Starting from the linear flow of homogeneous fluid, five modes are defined as eigenvectors of the basic system of conservation laws.
Quasi-plane geometry is considered. Projectors that separate overall perturbation of the fluid into specific modes are calculated and applied to nonlinear flow. Dynamic equations for the interacting modes are obtained in the frames of the method. A particular case of streaming caused by acoustic pulse is considered, illustrations on temporal behavior of streaming velocity and streamlines are presented.
The oscillations of ultrasound contrast agents are of particular importance to the understanding of the propagation of acoustic waves in the bubbly liquids (suspensions of ultrasound contrast agents). Acoustic waves propagating in bubbly liquids have been investigated extensively. Little has been dedicated to the resonance effects of the microbubbles on the propagating waves. Here a nonlinear partial differential equation for describing one-dimensional acoustic waves propagating near the resonance frequency of the microbubbles in bubbly liquids is obtained. The present equation recovers classi…
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 thermovisc…
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 …
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 freque…
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 pro…
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,…
The influences of blood vessels and focused location on temperature distribution during high-intensity focused ultrasound (HIFU) ablation of liver tumors is studied. A three-dimensional acoustics-thermal-fluid coupling model is employed to compute the temperature field in the hepatic cancerous region. The model is based on the linear Westervelt and bioheat equations as well as the nonlinear Navier-Stokes equations for the liver parenchyma and blood vessels. The effect of acoustic streaming is also taken into account in the present HIFU simulation study. Different blood vessel diameters and foc…
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…
Inaccurate slow streaming models of acoustically-induced fluid flow remain in use due to the lack of a generalized alternative. The Multiscale Articulated Differentials Method (MADaM; [see co-article]) solves this problem with a complete, scale-sensitive spatiotemporal expansion. Applied to classic axial Eckart streaming, the MADaM produces, in terms of a Burgers equation, a long-sought transient solution able to accommodate frequencies and amplitudes far beyond slow streaming models. Steady streaming is governed by a corresponding Riccati equation that, when solved, produces simple expression…
This paper reports the phenomenon of resonance weakening and streaming onset in two phase acoustofluidics by performing numerical simulations of a capillary droplet suspended in a microfluidic chamber. The simulations show that depending on the relative acoustic properties of the two phases, it is possible to observe (i)~the decrease in the total acoustic energy as the oscillation amplitude at the wall increases, and (ii)~the onset of acoustic streaming. The impact of these findings in terms of acoustic focusing inside droplets is also discussed.
Acoustic streaming can be generated around sharp structures, even when the acoustic wavelength is much larger than the vessel size. This sharp-edge streaming can be relatively intense, \textcolor{blue}{owing to the strongly focused inertial effect experienced by the acoustic flow near the tip.} We conducted experiments with Particle Image Velocimetry to quantify this streaming flow through the influence of liquid viscosity $ν$, from 1 mm$^2$/s to 30 mm$^2$/s, and acoustic frequency $f$ from 500 Hz to 3500 Hz. Both quantities supposedly influence the thickness of the viscous boundary layer $δ= …
Acoustic microstreaming has several industrial, therapeutic, and biomedical applications - Acoustic cleaning, micromixing, microfluid transport, hemolysis, sonoporation. The acoustic microstreaming due to the oscillation of ultrasound contrast microbubbles in the middle of the gap between two parallel walls is studied numerically. Axisymmetric Boundary Element Method along with theory of Nyborg is applied to study the streaming flow. Viscoelastic model with exponentially varying elasticity is used to simulate microbubble coating. The microstreaming streamlines near the plane walls and the indu…
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 sam…
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…
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 …
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 in…
Ultrasound-driven microbubbles rectify oscillatory motion into strong steady streaming flow [1, 2]. In this fluid dynamics video, we show size-dependent trapping, focusing and sorting of microparticles, utilizing the interaction between bubble streaming and the induced streaming around the mobile particles. This mechanism is purely passive and is selective for sizes and size differentials far smaller than any scale imposed by the device geometry.
Oscillating sharp edges have been employed to achieve rapid and homogeneous mixing in microchannels using acoustic streaming. Here we use 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 nonlin…
A time-domain numerical code based on the constitutive relations of nonlinear acoustics for simulating ultrasound propagation is presented. To model frequency power law attenuation, such as observed in biological media, multiple relaxation processes are included and relaxation parameters are fitted to both exact frequency power law attenuation and empirically measured attenuation of a variety of tissues that does not fit an exact power law. A computational technique based on artificial relaxation is included to correct the non-negligible numerical dispersion of the numerical method and to impr…
We describe a novel 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 as…
Inviscid hydrodynamics mediates forces through pressure and other, typically irrotational, external forces. Acoustically induced forces must be consistent with arising from such a pressure field. The use of "acoustic stress" is shown to have inconsistencies with such an analysis and generally arise from mathematical expediency but poor overall conceptualization of such systems. This contention is further supported by the poor agreement of experiment in many such approaches. The notion of momentum as being an intrinsic property of sound waves is similarly found to be paradoxical. Through an ana…
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…
Conformal mapping of a slab of a two-dimensional ultrasonic crystal generate a closed geometrical arrangement of ultrasonic scatterers with appealing acoustic properties. This acoustic shell is able to confine ultrasonic modes. Some of these internal resonances can be induced from an external wave source. The mapping of a linear defect produces a wave-guide that exhibits a spatial-frequency selection analogous to that characteristic of a synthetic "cochlea". Both, experimental and theoretical results are reported here.
The acoustic nonlinearity parameter B/A plays a significant role in the characterization of acoustic properties of various biomaterials and biological tissues. It has the potential to be a favorable imaging modality in contrast ultrasound imaging with coated microbubbles. However, the development of effective means for evaluating the nonlinearity parameter of suspensions of ultrasound contrast agents (UCAs, also known as bubbly liquids) remains open. The present paper formulates a new equation based on the thermodynamic method that correlates both attenuation and phase velocity of linear ultra…
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 combin…
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 …
The interaction of an acoustic wave with a stratified fluid can drive strong streaming flows owing to the baroclinic production of fluctuating vorticity, as recently demonstrated by Chini et al. (J. Fluid Mech., 744, 2014, pp. 329). In the present investigation, a set of wave/mean-flow interaction equations is derived that governs the coupled dynamics of a standing acoustic wave mode of characteristic (small) amplitude ε and the streaming flow it drives in a thin channel with walls maintained at differing temperatures. Unlike classical Rayleigh streaming, the resulting mean flow arises at O(ε)…
The efficient mixing of fluid samples in miniaturized total analysis systems is essential for numerous applications including biological screening assays, chemical extraction, polymerization, cell analysis, and protein folding. Miniaturized microfluidic platforms have recently emerged for microscale fluid mixing with their capabilities of high-throughput sample processing and reduced sample depletion. However, microscale fluid mixing is inherently hampered due to the characteristics of a low Reynolds number flows in diminutive channels. Microscale fluid mixing mainly depends on molecular diffu…
A viscoelastic theory for ultrasound-induced intracellular streaming
Institute for Theoretical Physics, Heidelberg University（海德堡大学理论物理研究所）；BioQuant, Heidelberg University（海德堡大学生物定量研究中心）；Max Planck Institute for Medical Research（马克斯·普朗克医学研究所）
Ultrasound-driven oscillating micro-bubbles have been used as active actuators in microfluidic devices to perform manifold tasks such as mixing, sorting and manipulation of microparticles. A common configuration consists on side-bubbles, created by trapping air pockets in blind channels perpendicular to the main channel direction. This configuration consists of acoustically excited bubbles with a semi-cylindrical shape that generate significant streaming flow. Due to the geometry of the channels, such flows have been generally considered as quasi two-dimensional. Similar assumptions are often …
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 pa…
Ultrasound contrast agents comprise gas microbubbles surrounded by stabilising elastic or viscoelastic shells. Microbubbles containing liquid or solid cores are referred to as antibubbles. The manufacturing process of long-lived antibubbles involves the adsorption of colloidal particles at the interfaces, a process called Pickering stabilisation. With and without cores present inside, Pickering-stabilised microbubbles generate a harmonic response, even at modest transmission amplitudes. Therefore, Pickering-stabilised ultrasound contrast agents may be of interest in contrast-enhanced ultrasoni…
Geometry of the fluid container plays a key role in the shape of acoustic streaming patterns. Inadvertent vortices can be troublesome in some cases, but if treated properly, the problem turns into a very useful parameter in acoustic tweezing or micromixing applications. In this paper, the effects of sinusoidal boundaries of a microchannel on acoustic streaming patterns are studied. Results show that while top and bottom sinusoidal walls are vertically actuated at the resonance frequency of basic hypothetical rectangular microchannel, some repetitive acoustic streaming patterns are recognized i…
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 cont…
Acoustic waves can generate steady streaming within a fluid owing to the generation of viscous boundary layers near walls, of typical thickness $δ$. In microchannels, the acoustic wavelength $λ$ is adjusted to twice the channel width $w$ to ensure a resonance condition, which implies the use of MHz transducers. Recently though, intense acoustic streaming was generated by acoustic waves of a few kHz (hence with $λ\gg w$), owing to the presence of sharp-tipped structures of curvature radius at the tip $r_c$ smaller than $δ$. The present study quantitatively investigates this sharp-edge acoustic …
We analyze acoustic streaming flows using an 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, …
Recent experiments showed that standing acoustic waves could be exploited to induce self-propulsion of rigid metallic particles in the direction perpendicular to the acoustic wave. We propose in this paper a physical mechanism for these observations based on the interplay between inertial forces in the fluid and the geometrical asymmetry of the particle shape. We consider an axisymmetric rigid near-sphere oscillating in a quiescent fluid along a direction perpendicular to its symmetry axis. The kinematics of oscillations can be either prescribed or can result dynamically from the presence of a…
High-resolution pressure imaging via background-oriented schlieren tomography: a spatiotemporal measurement for MHz ultrasound fields and hydrophone calibration
The attenuation of small-amplitude acoustic waves in a suspension containing ultrasound contrast agents (UCAs, coated microbubbles) is determined by the linear oscillation of the UCAs in the medium, which can be estimated via a linear attenuation theory. Recently, several nonlinear phenomena of energy attenuation at very low-intensity of acoustic pressures have been observed experimentally, raising concerns on the validity of the linear attenuation theory. Explanations of the nonlinear phenomenon are still lacking. Particularly, the interpretation of the pressure-dependent attenuation phenomen…
Acoustical and optical vortices have attracted large interest due to their ability in capturing and manipulating particles with the use of the radiation pressure. Here we show that acoustical vortices can also induce axial vortical flow reminiscent of cyclones whose topology can be controlled by adjusting the properties of the acoustical beam. In confined geometry, the phase singularity enables generating attractive streaming with a flow directed toward the transducer. This opens perspectives for contact-less vortical flow control.
When an acoustic wave travels in a lossy medium such as a liquid, it progressively transfers its pseudo-momentum to the fluid, which results in a steady acoustic streaming. Remarkably, the phenomenon involves a balance between sound attenuation and shear, such that viscosity vanishes in the final expression of the velocity field. For this reason, the effect of viscosity has long been ignored in acoustic streaming experiments. Here, we show experimentally that the viscosity plays a major role in cavities such as the streaming induced by surface acoustic waves in sessile droplets. We develop a n…
We report the theoretical and experimental demonstration of pattern formation in acoustics. The system is an acoustic resonator containing a viscous fluid. When the system is driven by an external periodic force, the ultrasonic field inside the cavity experiences different pattern-forming instabilities leading to the emergence of periodic structures. The system is also shown to possess bistable regimes, in which localized states of the ultrasonic field develop. The thermal nonlinearity in the viscous fluid, together with the far-from-equilibrium conditions, are is the responsible of the observ…
Ultrasound is an important imaging modality for biological systems. High-frequency ultrasound can also (e.g., via acoustical nonlinearities) be used to provide deeply penetrating and high-resolution imaging of vascular structure via catheterisation. The latter is an important diagnostic in vascular health. Typically, ultrasound requires sources and transducers that are greater than, or of order the same size as the wavelength of the acoustic wave. Here we design and theoretically demonstrate that single silver nanorods, acting as optical nonlinear dipole antennae, can be used to detect ultraso…
We study a horizontal streaming excited by means of a low frequency and intensity acoustic wave in 2D freely suspended film of thermotropic smectic liquid crystal. Acoustic pressure induces fast periodic transverse oscillations of the film, which produce in-plane stationary couples of vortices slowly rotating in opposite directions owing to hydrodynamic nonlinearity. The parameters of vortices are measured using a new method, based on tracking disk-shaped island defects. The horizontal motion occurs only when the amplitude of acoustic pressure exceeds threshold value, which can be explained by…
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 insi…
Understanding the acoustic cavitation threshold is essential for minimizing cavitation bioeffects in diagnostic ultrasound and for controlling cavitation--mediated tissue ablation in focused ultrasound procedures. The homogeneous cavitation threshold is an intrinsic material property of recognized importance to a variety of applications requiring cavitation control. However, acoustic measurements of the cavitation threshold in water differ from those predicted by classical nucleation theories. This persistent discrepancy is explained by combining novel methods for acoustically nucleating singl…
