Numerical investigation of acoustic radiation force and microstreaming in a viscoelastic fluid

We present a numerical model to study time-averaged acoustic radiation force and microstreaming around an elastic sphere immersed within an acoustically actuated viscoelastic fluid. We employ a perturbation approach to systematically identify limiting regimes where the viscoelastic fluid can be approximated as a purely viscous fluid at the acoustic and mean time scales. Unlike existing numerical models, we account for microstreaming and fluid elasticity contributions to the radiation force. We elucidate the inherent assumptions within reduced expressions considered in prior numerical models and highlight the divergence between the acoustic radiation force obtained from the reduced and general expressions. We also discuss numerical considerations to ensure the invariance of the acoustic radiation force with the choice of integration surface by recasting the time-averaged mass balance equation in terms of Stokes drift. Our results reveal that the acoustic radiation force exhibits a peak value for an optimal relaxation time, and both the peak acoustic radiation force and the optimal relaxation time increase with increasing polymer viscosity. The results also highlight the significant contribution of fluid elasticity to the radiation force and invalidate the previously employed reduced acoustic radiation force expressions for general viscoelastic regime.

An Acoustofluidic Picoinjector

Droplet microfluidics has emerged as a valuable technology for a multitude of chemical and biomedical applications, offering the capability to create independent microenvironments for high-throughput assays. Central to numerous droplet microfluidic applications is the picoinjection of materials into individual droplets, yet existing picoinjection methods often exhibit high power requirements, lack biocompatibility, and/or suffer from limited controllability. Here, we present an acoustofluidic picoinjector that generates acoustic pressure at the droplet interface to enable on-demand, energy-efficient, and biocompatible injection at high precision. We validate our platform by performing acid-base titrations by iteratively injecting picoliter volume reagents into droplets to induce pH transitions detectable by color change in solution. Additionally, we demonstrate the versatility of the acoustofluidic picoinjector in the synthesis of metallic nanoparticles, yielding highly monodisperse and reproducible particle morphologies compared to conventional bulk-phase techniques. By facilitating controlled delivery of reagents or biological samples with unparalleled accuracy, acoustofluidic picoinjection broadens the utility of droplet microfluidics for a myriad of applications in chemical and biological research.

The effect of microchannel height on the acoustophoretic motion of sub-micron particles

Acoustophoresis is an effective technique for particle manipulation. Acoustic radiation force scales with particle volume, enabling size separation. Yet, isolating sub-micron particles remains a challenge due to the acoustic streaming effect (ASE). While some studies confirmed the focusing ability of ASE, others reported continuous stirring effects. To investigate the parameters that influence ASE-induced particle motion in a microchannel, this study examined the effect of microchannel height and particle size. We employed standing surface acoustic wave (SSAW) to manipulate polystyrene particles suspended in the water-filled microchannel. The results show that ASE can direct particles as small as 0.31 µm in diameter to the centre of the streaming vortices, and increasing the channel height enhances the focusing effect. Smaller particles circulate in the streaming vortices continuously, with no movement towards the centres. We also discovered that when the channel height is at least 0.75 the fluid wavelength, particles transitioning from acoustic radiation-dominated to ASE-dominated share the same equilibrium position, which differs from the pressure nodes and the vortices' centres. The spatial distance between particles in different categories can lead to particle separation. Therefore, ASE is a potential alternative mechanism for sub-micron particle sorting when the channel height is accurately adjusted.

Skipping the Boundary Layer: High-Speed Droplet-Based Immunoassay Using Rayleigh Acoustic Streaming

Acoustic mixing of droplets is a promising way to implement biosensors that combine high speed and minimal reagent consumption. To date, this type of droplet mixing is driven by a volume force resulting from the absorption of high-frequency acoustic waves in the bulk of the fluid. Here, we show that the speed of these sensors is limited by the slow advection of analyte to the sensor surface due to the formation of a hydrodynamic boundary layer. We eliminate this hydrodynamic boundary layer by using much lower ultrasonic frequencies to excite the droplet, which drives a Rayleigh streaming that behaves essentially like a slip velocity. At equal average flow velocity in the droplet, both experiment and three-dimensional simulations show that this provides a three-fold speedup compared to Eckart streaming. Experimentally, we further shorten a SARS-CoV-2 antibody immunoassay from 20 min to 40 s taking advantage of Rayleigh acoustic streaming.

Modeling fast acoustic streaming: Steady-state and transient flow solutions

Traditionally, acoustic streaming is assumed to be a steady-state, relatively slow fluid response to passing acoustic waves. This assumption, the so-called slow streaming assumption, was made over a century ago by Lord Rayleigh. It produces a tractable asymptotic perturbation analysis from the nonlinear governing equations, separating the acoustic field from the acoustic streaming that it generates. Unfortunately, this assumption is often invalid in the modern microacoustofluidics context, where the fluid flow and acoustic particle velocities are comparable. Despite this issue, the assumption is still widely used today, as there is no suitable alternative. We describe a mathematical method to supplant the classic approach and properly treat the spatiotemporal scale disparities present between the acoustics and remaining fluid dynamics. The method is applied in this work to well-known problems of semi-infinite extent defined by the Navier-Stokes equations, and preserves unsteady fluid behavior driven by the acoustic wave. The separation of the governing equations between the fast (acoustic) and slow (hydrodynamic) spatiotemporal scales are shown to naturally arise from the intrinsic properties of the fluid under forcing, not by arbitrary assumption beforehand. Solution of the unsteady streaming field equations provides physical insight into observed temporal evolution of bulk streaming flows that, to date, have not been modeled. A Burgers equation is derived from our method to represent unsteady flow. By then assuming steady flow, a Riccati equation is found to represent it. Solving these equations produces direct, concise insight into the nonlinearity of the acoustic streaming phenomenon alongside an absolute, universal upper bound of 50% for the energy efficiency in transducing acoustic energy input to the acoustic streaming energy output. Rigorous validation with respect to experimental and theoretical results from the classic literature is presented to connect this work to past efforts by many authors.

Design of interdigitated transducers for acoustofluidic applications

Interdigitated transducers (IDTs) were originally designed as delay lines for radars. Half a century later, they have found new life as actuators for microfluidic systems. By generating strong acoustic fields, they trigger nonlinear effects that enable pumping and mixing of fluids, and moving particles without contact. However, the transition from signal processing to actuators comes with a range of challenges concerning power density and spatial resolution that have spurred exciting developments in solid-state acoustics and especially in IDT design. Assuming some familiarity with acoustofluidics, this paper aims to provide a tutorial for IDT design and characterization for the purpose of acoustofluidic actuation. It is targeted at a diverse audience of researchers in various fields, including fluid mechanics, acoustics, and microelectronics.

An ultrasonically actuated needle promotes the transport of nanoparticles and fluids

Non-invasive therapeutic ultrasound (US) methods, such as high-intensity focused ultrasound (HIFU), have limited access to tissue targets shadowed by bones or presence of gas. This study demonstrates that an ultrasonically actuated medical needle can be used to translate nanoparticles and fluids under the action of nonlinear phenomena, potentially overcoming some limitations of HIFU. A simulation study was first conducted to study the delivery of a tracer with an ultrasonically actuated needle (33 kHz) inside a porous medium acting as a model for soft tissue. The model was then validated experimentally in different concentrations of agarose gel showing a close match with the experimental results, when diluted soot nanoparticles (diameter < 150 nm) were employed as delivered entity. An additional simulation study demonstrated a threefold increase in the volume covered by the delivered agent in liver under a constant injection rate, when compared to without US. This method, if developed to its full potential, could serve as a cost effective way to improve safety and efficacy of drug therapies by maximizing the concentration of delivered entities within, e.g., a small lesion, while minimizing exposure outside the lesion.

Influences of microparticle radius and microchannel height on SSAW-based acoustophoretic aggregation

The use of acoustic waves for microfluidic aggregation has become widespread in chemistry, biology and medicine. Although numerous experimental and analytical studies have been undertaken to study the acoustophoretic aggregation mechanisms, few studies have been conducted to optimise the device design. This paper presents a numerical investigation of the acoustophoresis of microparticles suspended in compressible liquid. The wall of the rectangular microchannel is made of Polydimethylsiloxane (PDMS), and Standing Surface Acoustic Waves (SSAW) are introduced into the channel from the bottom wall. First, the relative amplitude of the acoustic radiation force and the viscous drag force is evaluated for particles of different radii ranging from 0.1μm to 15μm. Only when the particle size is larger than a critical value can the particles accumulate at acoustic pressure nodes (PNs). The efficiency of the particle accumulation depends on the microchannel height, so an extensive parametric study is then undertaken to identify the optimum microchannel height. The optimum height, when normalised by the acoustic wavelength, is found to be between 0.57 and 0.82. These findings provide insights into the design of acoustophoretic devices.

Theory and simulation of electroosmotic suppression of acoustic streaming

Acoustic handling of nanoparticles in resonating acoustofluidic devices is often impeded by the presence of acoustic streaming. For micrometer-sized acoustic chambers, this acoustic streaming is typically driven by viscous shear in the thin acoustic boundary layer near the fluid-solid interface. Alternating current (ac) electroosmosis is another boundary-driven streaming phenomenon routinely used in microfluidic devices for the handling of particle suspensions in electrolytes. Here, we study how streaming can be suppressed by combining ultrasound acoustics and ac electroosmosis. Based on a theoretical analysis of the electrokinetic problem, we are able to compute numerically a form of the electrical potential at the fluid-solid interface, which is suitable for suppressing the typical acoustic streaming pattern associated with a standing acoustic half-wave. In the linear regime, we even derive an analytical expression for the electroosmotic slip velocity at the fluid-solid interface and use this as a guiding principle for developing models in the experimentally more relevant nonlinear regime that occurs at elevated driving voltages. We present simulation results for an acoustofluidic device, showing how implementing a suitable ac electroosmosis results in a suppression of the resulting electroacoustic streaming in the bulk of the device by 2 orders of magnitude.

Visualization of Acoustic Energy Absorption in Confined Aqueous Solutions by PNIPAM Microgels: Effects of Bulk Viscosity

Ultrasound propagation in liquids is highly influenced by its attenuation due to viscous damping. The dissipated energy will be partially absorbed by the liquid due to its dynamic viscosity as well as its bulk viscosity. The former results in the generation of a flow that is called acoustic streaming, and the latter is associated with the vibrational and rotational relaxation of liquid molecules. Measuring the ultrasonic wave attenuation due to the bulk viscosity is presented as a novel method in this article. Poly(N-isopropylacrylamide) (PNIPAM) microgels, which are soluble in several solvents such as water, were used as acousto-responsive markers in water, which upon absorption of ultrasonic energy undergo a volume phase transition due to the breakage of their hydrogen bonds. Thus, they become insoluble in water, and due to shrinking, their optical density increases. As a result, their agglomeration can be seen as a turbid medium. We managed to visualize the ultrasonic energy absorption due to the bulk viscosity using the turbidity since the excess acoustic energy on top of the absorbed energy for the translational motion of liquid is spent to break the hydrogen bonds between PNIPAM and water. In addition, to quantify the turbidity phenomenon, the total energy required for breaking hydrogen bonds in the solution is calculated, and its evolution, according to the input power intensity, is quantified by image processing. The effect of viscosity by changing the microgel concentration was investigated, and it is shown that an increasing microgel concentration increases the acoustic energy absorption rate much greater than its dynamic viscosity. Therefore, the bulk viscosity, as the responsible parameter for this increase, is measured directly from the energy of broken hydrogen bonds. The results show that at low solution concentration (0.2 wt %) the bulk viscosity is in the same order of magnitude as its dynamic viscosity. Increasing the concentrations to 1 and 5 wt % increases the bulk viscosity and consequently the structural relaxation time by 1 and 2 orders of magnitude, respectively.

Suppression of Acoustic Streaming in Shape-Optimized Channels

Acoustic streaming is an ubiquitous phenomenon resulting from time-averaged nonlinear dynamics in oscillating fluids. In this theoretical study, we show that acoustic streaming can be suppressed by two orders of magnitude in major regions of a fluid by optimizing the shape of its confining walls. Remarkably, the acoustic pressure is not suppressed in this shape-optimized cavity, and neither is the acoustic radiation force on suspended particles. This basic insight may lead to applications, such as acoustophoretic handling of nm-sized particles, which is otherwise impaired by the streaming.

On-Chip Generation of Vortical Flows for Microfluidic Centrifugation

Microcentrifugation constitutes an important part of the microfluidic toolkit in a similar way that centrifugation is crucial to many macroscopic procedures, given that micromixing, sample preconcentration, particle separation, component fractionation, and cell agglomeration are essential operations in small scale processes. Yet, the dominance of capillary and viscous effects, which typically tend to retard flow, over inertial and gravitational forces, which are often useful for actuating flows and hence centrifugation, at microscopic scales makes it difficult to generate rotational flows at these dimensions, let alone with sufficient vorticity to support efficient mixing, separation, concentration, or aggregation. Herein, the various technologies-both passive and active-that have been developed to date for vortex generation in microfluidic devices are reviewed. Various advantages or limitations associated with each are outlined, in addition to highlighting the challenges that need to be overcome for their incorporation into integrated microfluidic devices.

Bulk-driven acoustic streaming at resonance in closed microcavities

Bulk-driven acoustic (Eckart) streaming is the steady flow resulting from the time-averaged acoustic energy flux density in the bulk of a viscous fluid. In simple cases, like the one-dimensional single standing-wave resonance, this energy flux is negligible, and therefore the bulk-driven streaming is often ignored relative to the boundary-driven (Rayleigh) streaming in the analysis of resonating acoustofluidic devices with length scales comparable to the acoustic wavelength. However, in closed acoustic microcavities with viscous dissipation, two overlapping resonances may be excited at the same frequency as a double mode. In contrast to single modes, the double modes can support a steady rotating acoustic energy flux density and thus a corresponding rotating bulk-driven acoustic streaming. We derive analytical solutions for the double modes in a rectangular-box-shaped cavity including the viscous boundary layers, and use them to map out possible rotating patterns of bulk-driven acoustic streaming. Remarkably, the rotating bulk-driven streaming may be excited by a nonrotating actuation, and we determine the optimal geometry that maximizes this excitation. In the optimal geometry, we finally simulate a horizontal 2×2, 4×4, and 6×6 streaming-roll pattern in a shallow square cavity. We find that the high-frequency 6×6 streaming-roll pattern is dominated by the bulk-driven streaming as opposed to the low-frequency 2×2 streaming pattern, which is dominated by the boundary-driven streaming.

Acoustic streaming induced by two orthogonal ultrasound standing waves in a microfluidic channel

A mathematical model is derived for acoustic streaming in a microfluidic channel confined between a solid wall and a rigid reflector. Acoustic streaming is produced by two orthogonal ultrasound standing waves of the same frequency that are created by two pairs of counter-propagating leaky surface waves induced in the solid wall. The magnitudes and phases of the standing waves are assumed to be different. Full analytical solutions are found for the equations of acoustic streaming. The obtained solutions are used in numerical simulations to reveal the structure of the acoustic streaming. It is shown that the interaction of two standing waves leads to the appearance of a cross term in the equations of acoustic streaming. If the phase lag between the standing waves is nonzero, the cross term brings about circular vortices with rotation axes perpendicular to the solid wall of the channel. The vortices make fluid particles rotate and move alternately up and down between the solid wall and the reflector. The obtained results are of immediate interest for acoustomicrofluidic applications such as the ultrasonic micromixing of fluids and the manipulation of microparticles.

Stokes drift

During its periodic motion, a particle floating at the free surface of a water wave experiences a net drift velocity in the direction of wave propagation, known as the Stokes drift (Stokes 1847 Trans. Camb. Philos. Soc.8, 441-455). More generally, the Stokes drift velocity is the difference between the average Lagrangian flow velocity of a fluid parcel and the average Eulerian flow velocity of the fluid. This paper reviews progress in fundamental and applied research on the induced mean flow associated with surface gravity waves since the first description of the Stokes drift, now 170 years ago. After briefly reviewing the fundamental physical processes, most of which have been established for decades, the review addresses progress in laboratory and field observations of the Stokes drift. Despite more than a century of experimental studies, laboratory studies of the mean circulation set up by waves in a laboratory flume remain somewhat contentious. In the field, rapid advances are expected due to increasingly small and cheap sensors and transmitters, making widespread use of small surface-following drifters possible. We also discuss remote sensing of the Stokes drift from high-frequency radar. Finally, the paper discusses the three main areas of application of the Stokes drift: in the coastal zone, in Eulerian models of the upper ocean layer and in the modelling of tracer transport, such as oil and plastic pollution. Future climate models will probably involve full coupling of ocean and atmosphere systems, in which the wave model provides consistent forcing on the ocean surface boundary layer. Together with the advent of new space-borne instruments that can measure surface Stokes drift, such models hold the promise of quantifying the impact of wave effects on the global atmosphere-ocean system and hopefully contribute to improved climate projections.This article is part of the theme issue 'Nonlinear water waves'.

Acoustic streaming: an arbitrary Lagrangian-Eulerian perspective

We analyse acoustic streaming flows using an arbitrary Lagrangian Eulerian (ALE) perspective. The formulation stems from an explicit separation of time scales resulting in two subproblems: a first-order problem, formulated in terms of the fluid displacement at the fast scale, and a second-order problem, formulated in terms of the Lagrangian flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the Lagrangian velocity, the formulation does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is formulated in terms of the displacement field, our formulation is directly applicable to more complex fluid-structure interaction problems in microacoustofluidic devices. After the formulation's exposition, we present numerical results that illustrate the advantages of the formulation with respect to current approaches.

Acoustic streaming in a microfluidic channel with a reflector: Case of a standing wave generated by two counterpropagating leaky surface waves

A theory is developed for the modeling of acoustic streaming in a microfluidic channel confined between an elastic solid wall and a rigid reflector. A situation is studied where the acoustic streaming is produced by two leaky surface waves that propagate towards each other in the solid wall and thus form a combined standing wave in the fluid. Full analytical solutions are found for both the linear acoustic field and the field of the acoustic streaming. A dispersion equation is derived that allows one to calculate the wave speed in the system under study. The obtained solutions are used to consider particular numerical examples and to reveal the structure of the acoustic streaming. It is shown that two systems of vortices are established along the boundaries of the microfluidic channel.

Acoustomicrofluidic application of quasi-shear surface waves

The paper analyzes the possibility of using predominantly boundary polarized surface acoustic waves for actuating fluidic effects in microchannels fabricated inside containers made of PDMS. The aim is to remove a shortcoming peculiar to conventionally utilized predominantly vertically polarized waves. Such waves strongly attenuate while they propagate under container side walls because of the leakage into them. Due to a specific feature of PDMS - extremely small shear elastic modulus - losses of boundary polarized modes should be far smaller. The amplitude of vertical mechanical displacements can be increased right inside the channel owing to the scattering of acoustic fields. As an example, the predominantly vertically polarized surface wave on 128YX LiNbO₃ is compared with the quasi-shear leaky wave on 64YX LiNbO₃. Our computations predict that, given the electric power supplied to the launching transducer, the quasi-shear wave will drive the fluid more efficiently than the surface wave on 128YX LiNbO₃ when the container wall thickness is larger than 25-30 wavelengths, if there are no additional scatterers inside the channel. In the presence of a scatterer, such as a thin gold strip, the quasi-shear wave can be more efficient when the wall thickness exceeds 10-15 wavelengths.

3D measurement and simulation of surface acoustic wave driven fluid motion: a comparison

The characterisation of the fluid motion induced by the acoustic streaming effect is of paramount interest for novel microfluidic devices based on surface acoustic waves (SAWs), e.g. for a detailed description of the achievable mixing efficiency and thus the design of such devices. Here, we present for the first time a quantitative 3D comparison between experimental measurements and numerical simulations of the acoustic streaming induced fluid flow inside a microchannel originating from a SAW. On the one hand, we performed fully three-dimensional velocity measurements using the astigmatism particle tracking velocimetry. On the other hand, we derived a novel streaming force approach solving the damped wave equation, which allows fast and easy 3D simulations of the acoustic streaming induced fluid flow. Furthermore, measurements of the SAW amplitude profile inside the fluid filled microchannel were performed. Based on these results, we obtained a very good agreement between the velocity measurements and the simulations of the fluid flow demonstrating the importance of comprising the actual shape of the SAW amplitude profile for quantitatively reliable simulations. It is shown that the novel streaming force approach is a valid approximation for the simulation of the acoustic streaming induced fluid flow, allowing a rapid and simple estimation of the flow field of SAW based microfluidic devices.

Comparing methods for the modelling of boundary-driven streaming in acoustofluidic devices

Numerical simulations of acoustic streaming flows can be used not only to explain the complex phenomena observed in acoustofluidic manipulation devices, but also to predict and optimise their performances. In this paper, two numerical methods based on perturbation theory are compared in order to demonstrate their viability and applicability for modelling boundary-driven streaming flows in acoustofluidic systems. It was found that the Reynolds stress method, which predicts the streaming fields from their driving terms, can effectively resolve both the inner and outer streaming fields and can be used to demonstrate the driving mechanisms of a broad range of boundary-driven streaming flows. However, computational efficiency typically limits its useful application to two-dimensional models. We highlight the close relationship between the classical boundary-driven streaming vortices and the rotationality of the Reynolds stress force field. The limiting velocity method, which ignores the acoustic boundary layer and solves the outer streaming fields by applying the 'limiting velocities' as boundary conditions, is more computationally efficient and can be used for predicting three-dimensional outer streaming fields and provide insight into their origins, provided that the radius of curvature of the channel surfaces is much greater than the acoustic boundary layer thickness ( δ v ). We also show that for the limiting velocity method to be valid the channel scales must exceed a value of approximately 100 δ v (for an error of ~5% on the streaming velocity magnitudes) for the case presented in this paper. Comparisons of these two numerical methods can provide effective guidance for researchers in the field of acoustofluidics on choosing appropriate methods to predict boundary-driven streaming fields in the design of acoustofluidic particle manipulation devices.

Numerical simulation of micro-particle rotation by the acoustic viscous torque

We present the first numerical simulation setup for the calculation of the acoustic viscous torque on arbitrarily shaped micro-particles inside general acoustic fields. Under typical experimental conditions, the particle deformation plays a minor role. Therefore, the particle is modeled as a rigid body which is free to perform any time-harmonic and time-averaged translation and rotation. Applying a perturbation approach, the viscoacoustic field around the particle is resolved to obtain the time-averaged driving forces for a subsequent acoustic streaming simulation. For some acoustic fields, the near-boundary streaming around the fluid-suspended particle induces surface forces on the nonrotating particle that integrate into a non-zero acoustic viscous torque. In the equilibrium state, this torque is compensated by an equal and opposite drag torque due to the particle rotation. The rotation-induced flow field is superimposed on the acoustic streaming field to obtain the total fluid motion around the rotating particle. In this work, we only consider cases within the Rayleigh limit even though the presented numerical model is not strictly limited to this regime. After a validation by analytical solutions, the numerical model is applied to challenging experimental cases. For an arbitrary particle density, we consider particle sizes that can be comparable to the viscous boundary layer thickness. This important regime has not been studied before because it lies beyond the validity limits of the available analytical solutions. The detailed numerical analysis in this work predicts nonintuitive phenomena, including an inversion of the rotation direction. Our numerical model opens the door to explore a wide range of experimentally relevant cases, including non-spherical particle rotation. As a step toward application fields such as micro-robotics, the rotation of a prolate ellipsoid is studied.

The importance of travelling wave components in standing surface acoustic wave (SSAW) systems

The use of ultrasonic fields to manipulate particles, cells and droplets has become widespread in lab on a chip (LOC) systems. There are two dominant actuation methods, the use of bulk acoustic waves (BAW) or surface acoustic waves (SAW). The development of BAW actuated systems have been underpinned by a robust understanding of the link between the ultrasonic field and forces which can be generated. In this work, we examine this link for standing surface acoustic waves (SSAW) comparing the relative strengths of streaming induced drag and acoustic radiation forces on suspended particles. To achieve this we have employed boundary conditions which accurately capture the travelling wave components of the pseudo-standing wave field, describe the key features of the acoustic radiation force fields and the acoustic streaming fields which can be generated, and finally we show that the relative importance of these two mechanisms is spatially dependant within a fluid chamber. The boundary condition used models the SSAW as two counter-propagating travelling waves, rather than assuming a standing wave directly. This allows the accurate inclusion of energy decay as the SAW couples into the fluid chamber and the resulting travelling wave component. This study shows that this previously neglected complexity of the SAW field is a critical factor in the nature of the resultant streaming field, as it gives rise to strong streaming rolls at the channel walls, which we validate experimentally. These rolls result in spatial variations of the dominant forces which in turn varies particle migration patterns spatially across the fluid domain.

Acoustofluidic actuation of in situ fabricated microrotors

We have demonstrated in situ fabricated and acoustically actuated microrotors. A polymeric microrotor with predefined oscillating sharp-edge structures is fabricated in situ by applying a patterned UV light to polymerize a photocrosslinkable polyethylene glycol solution inside a microchannel around a polydimethylsiloxane axle. To actuate the microrotors by oscillating the sharp-edge structures, we employed piezoelectric transducers which generate tunable acoustic waves. The resulting acoustic streaming flows rotate the microrotors. The rotation rate is tuned by controlling the peak-to-peak voltage applied to the transducer. A 6-arm microrotor can exceed 1200 revolutions per minute. Our technique is an integration of single-step microfabrication, instant assembly around the axle, and easy acoustic actuation for various applications in microfluidics and microelectromechanical systems (MEMS).

Controllable Acoustic Mixing of Fluids in Microchannels for the Fabrication of Therapeutic Nanoparticles

Fifteen years ago, surface acoustic waves (SAW) were found to be able to drive fluids and numerous applications in microfluidics have been developed since. Here, we review the progress made and report on new approaches in setting-up microfluidic, continuous flow acoustic mixing. In a microchannel, chaotic advection is achieved by generation of a SAW driven fluid jet perpendicular to the mean flow direction. Using a high speed video camera and particle image velocimetry, we measure the flow velocities and show that mixing is achieved in a particularly controllable and fast way. The mixing quality is determined as a function of system parameters: SAW power, volume flux and fluid viscosity. Exploring the parameter space of mixing provides a practical guide for acoustic mixing in microchannels and allows for adopting conditions to different solvents, as e.g., required for the generation of nanoscale particles from alcoholic phases. We exemplarily demonstrate the potential of SAW based continuous flow mixing for the production of therapeutic nucleic acid nanoparticles assembled from polymer and lipid solutions.

Computation of the pressure field generated by surface acoustic waves in microchannels

The high-frequency pressure induced by a surface acoustic wave in the fluid filling a microchannel is computed by solving the full scattering problem. The microchannel is fabricated inside a container attached to the top of a piezoelectric substrate where the surface wave propagates. The finite element method is used. The pressure found in this way is compared with the pressure obtained by solving boundary-value problems formulated on the basis of simplifications which have been introduced in earlier papers by other research studies. The considered example shows that the difference between the results can be significant, ranging from several tens of percent up to several times in different points inside the channel.

A comparative fluid flow characterisation in a low frequency/high power sonoreactor and mechanical stirred vessel

This study aims at analysing the jet-like acoustic streaming generated under low-frequency and high-power ultrasound irradiation and comparing it with fluid streaming generated by traditional mechanical mixing. The main characteristics of fluid flow, which include radial, axial and tangential terms of velocity and their effects on fluid flow pattern, pressure distribution, axial mixing time and turbulence intensity were considered at different power inputs. Both 3D CFD simulation and Particle Image Velocimetry (PIV) were used in this study. The CFD results indicated that the jet-like acoustic streaming reached the velocity magnitude of 145 cm/s at 400 W, which reduced the mixing time to 1.38 s. However, the minimum mixing time of 3.18 s corresponding to the impeller rotational speed of 800 RPM was observed for mechanical stirring. A uniform axial flow pattern was generated under ultrasound irradiation whereas the tangential flow pattern was more prominent in the stirred vessel. Besides, the highest turbulence was observed in the vicinity of the ultrasound transducer and impeller with the values of 138% and 82% for the ultrasonicator and stirred vessel, respectively. The predicted fluid flow pattern under ultrasound irradiation was in a reasonable agreement with that obtained from PIV, with a reasonable accuracy.

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.

Dynamics of liquid films exposed to high-frequency surface vibration

We derive a generalized equation that governs the spreading of liquid films under high-frequency (MHz-order) substrate vibration in the form of propagating surface waves and show that this single relationship is universally sufficient to collectively describe the rich and diverse dynamic phenomena recently observed for the transport of oil films under such substrate excitation, in particular, Rayleigh surface acoustic waves. In contrast to low-frequency (Hz- to kHz-order) vibration-induced wetting phenomena, film spreading at such high frequencies arises from convective drift generated by the viscous periodic flow localized in a region characterized by the viscous penetration depth β(-1)≡(2μ/ρω)(1/2) adjacent to the substrate that is invoked directly by its vibration; μ and ρ are the viscosity and the density of the liquid, respectively, and ω is the excitation frequency. This convective drift is responsible for driving the spreading of thin films of thickness h≪k(l)(-1), which spread self-similarly as t(1/4) along the direction of the drift corresponding to the propagation direction of the surface wave, k(l) being the wave number of the compressional acoustic wave that forms in the liquid due to leakage of the surface wave energy from the substrate into the liquid and t the time. Films of greater thicknesses h∼k(l)(-1)≫β(-1), in contrast, are observed to spread with constant velocity but in a direction that opposes the drift and surface wave propagation due to the attenuation of the acoustic wave in the liquid. The universal equation derived allows for the collective prediction of the spreading of these thin and thick films in opposing directions.

Investigation of acoustic streaming patterns around oscillating sharp edges

Oscillating sharp edges have been employed to achieve rapid and homogeneous mixing in microchannels using acoustic streaming. Here, we used a perturbation approach to study the flow around oscillating sharp edges in a microchannel. This work extends prior experimental studies to numerically characterize the effect of various parameters on the acoustically induced flow. Our numerical results match well with the experimental results. We investigated multiple device parameters such as the tip angle, oscillation amplitude, and channel dimensions. Our results indicate that, due to the inherent nonlinearity of acoustic streaming, the channel dimensions could significantly impact the flow patterns and device performance.

Boundary streaming with Navier boundary condition

In microfluidic applications involving high-frequency acoustic waves over a solid boundary, the Stokes boundary-layer thickness δ is so small that some non-negligible slip may occur at the fluid-solid interface. This paper assesses the impact of this slip by revisiting the classical problem of steady acoustic streaming over a flat boundary, replacing the no-slip boundary condition with the Navier condition u|_{y=0}=L_{s}∂_{y}u|_{y=0}, where u is the velocity tangent to the boundary y=0, and the parameter L_{s} is the slip length. A general expression is obtained for the streaming velocity across the boundary layer as a function of the dimensionless parameter L_{s}/δ. The limit outside the boundary layer provides an effective slip velocity satisfied by the interior mean flow. Particularizing to traveling and standing waves shows that the boundary slip respectively increases and decreases the streaming velocity.

Frequency effects on the scale and behavior of acoustic streaming

Acoustic streaming underpins an exciting range of fluid manipulation phenomena of rapidly growing significance in microfluidics, where the streaming often assumes the form of a steady, laminar jet emanating from the device surface, driven by the attenuation of acoustic energy within the beam of sound propagating through the liquid. The frequencies used to drive such phenomena are often chosen ad hoc to accommodate fabrication and material issues. In this work, we seek a better understanding of the effects of sound frequency and power on acoustic streaming. We present and, using surface acoustic waves, experimentally verify a laminar jet model that is based on the turbulent jet model of Lighthill, which is appropriate for acoustic streaming seen at micro- to nanoscales, between 20 and 936 MHz and over a broad range of input power. Our model eliminates the critically problematic acoustic source singularity present in Lighthill's model, replacing it with a finite emission area and enabling determination of the streaming velocity close to the source. At high acoustic power P (and hence high jet Reynolds numbers ReJ associated with fast streaming), the laminar jet model predicts a one-half power dependence (U∼P1/2∼ ReJ) similar to the turbulent jet model. However, the laminar model may also be applied to jets produced at low powers-and hence low jet Reynolds numbers ReJ-where a linear relationship between the beam power and streaming velocity exists: U∼P∼ReJ2. The ability of the laminar jet model to predict the acoustic streaming behavior across a broad range of frequencies and power provides a useful tool in the analysis of microfluidics devices, explaining peculiar observations made by several researchers in the literature. In particular, by elucidating the effects of frequency on the scale of acoustically driven flows, we show that the choice of frequency is a vitally important consideration in the design of small-scale devices employing acoustic streaming for microfluidics.

Surface acoustic wave microfluidics

The recent introduction of surface acoustic wave (SAW) technology onto lab-on-a-chip platforms has opened a new frontier in microfluidics. The advantages provided by such SAW microfluidics are numerous: simple fabrication, high biocompatibility, fast fluid actuation, versatility, compact and inexpensive devices and accessories, contact-free particle manipulation, and compatibility with other microfluidic components. We believe that these advantages enable SAW microfluidics to play a significant role in a variety of applications in biology, chemistry, engineering and medicine. In this review article, we discuss the theory underpinning SAWs and their interactions with particles and the contacting fluids in which they are suspended. We then review the SAW-enabled microfluidic devices demonstrated to date, starting with devices that accomplish fluid mixing and transport through the use of travelling SAW; we follow that by reviewing the more recent innovations achieved with standing SAW that enable such actions as particle/cell focusing, sorting and patterning. Finally, we look forward and appraise where the discipline of SAW microfluidics could go next.

Atomization off thin water films generated by high-frequency substrate wave vibrations

Generating aerosol droplets via the atomization of thin aqueous films with high frequency surface acoustic waves (SAWs) offers several advantages over existing nebulization methods, particularly for pulmonary drug delivery, offering droplet sizes in the 1-5-μm range ideal for effective pulmonary therapy. Nevertheless, the physics underlying SAW atomization is not well understood, especially in the context of thin liquid film formation and spreading and how this affects the aerosol production. Here, we demonstrate that the film geometry, governed primarily by the applied power and frequency of the SAW, indeed plays a crucial role in the atomization process and, in particular, the size of the atomized droplets. In contrast to the continuous spreading of low surface energy liquids atop similar platforms, high surface energy liquids such as water, in the present case, are found to undergo transient spreading due to the SAW to form a quasisteady film whose height is determined by self-selection of the energy minimum state associated with the acoustic resonance in the film and whose length arises from a competition between acoustic streaming and capillary effects. This is elucidated from a fundamental model for the thin film spreading behavior under SAW excitation, from which we show good agreement between the experimentally measured and theoretically predicted droplet dimension, both of which consistently indicate a linear relationship between the droplet diameter and the mechanical power coupled into the liquid by the SAW (the latter captured by an acoustic Weber number to the two thirds power, and the reciprocal of the SAW frequency).

Acoustofluidics 17: theory and applications of surface acoustic wave devices for particle manipulation

In this paper, number 17 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 surface acoustic waves (SAWs) and some related microfluidic applications. The equations describing SAWs are derived for a solid-vacuum interface before generalisations are made about solid-solid and solid-fluid interfaces. Techniques for SAW generation are discussed before an overview of applications is presented.