This addresses a significant challenge in the field, where traditional benchtop enrichment methods like filtration or centrifugation are often inadequate for efficiently processing small sample volumes or fragile cells. With reference being had to FIG. 4J, to evaluate the platform's performance, three different concentrations of 2ml white blood cell (WBC) solutions were passed through the microfluidic channel at a flow rate of 50 pL / min for 5 min. In each case, the cells were trapped and enriched at various points on the 20 x 20 array when the acoustics was turned on, with the number of trapped cells increasing proportionally with the initial concentration. Notably, even at the lowest concentration (1000 cells / mL), 100 ± 24 cells were found to be trapped within the observable array volume (0.34 pL), corresponding to a 294-fold enrichment within this localized region. FIG. 4K further illustrates the impact of acoustic trapping on cell enrichment, showing a marked increase in the number of captured cells over time, with an enhancement in the fluorescence intensity within the array when the acoustic field is applied. As a result, this enables rapid observation of rare cells, even in samples that fall below the threshold for microscopic detection, thereby enhancing diagnostic capabilities.

[0090] Whole blood samples from healthy donors were purchased through the Stanford University Blood Center. To isolate WBCs, whole blood was mixed with red blood cell (RBC) lysis buffer at a 1:10 ratio and incubated for 10 min to ensure complete lysis and effective WBC separation. After incubation, the mixture was centrifuged at 300 x g for 3 min and the resulting WBC cell pellet was collected and then resuspended in PBS for further studies. For enhanced on-chip visualization, WBCs were stained using CellTracker™ CMFDA green fluorescent probes (ThermoFisher Scientific Ltd of Waltham, MA) according to the manufacturer's protocol. In brief, lxio6cells in 1 mL of solution were incubated with 1 pL of the fluorescent probe for 30 min. After staining, the cells were fixed with 4% paraformaldehyde (PFA) for 30 min, followed by rinsing with PBS, which preserved cell morphology over an extended period and retained fluorescence.

[0091] With reference being made to FIGS. 4L and 4M, the system was also successfully applied to capture SK-MEL-28, a skin cancer cell line, showcasing its versatility in handling diverse cell types. SK-MEL-28 cells were used to demonstrate the platform's versatility in cell capture and assess cell viability post-release. The cells were cultured in Dulbecco's Modified Eagle Medium (DMEM) supplemented with 10% FBS and 100 units / mL penicillin-streptomycin at 37 °C in a humidified atmosphere with 5% CO2. As shown in FIG. 4L, to assess the effect of acoustics on cell viability, 25,000 cells / mL were trapped and released in triplicate. After releasing the trapped SK-MEL-28 cells, viability assessments indicated minimal impact on cell health due to acoustic exposure, confirming that the cells remain viable for downstream analytical processing as illustrated in FIG. 4M. These results collectively demonstrate the platform's ability to locally trap and visualize cells on a grid without surface modifications or sheath flows, thus offering a straightforward approach to enrichment and analysis of biological samples at high throughputs.

[0092] During all cell processing experiments, a flow rate of 50 pL / min was maintained to minimize mechanical stress and improve viability. Cell viability was assessed using the Countess™automated cell counter (available from Thermo Fisher Scientific) with trypan blue dye, both before and after acoustic trapping and release. To release and collect the trapped cells, the acoustics were turned off, and a PBS wash was applied. Approximately 150 pL of the cell suspension was then collected from the outlet for viability testing. For analysis, 10 pL of the sample was mixed with 10 pL of 0.4% trypan blue and loaded into the automated counter.

[0093] Finally, with reference to FIG. 5, the deformable membrane can be operated in collapsed mode (shown in the top panel). If the membranes and substrates have electrodes, this collapsing may be achieved by applying a large voltage is applied to the electrodes to cause the central portion of the deformable membrane to collapse and contact the bottom substrate. This collapsing creates multiple vibrating regions on the sides of the collapsed region on the same deformable membrane. Thus, by using electrostatic forces, the periodicity of the vibrating structure can be intentionally changed. By doing this, one can either reduce the periodicity or introduce variable periodicity. This may help to reduce the length of the evanescent waves, thereby increasing the acoustophoretic force, thus allowing the trapping of smaller particles / objects.

[0094] A collapse of a membrane of a resonator could also be achieved in other ways, more generally, without the use of an applied voltage. For example, the collapse of the central portion may be achieved by a pressure of air on the deformable membrane. As another example, if the weight of the membrane is not supported and the membrane bows in the middle, this also can effectively result in a collapsed mode of operation. Other forms of collapsing are also contemplated (as well as combinations of such modes of collapse), as long as they result in taking one vibrating surface of a respective membrane and turning it into multiple vibrating surfaces.

[0095] Since it is depicted in a side view, this appears to be two vibrating regions, but the actual number of vibrating sections would require consideration in three dimensions, as the geometry of the membrane and collapse mode will result in different numbers of vibrating regions. For example, a square-shaped membrane that has been collapsed in the center would result in four vibrating sections. As another example, a hexagonal-shaped membrane could have six vibrating regions, and an octagonal-shaped membrane could have eight vibrating sections. These vibrating regions can have a continuous form, even in the polygon shape, but there will n edge or side points in collapse mode in an n-agon (for instance, an octagon will have eight edge or side points when a center of the octagon membrane is collapsed to provide eight vibrating regions but still be formed of a single continuous membrane. Other geometries could also be used (e.g., circular, polygonal, and other shapes) and the number of vibrating sections and periodicity could vary based on the geometry and collapse point(s).

[0096] Comparing the top panel, showing operation in collapsed mode, to the bottom panel, showing operation in uncollapsed mode, one can see the differences in the periodicities of the array of resonators. In collapsed mode, a periodicity 1 is established between the vibrating regions on each respective resonator and a periodicity 2 is established between the adjacent vibrating sections of adjacent resonators. Because FIG. 5 is a side schematic, the periodicities are somewhat simplified; in three-dimensions, the geometry of the membrane will result in periodicity in at least two dimensions (and if the membranes are arranged not just along a plane, but stacked in three dimensions, could extend in three dimensions). In contrast, in uncollapsed mode, there is a single periodicity established by the spacing of the resonators from one another.

[0097] In summation, a novel class of membrane-based metasurfaces are introduced, providing a versatile platform for high-precision microscale particle manipulation. DReAM overcomes the limitations of conventional acoustofluidic manipulation techniques by enabling real-time adjustments to the spatial distribution of acoustic standing waves, eliminating the need for costly high-frequency IDTs or complex electronic systems. DReAM's unique capacity to support multiple subwavelength evanescent acoustic wavefields is facilitated by dynamic interactions between periodically arranged membrane resonators. It was demonstrated that the radiation force generated by these wavefields can be used to trap, pattern, and manipulate particles with precision at both individual and collective scales in a reversible and dexterous manner. The planar, 2D profile of the DReAM permits seamless integration with microfluidic channels, enabling the isolation and enrichment of microscale particles in high throughput flowing conditions. While the disclosure design presented challenges in trapping particles smaller than 2 microns, due to the scale of viscous forces involved, it is contemplated that redesigning DReAM with a smaller pitch could potentially enable the support of wavefields with shorter wavelengths, thus enhancing the trapping capability for smaller particles. Facilitating electrical actuation of individual membranes in the array could avoid the need for external acoustic sources, further refining the control over particle manipulation and allowing precise targeting of particles to specific locations on the metasurface.

[0098] The DReAM platform provides a delicate yet highly effective means of handling particles, opening opportunities to deepen understanding of intercellular adhesion forces and advancing personalized medicine by enabling precision 3D biomaterial synthesis for organoid engineering. Furthermore, DReAM's capacity for assembling and manipulating particulate structures has the potential to transform the study of colloidal and photonic crystals, enhancing the understanding of soft matter physics, and enabling the creation of dynamic living materials. In addition, DReAM's compatibility with readily available commercial transducers offers a low- cost approach for isolating micron-sized particles in a liquid medium. By harnessing additive manufacturing techniques and incorporating soft materials, DReAM holds the potential to extend its particle manipulation capabilities to the nanoscale, including the precise handling of exosomes and viruses. This advancement opens doors to innovative applications in the realms of liquid biopsy and early cancer detection.

[0099] There is a potential for broad impact in many areas of science, engineering, and medicine, wherein the trapping and manipulation of micro and nanoscale particles is of interest. The ability to manipulate particles at a subwavelength scale using commercially available piezoelectric transducers in the low-MHz frequencies avoids the need for expensive IDTs and sophisticated driving electronics to isolate and enrich small-scale biologies such as extracellular vesicles and viruses. Moreover, the capability to dynamically reconfigure the spatial distribution of the evanescent wavefield adds tremendous value in applications such as bio-assembly and spheroid engineering. Additionally, the metasurface is compatible with standard micromachining techniques and is easy to integrate with conventional microfluidic devices for biomedical applications. Further exploring the use of soft materials such as PDMS for the unit resonating element and utilizing additive manufacturing techniques such as 3D printing may result in the further development of a new class of unconventional metamaterials for microfluidic and lab-on-a-chip applications.

[0100] It should be appreciated that various other modifications and variations to the preferred embodiments can be made within the spirit and scope of the invention. Therefore, the invention should not be limited to the described embodiments. To ascertain the full scope of the invention, the following claims should be referenced.

Claims

CLAIMSWhat is claimed is:

1. A dynamically reprogrammable acoustofluidic metasurface comprising: an array of resonators in which each resonator in of the array of resonators are spaced from the other resonators; and one or more excitation sources positioned proximate the array of resonators to generate an acoustic wavefield that interacts with the array of resonators to reconfigurably displace the array of resonators and in which at least some of the array of resonators are acoustically coupled with one another via a fluid.

2. The dynamically reprogrammable acoustofluidic metasurface of claim 1, wherein each resonator in of the array of resonators has a respective deformable membrane.

3. The dynamically reprogrammable acoustofluidic metasurface of claim 2, wherein the dynamically reprogrammable acoustofluidic metasurface comprises a substrate having supports thereon, upon which supports the respective deformable membranes are supported.

4. The dynamically reprogrammable acoustofluidic metasurface of claim 3, wherein a vacuum gap exists between the substrate and the deformable membranes.

5. The dynamically reprogrammable acoustofluidic metasurface of claim 3, wherein the substrate comprises silicon and the respective deformable membranes comprise silicon nitride.

6. The dynamically reprogrammable acoustofluidic metasurface of claim 3, wherein the substrate supports one or more substrate electrodes and each of the respective deformable membrane supports a respective membrane electrode.

7. The dynamically reprogrammable acoustofluidic metasurface of claim 6, wherein, an electrical membrane actuator is connected to the one or more substrate electrodes and the respective membrane electrodes and is operable to excite the array of resonators.

8. The dynamically reprogrammable acoustofluidic metasurface of claim 2, wherein the respective deformable membranes comprise a 1.0 pm to 2.0 pm thick layer.

9. The dynamically reprogrammable acoustofluidic metasurface of claim 2, wherein the respective deformable membranes comprise a 1.5 pm thick layer of silicon nitride (SisN^.

10. The dynamically reprogrammable acoustofluidic metasurface of claim 1, wherein the array of resonators is a two-dimensional array.

11. The dynamically reprogrammable acoustofluidic metasurface of claim 10, wherein the array of resonators is at least ten by ten resonators large.

12. The dynamically reprogrammable acoustofluidic metasurface of claim 1, wherein the array of resonators is capable of supporting subwavelength evanescent waves, including at least some modes in the 50 kHz - 500 MHz frequency range.

13. The dynamically reprogrammable acoustofluidic metasurface of claim 1, wherein the one or more excitation sources are piezoelectric transducers.

14. A system for capturing particles from a flow of the fluid, the system comprising: a channel having an inlet for receiving the fluid and an outlet for outputting the fluid; and the dynamically reprogrammable acoustofluidic metasurface of claim 1 positioned in the channel between the inlet and the outlet.

15. The system of claim 14, wherein the fluid is a liquid.

16. A method of capturing and / or enriching particles in the fluid using the dynamically reprogrammable acoustofluidic metasurface of claim 1, the method comprising: introducing the fluid containing the particles over the dynamically reprogrammable acoustofluidic metasurface; displacing at least some of the resonators of the array of resonators; and at least one of trapping or manipulating particles from the fluid on the dynamically reprogrammable acoustofluidic metasurface while the at least some of the resonators the array of resonators are displaced.

17. The method of claim 16, wherein displacing at least some of the resonators the array of resonators involves generating an acoustic wavefield that interacts with the array of resonators to reconfigurably displace the array of resonators via acoustic interaction therewith, the array of resonators thereby generating a standing wave that interacts with the particles In the fluid to lead to at least one of trapping or manipulating particles from the fluid on the dynamically reprogrammable acoustofluidic metasurface.

18. The method of claim 17, wherein generating of the acoustic wavefield is produced by the one or more excitation sources positioned proximate the array of resonators.

19. The method of claim 16, wherein the dynamically reprogrammable acoustofluidic metasurface is received in a channel and wherein introducing the fluid containing the particles over the dynamically reprogrammable acoustofluidic metasurface involves the fluid flowing through the channel and over the dynamically reprogrammable acoustofluidic metasurface.

20. The method of claim 16, wherein the particles are label-free.

21. The method of claim 16, wherein displacing at least some of the resonators of the array of resonators results in generation of an acoustophoretic radiation force on the particles in a vicinity of the dynamically reprogrammable acoustofluidic metasurface to draw the particles toward the dynamically reprogrammable acoustofluidic metasurface.

22. A method of operating the dynamically reprogrammable acoustofluidic metasurface of claim 1 in a collapsed mode in which the resonators are deformable membranes, the method comprising: collapsing a central portion of at least one of the deformable membranes to contact the substrate, thereby creating multiple vibrating regions on either side of the central portion of the at least one of the deformable membranes and altering the periodicity of the array of resonators.

23. The method of claim 22, further comprising: displacing at least some of the deformable membranes that are collapsed to provide the multiple vibrating regions by generating an acoustic wavefield that interacts with the multiple vibrating regions of the deformable membranes that are collapsed to reconfigurably displace the multiple vibrating regions of the deformable membranes that are collapsed via acoustic interaction therewith.

24. The method of claim 22, wherein the collapse is achieved by applying a voltage across electrodes supported by at least one of the deformable membranes and a substrate to cause the collapse of the central portion.

25. The method of claim 22, wherein the collapse of the central portion is achieved by a pressure of air on the deformable membrane.

26. The method of claim 22, wherein the deformable membranes have a shape that is circular, rectangular, hexagonal, octagonal, or polygonal.

27. The method of claim 22, wherein operating in the collapsed mode results in multiple periodicities between the multiple vibrating regions as compared to operating in a non-collapsed mode.

28. The method of claim 27, wherein the multiple periodicities are dependent upon a shape or geometry of the membrane and the thickness of the membranes.

29. The method of claim 22, further comprising one or more pillars beneath the membranes and the interaction of the pillars with the membranes introduce additional periodicities in the collapsed mode of operation.

30. The method of claim 22, wherein the membranes are of variable thickness such that they are thicker at the central portion and thinner at an outer periphery to facilitate collapse or to change resonance modes.

31. A method of operating the dynamically reprogrammable acoustofluidic metasurface of claim 1 in a collapsed mode in which the resonators are deformable membranes that are circular, the method comprising: collapsing a central portion of at least one of the deformable membranes to contact the substrate, thereby creating a vibrating region that extends around the central portion of the at least one of the deformable membranes and altering the periodicity of the array of resonators.

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