arXiv subjects

Henrik Bruus

Publications and source records attributed to Henrik Bruus.

At least 37 records · Page 2Linked to original sources

arXiv2020

Particle-size-dependent acoustophoretic motion and depletion of micro- and nanoparticles at long time scales

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.

physics.flu-dyn↗

arXiv2020

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 acoustic~streaming.

physics.flu-dyn↗

arXiv2020

Theory of acoustic trapping of microparticles in capillary tubes

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.

physics.flu-dyn↗

arXiv2019

Three-dimensional numerical modeling of surface acoustic wave devices: Acoustophoresis of micro- and nanoparticles including streaming

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.

physics.app-ph↗

arXiv2019

Bulk-driven acoustic streaming at resonance in closed microcavities

Bulk-driven acoustic (Eckart) streaming is the steady flow resulting from the time-averaged acoustic energy flux density in the bulk of a viscous fluid. In simple cases, like the one-dimensional single standing-wave resonance, this energy flux is negligible, and therefore the bulk-driven streaming is often ignored relative to the boundary-driven (Rayleigh) streaming in the analysis of resonating acoustofluidic devices with length scales comparable to the acoustic wavelength. However, in closed acoustic microcavities with viscous dissipation, two overlapping resonances may be excited at the same frequency as a double mode. In contrast to single modes, the double modes can support a steady rotating acoustic energy flux density and thus a corresponding rotating bulk-driven acoustic streaming. We derive analytical solutions for the double modes in a rectangular box-shaped cavity including the viscous boundary layers, and use them to map out possible rotating patterns of bulk-driven acoustic streaming. Remarkably, the rotating bulk-driven streaming may be excited by a 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.

physics.flu-dyn↗

arXiv2018

Characterization of Acoustic Streaming in Gradients of Density and Compressibility

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 %.

physics.flu-dyn↗

arXiv2018

Whole-system ultrasound resonances as the basis for acoustophoresis in all-polymer microfluidic devices

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.

physics.flu-dyn↗

arXiv2018

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

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.

physics.flu-dyn↗

arXiv2018

Theoretical aspects of microscale acoustofluidics

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.

physics.flu-dyn↗

arXiv2017

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 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.

physics.flu-dyn↗

arXiv2017

Three-Dimensional Numerical Modeling of Acoustic Trapping in Glass Capillaries

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.

physics.flu-dyn↗

arXiv2017

Performance study of acoustophoretic microfluidic silicon-glass devices by characterization of material- and geometry-dependent frequency spectra

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.

physics.flu-dyn↗

arXiv2016

Acoustic Tweezing and Patterning of Concentration Fields in Microfluidics

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.

physics.flu-dyn↗

arXiv2016

Modeling of microdevices for SAW-based acoustophoresis --- a study of boundary conditions

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.

physics.flu-dyn↗

arXiv2016

The 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.

physics.flu-dyn↗

arXiv2015

A theoretical study of time-dependent, ultrasound-induced acoustic streaming in microchannels

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.

physics.flu-dyn↗

arXiv2015

Continuum Nanofluidics

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.

cond-mat.soft↗

arXiv2015

A sharp-interface model of electrodeposition and ramified growth

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.

physics.flu-dyn↗