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Vortex-based single-beam tweezers have the ability to precisely and selectively move a wide range of objects, including particles, bubbles, droplets, and cells with sizes ranging from the millimeter to micrometer scale. In 2017, Karlsen and Bruus [Phys. Rev. Appl. 7, 034017 (2017)] theoretically suggested that these tweezers could also address one of the most challenging issues: the patterning and manipulation of miscible fluids. In this paper, we experimentally demonstrate this ability using acoustic vortex beams generated by interdigital transducer-based active holograms. The experimental results are supported by a numerical model based on acoustic body force simulations. This work paves the way for the precise shaping of chemical concentration fields, a crucial factor in numerous chemical and biological processes.

Analytical expressions are derived for the time-averaged, quasi-steady, acoustic radiation force on a heated, spherical, elastic, solid microparticle suspended in a fluid and located in an axisymmetric incident acoustic wave. The heating is assumed to be spherically symmetric, and the effects of particle vibrations, sound scattering, and acoustic microstreaming are included in the calculations of the acoustic radiation force. It is found that changes in the speed of sound of the fluid due to temperature gradients can significantly change the force on the particle, particularly through perturbations to the microstreaming pattern surrounding the particle. For some fluid-solid combinations, the effects of particle heating even reverse the direction of the force on the particle for a temperature increase at the particle surface as small as 1 K., Comment: 13 pages, 3 pdf figures, RevTex 4.2

We derive general analytical expressions for the time-averaged acoustic radiation force on a small spherical particle suspended in a fluid and located in an axisymmetric incident acoustic wave. We treat the cases of the particle being either an elastic solid or a fluid particle. The effects of particle vibrations, acoustic scattering, acoustic microstreaming, heat conduction, and temperature-dependent fluid viscosity are all included in the theory. Acoustic streaming inside the particle is also taken into account for the case of a fluid particle. No restrictions are placed on the widths of the viscous and thermal boundary layers relative to the particle radius. We compare the resulting acoustic radiation force with that obtained from previous theories in the literature, and we identify limits, where the theories agree, and specific cases of particle and fluid materials, where qualitative or significant quantitative deviations between the theories arise., Comment: 29 pages, 4 pdf figures, RevTex 4.2

Supplying a piezoelectric transducer with constant voltage or constant power during a frequency sweep can lead to different results in the determination of the acoustofluidic resonance frequencies, which are observed when studying the acoustophoretic displacements and velocities of particles suspended in a liquid-filled microchannel. In this work, three cases are considered: (1) Constant input voltage into the power amplifier, (2) constant voltage across the piezoelectric transducer, and (3) constant average power dissipation in the transducer. For each case, the measured and the simulated responses are compared, and good agreement is obtained. It is shown that Case 1, the simplest and most frequently used approach, is largely affected by the impedance of the used amplifier and wiring, so it is therefore not suitable for a reproducible characterization of the intrinsic properties of the acoustofluidic device. Case 2 strongly favors resonances at frequencies yielding the lowest impedance of the piezoelectric transducer, so small details in the acoustic response at frequencies far from the transducer resonance can easily be missed. Case 3 provides the most reliable approach, revealing both the resonant frequency, where the power-efficiency is the highest, as well as other secondary resonances across the spectrum., Comment: 16 pages, 6 pdf-figures, RevTeX

A method is presented for the determination of complex-valued compression and shear elastic moduli of polymers for ultrasound applications. The resulting values, which are scarcely reported in the literature, are found with uncertainties typically around 1 % (real part) and 6 % (imaginary part). The method involves a setup consisting of a cm-radius, mm-thick polymer ring glued concentrically to a disk-shaped piezoelectric transducer. The ultrasound electrical impedance spectrum of the transducer is computed numerically and fitted to measured values as an inverse problem in a wide frequency range, typically from 500 Hz to 5 MHz, both on and off resonance. The method was validated experimentally by ultrasonic through-transmission around 1.9 MHz. Experimentally, the method is arguably simple and low cost, and it is not limited to specific geometries and crystal symmetries. Moreover, by involving off-resonance frequencies, it allows for determining the imaginary parts of the elastic moduli, equivalent to attenuation coefficients. Finally, the method has no obvious frequency limitations before severe attenuation sets in above 100 MHz., Comment: 10 pages, 5 pdf figures, RevTeX 4.2

Excitations of MHz acoustic modes are studied numerically in 10-um-thick silicon disk membranes with a radius of 100 and 500 um actuated by an attached 1-um-thick (AlSc)N thin-film transducer. It is shown how higher-harmonic membrane modes can be excited selectively and efficiently by appropriate patterning of the transducer electrodes. When filling the half-space above the membrane with a liquid, the higher-harmonic modes induce acoustic pressure fields in the liquid with interference patterns that result in the formation of a single, strong trapping region located 50 - 100 um above the membrane, where a single suspended cell can be trapped in all three spatial directions. The trapping strength depends on the acoustic contrast between the cell and the liquid, and as a specific example it is shown by numerical simulation that by using a 60% iodixanol solution, a cancer cell can be held in the trap., Comment: 14 pages, 5 pdf figures, REVTeX 4.2

Acoustic streaming is studied in a rectangular microfluidic channel. It is demonstrated theoretically, numerically, and experimentally with good agreement, frictional heating can alter the streaming pattern qualitatively at high acoustic energy densities E_ac above 500 J/m^3. The study shows, how as a function of increasing E_ac at fixed frequency, the traditional boundary-driven four streaming rolls created at a half-wave standing-wave resonance, transition into two large streaming rolls. This nonlinear transition occurs because friction heats up the fluid resulting in a temperature gradient, which spawns an acoustic body force in the bulk that drives thermoacoustic streaming., Comment: 6 pages, 2 pdf figures, REVTex 4.1

A theoretical model of thermal boundary layers and acoustic heating in microscale acoustofluidic devices is presented. It includes effective boundary conditions allowing for simulations in three dimensions. The model is extended by an iterative scheme to incorporate nonlinear thermoviscous effects not captured by standard perturbation theory. The model predicts that the dominant nonperturbative effects in these devices are due to the dependency of thermoacoustic streaming on gradients in the steady temperature induced by a combination of internal frictional heating, external heating, and thermal convection. The model enables simulations in a nonperturbative regime relevant for design and fabrication of high-throughput acoustofluidic devices., Comment: 15 pages, 6 pdf figures, REVTeX 4.2

A finite-element model is presented for numerical simulation in three dimensions of acoustophoresis of suspended microparticles in a microchannel embedded in a polymer chip and driven by an attached piezoelectric transducer at MHz frequencies. In accordance with the recently introduced principle of whole-system ultrasound resonances, an optimal resonance mode is identified that is related to an acoustic resonance of the combined transducer-chip-channel system and not to the conventional pressure half-wave resonance of the microchannel. The acoustophoretic action in the microchannel is of comparable quality and strength to conventional silicon-glass or pure glass devices. The numerical predictions are validated by acoustic focusing experiments on 5-um-diameter polystyrene particles suspended inside a microchannel, which was milled into a PMMA-chip. The system was driven anti-symmetrically by a piezoelectric transducer, driven by a 30-V peak-to-peak AC-voltage in the range from 0.5 to 2.5 MHz, leading to acoustic energy densities of 13 J/m^3 and particle focusing times of 6.6 s., Comment: 12 pages, 7 pdf figures, pdf-latex

We study acoustic streaming in liquids driven by a non-dissipative acoustic body force created by light-induced temperature gradients. This thermoacoustic streaming produces a velocity amplitude approximately 50 times higher than boundary-driven Rayleigh streaming and 90 times higher than Rayleigh-Benard convection at a temperature gradient of 10 K/mm in the channel. Further, Rayleigh streaming is altered by the acoustic body force at a temperature gradient of only 0.5 K/mm. The thermoacoustic streaming allows for modular flow control and enhanced heat transfer at the microscale. Our study provides the groundwork for studying microscale acoustic streaming coupled with temperature fields., Comment: 6 pages, 3 pdf figures, RevTex-4.1

In acoustofluidics, acoustic resonance modes for fluid and microparticle handling are traditionally excited by bulk piezoelectric transducers. In this work, we demonstrate by numerical simulation in three dimensions (3D) that integrated piezoelectric thin-film transducers constituting less than 0.1% of the device work equally well. The simulations are done using a well-tested and experimentally validated numerical model. Our proof-of-concept example is a water-filled straight channel embedded in a mm-sized glass chip with a 1-um thick thin-film transducer made of (Al,Sc)N. We compute the acoustic energy, streaming, and radiation force, and show that it is comparable to that of a conventional silicon-glass device actuated by a bulk PZT transducer. The ability of the thin-film transducer to create the desired acoustofluidic effects in bulk acoustofluidic devices rely on three physical aspects: The in-plane-expansion of the thin-film transducer under the orthogonal applied electric field, the acoustic whole-system resonance of the device, and the high Q-factor of the elastic solid constituting the bulk part of the device. Consequently, the thin-film device is surprisingly insensitive to the Q-factor and resonance properties of the thin-film transducer., Comment: 12 pages, 8 pdf figures, compiles using JASAnew.cls

We study by numerical simulation in two and three dimensions the coupling layer between the transducer and the microfluidic chip in ultrasound acoustofluidic devices. The model includes the transducer with electrodes, the microfluidic chip with a liquid-filled microchannel, and the coupling layer between the transducer and the chip. We consider two commonly used coupling materials, solid epoxy glue and viscous glycerol, as well as two commonly used device types, glass capillary tubes and silicon-glass chips. We study how acoustic resonances in ideal devices without a coupling layer is either sustained or attenuated as a coupling layer of increasing thickness is inserted. We establish a simple criterion based on the phase of the acoustic wave for whether a given zero-layer resonance is sustained or attenuated by the addition of a coupling layer. Finally, we show that by controlling the thickness and the material, the coupling layer can be used as a design component for optimal and robust acoustofluidic resonances., Comment: 10 pages, 9 pdf figures, compiled using JASAnew.cls

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 from the fluid-solid interface by viscous shear-stresses generated by the acoustic actuation. AC electroosmosis is another boundary-driven streaming phenomena routinely used in microfluidic devices for 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 a 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 streaming in the bulk of the device by two orders of magnitude., Comment: 12 pages, 8 pdf figures, compiled using JASAnew.cls

We present an effective thermoviscous theory of acoustofluidics including pressure acoustics, thermoviscous boundary layers, and streaming for fluids embedded in elastic cavities. By including thermal fields, we thus extend the effective viscous theory by Bach and Bruus, J. Acoust. Soc. Am. 144, 766 (2018). The acoustic temperature field and the thermoviscous boundary layers are incorporated analytically as effective boundary conditions and time-averaged body forces on the thermoacoustic bulk fields. Because it avoids resolving the thin boundary layers, the effective model allows for numerical simulation of both thermoviscous acoustic and time-averaged fields in 3D models of acoustofluidic systems. We show how the acoustic streaming depends strongly on steady and oscillating thermal fields through the temperature dependency of the material parameters, in particular the viscosity and the compressibility, affecting both the boundary conditions and spawning additional body forces in the bulk. We also show how even small steady temperature gradients (1 K/mm) induce gradients in compressibility and density that may result in very high streaming velocities (1 mm/s) for moderate acoustic energy densities (100 J/m^3)., Comment: 12 pages, 4 pdf figures, RevTex

We present fabrication of 570-um-thick, millimeter-sized soda-lime-silicate float glass blocks with a 1-um-thick AlN-thin-film piezoelectric transducer sandwiched between thin metallic electrodes and deposited on the top surface. The electro-mechanical properties are characterized by electrical impedance measurements in the frequency range from 0.1 to 10 MHz with a peak-to-peak voltage of 0.5 V applied to the electrodes. We measured the electrical impedance spectra of 35 devices, all of width 2 mm, but with 9 different lengths ranging from 2 to 6 mm and with 2-7 copies of each individual geometry. Each impedance spectrum exhibits many resonance peaks, of which we carefully measured the 5 most prominent ones in each spectrum. We compare the resulting 173 experimental resonance frequencies with the simulation result of a finite-element-method model that we have developed. When using material parameters from the manufacturer, we obtain an average relative deviation of the 173 simulated resonance frequencies from the experimental ones of (-4.2 +/-0.04)%. When optimizing the values of the Young's modulus and the Poisson ratio of the float glass in the simulation, this relative deviation decreased to (-0.03 +/- 0.04)%. Our results suggest a method for an accurate in-situ determination of the acoustic parameters at ultrasound frequencies of any elastic solid onto which a thin-film transducer can be attached, Comment: 9 pages, 5 pdf figures, RevTex

We present three-dimensional measurements of size-dependent acoustophoretic motion of microparticles with diameters from 4.8 um down to 0.5 um suspended in either homogeneous or inhomogeneous fluids inside a glass-silicon microchannel and exposed to a standing ultrasound wave. To study the cross-over from radiation force dominated to streaming dominated motion as the particle size is decreased, we extend previous studies to long time scales, where the particles smaller than the cross-over 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 cross-over 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., Comment: 12 pages, 7 figures, RevTex 4-1

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 acoustic~streaming., Comment: 6 pages, 4 figures, RevTex

We present a semi-analytical theory for the acoustic fields and particle-trapping forces in a viscous fluid inside a capillary tube with arbitrary cross section and ultrasound actuation at the walls. We find that the acoustic fields vary axially on a length scale proportional to the square root of the quality factor of the two-dimensional (2D) cross-section resonance mode. This axial variation is determined analytically based on the numerical solution to the eigenvalue problem in the 2D cross section. The analysis is developed in two steps: First, we generalize a recently published expression for the 2D standing-wave resonance modes in a rectangular cross section to arbitrary shapes, including the viscous boundary layer. Second, based on these 2D modes, we derive analytical expressions in three dimensions for the acoustic pressure, the acoustic radiation and trapping force, as well as the acoustic energy flux density. We validate the theory by comparison to three-dimensional numerical simulations., Comment: 13 pages, 7 pdf figures, RevTex

Surface acoustic wave (SAW) devices form an important class of acoustofluidic devices, in which the acoustic waves are generated and propagate along the surface of a piezoelectric substrate. Despite their wide-spread use, only a few fully three-dimensional (3D) numerical simulations have been presented in the literature. In this paper, we present a 3D numerical simulation taking into account the electromechanical fields of the piezoelectric SAW device, the acoustic displacement field in the attached elastic material, in which the liquid-filled microchannel is embedded, the acoustic fields inside the microchannel, as well as the resulting acoustic radiation force and streaming-induced drag force acting on micro- and nanoparticles suspended in the microchannel. A specific device design is presented, for which the numerical predictions of the acoustic resonances and the acoustophoretic repsonse of suspended microparticles in 3D are successfully compared with experimental observations. The simulation provides a physical explanation of the the observed qualitative difference between devices with an acoustically soft and hard lid in terms of traveling and standing waves, respectively. The simulations also correctly predict the existence and position of the observed in-plane streaming flow rolls. The presented simulation model may be useful in the development of SAW devices optimized for various acoustofluidic tasks., Comment: 16 pages, 8 pdf figures, RevTex

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 non-rotating actuation, and we determine the optimal geometry that maximizes this excitation. In the optimal geometry, we finally simulate a horizontal 2-by-2, 4-by-4, and 6-by-6 streaming-roll pattern in a shallow square cavity. We find that the high-frequency 6-by-6 streaming-roll pattern is dominated by the bulk-driven streaming as opposed to the low-frequency 2-by-2 streaming pattern, which is dominated by the boundary-driven streaming., Comment: 22 pages, 9 pdf figures, Revtex 4-1

Suppression of boundary-driven Rayleigh streaming has recently been demonstrated for fluids of spatial inhomogeneity in density and compressibility owing to the competition between the boundary-layer-induced streaming stress and the inhomogeneity-induced acoustic body force. Here we characterize acoustic streaming by general defocusing particle tracking inside a half-wavelength acoustic resonator filled with two miscible aqueous solutions of different density and speed of sound controlled by the mass fraction of solute molecules. We follow the temporal evolution of the system as the solute molecules become homogenized by diffusion and advection. Acoustic streaming rolls is suppressed in the bulk of the microchannel for 70-200 seconds dependent on the choice of inhomogeneous solutions. From confocal measurements of the concentration field of fluorescently labelled Ficoll solute molecules, we conclude that the temporal evolution of the acoustic streaming depends on the diffusivity and the initial distribution of these molecules. Suppression and deformation of the streaming rolls are observed for inhomogeneities in the solute mass fraction down to 0.1 %., Comment: RevTex, pdfLaTex, 10 pages, 10 pdf figures

Using a previously well-tested numerical model, we demonstrate theoretically that good acoustophoresis can be obtained in a microchannel embedded in an acoustically soft, all-polymer chip, by excitation of whole-system ultrasound resonances. In contrast to conventional techniques based on a standing bulk acoustic wave inside a liquid-filled microchannel embedded in an elastic, acoustically hard material, such as glass or silicon, the proposed whole-system resonance does not need a high acoustic contrast between the liquid and surrounding solid. Instead, it relies on the very high acoustic contrast between the solid and the surrounding air. In microchannels of usual dimensions, we demonstrate the existence of whole-system resonances in an all-polymer device, which support acoustophoresis of a quality fully comparable to that of a conventional hard-walled system. Our results open up for using cheap and easily processable polymers in a controlled manner to design and fabricate microfluidic devices for single-use acoustophoresis., Comment: 12 pages, 8 pdf figures, RevTex

The acoustic fields and streaming in a confined fluid depend strongly on the acoustic boundary layer forming near the wall. The width of this layer is typically much smaller than the bulk length scale set by the geometry or the acoustic wavelength, which makes direct numerical simulations challenging. Based on this separation in length scales, we extend the classical theory of pressure acoustics by deriving a boundary condition for the acoustic pressure that takes boundary-layer effects fully into account. Using the same length-scale separation for the steady second-order streaming, and combining it with time-averaged short-range products of first-order fields, we replace the usual limiting-velocity theory with an analytical slip-velocity condition on the long-range streaming field at the wall. The derived boundary conditions are valid for oscillating cavities of arbitrary shape and wall motion as long as the wall curvature and displacement amplitude are both sufficiently small. Finally, we validate our theory by comparison with direct numerical simulation in two examples of two-dimensional water-filled cavities: The well-studied rectangular cavity with prescribed wall actuation, and the more generic elliptical cavity embedded in an externally actuated rectangular elastic glass block., Comment: 18 pages, 5 figures, pdfLatex, RevTex

Henrik Bruus is professor of lab-chip systems and theoretical physics at the Technical University of Denmark. In this contribution, he summarizes some of the recent results within theory and simulation of microscale acoustofluidic systems that he has obtained in collaboration with his students and international colleagues. The main emphasis is on three dynamical effects induced by external ultrasound fields acting on aqueous solutions and particle suspensions: The acoustic radiation force acting on suspended micro- and nanoparticles, the acoustic streaming appearing in the fluid, and the newly discovered acoustic body force acting on inhomogeneous solutions., Comment: Nobel Symposium 162, Stockholm, Sweden, 2017 arXiv:1712.08369v1 Report-no: Nobel162/2017/04

We present a theoretical and experimental study of boundary-driven acoustic streaming in an inhomogeneous fluid with variations in density and compressibility. In a homogeneous fluid this streaming results from dissipation in the boundary layers (Rayleigh streaming). We show that in an inhomogeneous fluid, an additional non-dissipative force density acts on the fluid to stabilize particular inhomogeneity configurations, which markedly alters and even suppresses the streaming flows. Our theoretical and numerical analysis of the phenomenon is supported by ultrasound experiments performed with inhomogeneous aqueous iodixanol solutions in a glass-silicon microchip., Comment: 6 pages, 3 pdf figures, RevTex 4-1

Acoustic traps are used to capture and handle suspended microparticles and cells in microfluidic applications. A particular simple and much-used acoustic trap consists of a commercially available, millimeter-sized, liquid-filled glass capillary actuated by a piezoelectric transducer. Here, we present a three-dimensional numerical model of the acoustic pressure field in the liquid coupled to the displacement field of the glass wall, taking into account mixed standing and traveling waves as well as absorption. The model predicts resonance modes well suited for acoustic trapping, their frequencies and quality factors, the magnitude of the acoustic radiation force on a single test particle as a function of position, and the resulting acoustic retention force of the trap. We show that the model predictions are in agreement with published experimental results, and we discuss how improved and more stable acoustic trapping modes might be obtained using the model as a design tool., Comment: 13 pages, 15 pdf figures, pdfLatex/Revtex

We demonstrate theoretically that acoustic forces acting on inhomogeneous fluids can be used to pattern and manipulate solute concentration fields into spatio-temporally controllable configurations stabilized against gravity. A theoretical framework describing the dynamics of concentration fields that weakly perturb the fluid density and speed of sound is presented and applied to study manipulation of concentration fields in rectangular-channel acoustic eigenmodes and in Bessel-function acoustic vortices. In the first example, methods to obtain horizontal and vertical multi-layer stratification of the concentration field at the end of a flow-through channel are presented. In the second example, we demonstrate acoustic tweezing and spatio-temporal manipulation of a local high-concentration region in a lower-concentration medium, thereby extending the realm of acoustic tweezing to include concentration fields., Comment: Revtex, 9 pages, 5 eps figures

The mechanical and electrical response of acoustophoretic microfluidic devices attached to an ac-voltage-driven piezoelectric transducer is studied by means of numerical simulations. The governing equations are formulated in a variational framework that, introducing Lagrangian and Hamiltonian densities, is used to derive the weak form for the finite element discretization of the equations and to characterize the device response in terms of frequency-dependent figures of merit or indicators. The effectiveness of the device in focusing microparticles is quantified by two mechanical indicators: the average direction of the pressure gradient and the amount of acoustic energy localized in the microchannel. Further, we derive the relations between the Lagrangian, the Hamiltonian and three electrical indicators: the resonance Q-value, the impedance and the electric power. The frequency response of the hard-to-measure mechanical indicators is correlated to that of the easy-to-measure electrical indicators, and by introducing optimality criteria, it is clarified to which extent the latter suffices to identify optimal driving frequencies as the geometric configuration and the material parameters vary., Comment: 15 pages, 10 figures, Supplementary Material

We present a finite-element method modeling of acoustophoretic devices consisting of a single, long, straight, water-filled microchannel surrounded by an elastic wall of either borosilicate glass (pyrex) or the elastomer polydimethylsiloxane (PDMS) and placed on top of a piezoelectric transducer that actuates the device by surface acoustic waves (SAW). We compare the resulting acoustic fields in these full solid-fluid models with those obtained in reduced fluid models comprising of only a water domain with simplified, approximate boundary conditions representing the surrounding solids. The reduced models are found to only approximate the acoustically hard pyrex systems to a limited degree for large wall thicknesses and not at all for the acoustically soft PDMS systems., Comment: pdf-latex, 13 pages, and 6 pdf figures

We present a theory for the acoustic force density acting on inhomogeneous fluids in acoustic fields on time scales that are slow compared to the acoustic oscillation period. The acoustic force density depends on gradients in the density and compressibility of the fluid. For microfluidic systems, the theory predicts a relocation of the inhomogeneities into stable field-dependent configurations, which are qualitatively different from the horizontally layered configurations due to gravity. Experimental validation is obtained by confocal imaging of aqueous solutions in a glass-silicon microchip., Comment: RevTex, 5 pages, 3 eps figures

Based on first- and second-order perturbation theory, we present a numerical study of the temporal build-up and decay of unsteady acoustic fields and acoustic streaming flows actuated by vibrating walls in the transverse cross-sectional plane of a long straight microchannel under adiabatic conditions and assuming temperature-independent material parameters. The unsteady streaming flow is obtained by averaging the time-dependent velocity field over one oscillation period, and as time increases, it is shown to converge towards the well-known steady time-averaged solution calculated in the frequency domain. Scaling analysis reveals that the acoustic resonance builds up much faster than the acoustic streaming, implying that the radiation force may dominate over the drag force from streaming even for small particles. However, our numerical time-dependent analysis indicates that pulsed actuation does not reduce streaming significantly due to its slow decay. Our analysis also shows that for an acoustic resonance with a quality factor Q, the amplitude of the oscillating second-order velocity component is Q times larger than the usual second-order steady time-averaged velocity component. Consequently, the well-known criterion v << c for the validity of the perturbation expansion is replaced by the more restrictive criterion v << c/Q. Our numerical model is available in the supplemental material in the form of Comsol model files and Matlab scripts., Comment: 14 pages, Revtex, 8 eps figures

We present a theoretical analysis of the acoustic radiation force on a single small particle, either a thermoviscous fluid droplet or a thermoelastic solid particle, suspended in a viscous and heat-conducting fluid medium. Our analysis places no restrictions on the length scales of the viscous and thermal boundary layer thicknesses $\delta_\mathrm{s}$ and $\delta_\mathrm{t}$ relative to the particle radius $a$, but it assumes the particle to be small in comparison to the acoustic wavelength $\lambda$. This is the limit relevant to scattering of sound and ultrasound waves from micrometer-sized particles. For particles of size comparable to or smaller than the boundary layers, the thermoviscous theory leads to profound consequences for the acoustic radiation force. Not only do we predict forces orders of magnitude larger than expected from ideal-fluid theory, but for certain relevant choices of materials, we also find a sign change in the acoustic radiation force on different-sized but otherwise identical particles. This phenomenon may possibly be exploited in handling of submicrometer-sized particles such as bacteria and vira in lab-on-a-chip systems., Comment: Revtex, 23 pages, 4 eps figures

We present a sharp-interface model of two-dimensional ramified growth during quasi-steady electrodeposition. Our model differs from previous modeling methods in that it includes the important effects of extended space-charge regions and nonlinear electrode reactions. The model is validated by comparing its behavior in the initial stage with the predictions of a linear stability analysis., Comment: RevTex, 14 pages, 12 eps figures

This paper introduces the fundamental continuum theory governing momentum transport in isotropic nanofluidic flows. The theory is an extension to the classical Navier-Stokes equation, which includes coupling between translational and rotational degrees of freedom, as well as non-local response functions that incorporates spatial correlations. The continuum theory is compared with molecular dynamics simulation data for both relaxation processes and fluid flows showing excellent agreement on the nanometer length scale. We also present practical tools to estimate when the extended theory should be used.

We present a linear stability analysis of a planar metal electrode during steady electrodeposition. We extend the previous work of Sundstrom and Bark by accounting for the extended space-charge density, which develops at the cathode once the applied voltage exceeds a few thermal voltages. In accordance with Chazalviel's conjecture, the extended space-charge region is found to greatly affect the morphological stability of the electrode. To supplement the numerical solution of the stability problem, we have derived analytical expressions valid in limit of low and high voltage, respectively., Comment: 10 pages, 6 eps figures, Revtex 4-1

We present a theoretical expression for the acoustic interaction force between small spherical particles suspended in an ideal fluid exposed to an external acoustic wave. The acoustic interaction force is the part of the acoustic radiation force on one given particle involving the scattered waves from the other particles. The particles, either compressible liquid droplets or elastic microspheres, are considered to be much smaller than the acoustic wavelength. In this so-called Rayleigh limit, the acoustic interaction forces between the particles are well approximated by gradients of pair-interaction potentials with no restriction on the inter-particle distance. The theory is applied to studies of the acoustic interaction force on a particle suspension in either standing or traveling plane waves. The results show aggregation regions along the wave propagation direction, while particles may attract or repel each other in the transverse direction. In addition, a mean-field approximation is developed to describe the acoustic interaction force in an emulsion of oil droplets in water., Comment: 11 pages, 5 eps figures, RevTex 4.1

We present a numerical study of thermoviscous effects on the acoustic streaming flow generated by an ultrasound standing-wave resonance in a long straight microfluidic channel containing a Newtonian fluid. These effects enter primarily through the temperature and density dependence of the fluid viscosity. The resulting magnitude of the streaming flow is calculated and characterized numerically, and we find that even for thin acoustic boundary layers, the channel height affects the magnitude of the streaming flow. For the special case of a sufficiently large channel height we have successfully validated our numerics with analytical results from 2011 by Rednikov and Sadhal for a single planar wall. We analyze the time-averaged energy transport in the system and the time-averaged second-order temperature perturbation of the fluid. Finally, we have made three main changes in our previously published numerical scheme to improve the numerical performance: (i) The time-averaged products of first-order variables in the time-averaged second-order equations have been recast as flux densities instead of as body forces. (ii) The order of the finite element basis functions has been increased in an optimal manner. (iii) Based on the International Association for the Properties of Water and Steam (IAPWS 1995, 2008, and 2011), we provide accurate polynomial fits in temperature for all relevant thermodynamic and transport parameters of water in the temperature range from 10 C to 50 C., Comment: 13 pages, 8 eps figures, Revtex 4.1

We present a comprehensive analysis of salt transport and overlimiting currents in a microchannel during concentration polarization. We have carried out full numerical simulations of the coupled Poisson-Nernst-Planck-Stokes problem governing the transport and rationalized the behaviour of the system. A remarkable outcome of the investigations is the discovery of strong couplings between bulk advection and the surface current; without a surface current, bulk advection is strongly suppressed. The numerical simulations are supplemented by analytical models valid in the long channel limit as well as in the limit of negligible surface charge. By including the effects of diffusion and advection in the diffuse part of the electric double layers, we extend a recently published analytical model of overlimiting current due to surface conduction., Comment: 15 pages, 11 figures, Revtex 4.1

We present an analytical model of salt- and water-ion transport across an ion-selective interface based on an assumption of local equilibrium of the water-dissociation reaction. The model yields current-voltage characteristics and curves of water-ion current versus salt-ion current, which are in qualitative agreement with experimental results published in the literature. The analytical results are furthermore in agreement with direct numerical simulations. As part of the analysis, we find approximate solutions to the classical problem of pure salt transport across an ion-selective interface. These solutions provide closed-form expressions for the current-voltage characteristics, which include the overlimiting current due to the development of an extended space charge region. Finally, we discuss how the addition of an acid or a base affects the transport properties of the system and thus provide predictions accessible to further experimental tests of the model., Comment: 14 pages, 12 figures, RevTex

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 um and 5.33 um. 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-um-diam particles, allowing for quantitative comparison between theoretical predictions and measurements of the streaming induced motion of small 0.5-um-diam particles., Comment: 13 pages, 8 figures, Revtex 4.1

Sound can move particles. A good example of this phenomenon is the Chladni plate, in which an acoustic wave is induced in a metallic plate and particles migrate to the nodes of the acoustic wave. For several years, acoustophoresis has been used to manipulate microparticles in microscopic scales. In this fluid dynamics video, submitted to the 30th Annual Gallery of Fluid Motion, we show the basic mechanism of the technique and a simple way of visualize it. Since acoustophoretic phenomena is essentially a three-dimensional effect, we employ a simple technique to visualize the particles in 3D. The technique is called Astigmatism Particle Tracking Velocimetry and it consists in the use of cylindrical lenses to induce a deformation in the particle shape, which will be then correlated with its distance from the observer. With this method we are able to dive with the particles and observe in detail particle motion that would otherwise be missed. The technique not only permits visualization but also precise quantitative measurements that can be compared with theory and simulations., Comment: Fluid dynamics video for the 30th Annual Gallery of Fluid Motion, Entry #84160 65th Annual Meeting of the American Physical Society, Division of Fluid Dynamics San Diego, CA, Nov 2012

We present micro-PIV measurements of suspended microparticles of diameters from 0.6 um to 10 um undergoing acoustophoresis in an ultrasound symmetry plane in a microchannel. The motion of the smallest particles are dominated by the Stokes drag from the induced acoustic streaming flow, while the motion of the largest particles are dominated by the acoustic radiation force. For all particle sizes we predict theoretically how much of the particle velocity is due to radiation and streaming, respectively. These predictions include corrections for particle-wall interactions and ultrasonic thermoviscous effects, and they match our measurements within the experimental uncertainty. Finally, we predict theoretically and confirm experimentally that the ratio between the acoustic radiation- and streaming-induced particle velocities is proportional to the square of the particle size, the actuation frequency and the acoustic contrast factor, while it is inversely proportional to the kinematic viscosity., Comment: 11 pages, 9 figures, RevTex 4-1

We calculate the acoustic radiation force from an ultrasound wave on a compressible, spherical particle suspended in a viscous fluid. Using Prandtl--Schlichting boundary-layer theory, we include the kinematic viscosity of the solvent and derive an analytical expression for the resulting radiation force, which is valid for any particle radius and boundary-layer thickness provided that both of these length scales are much smaller than the wavelength of the ultrasound wave (mm in water at MHz frequencies). The acoustophoretic response of suspended microparticles is predicted and analyzed using parameter values typically employed in microchannel acoustophoresis., Comment: 12 pages, 4 figures

We study the response of a model micro-electrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes, ignoring any transverse instability or fluid flow. We analyze the resulting one-dimensional problem by matched asymptotic expansions in the limit of thin double layers and extend previous work into the strongly nonlinear regime, which is characterized by two novel features - significant salt depletion in the electrolyte near the electrodes and, at very large voltage, the breakdown of the quasi-equilibrium structure of the double layers. The former leads to the prediction of "ac capacitive desalination", since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion layers. The latter is associated with transient diffusion limitation, which drives the formation and collapse of space-charge layers, even in the absence of any net Faradaic current through the cell. We also predict that steric effects of finite ion sizes (going beyond dilute solution theory) act to suppress the strongly nonlinear regime in the limit of concentrated electrolytes, ionic liquids and molten salts. Beyond the model problem, our reduced equations for thin double layers, based on uniformly valid matched asymptotic expansions, provide a useful mathematical framework to describe additional nonlinear responses to large ac voltages, such as Faradaic reactions, electro-osmotic instabilities, and induced-charge electrokinetic phenomena., Comment: 30 pages, 17 eps-figures, RevTex

The advent in recent years of highly parallelized microfluidic chemical reaction systems necessitates an understanding of all fluid dynamic time scales including the often neglected millisecond time scale of the inertia of the liquid. We propose the use of harmonically oscillating microfluidics in the low kilohertz range as an analytical tool for the deduction of these time scales. Furthermore, we suggest the use of systems-level equivalent circuit theory as an adequate theory of the behavior of the system. A novel pressure source capable of operation in the desired frequency range is presented for this generic analysis. As a proof of concept, we study the fairly complex system of water-filled interconnected elastic microfluidic tubes containing a large, trapped air-bubble and driven by a pulsatile pressure difference. We demonstrate good agreement between the systems-level model and the experimental results, allowing us to determine the dynamic time scales of the system., Comment: This paper has been removed from arXiv.org due to copyright issues. 1 page, RevTex

To ensure homogeneous conditions within the complete area of perfused microfluidic bio-reactors, we develop a general design of a continuously feed bio-reactor with uniform perfusion flow. This is achieved by introducing a specific type of perfusion inlet to the reaction area. The geometry of these inlets are found using the methods of topology optimization and shape optimization. The results are compared with two different analytic models, from which a general parametric description of the design is obtained and tested numerically. Such a parametric description will generally be beneficial for the design of a broad range of microfluidic bioreactors used for e.g. cell culturing and analysis, and in feeding bio-arrays., Comment: 15 pages, 8 figures

For a microchamber filled with a binary electrolyte and containing a flat un-biased center electrode at one wall, we employ three numerical models to study the strength of the resulting induced-charge electro-osmotic (ICEO) flow rolls: (i) a full nonlinear continuum model resolving the double layer, (ii) a linear slip-velocity model not resolving the double layer and without tangential charge transport inside this layer, and (iii) a nonlinear slip-velocity model extending the linear model by including the tangential charge transport inside the double layer. We show that compared to the full model, the slip-velocity models significantly overestimate the ICEO flow. This provides a partial explanation of the quantitative discrepancy between observed and calculated ICEO velocities reported in the literature. The discrepancy increases significantly for increasing Debye length relative to the electrode size, i.e. for nanofluidic systems. However, even for electrode dimensions in the micrometer range, the discrepancies in velocity due to the finite Debye length can be more than 10% for an electrode of zero height and more than 100% for electrode heights comparable to the Debye length., Comment: 11 pages, Revtex, 7 eps figures