Inversion of Chladni patterns by tuning the vibrational acceleration

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.

Acoustofluidics-Assisted Multifunctional Paper-Based Analytical Devices

Microfluidic paper-based analytical devices (μPADs) feature an economic and sensitive nature, while acoustofluidics displays contactless and versatile virtue, and both of them gained tremendous interest in the past decades. Integrating μPADs with acoustofluidic techniques provides great potential to overcome the inherent shortcomings and make appealing achievements. Here, we present acoustofluidics-assisted multifunctional paper-based analytical devices that leverage bulk acoustic waves to realize multiple applications on paper substrates, including uniform colorimetric detection, microparticle/cell enrichment, fluorescence amplification, homogeneous mixing, and nanomaterial synthesis. The glucose detection in the range of 5-15 mM was conducted to perform uniform colorimetric detection. Various types (brass powder, copper powder, diamond powder, and yeast cells) and sizes (5-200 μm) of solid particles and biological cells can be enriched on paper in a few seconds or minutes; thus, fluorescence amplification by 3 times was realized with the enrichment. The high-throughput and homogeneous mixing of two fluids can be achieved, and based on the mixing, nanomaterials (ZnO nanosheets) were synthesized on paper. We analyzed the underlying mechanisms of these applications in the devices, which are attributed to Faraday waves and Chladni patterns. With their simple fabrication and prominent effectiveness, the devices open up new possibilities for paper-based microfluidic devices.

Forced free vibrations of a square plate

The vibrations of a square plate with free edges that is forced at its center has been investigated experimentally and numerically. A two-step finite volume scheme is proposed and is tested against an exact solution to a related problem. The governing equation and numerical solution procedure were constructed to closely mimic the experiment. Good agreement was found between the numerical simulations and the experiments.

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.

Motion of Heavy Particles on a Submerged Chladni Plate

Heavy particles are traditionally believed to gather at the nodes of a resonating plate, forming standard Chladni patterns. Here, for the first time, we experimentally show that heavy particles, i.e., sub-mm particles, can move towards the antinodes of a resonating plate. By submerging the resonating plate inside a fluidic medium, the acoustic radiation force and the lateral effective weight become dominant at the sub-mm scale. Those forces, averaged over a vibration cycle, move the particles towards the antinodes and generate sophisticated patterns. We create a statistical model that relates the complex motion of particles to their locations and plate vibration frequencies in a wide spectrum of both resonant and nonresonant frequencies. Additionally, we employ our model to control the motion of single particles and a swarm of particles on the submerged plate. Our device can move particles with sufficient power at an exceptionally wide frequency range, potentially opening a path to new particle manipulation techniques at sub-mm scale in fluidic media.

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 .

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.

Phase transition and flow-rate behavior of merging granular flows

Merging of granular flows is ubiquitous in industrial, mining, and geological processes. However, its behavior remains poorly understood. This paper studies the phase transition and flow-rate behavior of two granular flows merging into one channel. When the main channel is wider than the side channel, the system shows a remarkable two-sudden-drops phenomenon in the outflow rate when gradually increasing the main inflow. When gradually decreasing the main inflow, the system shows obvious hysteresis phenomenon. We study the flow-rate-drop phenomenon by measuring the area fraction and the mean velocity at the merging point. The phase diagram of the system is also presented to understand the occurrence of the phenomenon. We find that the dilute-to-dense transition occurs when the area fraction of particles at the joint point exceeds a critical value ϕ(c)=0.65±0.03.

Stop and restart of granular clock in a vibrated compartmentalized bidisperse granular system

This paper studies a bidisperse granular mixture consisting of two species of stainless steel spheres in a vertically vibrated compartmentalized container. The experiments show that with proper vibration acceleration, the granular clock stops when horizontal segregation of the large spheres residing in the far end from the barrier wall occurs. When the segregation is broken, the granular clock restarts. We present the phase diagrams of vibration acceleration versus container width and small particle number, which exhibits three different regions, namely, clustering state, stop-restart of the granular clock, and the granular clock. A generalized flux model is proposed to reproduce the phenomenon of stop and restart of the granular clock.