Chladni figures revisited based on nanomechanics

Acoustophoresis-driven particle focusing and separation with standard/inverse Chladni patterns

Manipulating objects with acoustics has been developed for hundreds of years since Chladni patterns in gaseous environments were exhibited. In recent decades, acoustic manipulation in microfluidics, known as acoustofluidics, has rapidly thrived and many sophisticated technologies were born. However, the basic background motion of particles under acoustic excitation is usually neglected and the classical Chladni patterns haven't been reproduced in an aqueous environment. In this study, we investigated the basic mechanism and the motion of suspended particles and sinking particles in a plain microchamber under low-frequency excitation (3-5 kHz). The mechanisms were clearly distinguished by comparing the differences among colored fluids, suspended particles, and sinking particles. The suspended particles rotated around the antinode with a speed up to 55.1 μm s-1 at 100 Vpp by the acoustic streaming and they approached each other by the secondary acoustic radiation force. The sinking particles concentrated at the node with a speed up to 22.3 μm s-1 at 100 Vpp by bouncing on the vibrating surface and the primary acoustic radiation force. We have reproduced the classical standard/inverse Chladni patterns in an aqueous environment for the first time, and they were leveraged to separate SiO2 particles with different sizes. The big particles with an average diameter of 9.68 μm were concentrated at the node while the small particles with an average diameter of 2.72 μm were collected at the antinode within 2 min. These results not only provide insightful perspectives of basic mechanisms, but also open up new possibilities for advanced acoustic tweezers.

Cavity-agnostic acoustofluidic manipulations enabled by guided flexural waves on a membrane acoustic waveguide actuator

This article presents an in-depth exploration of the acoustofluidic capabilities of guided flexural waves (GFWs) generated by a membrane acoustic waveguide actuator (MAWA). By harnessing the potential of GFWs, cavity-agnostic advanced particle manipulation functions are achieved, unlocking new avenues for microfluidic systems and lab-on-a-chip development. The localized acoustofluidic effects of GFWs arising from the evanescent nature of the acoustic fields they induce inside a liquid medium are numerically investigated to highlight their unique and promising characteristics. Unlike traditional acoustofluidic technologies, the GFWs propagating on the MAWA's membrane waveguide allow for cavity-agnostic particle manipulation, irrespective of the resonant properties of the fluidic chamber. Moreover, the acoustofluidic functions enabled by the device depend on the flexural mode populating the active region of the membrane waveguide. Experimental demonstrations using two types of particles include in-sessile-droplet particle transport, mixing, and spatial separation based on particle diameter, along with streaming-induced counter-flow virtual channel generation in microfluidic PDMS channels. These experiments emphasize the versatility and potential applications of the MAWA as a microfluidic platform targeted at lab-on-a-chip development and showcase the MAWA's compatibility with existing microfluidic systems.

Dynamics of a two-layer immiscible fluid system exposed to ultrasound

The relocation dynamics of a two-layer immiscible fluid system exposed to bulk acoustic waves using simulations and experiments are reported. A theoretical formulation of the acoustic radiation pressure (ARP) acting on the interface reveals that ARP is a nonlinear function of the impedance contrast. It has been shown that the force acting on the interface is the simple sum of the ARP and the interfacial tension, which is dependent on the angle of the interface. It was discovered that although the acoustic radiation force is directed from high-impedance fluid (HIF) to low-impedance fluid (LIF), the final steady-state configuration depends on the wall-fluid contact angle (CA). Our study reveals that the HIF and LIF would relocate to the channel center for CA>110°, and CA<70°, respectively, while complete flipping of the fluids is observed for intermediate angles. The forces relocate the fluids in the channel, generally, by a clockwise or anticlockwise rotation. Here, it is demonstrated that the direction of this twist can be determined by the relative densities and wettabilities of the two fluids.

Microfabricated acoustofluidic membrane acoustic waveguide actuator for highly localized in-droplet dynamic particle manipulation

Precision manipulation techniques in microfluidics often rely on ultrasonic actuators to generate displacement and pressure fields in a liquid. However, strategies to enhance and confine the acoustofluidic forces often work against miniaturization and reproducibility in fabrication. This study presents microfabricated piezoelectric thin film membranes made via silicon diffusion for guided flexural wave generation as promising acoustofluidic actuators with low frequency, voltage, and power requirements. The guided wave propagation can be dynamically controlled to tune and confine the induced acoustofluidic radiation force and streaming. This provides for highly localized dynamic particle manipulation functionalities such as multidirectional transport, patterning, and trapping. The device combines the advantages of microfabrication and advanced acoustofluidic capabilities into a miniature "drop-and-actuate" chip that is mechanically robust and features a high degree of reproducibility for large-scale production. The membrane acoustic waveguide actuators offer a promising pathway for acoustofluidic applications such as biosensing, organoid production, and in situ analyte transport.

Exploring the Origin of Maximum Entropy States Relevant to Resonant Modes in Modern Chladni Plates

Abstract: The resonant modes generated from the modern Chladni experiment are systematically confirmed to intimately correspond to the maximum entropy states obtained from the inhomogeneous Helmholtz equation for the square and equilateral triangle plates [...]

Programmable assembly of particles on a Chladni plate

In nature, simple building units can be assembled into complex shapes through long-term time-varying external stimuli that are often spatially nonlinear. In contrast, most artificial methods of externally directed assembly rely on field- or template-based energy minimization. However, methods directing the assembly process by controlling time-varying external stimuli instead of attaining the lowest-energy state remain largely unexplored. In this study, we introduce a method that applies time-varying and spatially nonlinear vibration fields to assemble particles into a desired two-dimensional shape. Our assembly method predicts, controls, and monitors the vibration-induced particle motion to iteratively minimize the difference between the desired shape and the actual particle distribution. We applied our method to a centrally actuated vibrating plate, also known as a Chladni plate, and assembled up to a hundred submillimeter particles into complex recognizable shapes. The method allows programmable formation of shapes beyond the intrinsic limits of periodic patterning of the plate.

Deformation of Al85Y8Ni5Co2 Metallic Glasses under Cyclic Mechanical Load and Uniform Heating

Modelling of the deformation process of Al85Y8Ni5Co2 amorphous alloys was carried out under simultaneous application of cyclic mechanical load (at 0.3 or 3 Hz frequencies) and continuously increasing temperature (heating rate 5 K/min). It is shown that deformation of the amorphous specimens occurs by the hyperbolic temporal dependence. It is analytically determined and experimentally proved that for non-isothermal cyclic deformation, the wave effects take place as a result of the superposition of thermal-activated and mechanical components. The behaviour of the material under thermo-mechanical action was described qualitatively within the framework of Spaepen’s model. The dependencies for the reaction force of the samples were obtained as two-parameter functions of the frequency and temperature. A reaction force surface of a specimen, as a function of the different forcing frequencies and time, has been plotted.

Reconfigurable Particle Swarm Robotics Powered by Acoustic Vibration Tweezer

Inspired by natural swarms such as bees and ants, various types of swarm robotic systems have been developed to work together to complete tasks that transcend individual capabilities. Autonomous robots controlled by collective algorithm and colloidal swarms energized by external field have been designed in an attempt to emulate collective behaviors in nature. However, either sophisticated hardware designs or active agents with special electromagnetic properties and microstructural designs are needed. Here, for the first time, we create a swarm robotic system that can make any granular materials an active swarm robot by acoustic vibration tweezer. It should be noted that the particles energized by only one vibration generator are ordinary sand without any microstructural design. Therefore, it is the simplest and lowest cost swarm robot. Particles can display a solid-like aggregate, which is capable of robustly carrying and transporting an object that is about 1 million times heavier than a single particle. Moreover, through the cooperation of two swarm robots, we can achieve cooperative transport of a stick with a length of 1000 times the diameter of a single particle. The particle robot can move in a fluid-like amorphous group, which can change its own shape to adapt to the surrounding environment, thus having a strong environmental adaptability. Besides, it can move quickly (about 600 times the particle diameter per second) in a discrete state. Within one certain particle system, the particle swarm robot can emulate diverse biomimetic collective behaviors through navigated locomotion, multimode transformation, and cooperative transport.

Acoustic Microfluidics

Acoustic microfluidic devices are powerful tools that use sound waves to manipulate micro- or nanoscale objects or fluids in analytical chemistry and biomedicine. Their simple device designs, biocompatible and contactless operation, and label-free nature are all characteristics that make acoustic microfluidic devices ideal platforms for fundamental research, diagnostics, and therapeutics. Herein, we summarize the physical principles underlying acoustic microfluidics and review their applications, with particular emphasis on the manipulation of macromolecules, cells, particles, model organisms, and fluidic flows. We also present future goals of this technology in analytical chemistry and biomedical research, as well as challenges and opportunities.

Design of acoustofluidic device for localized trapping

State of the art acoustofluidics typically treat micro-particles in a multi-wavelength range due to the scale limitations of the established ultrasound field. Here, we report a spatial selective acoustofluidic device that allows trapping micro-particles and cells in a wavelength scale. A pair of interdigital transducers with a concentric-arc shape is used to compress the beam width, while pulsed actuation is adopted to localize the acoustic radiation force in the wave propagating direction. Unlike the traditional usage of geometrical focus, the proposed device is designed by properly superposing the convergent section of two focused surface acoustic waves. We successfully demonstrate a single-column alignment of 15-μm polystyrene particles and double-column alignment of 8-μm T cells in a wavelength scale. Through proof-of-concept experiments, the proposed acoustofluidic device shows potential applications in on-chip biological and chemical analyses, where localized handing is required.

Robotic Trajectories and Morphology Manipulation of Single Particle and Granular Materials by a Vibration Tweezer

Robotic self-assembly of deformable materials holds potential for the automatic construction of complex robots. Current manipulation for deformable manipulation mainly focuses on a soft robot. It still remains a great challenge for morphology manipulation of a swarm of particles. Chladni patterns have raised great interest in the field of self-assembly for different materials. The formation of Chladni patterns is driven by the vibration process that involves the particles moving from disorder to order. Particles bounce randomly on the plate, and gradually accumulate along nodal lines, whereas the instantaneous random effect is inevitable, meaning that the trajectories of particles are uncertain. Here, the vibration tweezer is proposed by programmable two-frequency driving Chladni patterns. Different materials can be precisely and flexibly trapped to the vibration node. The vibration tweezer is further programmed for arbitrary positions by solving the vibration inverse problem. Then, different controllable trajectories "PKU" manipulation of particle can be achieved through switching the tweezer positions. Most importantly, the vibration tweezer exhibits the morphology of granular materials assemblages with collection, motion, and rotation. This work paves the way for the control of complex self-assembly, thereby enabling programmable manipulation of granular materials and micro robots.

Deep, sub-wavelength acoustic patterning of complex and non-periodic shapes on soft membranes supported by air cavities

Arbitrary patterning of micro-objects in liquid is crucial to many biomedical applications. Among conventional methodologies, acoustic approaches provide superior biocompatibility but are intrinsically limited to producing periodic patterns at low resolution due to the nature of standing waves and the coupling between fluid and structure vibrations. This work demonstrates a near-field acoustic platform capable of synthesizing high resolution, complex and non-periodic energy potential wells. A thin and viscoelastic membrane is utilized to modulate the acoustic wavefront on a deep, sub-wavelength scale by suppressing the structural vibration selectively on the platform. Using 3 MHz excitation (λ∼ 500 μm in water), we have experimentally validated such a concept by realizing patterning of microparticles and cells with a line resolution of 50 μm (one tenth of the wavelength). Furthermore, massively parallel patterning across a 3 × 3 mm² area has been achieved. This new acoustic wavefront modulation mechanism is powerful for manufacturing complex biologic products.

Impact Excitation of a Seismic Pulse and Vibrational Normal Modes on Asteroid Bennu and Associated Slumping of Regolith

We consider an impact on an asteroid that is energetic enough to cause resurfacing by seismic reverberation and just below the catastrophic disruption threshold, assuming that seismic waves are not rapidly attenuated. In asteroids with diameter less than 1 km we identify a regime where rare energetic impactors can excite seismic waves with frequencies near those of the asteroid's slowest normal modes. In this regime, the distribution of seismic reverberation is not evenly distributed across the body surface. With mass-spring model elastic simulations, we model impact excitation of seismic waves with a force pulse exerted on the surface and using three different asteroid shape models. The simulations exhibit antipodal focusing and normal mode excitation. If the impulse excited vibrational energy is long lasting, vibrations are highest at impact point, its antipode and at high surface elevations such as an equatorial ridge. A near equatorial impact launches a seismic impulse on a non-spherical body that can be focused on two additional points on an the equatorial ridge. We explore simple flow models for the morphology of vibration induced surface slumping. We find that the initial seismic pulse is unlikely to cause large shape changes. Long lasting seismic reverberation on Bennu caused by a near equatorial impact could have raised the height of its equatorial ridge by a few meters and raised two peaks on it, one near impact site and the other near its antipode.

Protocol for assembling micro- and nanoparticles in a viscous liquid above a vibrating plate

In this protocol, we demonstrate the use of a vibrating plate to drive the assembly of micro- and nanoparticles as an approach to high-throughput, large-scale directed assembly in a viscous liquid. Vibration drives the assembly of glass bead microparticles and iron oxide nanoparticles in contact with water over an area of 6400 mm². We use a scaling analysis to show that there is a competition between acoustic radiation force and vibration-generated fluid flow in a viscous medium, which determines particle transport characteristics. For assembly in a viscous liquid, we find close agreement between the observed experimental results when compared to a numerical solution of the 2D wave equation that describes plate displacement. This model indicates that microparticles migrate along displacement gradients towards displacement anti-nodes where the magnitude of displacement is maximum. We also observe that nanoparticles migrate toward displacement nodes where the magnitude of displacement is zero.

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Cost-effective directed assembly technique without the need for microfabrication facilities

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Large-scale assembly produces heterogeneously ordered structures on a vibrating substrate

Point-driven modern Chladni figures with symmetry breaking

Point-driven modern Chladni figures subject to the symmetry breaking are systematically unveiled by developing a theoretical model and making experimental confirmation in the orthotropic brass. The plates with square shape are employed in the exploration based on the property that the orientation-dependent elastic anisotropy can be controlled by cutting the sides with a rotation angle with respect to the characteristic axes of the brass. Experimental results reveal that the orientation symmetry breaking not only causes the redistribution of resonant frequencies but also induces more resonant modes. More intriguingly, the driving position in some of new resonant modes can turn into the nodal point, whereas this position is always the anti-node in the isotropic case. The theoretical model is analytically developed by including a dimensionless parameter to consider the orientation symmetry-breaking effect in a generalized way. It is numerically verified that all experimental resonant frequencies and Chladni patterns can be well reconstructed with the developed model. The good agreement between theoretical calculations and experimental observations confirms the feasibility of using the developed model to analyze the modern Chladni experiment with orientation symmetry breaking. The developed model is believed to offer a powerful tool to build important database of plate resonant modes for the applications of controlling collective motions of micro objects.

Formation of inverse Chladni patterns in liquids at microscale: roles of acoustic radiation and streaming-induced drag forces

While Chladni patterns in air over vibrating plates at macroscale have been well studied, inverse Chladni patterns in water at microscale have recently been reported. The underlying physics for the focusing of microparticles on the vibrating interface, however, is still unclear. In this paper, we present a quantitative three-dimensional study on the acoustophoretic motion of microparticles on a clamped vibrating circular plate in contact with water with emphasis on the roles of acoustic radiation and streaming-induced drag forces. The numerical simulations show good comparisons with experimental observations and basic theory. While we provide clear demonstrations of three-dimensional particle size-dependent microparticle trajectories in vibrating plate systems, we show that acoustic radiation forces are crucial for the formation of inverse Chladni patterns in liquids on both out-of-plane and in-plane microparticle movements. For out-of-plane microparticle acoustophoresis, out-of-plane acoustic radiation forces are the main driving force in the near-field, which prevent out-of-plane acoustic streaming vortices from dragging particles away from the vibrating interface. For in-plane acoustophoresis on the vibrating interface, acoustic streaming is not the only mechanism that carries microparticles to the vibrating antinodes forming inverse Chladni patterns: In-plane acoustic radiation forces could have a greater contribution. To facilitate the design of lab-on-a-chip devices for a wide range of applications, the effects of many key parameters, including the plate radius R and thickness h and the fluid viscosity μ, on the microparticle acoustophoresis are discussed, which show that the threshold in-plane and out-of-plane particle sizes balanced from the acoustic radiation and streaming-induced drag forces scale linearly with R and μ , but inversely with h .

Artificial Swimmers Propelled by Acoustically Activated Flagella

Recent studies have garnered considerable interest in the field of propulsion to maneuver micro- and nanosized objects. Acoustics provide an alternate and attractive method to generate propulsion. To date, most acoustic-based swimmers do not use structural resonances, and their motion is determined by a combination of bulk acoustic streaming and a standing-wave field. The resultant field is intrinsically dependent on the boundaries of their resonating chambers. Though acoustic based propulsion is appealing in biological contexts, existing swimmers are less efficient, especially when operating in vivo, since no predictable standing-wave can be established in a human body. Here we describe a new class of nanoswimmer propelled by the small-amplitude oscillation of a flagellum-like flexible tail in standing and, more importantly, in traveling acoustic waves. The artificial nanoswimmer, fabricated by multistep electrodeposition techniques, compromises a rigid bimetallic head and a flexible tail. During acoustic excitation of the nanoswimmer the tail structure oscillates, which leads to a large amplitude propulsion in traveling waves. FEM simulation results show that the structural resonances lead to high propulsive forces.

Chladni Patterns in a Liquid at Microscale

By means of ultrathin silicon membranes excited in the low ultrasound range, we show for the first time that it is possible to form two-dimensional Chladni patterns of microbeads in liquid. Unlike the well-known effect in a gaseous environment at the macroscale, where gravity effects are generally dominant, leading particles towards the nodal regions of displacement, we show that the combined effects of an ultrathin plate excited at low frequency (yielding to subsonic waves) together with reduced gravity (arising from buoyancy) will enhance the importance of microstreaming in the Chladni problem. Here, we report that for micrometric beads larger than the inner streaming layer, the microscale streaming in the vicinity of the plate tends to gather particles in antinodal regions of vibrations yielding to patterns in good agreement with the predicted modes for a liquid-loaded plate. Interestingly, a symmetry breaking phenomenon together with the streaming can trigger movements of beads departing from one cluster to another. We show that, for higher modes, this movement can appear as a collective rotation of the beads in the manner of a "farandole."

Exploring the resonant vibration of thin plates: Reconstruction of Chladni patterns and determination of resonant wave numbers

The Chladni nodal line patterns and resonant frequencies for a thin plate excited by an electronically controlled mechanical oscillator are experimentally measured. Experimental results reveal that the resonant frequencies can be fairly obtained by means of probing the variation of the effective impedance of the exciter with and without the thin plate. The influence of the extra mass from the central exciter is confirmed to be insignificant in measuring the resonant frequencies of the present system. In the theoretical aspect, the inhomogeneous Helmholtz equation is exploited to derive the response function as a function of the driving wave number for reconstructing experimental Chladni patterns. The resonant wave numbers are theoretically identified with the maximum coupling efficiency as well as the maximum entropy principle. Substituting the theoretical resonant wave numbers into the derived response function, all experimental Chladni patterns can be excellently reconstructed. More importantly, the dispersion relationship for the flexural wave of the vibrating plate can be determined with the experimental resonant frequencies and the theoretical resonant wave numbers. The determined dispersion relationship is confirmed to agree very well with the formula of the Kirchhoff-Love plate theory.

Surface adsorbate fluctuations and noise in nanoelectromechanical systems

Physisorption on solid surfaces is important in both fundamental studies and technology. Adsorbates can also be critical for the performance of miniature electromechanical resonators and sensors. Advances in resonant nanoelectromechanical systems (NEMS), particularly mass sensitivity attaining the single-molecule level, make it possible to probe surface physics in a new regime, where a small number of adatoms cause a detectable frequency shift in a high quality factor (Q) NEMS resonator, and adsorbate fluctuations result in resonance frequency noise. Here we report measurements and analysis of the kinetics and fluctuations of physisorbed xenon (Xe) atoms on a high-Q NEMS resonator vibrating at 190.5 MHz. The measured adsorption spectrum and frequency noise, combined with analytic modeling of surface diffusion and adsorption-desorption processes, suggest that diffusion dominates the observed excess noise. This study also reveals new power laws of frequency noise induced by diffusion, which could be important in other low-dimensional nanoscale systems.

Nanoscale self-organization using standing surface acoustic waves

The diffusion of an adatom on a substrate submitted to a standing surface acoustic wave is theoretically studied. By performing large scale molecular dynamic simulations, we show that the wave dynamically structures the substrate by encouraging the presence of the adatom in the vicinity of the maximum displacements of the substrate. Using an analytical model, we explain this feature introducing an effective potential induced by the wave. Applied in an atomic deposition experiment, this dynamic structuring process should govern the nucleation sites distribution opening the route to accurately control the self-organization process at the nanoscale.

Inversion of Chladni patterns by tuning the vibrational acceleration

Inverse Chladni patterns, i.e., grains collecting at the antinodes of a resonating plate, are traditionally believed to occur only when the particles are small enough to be carried along by the ambient air. We now show--theoretically and numerically--that air currents are not the only mechanism leading to inverse patterns: When the acceleration of the resonating plate does not exceed g , particles will always roll to the antinodes, irrespective of their size, even in the absence of air. We also explain why this effect has hitherto escaped detection in standard Chladni experiments.

Mass sensing based on deterministic and stochastic responses of elastically coupled nanocantilevers

Coupled nanomechanical systems and their entangled eigenstates offer unique opportunities for the detection of ultrasmall masses. In this paper we show theoretically and experimentally that the stochastic and deterministic responses of a pair of coupled nanocantilevers provide different and complementary information about the added mass of an analyte and its location. This method allows the sensitive detection of minute quantities of mass even in the presence of large initial differences in the active masses of the two cantilevers. Finally, we show the fundamental limits in mass detection of this sensing paradigm.

Quantitative time-resolved measurement of membrane protein-ligand interactions using microcantilever array sensors

Membrane proteins are central to many biological processes, and the interactions between transmembrane protein receptors and their ligands are of fundamental importance in medical research. However, measuring and characterizing these interactions is challenging. Here we report that sensors based on arrays of resonating microcantilevers can measure such interactions under physiological conditions. A protein receptor--the FhuA receptor of Escherichia coli--is crystallized in liposomes, and the proteoliposomes then immobilized on the chemically activated gold-coated surface of the sensor by ink-jet spotting in a humid environment, thus keeping the receptors functional. Quantitative mass-binding measurements of the bacterial virus T5 at subpicomolar concentrations are performed. These experiments demonstrate the potential of resonating microcantilevers for the specific, label-free and time-resolved detection of membrane protein-ligand interactions in a micro-array format.

Statistics of nodal points of in-plane random waves in elastic media

We consider the nodal points (NPs) u=0 and v=0 of the in-plane vectorial displacements u=(u,v) which obey the Navier-Cauchy equation. Similar to the Berry conjecture of quantum chaos, we present the in-plane eigenstates of chaotic billiards as the real part of the superposition of longitudinal and transverse plane waves with random phases. By an average over random phases we derive the mean density and correlation function of NPs. Consequently we consider the distribution of the nearest distances between NPs.