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 nonlinearity of acoustic streaming, the channel dimensions could significantly impact the flow patterns and device performance.
A novel mechanism for the transport of microscale particles in viscous fluids is demonstrated. The mechanism exploits the trapping of such particles by rotational streaming cells established in the vicinity of an oscillating cylinder, recently analyzed in previous work. The present work explores a strategy of transporting particles between the trapping points established by multiple cylinders undergoing oscillations in sequential intervals. It is demonstrated that, by controlling the sequence of oscillation intervals, an inertial particle is effectively and predictably transported between the …
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,…
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= …
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…
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…
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 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…
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 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…
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…
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 …
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…
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 …
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…
In this paper, it is shown that in interaction with an oscillating bubbles cluster the fluid becomes inhomogeneous. The radial variation of the acoustic refractive index of the fluid generates an acoustic lens with spherical symmetry. When the focal length of the lens associated with the bubbles cluster is equal to the length of the position vector then the bubbles cluster behaves like a dumb hole. Unlike the properties of a bubble, the cluster, by compression under the action of attractive internal forces, can shrink its radius to become a dumb hole.
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, …
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 …
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.
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…
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…
The interaction of waves and flows is a challenging topic where a complete resolution has been frustrated by the essential nonlinear features in the hydrodynamic case. Even in the case of EM waves in flowing media, the results are subtle. For a simple shear flow of constant n fluid, incident radiation is shown to be reflected and refracted in an analogous manner to Snell's law. However, the beam intensities differ and the system has an asymmetry in that an internal reflection gap opens at steep incident angles nearly oriented with the shear. For EM waves these effects are generally negligible …
Acoustic streaming is the net time-averaged flow that results from the nonlinearities in an oscillating flow. Extensive research has sought to identify different physical mechanisms and types of acoustic streaming in systems of various geometries. While streaming in a channel maintains one of the simplest geometries, dimensional analysis of the governing equations reveals that multiple regimes of streaming may occur within a channel. In this study, a framework is developed for investigating and understanding the physical streaming regimes in a two-dimensional channel. By taking different limit…
Recently, the phenomena of streaming suppression and relocation of inhomogeneous miscible fluids under acoustic fields were explained using the hypothesis on mean Eulerian pressure. In this letter, we show that this hypothesis is unsound and any assumption on mean Eulerian pressure is needless. We present a theory of non-linear acoustics for inhomogeneous fluids from the first principles, which explains streaming suppression and acoustic relocation in both miscible and immiscible inhomogeneous fluids inside a microchannel. This theory predicts the relocation of higher impedance fluids to press…
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…
Analytical solutions in fluid dynamics can be used to elucidate the physics of complex flows and to serve as test cases for numerical models. In this work, we present the analytical solution for the acoustic boundary layer that develops around a rigid sphere executing small amplitude harmonic rectilinear motion in a compressible fluid. The mathematical framework that describes the primary flow is identical to that of wave propagation in linearly elastic solids, the difference being the appearance of complex instead of real valued wave numbers. The solution reverts to well-known classical solut…
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…
In microfluidic applications involving high-frequency acoustic waves over a solid boundary, the Stokes boundary-layer thickness $δ$ is so small that some non-negligible slip may occur at the fluid-solid interface. This paper assesses the impact of the slip by revisiting the classical problem of steady acoustic streaming over a flat boundary with the Navier boundary condition $u|_{y=0} = L_\mathrm{s} \partial_y u|_{y=0}$, where $u$ is the velocity tangent to the boundary $y=0$, and the parameter $L_\mathrm{s}$ is the slip length. The limit outside the boundary layer provide an effective slip ve…
Acoustically actuated sessile bubbles can be used as a tool to manipulate microparticles, vesicles and cells. In this work, using acoustically actuated sessile semi-cylindrical microbubbles, we demonstrate experimentally that finite-sized microparticles undergo size-sensitive migration and trapping towards specific spatial positions in three dimensions with high reproducibility. The particle trajectories are successfully reproduced by passive advection of the particles in a steady three-dimensional streaming flow field augmented with volume exclusion from the confining boundaries. For differen…
Damped internal wave beams in stratified fluids have long been known to generate strong mean flows through a mechanism analogous to acoustic streaming. While the role of viscous boundary layers in acoustic streaming has thoroughly been addressed, it remains largely unexplored in the case of internal waves. Here we compute the mean flow generated close to an undulating wall that emits internal waves in a viscous, linearly stratified two-dimensional Boussinesq fluid. Using a quasi-linear approach, we demonstrate that the form of the boundary conditions dramatically impacts the generated boundary…
The source of the hummingbirds distinctive hum is not well understood, but there are clues to its origin in the acoustic nearfield and farfield. To unravel this mystery, we recorded the acoustic nearfield generated by six freely hovering Annas hummingbirds using a 2176 microphone array. We also directly measured the 3D aerodynamic forces generated by the hummingbird in vivo using a new aerodynamic force platform. To determine the degree to which the aerodynamic forces cause the hum, we developed a simple first-principles model to predict the acoustic field radiated by the 3D oscillating forces…
We investigate the flow around an oscillating nearly-spherical particle at low, yet non-vanishing, Reynolds numbers, and the potential resulting locomotion. We analytically demonstrate that no net motion can arise up to order one in Re and order one in the asphericity parameter, regardless of the particle's shape. Therefore, geometry-induced acoustic streaming propulsion, if any, must arise at higher order.
The aim of this paper is to derive a new equation (the \emph{acoustic-drift equation} (ADE)) describing the generation of a flow by an acoustic wave. We consider acoustic waves of perfect barotropic gas as the zero-order solution and derive the equation for the averaged flow of the first order. The used small parameter of our asymptotic study is dimensionless inverse frequency, and the leading term for a velocity field is chosen to be a purely oscillating acoustic field. The employed mathematical approach combines the two-timing method and the notion of a distinguished limit. The properties of…
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 microstreaming due to an oscillating microbubble is analytically investigated to obtain the circular streaming motion adjacent to a nearby wall. Classical theory due to Nyborg is carefully derived in the radial coordinates. The theory is used to obtain the flow field and the vortical motion caused by the microbubble motion. The length of the vertices are decreasing when the microbubble is excited at distances close to the rigid wall, while the maximum shear stress is increasing.
We study the secondary time-averaged flow (streaming) generated by an oscillating cylinder immersed within a fluid, under high amplitude forcing so that inertial effects are significant. This streaming is decomposed into a viscous boundary layer flow where vorticity is created, and an outer flow of larger size. We operate under conditions of relatively low viscosity, so that the boundary layer is smaller than the object diameter. While for low Keulegan-Carpenter (KC) number (small enough amplitude), the size of the outer flow is typically that of the object, here we show that at large enough f…
