arXiv subjects

Henrik Bruus

Publications and source records attributed to Henrik Bruus.

At least 55 records · Page 3Linked to original sources

arXiv2015

Forces acting on a small particle in an acoustical field in a thermoviscous fluid

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

physics.flu-dyn↗

arXiv2015

Morphological instability during steady electrodeposition at overlimiting currents

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

physics.flu-dyn↗

arXiv2014

Acoustic interaction forces between small particles in an ideal fluid

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

physics.flu-dyn↗

arXiv2014

A numerical study of thermoviscous effects in ultrasound-induced acoustic streaming in microchannels

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

physics.flu-dyn↗

arXiv2014

Concentration polarization, surface currents, and bulk advection in a microchannel

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

physics.flu-dyn↗

arXiv2013

Transport-limited water splitting at ion-selective interfaces during concentration polarization

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

physics.flu-dyn↗

arXiv2013

Ultrasound-induced acoustophoretic motion of microparticles in three dimensions

We derive analytical expressions for the three-dimensional (3D) acoustophoretic motion of spherical microparticles in rectangular microchannels. The motion is generated by the acoustic radiation force and the acoustic streaming-induced drag force. In contrast to the classical theory of Rayleigh streaming in shallow, infinite, parallel-plate channels, our theory does include the effect of the microchannel side walls. The resulting predictions agree well with numerics and experimental measurements of the acoustophoretic motion of polystyrene spheres with nominal diameters of 0.537 um and 5.33 um. The 3D particle motion was recorded using astigmatism particle tracking velocimetry under controlled thermal and acoustic conditions in a long, straight, rectangular microchannel actuated in one of its transverse standing ultrasound-wave resonance modes with one or two half-wavelengths. The acoustic energy density is calibrated in situ based on measurements of the radiation dominated motion of large 5-um-diam particles, allowing for quantitative comparison between theoretical predictions and measurements of the streaming induced motion of small 0.5-um-diam particles.

physics.flu-dyn↗

arXiv2012

Diving with microparticles in acoustic fields

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

physics.flu-dyn↗

arXiv2012

Acoustic radiation- and streaming-induced microparticle velocities determined by micro-PIV in an ultrasound symmetry plane

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

physics.flu-dyn↗

arXiv2011

On the forces acting on a small particle in an acoustical field in a viscous fluid

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

physics.flu-dyn↗

arXiv2009

Strongly nonlinear dynamics of electrolytes in large ac voltages

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

physics.flu-dyn↗

arXiv2009

Kilohertz microfluidics as an analytical tool for determining dynamic characteristics of microfluidic systems

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

physics.flu-dyn↗

arXiv2009

Optimal homogenization of perfusion flows in microfluidic bio-reactors; a numerical study

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

physics.flu-dyn↗

arXiv2009

A numerical analysis of finite Debye-length effects in induced-charge electro-osmosis

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

physics.flu-dyn↗

arXiv2009

Topology and shape optimization of induced-charge electro-osmotic micropumps

For a dielectric solid surrounded by an electrolyte and positioned inside an externally biased parallel-plate capacitor, we study numerically how the resulting induced-charge electro-osmotic (ICEO) flow depends on the topology and shape of the dielectric solid. In particular, we extend existing conventional electrokinetic models with an artificial design field to describe the transition from the liquid electrolyte to the solid dielectric. Using this design field, we have succeeded in applying the method of topology optimization to find system geometries with non-trivial topologies that maximize the net induced electro-osmotic flow rate through the electrolytic capacitor in the direction parallel to the capacitor plates. Once found, the performance of the topology optimized geometries has been validated by transferring them to conventional electrokinetic models not relying on the artificial design field. Our results show the importance of the topology and shape of the dielectric solid in ICEO systems and point to new designs of ICEO micropumps with significantly improved performance.

physics.flu-dyn↗

arXiv2008

Osmotically driven flows in microchannels separated by a semipermeable membrane

We perform experimental investigations of osmotically driven flows in artificial microchannels by studying the dynamics and structure of the front of a sugar solution traveling in 200 um wide and 50-200 um deep microchannels. We find that the sugar front travels with constant speed, and that this speed is proportional to the concentration of the sugar solution and inversely proportional to the depth of the channel. We propose a theoretical model, which, in the limit of low axial flow resistance, predicts that the sugar front indeed should travel with a constant velocity. The model also predicts an inverse relationship between the depth of the channel and the speed and a linear relation between the sugar concentration and the speed. We thus find good agreement between the experimental results and the predictions of the model. Our motivation for studying osmotically driven flows is that they are believed to be responsible for the translocation of sugar in plants through the phloem sieve element cells. Also, we suggest that osmotic elements can act as integrated pumps with no movable parts in lab-on-a-chip systems.

physics.flu-dyn↗

arXiv2008

Multi-directional sorting modes in deterministic lateral displacement devices

Deterministic lateral displacement (DLD) devices separate micrometer-scale particles in solution based on their size using a laminar microfluidic flow in an array of obstacles. We investigate array geometries with rational row-shift fractions in DLD devices by use of a simple model including both advection and diffusion. Our model predicts novel multi-directional sorting modes that could be experimentally tested in high-throughput DLD devices containing obstacles that are much smaller than the separation between obstacles.

physics.flu-dyn↗

arXiv2007

A theoretical analysis of the resolution due to diffusion and size-dispersion of particles in deterministic lateral displacement devices

We present a model including diffusion and particle-size dispersion for separation of particles in deterministic lateral displacement devices also known as bumper arrays. We determine the upper critical diameter for diffusion-dominated motion and the lower critical diameter for pure convection-induced displacement. Our model explains the systematic deviation, observed for small particles in several experiments, from the critical diameter for separation given by simple laminar flow considerations.

physics.flu-dyn↗