Acoustofluidic Properties of Polystyrene Microparticles.

Acoustophoresis has become a powerful tool to separate microparticles and cells, based on their material and biophysical properties, and is gaining popularity in clinical and biomedical research. One major application of acoustophoresis is to measure the compressibility of cells and small organisms, which is related to their contents. The cell compressibility can be extracted from the acoustic mobility, which is the main output of acoustic migration experiments, if the material properties and sizes of reference particles, the size of the cells, and the surrounding medium are known. Accurate methods to measure and calibrate the acoustic energy density in acoustophoresis systems are therefore critical. In this Perspective, polystyrene microparticles have become the most commonly used reference particles in acoustophoresis, due to their similar biophysical properties to cells. We utilized a two-step focusing method to measure the relative acoustic mobility of polystyrene beads of various sizes and colors and present a quantitative analysis of the variation in acousto-mechanical properties of polystyrene microparticles, showing a large spread in their material properties. A variation of more than 25% between different particle types was found. Thus, care is required when relying on polystyrene particles as a reference when characterizing acoustofluidics systems or acousto-mechanical properties of cells.

Reduced acoustic resonator dimensions improve focusing efficiency of bacteria and submicron particles.

In this study, we demonstrate an acoustofluidic device that enables single-file focusing of submicron particles and bacteria using a two-dimensional (2D) acoustic standing wave. The device consists of a 100 µm × 100 µm square channel that supports 2D particle focusing in the channel center at an actuation frequency of 7.39 MHz. This higher actuation frequency compared with conventional bulk acoustic systems enables radiation-force-dominant motion of submicron particles and overcomes the classical size limitation (≈2 µm) of acoustic focusing. We present acoustic radiation force-based focusing of particles with diameters less than 0.5 µm at a flow rate of 12 µL min-1, and 1.33 µm particles at flow rates up to 80 µL min-1. The device focused 0.25 µm particles by the 2D acoustic radiation force while undergoing a channel cross-section centered, single-vortex acoustic streaming. A suspension of bacteria was also investigated to evaluate the biological relevance of the device, which demonstrated the alignment of bacteria in the channel at a flow rate of up to 20 µL min-1. The developed acoustofluidic device can align submicron particles within a narrow flow stream in a highly robust manner, validating its use as a flow-through focusing chamber to perform high-throughput and accurate flow cytometry of submicron objects.

Acoustic Compressibility of Caenorhabditis elegans.

The acoustic compressibility of Caenorhabditis elegans is a necessary parameter for further understanding the underlying physics of acoustic manipulation techniques of this widely used model organism in biological sciences. In this work, numerical simulations were combined with experimental trajectory velocimetry of L1 C. elegans larvae to estimate the acoustic compressibility of C. elegans. A method based on bulk acoustic wave acoustophoresis was used for trajectory velocimetry experiments in a microfluidic channel. The model-based data analysis took into account the different sizes and shapes of L1 C. elegans larvae (255 ± 26 µm in length and 15 ± 2 µm in diameter). Moreover, the top and bottom walls of the microfluidic channel were considered in the hydrodynamic drag coefficient calculations, for both the C. elegans and the calibration particles. The hydrodynamic interaction between the specimen and the channel walls was further minimized by acoustically levitating the C. elegans and the particles to the middle of the measurement channel. Our data suggest an acoustic compressibility κCe of 430 TPa-1 with an uncertainty range of ±20 TPa-1 for C. elegans, a much lower value than what was previously reported for adult C. elegans using static methods. Our estimated compressibility is consistent with the relative volume fraction of lipids and proteins that would mainly make up for the body of C. elegans. This work is a departing point for practical engineering and design criteria for integrated acoustofluidic devices for biological applications.

Acoustofluidic particle dynamics: Beyond the Rayleigh limit.

In this work a numerical model to calculate the trajectories of multiple acoustically and hydrodynamically interacting spherical particles is presented. The acoustic forces are calculated by solving the fully coupled three-dimensional scattering problem using finite element software. The method is not restricted to single re-scattering events, mono- and dipole radiation, and long wavelengths with respect to the particle diameter, thus expanding current models. High frequency surface acoustic waves have been used in the one cell per well technology to focus individual cells in a two-dimensional wave-field. Sometimes the cells started forming clumps and it was not possible to focus on individual cells. Due to a lack of existing theory, this could not be fully investigated. Here, the authors use the full dynamic simulations to identify limiting factors of the one-cell-per-well technology. At first, the authors demonstrate good agreement of the numerical model with analytical results in the Rayleigh limiting case. A frequency dependent stability exchange between the pressure and velocity was then demonstrated. The numerical formulation presented in this work is relatively general and can be used for a multitude of different high frequency applications. It is a powerful tool in the analysis of microscale acoustofluidic devices and processes.

Multibody dynamics in acoustophoresis.

Determining the trajectories of multiple acoustically and hydrodynamically interacting as well as colliding particles is one of the challenges in numerical acoustophoresis. Although the acoustic forces between multiple small spherical particles can be obtained analytically, previous research did not address the particle-particle contacts in a rigorous way. This article extends existing methods by presenting an algorithm on displacement level which models the hard contacts using set-valued force laws, hence allowing for the first time the computation of a first approximation of complete trajectories of multiple hydrodynamically and acoustically interacting particles. This work uses a semi-analytical method to determine the acoustic forces, which is accurate up to the dipole contributions of the multipole expansion. The hydrodynamic interactions are modeled using the resistance and mobility functions of the Stokes' flow. In previous experimental work particles have been reported to interact acoustically, ultimately forming stacked lines near the pressure nodes of a standing wave. This phenomenon is examined experimentally and numerically, the simulation shows good agreement with the experimental results. To demonstrate the capabilities of the method, the rotation of a particle clump in two orthogonal waves is simulated. The presented method allows further insight in self-assembly applications and acoustic particle manipulation.

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.

Acoustic streaming outside and inside a fluid particle undergoing monopole and dipole oscillations.

An analytical theory is developed for acoustic streaming induced by an acoustic wave field inside and outside a spherical fluid particle, which can be a liquid droplet or a gas bubble. The particle is assumed to undergo the monopole (pulsation) and the dipole (translation) oscillation modes. The dispersed phase and the carrier medium are considered to be immiscible, compressible, and viscous. The developed theory allows one to calculate the acoustic streaming both outside and inside the fluid particle. In contrast to earlier works, no restrictions are imposed on the thickness of the outer and inner viscous boundary layers with respect to the particle radius. A numerical implementation of the obtained analytical results is used to evaluate the acoustic streaming for different experimentally relevant configurations, such as an air bubble in water, a water droplet in oil, and a water droplet in air, considering both traveling and standing acoustic waves. The results show the richness of streaming pattern variations that arise in bubbles and droplets.

Acoustic radiation force acting on a heavy particle in a standing wave can be dominated by the acoustic microstreaming.

We numerically investigate the contribution of the microstreaming to the acoustic radiation force acting on a small elastic spherical particle placed into an ultrasonic standing wave. When an acoustic wave scatters on a particle the acoustic radiation force and the microstreaming appear as nonlinear time-averaged effects. The compressible Navier-Stokes equations are solved up to second order in terms of the small Mach number using a finite element method. We show that when the viscous boundary layer thickness to particle radius ratio is sufficiently large and the particle is sufficiently dense, the acoustic microstreaming dominates the acoustic radiation force. In this case, our theory predicts migration of the particle to the velocity node (pressure antinode).

Neutrophil-inspired propulsion in a combined acoustic and magnetic field.

Systems capable of precise motion in the vasculature can offer exciting possibilities for applications in targeted therapeutics and non-invasive surgery. So far, the majority of the work analysed propulsion in a two-dimensional setting with limited controllability near boundaries. Here we show bio-inspired rolling motion by introducing superparamagnetic particles in magnetic and acoustic fields, inspired by a neutrophil rolling on a wall. The particles self-assemble due to dipole-dipole interaction in the presence of a rotating magnetic field. The aggregate migrates towards the wall of the channel due to the radiation force of an acoustic field. By combining both fields, we achieved a rolling-type motion along the boundaries. The use of both acoustic and magnetic fields has matured in clinical settings. The combination of both fields is capable of overcoming the limitations encountered by single actuation techniques. We believe our method will have far-reaching implications in targeted therapeutics.Devising effective swimming and propulsion strategies in microenvironments is attractive for drug delivery applications. Here Ahmed et al. demonstrate a micropropulsion strategy in which a combination of magnetic and acoustic fields is used to assemble and propel colloidal particles along channel walls.

Imaging the position-dependent 3D force on microbeads subjected to acoustic radiation forces and streaming.

Acoustic particle manipulation in microfluidic channels is becoming a powerful tool in microfluidics to control micrometer sized objects in medical, chemical and biological applications. By creating a standing acoustic wave in the channel, the resulting pressure field can be employed to trap or sort particles. To design efficient and reproducible devices, it is important to characterize the pressure field throughout the volume of the microfluidic device. Here, we used an optically trapped particle as probe to measure the forces in all three dimensions. By moving the probe through the volume of the channel, we imaged spatial variations in the pressure field. In the direction of the standing wave this revealed a periodic energy landscape for 2 µm beads, resulting in an effective stiffness of 2.6 nN m(-1) for the acoustic trap. We found that multiple fabricated devices showed consistent pressure fields. Surprisingly, forces perpendicular to the direction of the standing wave reached values of up to 20% of the main-axis-values. To separate the direct acoustic force from secondary effects, we performed experiments with different bead sizes, which attributed some of the perpendicular forces to acoustic streaming. This method to image acoustically generated forces in 3D can be used to either minimize perpendicular forces or to employ them for specific applications in novel acoustofluidic designs.

Numerical simulation of acoustofluidic manipulation by radiation forces and acoustic streaming for complex particles.

The numerical prediction of acoustofluidic particle motion is of great help for the design, the analysis, and the physical understanding of acoustofluidic devices as it allows for a simple and direct comparison with experimental observations. However, such a numerical setup requires detailed modeling of the acoustofluidic device with all its components and thorough understanding of the acoustofluidic forces inducing the particle motion. In this work, we present a 3D trajectory simulation setup that covers the full spectrum, comprising a time-harmonic device model, an acoustic streaming model of the fluid cavity, a radiation force simulation, and the calculation of the hydrodynamic drag. In order to make quantitatively accurate predictions of the device vibration and the acoustic field, we include the viscous boundary layer damping. Using a semi-analytical method based on Nyborg's calculations, the boundary-driven acoustic streaming is derived directly from the device simulation and takes into account cavity wall vibrations which have often been neglected in the literature. The acoustic radiation forces and the hydrodynamic drag are calculated numerically to handle particles of arbitrary shape, structure, and size. In this way, complex 3D particle translation and rotation inside experimental microdevices can be predicted. We simulate the rotation of a microfiber in an amplitude-modulated 2D field and analyze the results with respect to experimental observations. For a quantitative verification, the motion of an alumina microdisk is compared to a simple experiment. Demonstrating the potential of the simulation setup, we compute the trajectory of a red blood cell inside a realistic microdevice under the simultaneous effects of acoustic streaming and radiation forces.