Transition from Boundary-Driven to Bulk-Driven Acoustic Streaming Due to Nonlinear Thermoviscous Effects at High Acoustic Energy Densities.

Acoustic streaming at high acoustic energy densities E_{ac} is studied in a microfluidic channel. It is demonstrated theoretically, numerically, and experimentally with good agreement that frictional heating can alter the streaming pattern qualitatively at high E_{ac} above 400 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.

Fast Microscale Acoustic Streaming Driven by a Temperature-Gradient-Induced Nondissipative Acoustic Body Force.

We study acoustic streaming in liquids driven by a nondissipative acoustic body force created by light-induced temperature gradients. This thermoacoustic streaming produces a velocity amplitude nearly 100 times higher than the boundary-driven Rayleigh streaming and the Rayleigh-Bénard convection at a temperature gradient of 10 K/mm in the channel. The 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.

Theory of pressure acoustics with thermoviscous boundary layers and streaming in elastic cavities.

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 three-dimensional 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/m3).

Numerical study of the coupling layer between transducer and chip in acoustofluidic devices.

By numerical simulation in two and three dimensions, the coupling layer between the transducer and microfluidic chip in ultrasound acoustofluidic devices is studied. The model includes the transducer with electrodes, microfluidic chip with a liquid-filled microchannel, and coupling layer between the transducer and chip. 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, are considered. It is studied how acoustic resonances in ideal devices without a coupling layer are either sustained or attenuated as a coupling layer of increasing thickness is inserted. 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 is established. Finally, by controlling the thickness and the material, it is shown that the coupling layer can be used as a design component for optimal and robust acoustofluidic resonances.

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.

Numerical study of bulk acoustofluidic devices driven by thin-film transducers and whole-system resonance modes.

In bulk acoustofluidic devices, acoustic resonance modes for fluid and microparticle handling are traditionally excited by bulk piezoelectric (PZE) transducers. In this work, it is demonstrated by numerical simulations in three dimensions that integrated PZE thin-film transducers, constituting less than 0.1% of the bulk device, work equally well. The simulations are performed using a well-tested and experimentally validated numerical model. A water-filled straight channel embedded in a mm-sized bulk glass chip with a 1- µm-thick thin-film transducer made of Al0.6Sc0.4N is presented as a proof-of-concept example. The acoustic energy, radiation force, and microparticle focusing times are computed and shown to be comparable to those of a conventional bulk silicon-glass device actuated by a bulk lead-zirconate-titanate transducer. The ability of thin-film transducers to create the desired acoustofluidic effects in bulk acoustofluidic devices relies on three physical aspects: the in-plane-expansion of the thin-film transducer under the applied orthogonal 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 remarkably insensitive to the Q-factor and resonance properties of the thin-film transducer.

Acoustophoresis in polymer-based microfluidic devices: Modeling and experimental validation.

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-µm-diameter polystyrene particles suspended inside a microchannel, which was milled into a polymethylmethacrylate chip. The system was driven anti-symmetrically by a piezoelectric transducer, driven by a 30-V peak-to-peak alternating voltage in the range from 0.5 to 2.5 MHz, leading to acoustic energy densities of 13 J/m3 and particle focusing times of 6.6 s.

Acoustic trapping based on surface displacement of resonance modes.

Acoustic trapping is a promising technique for aligning particles in two-dimensional arrays, as well as for dynamic manipulation of particles individually or in groups. The actuating principles used in current systems rely on either cavity modes in enclosures or complex arrangements for phase control. Therefore, available systems either require high power inputs and costly peripheral equipment or sacrifice flexibility. This work presents a different concept for acoustic trapping of particles and cells that enables dynamically defined trapping patterns inside a simple and inexpensive setup. Here, dynamic operation and dexterous trapping are realized through the use of a modified piezoelectric transducer in direct contact with the liquid sample. Physical modeling shows how the transducer induces an acoustic force potential where the conventional trapping in the axial direction is supplemented by surface displacement dependent lateral trapping. The lateral field is a horizontal array of pronounced potential minima with frequency-dependent locations. The resulting system enables dynamic arraying of levitated trapping sites at low power and can be manufactured at ultra-low cost, operated using low-cost electronics, and assembled in less than 5 min. We demonstrate dynamic patterning of particles and biological cells and exemplify potential uses of the technique for cell-based sample preparation and cell culture.

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.

Toward optimal acoustophoretic microparticle manipulation by exploiting asymmetry.

The performance of a micro-acousto-fluidic device designed for microparticle trapping is simulated using a three-dimensional (3D) numerical model. It is demonstrated by numerical simulations that geometrically asymmetric architecture and actuation can increase the acoustic radiation forces in a liquid-filled cavity by almost 2 orders of magnitude when setting up a standing pressure half wave in a microfluidic chamber. Similarly, experiments with silicon-glass devices show a noticeable improvement in acoustophoresis of 20-µm silica beads in water when asymmetric devices are used. Microparticle acoustophoresis has an extensive array of applications in applied science fields ranging from life sciences to 3D printing. A more efficient and powerful particle manipulation system can boost the overall effectiveness of an acoustofluidic device. The numerical simulations are developed in the COMSOL Multiphysics® software package (COMSOL AB, Stockholm, Sweden). By monitoring the modes and magnitudes of simulated acoustophoretic fields in a relatively wide range of ultrasonic frequencies, a map of device performance is obtained. 3D resonant acoustophoretic fields are identified to quantify the improved performance of the chips with an asymmetric layout. Four different device designs are analyzed experimentally, and particle tracking experimental data qualitatively supports the numerical results.

Acoustic Streaming and Its Suppression in Inhomogeneous Fluids.

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 nondissipative 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.

Theory of pressure acoustics with viscous boundary layers and streaming in curved elastic cavities.

The acoustic fields and streaming in a confined fluid depend strongly on the viscous 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, the classical theory of pressure acoustics is extended by deriving a boundary condition for the acoustic pressure that takes viscous 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, the usual limiting-velocity theory is replaced 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 both the wall curvature and displacement amplitude are sufficiently small. Finally, the theory is validated 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 a more generic elliptical cavity embedded in an externally actuated rectangular elastic glass block.

Ultrasound Characterization of Microbead and Cell Suspensions by Speed of Sound Measurements of Neutrally Buoyant Samples.

We present an experimental method including error analysis for the measurement of the density and compressibility of cells and microbeads; these being the two central material properties in ultrasound-based acoustophoretic applications such as particle separation, trapping, and up-concentration. The density of the microparticles is determined by using a neutrally buoyant selection process that involves centrifuging of microparticles suspended in different density solutions, CsCl for microbeads and Percoll for cells. The speed of sound at 3 MHz in the neutrally buoyant suspensions is measured as a function of the microparticle volume fraction, and from this the compressibility of the microparticles is inferred. Finally, from the obtained compressibility and density, the acoustic scattering coefficients and contrast factor of the microparticles are determined, and in a sensitivity analysis, the impact of the measurement errors on the computed acoustic properties is reported. The determination of these parameters and their uncertainties allow for accurate predictions of the acoustophoretic response of the microparticles. The method is validated by determining the density (0.1-1% relative uncertainty) and compressibility (1-3% relative uncertainty) of previously well-characterized polymer microbeads and subsequently applied to determine the density (0.1-1% relative uncertainty), compressibility (1% relative uncertainty), scattering coefficients, and acoustic contrast factors for nonfixed and fixed cells, such as red blood cells, white blood cells, DU-145 prostate cancer cells, MCF-7 breast cancer cells, and LU-HNSCC-25 head and neck squamous carcinoma cells in phosphate buffered saline. The results show agreement with published data obtained by other methods.

Acoustic Force Density Acting on Inhomogeneous Fluids in Acoustic Fields.

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.

Migration of cells in a social context.

In multicellular organisms and complex ecosystems, cells migrate in a social context. Whereas this is essential for the basic processes of life, the influence of neighboring cells on the individual remains poorly understood. Previous work on isolated cells has observed a stereotypical migratory behavior characterized by short-time directional persistence with long-time random movement. We discovered a much richer dynamic in the social context, with significant variations in directionality, displacement, and speed, which are all modulated by local cell density. We developed a mathematical model based on the experimentally identified "cellular traffic rules" and basic physics that revealed that these emergent behaviors are caused by the interplay of single-cell properties and intercellular interactions, the latter being dominated by a pseudopod formation bias mediated by secreted chemicals and pseudopod collapse following collisions. The model demonstrates how aspects of complex biology can be explained by simple rules of physics and constitutes a rapid test bed for future studies of collective migration of individual cells.

Continuum Nanofluidics.

This paper introduces the fundamental continuum theory governing momentum transport in isotropic nanofluidic systems. The theory is an extension of the classical Navier-Stokes equation, and includes coupling between translational and rotational degrees of freedom as well as nonlocal response functions that incorporate 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. It is shown that in the wall-fluid region the fluid molecules align with the wall, and in this region the isotropic model may fail and a full anisotropic description is necessary.

Generalized extended Navier-Stokes theory: correlations in molecular fluids with intrinsic angular momentum.

The extended Navier-Stokes theory accounts for the coupling between the translational and rotational molecular degrees of freedom. In this paper, we generalize this theory to non-zero frequencies and wavevectors, which enables a new study of spatio-temporal correlation phenomena present in molecular fluids. To discuss these phenomena in detail, molecular dynamics simulations of molecular chlorine are performed for three different state points. In general, the theory captures the behavior for small wavevector and frequencies as expected. For example, in the hydrodynamic regime and for molecular fluids with small moment of inertia like chlorine, the theory predicts that the longitudinal and transverse intrinsic angular velocity correlation functions are almost identical, which is also seen in the molecular dynamics simulations. However, the theory fails at large wavevector and frequencies. To account for the correlations at these scales, we derive a phenomenological expression for the frequency dependent rotational viscosity and wavevector and frequency dependent longitudinal spin viscosity. From this we observe a significant coupling enhancement between the molecular angular velocity and translational velocity for large frequencies in the gas phase; this is not observed for the supercritical fluid and liquid state points.

Theory and modeling of nonperturbative effects in thermoviscous acoustofluidics.

A theoretical model of thermal boundary layers and acoustic heating in microscale acoustofluidic devices is presented. Based on it, an iterative numerical model is developed that enables numerical simulation of nonlinear thermoviscous effects due to acoustic heating and thermal advection. Effective boundary conditions are derived and used to enable simulations in three dimensions. The theory shows how friction in the viscous boundary layers causes local heating of the acoustofluidic device. The resulting temperature field spawns thermoacoustic bulk streaming that dominates the traditional boundary-driven Rayleigh streaming at relatively high acoustic energy densities. The model enables simulations of microscale acoustofluidics with high acoustic energy densities and streaming velocities in a range beyond the reach of perturbation theory, and is relevant for design and fabrication of high-throughput acoustofluidic devices.

Acoustic radiation force on a spherical thermoviscous particle in a thermoviscous fluid including scattering and microstreaming.

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.

Acoustic radiation force on a heated spherical particle in a fluid including scattering and microstreaming from a standing ultrasound wave.

Analytical expressions are derived for the time-averaged, quasisteady, 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.