Acoustophoretic Motion Research Articles

Comparisons of the acoustic radiation force of ultrasonic standing waves in half-wavelength and quarter-wavelength micro-resonators of cylindrical geometry

Ultrasonic standing waves with specific wavelengths generated in the multi-layered micro-resonators were numerically and experimentally analyzed. Using a three-dimensional scanning fluorescence microscope, the acoustophoretic motion of fluorescent microparticles within the micro-resonators was carefully and accurately measured. The manufactured micro-resonators were validated by comparing the location of the acoustic pressure nodal plane and the average energy density curves derived from numerical and experimental results. Results confirmed that the acoustic radiation force of the induced ultrasonic standing waves drives the microparticles vertically within the micro-resonators and their average energy density increases as the sinusoidal voltage applied to the piezoelectric transducer increases. Semi-empirical correlations were developed for the average energy density, based on experimental results for a wide range of the applied voltage amplitudes. The correlations were in good agreement, within less than 20 % of the experimental values measured for both the half-wavelength and quarter-wavelength micro-resonators.

Acoustofluidic Three-Dimensional Motion of Suspended Cells at Near-Zero Acoustic Contrast in Homogeneous Media

Acoustic separation of suspension cells can be achieved by altering the properties of the cell medium. Cells of different types can then migrate in opposing directions in the sound field due to differences in their relative density and compressibility with respect to the surrounding fluid. For near-zero acoustic contrast the acoustic radiation force on cells becomes negligible, and it is the primary objective of this paper to study the interplay of acoustic radiation, acoustic streaming, and buoyancy in this regime and how it may affect the separation outcome. We study the three-dimensional acoustophoretic motion of suspension cells in homogeneous suspending media and link this to the underlying acoustofluidic mechanisms. Cell trajectories are measured by a defocused-image tracking approach, and we assess the technique's applicability for tracking cells by determining the associated error when measuring the out-of-image-plane component of the tracks. For cells at near-zero acoustic contrast, we observe strong effects of buoyancy and acoustic streaming and that small distributions of cell properties within a population leads to large differences in the cell motion patterns. A neural network was developed to classify experimental cell trajectories according to their acoustic contrast in different suspending media. Further, we compare the experimentally measured trajectories to a numerical model by generating simulated trajectories of cells.

Continuous Particle Aggregation and Separation in Acoustofluidic Microchannels Driven by Standing Lamb Waves

In this study, we realize acoustic aggregation and separation of microparticles in fluid channels driven by standing Lamb waves of a 300-μm-thick double-side polished lithium-niobate (LiNbO3) plate. We demonstrate that the counter-propagating lowest-order antisymmetric and symmetric Lamb modes can be excited by double interdigitated transducers on the LiNbO3 plate to produce interfacial coupling with the fluid in channels. Consequently, the solid-fluid coupling generates radiative acoustic pressure and streaming fields to actuate controlled acoustophoretic motion of particles by means of acoustic radiation and Stokes drag forces. We conducted finite-element simulations based on the acoustic perturbation theory with full-wave modeling to tailor the acoustic and streaming fields in the channels driven by the standing Lamb waves. As a result, the acoustic process and the mechanism of particle aggregation and separation were elucidated. Experiments on acoustic manipulation of particles in channels validate the capability of aggregation and separation by the designed devices. It is observed that strong streaming dominates the particle aggregation while the acoustic radiation force differentially expels particles with different sizes from pressure antinodes to achieve continuous particle separation. This study paves the way for Lamb-wave acoustofluidics and may trigger more innovative acoustofluidic systems driven by Lamb waves and other manipulating approaches incorporated on a thin-plate platform.

Investigation of effective parameters on streaming-induced acoustophoretic particle manipulation in a microchannel via three-dimensional numerical simulation

Particle manipulation using ultrasonic standing waves has gained increased attention in recent years as it is efficient and noninvasive. In order to predict the effects of acoustic streaming on the concentration of particles in the actual microchannel geometry, this paper presents a 3D numerical study on the transient motion of microparticles suspended in a liquid-filled microchannel, considering the mixed standing and traveling waves. The motion was generated by the acoustic radiation force and acoustic streaming-induced drag force arising from an imposed bulk acoustic wave and the hydrodynamic drag. The acoustic streaming patterns in the 3D microchannel were investigated using the limiting velocity method. In addition, the effects of the 3D streaming pattern in an acoustofluidic device on the acoustophoretic motion of microparticles were evaluated. The concentration of polystyrene particles was simulated for many particles with diameters of 0.5, 2, and 5 μm released from random initial locations. The obtained results indicate a balance between the flow rate and the particle diameter to achieve the highest concentration percentage. Increasing the height increased the concentration of large 5-μm-diameter particles to more than 80%. By doubling the length of the piezoelectrically actuated region, the concentration of 2-μm particles improved by approximately 20%. Finally, increasing the viscosity of the fluid by using a 50% glycerol-in-water mixture resulted in a greater effect of acoustic streaming. This study can provide helpful guidance for optimizing the design of acoustofluidic devices to enhance experiments.

3D numerical simulation of acoustophoretic motion induced by boundary-driven acoustic streaming in standing surface acoustic wave microfluidics

Standing surface acoustic waves (SSAWs) have been widely utilized in microfluidic devices to manipulate various cells and micro/nano-objects. Despite widespread application, a time-/cost-efficient versatile 3D model that predicts particle behavior in such platforms is still lacking. Herein, a fully-coupled 3D numerical simulation of boundary-driven acoustic streaming in the acoustofluidic devices utilizing SSAWs has been conducted based on the limiting velocity finite element method. Through this efficient computational method, the underlying physical interplay from the electromechanical fields of the piezoelectric substrate to different acoustofluidic effects (acoustic radiation force and streaming-induced drag force), fluid–solid interactions, the 3D influence of novel on-chip configuration like tilted-angle SSAW (taSSAW) based devices, required boundary conditions, meshing technique, and demanding computational cost, are discussed. As an experimental validation, a taSSAW platform fabricated on YX 128 ^circ LiNbO3 substrate for separating polystyrene beads is simulated, which demonstrates acceptable agreement with reported experimental observations. Subsequently, as an application of the presented 3D model, a novel sheathless taSSAW cell/particle separator is conceptualized and designed. The presented 3D fully-coupled model could be considered a powerful tool in further designing and optimizing SSAW microfluidics due to the more time-/cost-efficient performance than precedented 3D models, the capability to model complex on-chip configurations, and overcome shortcomings and limitations of 2D simulations.

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

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

Acoustophoretic Motion of Erythrocyte‐mimicking Hemoglobin Micromotors

Summary of main observation and conclusionBiocompatible micromotors have received increasing attention, due to their powerful motion, diverse functionalities and autonomous navigation in the field of biomedical applications. Herein, we report an acoustically‐propelled, magnetic‐guided, erythrocyte‐mimicking hemoglobin micromotor with oxygen‐carrying capability. These hemoglobin micromotors were fabricated by encapsulating magnetic nanoparticles in hybrid hemoglobin/calcium carbonate microparticles, followed by covalently layer‐by‐layer assembly of hemoglobin multilayers. The asymmetric distribution of magnetic nanoparticles enables these micromotors to move rapidly under the propulsion of an acoustic field. The velocity of acoustophoretic motion of hemoglobin micromotors increases with the increase of input voltage of acoustic field, up to 58.2 μm·s–1 at 10 V. The hemoglobin micromotors are directionally navigated by applying an external magnetic field, and also could pass through microchannels toward the targeted region. Moreover, such hemoglobin micromotors show effective oxygen loading and releasing capability, holding considerable promise as a new platform for oxygen delivery applications.

Full-wave modeling of micro-acoustofluidic devices driven by standing surface acoustic waves for microparticle acoustophoresis

Surface acoustic wave (SAW)-based acoustofluidic systems are emerging as an important tool for acoustophoresis. In this paper, we present a full cross-sectional model of standing SAW acoustofluidic devices for obtaining full-wave results. Our model involves a piezoelectric substrate with interdigitated electrodes and a rectangular water channel enclosed in a finite soft elastic solid. This model accounts for piezoelectric SAWs with electromechanical coupling, simultaneous transverse and longitudinal wave fields in the elastic solid from SAW radiation, and acoustic and streaming fields in the enclosed water channel in an integrated system by solving the elastodynamic and Navier–Stokes field equations. Accordingly, the acoustic radiation force and streaming-induced Stokes drag force are obtained to analyze the acoustophoretic motion of microparticles of different sizes. Using the full-wave results, we reveal the influences of the channel wall displacements and acoustic and flow fields in the water domain. The full-wave field also allows us to determine the effects of the channel dimensions and its location in the finite elastic solid on the force strengths. We demonstrate that the critical diameter of the microparticles can be reduced by an order of magnitude by changing the channel location, while maintaining the same acoustic frequency. We note that the results, mechanisms, and method presented in this study can be usefully applied to the rational design of standing SAW acoustofluidic devices and for developing innovative acoustophoretic systems involving complex structure–fluid interactions.

Particle-size-dependent acoustophoretic motion and depletion of micro- and nano-particles at long timescales.

We present three-dimensional measurements of particle-size-dependent acoustophoretic motion of microparticles with diameters from 4.8 μm down to 0.5 μm suspended in either homogeneous or inhomogeneous fluids inside a glass-silicon microchannel and exposed to a standing ultrasound wave. To study the crossover from radiation force dominated to streaming dominated motion as the particle size is decreased, we extend previous studies to long timescales, where the particles smaller than the crossover size move over distances comparable to the channel width. We observe a particle-size-dependent particle depletion at late times for the particles smaller than the crossover size. The mechanisms behind this depletion in homogeneous fluids are rationalized by numerical simulations which take the Brownian motion into account. Experimentally, the particle trajectories in inhomogeneous fluids show focusing in the bulk of the microchannel at early times, even for the particles below the critical size, which clearly demonstrates the potential to manipulate submicrometer particles.

Rapid acoustophoretic motion of microparticles manipulated by phononic crystals

We present the acoustophoretic motion of microparticles simultaneously driven by the acoustic streaming induced drag force (ASF) and acoustic radiation force (ARF) on a phononic crystal plate (PCP). A much faster acoustophoresis can be achieved via a PCP than a traditional standing wave in bulk and surface acoustic wave devices. The mechanism is attributed to the significantly enhanced ASF and ARF originating from the resonant excitation of a nonleaky zero-order antisymmetric Lamb mode intrinsically in the plate, which generates the highly localized field vertical to the surface and periodic field parallel to the surface. We also demonstrate the transition from the ASF dominated acoustophoresis to ARF dominated acoustophoresis as a function of particle size. The predicted trajectories and velocity of acoustophoretic particles by the proposed finite element model are in reasonable agreement with experimental phenomena. This study would aid the development of simple, scalable, integrated, and disposable phononic crystal based acoustofluidic systems for biomedical applications such as rapid mixing, cell trapping, sorting, and patterning.

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 sqrt mu, but inversely with sqrt h.

Effects of fluid medium flow and spatial temperature variation on acoustophoretic motion of microparticles in microfluidic channels.

A numerical modeling method for accurately predicting the acoustophoretic motion of compressible microparticles in microfluidic devices is presented to consider the effects of fluid medium flow and spatial temperature variation that can significantly influence the acoustophoretic motion. In the proposed method, zeroth-order fluid medium flow and temperature, and first- and second-order acoustic fields in the microfluidic devices are first calculated by applying quadratic mapping functions and a second-order finite difference method (FDM) to perturbed mass, momentum, and energy conservation equations and state equation. Then, the acoustic radiation force is obtained based on the Gorkov's acoustic radiation force equation and applied to the Newton's Equation of Motion to calculate the microparticle motion. The proposed method was validated by comparing its results to a commercial software package, COMSOL Multiphysics results, one-dimensional, analytical modeling results, and experimental results. It is shown that the fluid medium flow affects the acoustic radiation force and streaming significantly, resulting in the acoustic radiation force and streaming prediction errors of 10.9% and 67.4%, respectively, when the fluid medium flow speed is increased from 0 to 1 m/s. A local temperature elevation from 20 °C to 22 °C also results in the prediction errors of 88.4% and 73.4%.

Numerical study of acoustophoretic motion of particles in a PDMS microchannel driven by surface acoustic waves.

We present a numerical study of the acoustophoretic motion of particles suspended in a liquid-filled PDMS microchannel on a lithium niobate substrate acoustically driven by surface acoustic waves. We employ a perturbation approach where the flow variables are divided into first- and second-order fields. We use impedance boundary conditions to model the PDMS microchannel walls and we model the acoustic actuation by a displacement function from the literature based on a numerical study of piezoelectric actuation. Consistent with the type of actuation, the obtained first-order field is a horizontal standing wave that travels vertically from the actuated wall towards the upper PDMS wall. This is in contrast to what is observed in bulk acoustic wave devices. The first-order fields drive the acoustic streaming, as well as the time-averaged acoustic radiation force acting on suspended particles. We analyze the motion of suspended particles driven by the acoustic streaming drag and the radiation force. We examine a range of particle diameters to demonstrate the transition from streaming-drag-dominated acoustophoresis to radiation-force-dominated acoustophoresis. Finally, as an application of our numerical model, we demonstrate the capability to tune the position of the vertical pressure node along the channel width by tuning the phase difference between two incoming surface acoustic waves.

Effects of fluid medium flow and spatial temperature variation on acoustophoretic motion of microparticles in microfluidic channels

Effects of fluid medium flow and spatial temperature variation on acoustophoretic motion of microparticles in microfluidic channels

Numerical simulation of 3D boundary-driven acoustic streaming in microfluidic devices

This article discusses three-dimensional (3D) boundary-driven streaming in acoustofluidic devices. Firstly, the 3D Rayleigh streaming pattern in a microchannel is simulated and its effect on the movement of microparticles of various sizes is demonstrated. The results obtained from this model show good comparisons with 3D experimental visualisations and demonstrate the fully 3D nature of the acoustic streaming field and the associated acoustophoretic motion of microparticles in acoustofluidic devices. This method is then applied to another acoustofluidic device in order to gain insights into an unusual in-plane streaming pattern. The origin of this streaming has not been fully described and its characteristics cannot be explained from the classical theory of Rayleigh streaming. The simulated in-plane streaming pattern was in good agreement with the experimental visualisation. The mechanism behind it is shown to be related to the active sound intensity field, which supports our previous findings on the mechanism of the in-plane acoustic streaming pattern visualised and modelled in a thin-layered capillary device.

Ultrasound-induced acoustophoretic motion of microparticles in three dimensions

We derive analytical expressions for the three-dimensional (3D) acoustophoretic motion of spherical microparticles in rectangular microchannels. The motion is generated by the acoustic radiation force and the acoustic streaming-induced drag force. In contrast to the classical theory of Rayleigh streaming in shallow, infinite, parallel-plate channels, our theory does include the effect of the microchannel side walls. The resulting predictions agree well with numerics and experimental measurements of the acoustophoretic motion of polystyrene spheres with nominal diameters of 0.537 and 5.33 μm. The 3D particle motion was recorded using astigmatism particle tracking velocimetry under controlled thermal and acoustic conditions in a long, straight, rectangular microchannel actuated in one of its transverse standing ultrasound-wave resonance modes with one or two half-wavelengths. The acoustic energy density is calibrated in situ based on measurements of the radiation dominated motion of large 5-μm-diameter particles, allowing for quantitative comparison between theoretical predictions and measurements of the streaming-induced motion of small 0.5-μm-diameter particles.

Numerical modeling for analyzing microfluidic acoustophoretic motion of cells and particles with application to identification of vibro-acoustic properties

Microfluidic, acoustophoretic cell/particle separation has gained significant interest recently. In order to analyze the motion of cells/particles in the acoustophoretic separation, a one-dimensional (1-D) analytical model in a “static” fluid medium has been widely used, while the effects of acoustic streaming, viscous boundary layers, and 2-D and 3-D geometries are usually not considered. Therefore, it is not sufficient to accurately predict the cell/particle motion. Thus, a numerical modeling procedure for analyzing the acoustophoretic cell/particle motion is presented to include the aforementioned effects. Here, the first-order acoustic pressure and the second-order acoustic streaming velocity are first calculated by using a high-order finite difference method. Then, acoustophoretic force is calculated based on the acoustophoretic force equation proposed by Gorkov and is applied to the Newton’s equation of motion to calculate the motion of cells/particles. Through various simulations, the effects of acoustic streaming on the motion of cells/particles are studied. Since the acoustophoretic motion depends on the vibro-acoustic properties (e.g., density, compressibility, and size) of particles/cells, the vibro-acoustic properties can be estimated by optimally fitting the experimental and simulated trajectories. The properties obtained from experimental results with polystyrene beads show good agreement with the data reported in literature.

A numerical study of microparticle acoustophoresis driven by acoustic radiation forces and streaming-induced drag forces

We present a numerical study of the transient acoustophoretic motion of microparticles suspended in a liquid-filled microchannel and driven by the acoustic forces arising from an imposed standing ultrasound wave: the acoustic radiation force from the scattering of sound waves on the particles and the Stokes drag force from the induced acoustic streaming flow. These forces are calculated numerically in two steps. First, the thermoacoustic equations are solved to first order in the imposed ultrasound field taking into account the micrometer-thin but crucial thermoviscous boundary layer near the rigid walls. Second, the products of the resulting first-order fields are used as source terms in the time-averaged second-order equations, from which the net acoustic forces acting on the particles are determined. The resulting acoustophoretic particle velocities are quantified for experimentally relevant parameters using a numerical particle-tracking scheme. The model shows the transition in the acoustophoretic particle motion from being dominated by streaming-induced drag to being dominated by radiation forces as a function of particle size, channel geometry, and material properties.

Acoustofluidics 7: The acoustic radiation force on small particles

In this paper, Part 7 of the thematic tutorial series "Acoustofluidics-exploiting ultrasonic standing waves, forces and acoustic streaming in microfluidic systems for cell and particle manipulation", we present the theory of the acoustic radiation force; a second-order, time-averaged effect responsible for the acoustophoretic motion of suspended, micrometre-sized particles in an ultrasound field.

Acoustophoresis in shallow microchannels

Acoustophoretic (AP) motion of spherical polystyrene particles in a steady pressure driven flow is investigated in shallow microchannels, where the channel height is comparable to the particle diameter. Particle trajectories at different ultrasonic actuation amplitudes are extracted by a particle tracking algorithm. Depths of the particles are predicted using the streamwise particle speed that is due to the pressure driven flow. The particle depths are shown to be influenced by the actuation voltage. The particle migration along the channel height is explained using the second-order perturbation theory. The particle equation of motion is employed to extract the AP force. Wall effects are included in the analysis of both particle depth and force predictions. Differences as large as 20% in the AP force magnitude due to the wall corrections are reported. The AP force is also calculated using the theoretical force expression, and compared with the experimental results. The focal length, which is the necessary distance to effectively concentrate particles in a microchannel, is calculated using the analytical solution of the particle equation of motion. The calculated force and the focusing length agree well with the experimental results. The focal length is critical for the design of micro sample concentration devices.