Otto Manneberg PhD Thesis: Multidimensional Ultrasonic Standing Wave Manipulation in Microfluidic...

Multidimensional UltrasonicStanding Wave Manipulation

in Microfluidic Chips

OTTO MANNEBERG

Doctoral ThesisDepartment of Applied PhysicsRoyal Institute of Technology

Stockholm, Sweden 2009

TRITA-FYS 2009:44ISSN 0280-316XISRN KTH/FYS/--09:4--SEISBN 978-91-7415-398-9

KTHSE-100 44 Stockholm

SWEDEN

Akademisk avhandling som med tillstånd av Kungl Tekniska Högskolan framläggestill offentlig granskning för avläggande av teknologie doktorsexamen fredagen den11:e september 2009 kl. 14:00 i sal FD5, Roslagstullsbacken 21,AlbaNova Universitetscentrum, Kungl Tekniska Högskolan, Stockholm.

© Otto Manneberg, 11 september, 2009

Tryck: Universitetsservice US AB

Errata

Page 7: The conclusion that the two potentials describe pure shear and longitudinal waves, respectively, is valid for plane waves of the two types.

Page 9: The cut-off condition given for Lamb modes does not discern

between the different types of modes. For a more extensive treatment of cut-off conditions, see Ref. [18] pp. 167-168.

Page 18: The caption to Fig. 3.1 is erroneous. A streamline is a line at all

points and times tangent to the velocity field. Page 61: The last author of Ref. [96] should be “Laurell, T”

Docendo Discimus

Abstract

The use of ultrasonic standing waves for contactless manipulation of microparticlesin microfluidic systems is a field with potential to become a new standard tool in lab-on-chip systems. Compared to other contactless manipulation methods ultrasonicstanding wave manipulation shows promises of gentle cell handling, low cost, andprecise temperature control. The technology can be used both for batch handling,such as sorting and aggregation, and handling of single particles.

This doctoral Thesis presents multi-dimensional ultrasonic manipulation, i.e., ma-nipulation in both two and three spatial dimensions as well as time-dependentmanipulation of living cells and microbeads in microfluidic systems. The lab-on-chip structures used allow for high-quality optical microscopy, which is central tomany bio-applications. It is demonstrated how the ultrasonic force fields can bespatially confined to predefined regions in the system, enabling sequential manipu-lation functions. Furthermore, it is shown how frequency-modulated signals can beused both for spatial stabilization of the force fields as well as for flow-free transportof particles in a microchannel. Design parameters of the chip-transducer systemsemployed are investigated experimentally as well as by numerical simulations. It isshown that three-dimensional resonances in the solid structure of the chip stronglyinfluences the resonance shaping in the channel.

v

List of Papers

Paper I J. Hultström, O. Manneberg, K. Dopf, H. M. Hertz, H. Brismar andM. Wiklund. “Proliferation and viability of adherent cells manipulatedby standing-wave ultrasound in a microfluidic chip”, Ultrasound Med.Biol. 33, 145-151, 2007.

Paper II J. Svennebring, O. Manneberg, and M. Wiklund. “Temperature regu-lation during ultrasonic manipulation for long-term cell handling in amicrofluidic chip”, J. Micromech. Microeng. 17, 2469-2474, 2007.

Paper III O. Manneberg, S. M. Hagsäter, J. Svennebring, H. M. Hertz, J. P.Kutter, H. Bruus, and M. Wiklund. “Spatial confinement of ultrasonicforce fields in microfluidic channels”, Ultrasonics 49, 112-119, 2009.

Paper IV O. Manneberg, J. Svennebring, H. M. Hertz, and M. Wiklund. “Wedgetransducer design for two-dimensional ultrasonic manipulation in a mi-crofluidic chip”, J. Micromech. Microeng. 18, 095025 (9 pp), 2008.

Paper V O. Manneberg, B. Vanherberghen, J. Svennebring, H. M. Hertz, B.Önfelt and M. Wiklund. “A three-dimensional ultrasonic cage for char-acterization of individual cells”, Appl. Phys. Lett. 93, 063901 (3 pp),2008.

Paper VI J. Svennebring, O. Manneberg, P. Skafte-Pedersen, H. Bruus, and M.Wiklund. “Selective bioparticle manipulation and characterization ina chip-integrated confocal ultrasonic cavity”, Biotechnol. Bioeng. 103,323-328, 2009.

Paper VII O. Manneberg, B. Vanherberghen, B. Önfelt and M. Wiklund. “Flow-free transport of cells in microchannels by frequency-modulated ultra-sound”, Lab Chip 9, 833-837, 2009.

vii

List of Abbreviations

AC Alternating current

DC Direct current

(n/p)DEP (negative/positive) Dielectrophoresis

FEM Finite element method

OT Optical tweezer

PBS Phosphate buffered saline

PDMS Polydimethylsiloxane

PRF Primary radiation force

PZT Lead zirconate titanate

SRF Secondary radiation force

USW Ultrasonic standing wave

ix

Contents

Abstract v

List of Papers vii

List of Abbreviations ix

Contents x

1 Introduction and Background 1

2 Ultrasound Acoustics 52.1 Ultrasound in fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Ultrasound in solids . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Ultrasonic standing waves . . . . . . . . . . . . . . . . . . . . . . . . 92.4 Radiation forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4.1 Primary radiation force . . . . . . . . . . . . . . . . . . . . . 102.4.2 Time-harmonic fields . . . . . . . . . . . . . . . . . . . . . . . 122.4.3 Secondary radiation force . . . . . . . . . . . . . . . . . . . . 13

2.5 Acoustic streaming . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 Microfluidics 17

4 Alternative Contactless Manipulation Methods 214.1 Optical tweezers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2 Dielectrophoresis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5 Ultrasonic Standing Wave Manipulation 275.1 One-dimensional manipulation . . . . . . . . . . . . . . . . . . . . . 275.2 Multi-dimensional manipulation . . . . . . . . . . . . . . . . . . . . . 29

5.2.1 Single-frequency manipulation . . . . . . . . . . . . . . . . . 295.2.2 Multiple-fixed-frequency manipulation . . . . . . . . . . . . . 305.2.3 Frequency-modulated manipulation . . . . . . . . . . . . . . . 33

5.3 Design of USW manipulation systems . . . . . . . . . . . . . . . . . 34

x

CONTENTS xi

5.3.1 Wedge transducers and microfluidic chips . . . . . . . . . . . 365.4 Numerical simulations of ultrasonic resonances . . . . . . . . . . . . 38

5.4.1 Straight channels . . . . . . . . . . . . . . . . . . . . . . . . . 395.4.2 Non-straight channels . . . . . . . . . . . . . . . . . . . . . . 40

6 Applications of USW Manipulation in Microfluidic Systems 436.1 Batch manipulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.1.1 Flowthrough batch manipulation . . . . . . . . . . . . . . . . 446.1.2 No-flow batch manipulation . . . . . . . . . . . . . . . . . . . 44

6.2 Single-particle manipulation . . . . . . . . . . . . . . . . . . . . . . . 45

7 Conclusions and Outlook 49

Summary of Original Work 51

Acknowledgments 53

Bibliography 55

A Appendix: Walkthrough of Gor’kov 63A.1 The first three equations from first principles . . . . . . . . . . . . . 64

A.1.1 Derivation of the momentum flux tensor . . . . . . . . . . . . 64A.1.2 The second numbered equation . . . . . . . . . . . . . . . . . 65A.1.3 Derivation of the second-order pressure field . . . . . . . . . . 65

A.2 Derivation of the scattered wave field . . . . . . . . . . . . . . . . . . 69A.2.1 Derivation of the first constant a . . . . . . . . . . . . . . . . 70A.2.2 Derivation of the second constant Ai . . . . . . . . . . . . . . 72

A.3 The force potential in a non-plane wave . . . . . . . . . . . . . . . . 79

Chapter 1

Introduction and Background

This Thesis concerns the contactless manipulation of living cells and microbeads inmicrofluidic systems, i.e., systems with fluid channels or reservoirs of dimension afew hundred micrometers or smaller. The developed methods use ultrasound as themanipulation tool, more precisely the force field created by a resonant ultrasonicfield. Thus, we begin with a very brief history of the theory and practice of sonicmanipulation.

In 1866, German physicist August Kundt presented a method for measuring thespeed of sound in gases.[1] The method was based on the observation that when astanding acoustic wave was set up in a transparent tube, fine powder (Lycopodiumspores or ground cork) strewn on the bottom of the tube would be collected to-wards the pressure nodal planes of the sound field, enabling measurement of thewavelength. Knowing the frequency of the sound, the speed of sound in the gasin the tube could easily be calculated. The experimental setup lives on today as apopular physics experiment in high schools and undergraduate physics, bearing thename of its inventor - Kundt’s tube. However, the origin of the force is very seldommentioned when the experiment is performed at said levels, and the hand-wavingexplanation on Wikipedia [2] makes the (as we shall see, erroneous) predicion thatthe dust would move to the displacement nodes instead of the pressure nodes (as isthe actual case). Thus, we are led to suspect that the origin of the force is in factnot all that easy to grasp.

During the beginning of the 20th century, giants such as Lord Rayleigh and Bril-louin investigated the theory behind acoustic radiation pressure, i.e., the fact that asound wave (just like a light wave) can exert a time-averaged, directed pressure onan object even though the pressure in the sound field (to first order) changes signperiodically. In 1932, King wrote what came to be a seminal paper systematicallyderiving expressions for the acoustic radiation force on incompressible spherical

1

2 CHAPTER 1. INTRODUCTION AND BACKGROUND

particles.[3] King noted in the introduction to his paper that “the effects of com-pressibility . . . and viscosity . . . are not taken into account, although the analysismay be extended to include these effects”. However, it was not until 1955 that theeffects of compressibility of involved materials were investigated by Yosioka andKawasima [4], and viscosity came to take even longer. In 1962 Gor’kov wrote ashort (only 2.5 pages) paper deriving the expression for the force on a compressiblesphere in a resonant sound field [5] that most experimental physicists use as theirstarting point today. The last theorist in the area to be mentioned in this very briefbackground of the theory of the field will be Doinikov, who during the last decadeof the 20th century extended the theory to include, e.g., viscosity [6] and thermaldissipation effects [7].

Many experimental studies have been conducted to verify the theory and developapplications thereof. As the focus of this Thesis is on ultrasonic manipulation inmicrofluidic systems, the reader interested in the history of acoustic manipulationin macro-scale systems, other usages of ultrasound in cell-biological applications, oracoustic levitation, is urged towards the literature on said subjects, such as Refs.[8–10].

Microfluidic systems have been around for millions of years in nature - capillaries inbiological organisms are a nice example. It would seem that the first “microfluidic”system in which particles were manipulated with ultrasound actually was a nature-made one; blood vessels. Dyson et al. reported on being able to stop blood cellsbut not the serum in blood flow in living tissue in 1971.[11] When it comes tomanipulation in man-made microfluidic systems, the field really took off in the late90’s and early 2000’s, as the field was developed more or less in parallel by, e.g., thegroups of Hawkes, Hill, and Coakley in Great Britain, Dual in Switzerland, Benesin Austria, and Laurell and Hertz, both in Sweden. For an extensive list of workdone during this period, see, e.g., the references in the review papers [12–14].

In the current ultrasound manipulation group at KTH in Stockholm, the work inmicrofluidic systems was started by Hertz and Wiklund in the early 2000’s, withthe doctoral Thesis work by Wiklund [15] (preceded by a 1995 paper by Hertz[16]). The present Thesis work started out under the auspices of the EuropeanCommission project “CellPROM”, aiming to construct an automated microfluidicplatform for assaying and directed differentiation of stem cells [17]. This Thesisfocuses on the design and operation of chip-transducer systems, and on creatingmanipulation functions that can be used for a variety of bio-assays using function-alized microbeads and/or living cells. The aim has been to create force fields intwo or three dimensions and spatially confine these fields to pre-decided parts ofthe microfluidic system.

The Thesis outline is as follows: Chapter 2 aims to give a very brief outline ofthe theory of ultrasound acoustics, and introduce the radiation forces used forthe manipulation. In Chapter 3, the microfluidic principles most central to the

3

present work are presented. Chapter 4 deals with contactless particle manipulationmethods other than ultrasound. Chapter 5 is dedicated to ultrasonic standing wavemanipulation, the chip-transducer systems used and numerical simulations thereof.Lastly, Chapter 6 gives some application examples of ultrasonic manipulation inmicrofluidic systems. A detailed walk-through of the seminal paper [5] by Gor’kovis included as an Appendix.

Chapter 2

Ultrasound Acoustics

Sound can, in a very general way, be described as the propagation of a deviationfrom static conditions in a mechanical property of a medium. Most often, thisproperty is taken to be displacement or velocity of a medium particle as a functionof time and space (in acoustics, “particle” is understood to mean a volume elementof very small size, but large enough to retain thermodynamic properties), or stressesand strains, which in the simpler case of a fluid medium would give us the soundpressure field. However, it is possible to use, e.g., density variations instead ofpressure variations (and indeed in first order calculations the transition betweenthem is trivial), but it is much less commonly done. Ultrasound is simply a case ofsound where the frequency (assuming a harmonic time-dependence, as will be thecase throughout this text) is greater than the hearing threshold for a human. This,of course, varies from person to person, but the ultrasonic regime is generally takento begin around 20 kHz. The exact lower limit is somewhat of a moot point in thistext anyway, as we shall be working with frequencies in the range of 1-10 MHz. Aswe shall see, sound behaves somewhat differently in solids and fluids, with fluidsbeing the mathematically more simple case. Thus, we begin with a sound in a fluidmedium.

2.1 Ultrasound in fluids

The main reason that the description of sound in a fluid medium (liquid or gas) ismathematically simpler than that for a solid is the fact that fluids, in contrast tosolids, deform more or less continuously under shear stresses. This means that theonly stress that can exist to any greater degree is normal stress, which most often istermed pressure. Here, one must take care to separate the pressure field induced bythe presence of a sound field from the equilibrium pressure in the fluid such as the

5

6 CHAPTER 2. ULTRASOUND ACOUSTICS

hydrostatic pressure. We shall assume this to be constant throughout the volumeof our fluid and, thus, by “pressure” mean the sound pressure. We shall also assumethat the bulk velocity of our fluid, in the case it is flowing, is much smaller thanthe speed of sound, and by “velocity field” in this Section mean the velocity fieldimparted to the fluid by the sound. The basic acoustic theory presented in this andthe following Section is based largely on the book by Cheeke [18], but can be foundin any basic textbook on the subject.

Anticipating the practicality of a single scalar entity to describe the sound field, wenow introduce the (scalar) velocity potential ϕ, which relates to the pressure andvelocity fields as

v (r, t) = ∇ϕ (r, t)

p (r, t) = −ρ ∂∂tϕ (r, t) ,

(2.1)

where v is the velocity at position r and time t, p is the (sound) pressure and ρ is the(bulk) density of the fluid. It might be of interest to note that the second equationis a first-order approximation, as is shown in the Appendix. It can be shown thatthe velocity potential satisfies the expected wave equation for any entity proper fordescribing the sound field, so we have that

∇2ϕ = 1c2∂2ϕ

∂t2. (2.2)

Here, c is the speed of sound in the medium. This of course means that the entiremachinery of basic wave mechanics carries over and can be used.

In what follows, the reader is assumed to have some previous familiarity with con-cepts such as plane waves, standing waves, and so on. It should also be mentionedthat we have now neglected effects of viscosity entirely. If the medium is assumed tobe viscous, the viscosity will give rise to damping of the sound field due to viscouslosses (heating) in the fluid. However, for water-like substances at MHz frequenciesover the distance scales relevant to us (i.e., hundreds of µm), this effect will be smalleven when taking into account the fact that we might be interested in thousandsor tens of thousands of roundtrips in such a resonator.[19] Viscous properties canhowever influence the expression for the force on a particle in a standing wave, aswe shall briefly discuss below. Effects of fluid viscosity also appear in a more impor-tant context for this work, acoustic streaming. This phenomenon will be discussedin Section 2.5.

2.2 Ultrasound in solids

When considering the propagation of sound in a solid material, the descriptionmust necessarily be more mathematically complex. Apart from the compressional

2.2. ULTRASOUND IN SOLIDS 7

(longitudinal) waves that exist in a fluid, a solid can uphold shear (transverse)waves. If we also, in addition to bulk waves, i.e., waves travelling in an infinite (verylarge), solid, would like to include effects taking place at the boundary of a half-infinite solid, or in thin solid plates, a plethora of phenomena appear. This Sectionis not intended to cover all of these and the interested reader is recommended togo to the literature, e.g., Ref. [18], on which the following is based. The increasednumber of possible polarizations of the wave in three dimensions makes the scalarpotential description from the previous Section incomplete. The traditional wayto solve this in a solid is to express the (vectorial) displacement field s (r, t) in thesolid as a sum of a divergence and a rotation, so that we have

s (r, t) = ∇φ (r, t) +∇×ψ (r, t) , (2.3)

where we have introduced the scalar and vector displacement potentials φ and ψ.These entities are nicely coupled to the longitudinal and transverse displacementcomponents sL and sT :

sL = ∇φsT = ∇×ψ.

(2.4)

This can be understood slightly heuristically by noting that, from basic vectoranalysis, we have that

∇× sL = ∇× (∇φ) ≡ 0∇ · sT = ∇ · (∇×ψ) ≡ 0,

(2.5)

the interpretation of which is that sL can only be connected to changes in volumeof an element - not angle between elements or rotations, and vice versa for sT .In fact, in bulk material, both potentials fulfill wave equations, but with differentspeeds of sound; the aptly named longitudinal and transverse (or shear) speeds ofsound cL and cT :

∇2φ = 1c2L

∂2φ

∂t2

∇2ψ = 1c2T

∂2ψ

∂t2.

(2.6)

Figure 2.1 shows the displacement fields for longitudinal (center) and shear (bot-tom) waves in a deformed-grid diagram covering two wavelengths. The undeformedsolid is shown at the top for comparison.

As previously mentioned, if the solid in question is, e.g., only half-infinite, surfacephenomena such as Rayleigh waves, waves guided along the surface of the solid,might appear (see, e.g., Ref. [18] Chapter 8). However, a microfluidic chip struc-ture, such as those to be considered in this Thesis, has a thickness of the order of


x

y

Figure 2.1: Schematic of bulk waves in a solid; longitudinal (middle) and shear (bottom)waves travelling in the x direction. The top diagram shows the undeformed solid forcomparison. Bold lines indicate planes of zero displacement.

x

yd

Figure 2.2: Schematic of zero-order Lamb modes propagating in the x direction; unde-formed plate (top), compressional mode (middle), and flexural mode (bottom). Displace-ment amplitudes are exaggerated for clarity.

2.3. ULTRASONIC STANDING WAVES 9

the wavelength of the sound. Hence, we need to consider propagation of sound inthin plates.

The propagation of sound in thin plates, known as Lamb waves [20], is a mathemat-ically fairly cumbersome topic which nonetheless is well understood. For a rigorousand extensive treatment see, e.g., Ref. [21]. Here, it will suffice to state some basicproperties of such waves. For sake of simplicity, we shall consider an infinite thinplate of thickness d, and bear in mind that the finite extension of a microfluidicchip will impose further restrictions on what modes will appear due to resonanceconditions in the dimensions along the chip surface. Firstly, Lamb modes come intwo distinctive varieties: Flexural (shear, antisymmetric) and extensional (longitu-dinal, symmetric), as can be seen in Figure 2.2, showing the lowest order flexuraland compressional modes propagating in the x direction. Secondly, Lamb modesare strongly dispersive, with the mode of order n (except the zero-order modes,which exist at arbitrarily low frequencies) having a lower cut-off frequency set bythe condition that d = nλ

2 where n is a positive integer. It is important to realizethat once the frequency is above the cut-off for a certain mode, the actual displace-ment field in the plate will be a superposition of that mode and the lower modes,sometimes making it very hard indeed to distinguish “pure” higher modes. In thecontext of this Thesis, basic knowledge of Lamb modes will be important whenwe attempt to analyze the displacement field in the solid chip structure throughinterpretation of simulation results, cf. Section 5.4. We now move on to considerresonant fields in fluids - standing waves.

2.3 Ultrasonic standing waves

This Thesis concerns use of ultrasonic standing wave (USW) fields for manipulationof microparticles, so this section gives a very brief introduction to resonant fields andstanding waves. A standing wave field in this context is taken to be one where thespatial and time-dependent parts of the field separate. Consider first the simplestof waves, a plane running wave travelling in the positive x direction in a fluid. Thiswave can be characterized by, e.g., its pressure amplitude p0, its angular frequencyω = 2πf , and its wave number k = 2πλ−1, thus:

p (x, t) = p0 sin (ωt− kx) . (2.7)

The simplest example of a standing wave is then realized by considering the super-position of such a wave with an identical wave running in the other direction. Basictrigonometry shows that in this case, the total wave field will be

ptot (x, t) = p0 sin (ωt− kx) + p0 sin (ωt+ kx)= 2p0 sin (ωt) cos (kx) ,

(2.8)


i.e., a field with twice the amplitude and the temporal part separated from thespatial part. We shall call this a spatially harmonic standing wave. As it will beshown below that the spatial part of the sound field in a microfluidic channel is notnecessarily harmonic, especially not in several directions simultaneously, we take“standing wave” henceforth to mean simply any sound field where the temporal partis separated from the spatial, but assume the temporal part to still be harmonic intime, so we can write the pressure P in a general standing wave field as

P (r, t) = p (r) sin (ωt) . (2.9)

2.4 Radiation forces

As has been previously stated, a particle (we now use “particle” as meaning a smallphysical body) immersed in a fluid medium and subjected to a sound field will alsobe acted upon by time-averaged (steady-state) forces which are due to the presenceof the sound field. These forces are termed “radiation forces”, and this Sectionaims to describe the two most central to this Thesis work: The primary radiationforce (PRF) FPRF in an USW in Section 2.4.1, and the (often weaker) secondaryradiation force (SRF) FSRF, also termed the Bjerknes force in Section 2.4.3. Pre-emptively, we state that in the case of polymer microbeads or cells immersed in awater-like medium, the PRF will tend to drive the particles towards the pressurenodes of the field, where the SRF will be an attractive interparticle force. Figure2.3 summarizes these effects graphically.

During the last century, authors have discussed different interpretations of whatthe radiation force, most often on a flat surface and using plane waves, should beinterpreted as in terms of other quantities (cf., e.g., the 1982 review on the subjectby Chu and Apfel [22]). Others taking a more pragmatic approach to the issue andsimply derive the expression for the force (cf., e.g., Refs [3–7]). In this work, weshall concentrate on the latter approach and leave the interested reader to form herown philosophical opinion.

2.4.1 Primary radiation force

This Section will deal with the PRF in standing-wave fields only. It has been shownthat the magnitude of the radiation force on a small particle in a running planewave is orders of magnitude smaller [4, 6], and hence not of interest in the presentwork. The most often-used expression for the force in an arbitrary sound field notresembling a running wave is the one given by Gor’kov. In his 1962 paper [5],Gor’kov gives the (time-averaged) PRF on a particle of volume V in an inviscid

2.4. RADIATION FORCES 11

v, p

x

pv

t1 t 2 t3

PRFsSRFs

a) b) c) d)

Figure 2.3: Schematic summary of PRF and SRF: a) Pressure and velocity fields ina one-dimensional standing wave. b-d) Location of particles at three consecutive timest1 − t3. PRFs are drawn as black arrows, SRFs as gray arrows. The lengths of the arrowsare adjusted for clarity, and omitted from d) altogether.

fluid with density ρ and speed of sound c as the gradient of a potential functionthus:

FPRF = −∇U = −∇V(

f1

2ρc2

⟨p2 (r, t)

⟩T− 3

4ρf2⟨v2 (r, t)

⟩T

), (2.10)

where the brackets 〈· · · 〉T denote time-averaging, and where f1 and f2 are contrastfactors describing the effect of the relevant material parameters of the medium andfluid, defined as

f1 = 1− ρc2

ρpc2p

= 1− βpβ,

f2 = 2 (ρp − ρ)2ρp + ρ

.

(2.11)

Here, index “p” means parameters pertaining to the particle, and β is the (isen-tropic) compressibility. As a numerical example relevant to this Thesis, we havefor cells (erythrocytes) in a water-like fluid,with values for the cells taken fromGherardini et al. [23], that

ρp = 1094 kg/m3 βp = 3.4 · 10−10 ms2/kgρ ≈ 1000 kg/m3 β ≈ 4.5 · 10−10 ms2/kg,

which gives the contrast factors f1 = 0.24 and f2 = 0.06. For a pressure amplitudeof 0.85 MPa (as in Paper I) and a particle/cell with a diameter of ∼ 10 µm, this


would in a spatially harmonic standing wave (cf. Eq. 2.8) give a maximum force of(cf. Eq. 2.18) some tens of pN at frequencies of a few MHz. Using, e.g., a stronglyfocused resonator (as in Paper VI) this can be increased to a few hundred pN.

For the reader interested in a complete derivation of Gor’kov’s equation (Eq. (2.10))for the PRF, a walk-through of the paper can be found in the Appendix of thisThesis. Here, we shall just state that the derivation is done by considering theflux of momentum through a surface surrounding the particle, and carrying outthe calculations using a second-order expression for the sound field. Using the“normal” first-order expressions yields a time-averaged force of zero, as all fieldswill be harmonic in time. The total field is expressed as a sum of the incident fieldand the scattered field, the latter taken to be approximately equal to the first twoterms in a multipole expansion. It is also important to note that the calculations aredone in an inviscid fluid, meaning that no effects of viscosity are accounted for, andneither is heat conduction. These derivations have been carried out by Doinikov[6, 7] but the reader is warned that there is a large quantity of mathematics in thosepapers. With this said, it should be noted that in the applications discussed herein,i.e., manipulation of living cells and polymer microbeads, good agreement betweentheory and experiments is found by entering first-order fields (not second-order)into the equation for the force as given by Gor’kov (thus also disregarding viscouseffects).

2.4.2 Time-harmonic fields

For the case of a time-harmonic field, it is possible to carry out the time-averagingin Eq. (2.10) explicitly, and rewrite the expression into one giving the force as afunction of the pressure (or velocity) field only, as done in Paper IV. This facilitates,e.g., numerical calculations based on a simulated pressure field as discussed inSection 5.4, and done in Papers IV-VI. Let us start by assuming a velocity potentialthat separates in time and space, as discussed in Section 2.3:

Φ (r, t) = ϕ (r) cos (ωt) , (2.12)

with ω = 2πf being the angular frequency and ϕ (r) the spatial velocity potentialdistribution. This yields a pressure field according to Eq. (2.1):

P (r, t) = −ρ ∂∂t

Φ (r, t) = −ρωϕ (r)︸︷︷︸p(r)

(− sin (ωt)) , (2.13)

which we now want to use to express our velocity field as a function of. We have,also from Eq. (2.1), that

Φ (r, t) = ∂

∂t

∫Φ (r, t) dt = −1

ρ

∫P (r, t) dt, (2.14)

2.4. RADIATION FORCES 13

giving us a velocity field as the gradient of the last integral equal to

v (r, t) = −∇1ρ

∫P (r, t) dt

= −1ρ

cos (ωt)ω

∇p (r) .(2.15)

We thus have both the velocity and pressure fields separated in time and space,and expressed as functions of the spatial pressure distribution p (r). Carrying outthe time-averaging now yields

⟨P 2 (r, t)

⟩T

= p2 (r) 1T

T∫0

(− sin (ωt))2dt = 1

2p2 (r) and

⟨v2 (r, t)

⟩T

=(−1ρω

)2(∇p (r))2

T∫0

cos2 (ωt) dt = 12ρ2ω2 (∇p (r))2

.

(2.16)

Entering these two expressions into Eq. (2.10) and carrying out some simplifica-tions, we end up with a potential and force according to

U = V β

4

[f1p

2 (r)− 3f2

2k2 (∇p (r))2]

and

FPRF = −V β2

[f1p (r)∇p (r)− 3f2

2k2 (∇p (r) · ∇)∇p (r)],

(2.17)

respectively. Here, k is the wavenumber of the sound field, defined as k = ωc−1.This force, then, is the primary force used for the manipulation of microbeads andcells throughout this Thesis.

To get a feeling for how the force works, the classic example is to consider a one-dimensional spatially harmonic standing wave. Assuming a pressure field p (x) =p0 sin (kx) and using Eq. (2.17), some simple calculations yield a force field

FPRF = −V β4 p20k

(f1 + 3f2

2

)sin (2kx) . (2.18)

However, it is important to note that the derivation is done for a single particle.Thus, the equations do not contain any effect of particle-particle or particle-wallinteractions through scattered fields. The first of these is instead the topic of thenext Section.

2.4.3 Secondary radiation force

When more than one particle is present in the fluid, as is very often the case,each particle will produce a scattered sound field which will influence the other


particles. This interaction gives rise to the secondary radiation force (SRF) [24,25], often called the Bjerknes force (also secondary Bjerknes force or König forcedepending on literature). Assuming, just as for the PRF, that the particles aresmall compared to the wavelength (particle radius Rp λ), and additionally thatthe interparticle distance, measured center-to-center, is also small compared to thewavelength (d λ), it has been shown by Weiser et al. [26] that the SRF can bewritten as

FSRF = 4πR6p

((ρp − ρ)2 (3 cos2 α− 1

)6ρd4 v2 (x)− ω2ρ (βp − β)2

9d2 p2 (x)), (2.19)

where α is the angle between the line connecting the particle centers and the “prop-agation direction” of the sound field, and we have assumed a one-dimensional stand-ing wave in the x direction. By convention, a positive SRF means a repulsive force.We also note that the force is inherently short-ranged, so that it comes into playfirst when the particles are closely spaced. As the particles in our applicationswill tend to gather quickly in the pressure nodes due to the PRF, the second termin the parenthesis can be taken to be negligible, and the SRF becomes attractive(as α ≈ 90 when the particles are close to the pressure nodal plane). Thus, thephysical effect of the SRF is to create closely packed aggregates in the nodal plane,as shown in, e.g., Paper I.

2.5 Acoustic streaming

Acoustic streaming is a phenomenon characterized by static (time-independent)flow patterns caused by the presence of a sound field in the fluid. The phenomenonis usually split into three types [27] with different inherent length scales: Schlichtingstreaming, Rayleigh streaming, and Eckart streaming, the latter also known as the“quartz wind”. All types of streaming have their origin in viscous losses in the fluid,the differences in length scale stemming from where the losses occur.

Schlichting streaming [28] is a name given to streaming occuring in the viscousboundary layer close to a surface and has vortices of a scale much smaller thanthe acoustic wavelength. In systems for ultrasonic manipulation of microparticles,this type of streaming does not, to the best of our knowledge, have any noticeableeffect on the manipulation, and thus will be disregarded henceforth. Rayleigh-typestreaming [29], stems from losses in boundary layers driving streaming vortices onthe scale of a quarter wavelength outside the boundary layer itself [30, 31]. Theinherent length scale of the streaming means that it can greatly influence the be-havior of the fluid and thus the particles, in a microfluidic system for ultrasonicmanipulation. Eckart streaming [32] is large-scale (container-scale) streaming dueto absorption in the fluid. Rather than giving a vortical pattern like Rayleigh

2.5. ACOUSTIC STREAMING 15

streaming, Eckart streaming typically gives a flow in the direction of the propaga-tion of the sound. In a closed system, however, counterflows will of course occur asthe fluid cannot escape the cavity. It has been shown that Eckart streaming canbe minimized in several ways, such as minimizing the size of the resonator (thuspreventing the Eckart streaming to build up), or by designing a resonator contain-ing acoustically transparent foils [16, 33]. Figure 2.4 illustrates the length scalesand vortical pattern of Rayleigh and Eckart streaming. Note that the Rayleighstreaming will always be directed “outwards” in the pressure nodal plane.

For applications where it is important to stably trap particles using ultrasound,acoustic streaming is often considered an unwanted effect, as the streaming flowgives drag forces (Stokes’ drag) on the particles according to (assuming sphericalparticles of radius Rp) FStokes = 6πηRpv, where η is the viscosity of the fluid andv the velocity of the same (cf. Chapter 3). As this force is proportional to theradius of the particle, and the PRF is proportional to the volume, we see that forlarger particles the PRF will dominate while for smaller particles the Stokes’ dragwill dominate. The particle size limit where this happens depends on the geometryof the resonating channel, which has a large influence on the amount of streaming,but it is generally around 1 µm for polymer particles in water-like media in systemsof the kind discussed in the Thesis (cf. Ref. [34] and Paper VII). This effect can beused for characterization both of ultrasonic force fields as done in Paper III, andof fluid flows while manipulating particles as done in Paper VII. In the latter case,1-µm particles were used as fluid tracers while manipulating 5-µm particles. As alast note, the phenomenon of acoustic streaming can also be used as a desired effect,e.g., to create acoustic micromixers.[35] It has also been shown to be employable toincrease the efficiency of bead bio-assays by using the mixing property to enhancebinding rates.[36]

16 CHAPTER 2. ULTRASOUND ACOUSTICSd

> > l

a) b) Sound source

Reflector

d =

l/2

Sound source

Pres

sure

nod

eFigure 2.4: Two different types of acoustic streaming: a) Cavity-scale Eckart streaming.b) Rayleigh streaming with λ4 -scale vortices in a resonator.

Chapter 3

Microfluidics

This chapter presents some aspects of microfluidics pertinent to the Papers under-lying this Thesis. Loosely defined, a microfluidic system is any fluidic system wherethe fluid is confined in at least one dimension to the micrometer domain. Today,microfluidic systems are often the central part in what is called a lab-on-chip (LoC)or micro total analysis system (µTAS) [37]. Due to scaling laws (cf. below), suchsystems are attractive for a number of reasons, including short reaction and anal-ysis times, low sample and reagent volumes, and laminar flows. Additionally, theyalso often show low power consumption and manufacturing cost.

For a good review paper of the field of microfluidics and a very nice book on thesubject, the reader is recommended Refs. [38] and [39]. From the perspective ofconducting physical and chemical experiments in microsystems, the most importantfeature are the scaling effects (for an extensive table, see Ref. [39] Section 1.2).As an important but simple example, take surface- and volume-dependent forces:Examples of volume forces are, e.g., inertia and gravity, while surface tension andviscosity depend on surface properties but not volume. In “every-day life” we arevery used to dealing with volume forces, but as we decrease the length scale d of asystem, we see that the ratio between surface and volume goes to infinity, as it isproportional to d−1. Thus, surface forces will dominate and give rise to importantproperties of microfluidic systems. Of these, the most central might be that viscouseffects tends to dominate over inertial in flows, rendering the flows laminar.

A laminar flow (as opposed to a turbulent flow) is characterized by the fluid flowingin “sheets” (laminae) with no intermixing of fluid between adjacent laminae, asindicated in Figure 3.1. The most important parameter to predict whether a flowwill be laminar or turbulent is the Reynolds number Re, generally defined for afluid of (dynamic) viscosity η and density ρ as

Re = ρv0d0

η, (3.1)

17

18 CHAPTER 3. MICROFLUIDICS

Figure 3.1: FEM simulation of flow in an arbitrary microfluidic system with Remax ≈ 1,showing laminar flow. The grayscale indicates flow speed, and the white lines are sixstreamlines (lines of constant flow speed).

where v0 is a characteristic flow velocity, and d0 is a characteristic length scaleof the system. Turbulent flows occur at Re larger than about 4000, and flowsat Re larger than about 1500 are often termed transitional flows. For a typicalmicrofluidic system, the Reynolds number is often around or smaller than unity,giving a laminar flow and greatly simplifying flow profile calculations.

The laminar flows in microfluidics means that mixing is more or less controlled bydiffusion. Albeit diffusion is a slow process in the macroscopic world, the smalllength scales of microfluidics, together with different schemes for maximizing the“contact area” between fluids with different solutes to be mixed, makes mixingpossible. As was mentioned in Section 2.5, acoustic streaming can be utilized tothis purpose, as can the radiation force in the case of the fluids showing acousticcontrast according to Eq. (2.11) [40]. A review of different mixing schemes can befound in Ref. [41]. It should be mentioned that the microbeads employed in theexperiments this Thesis is based on are too large for diffusion to be of importanceto their movements in the arragements considered. Instead of being transported bydiffusion, they are moved by the ultrasonic PRF or by the Stokes’ drag force, whichfor a particle of radius Rp in a flow with low Reynolds number can be expressed as

FStokes = 6πηRpv, (3.2)

where v is the velocity of the flow. This drag force is what carries the particles alongin a fluid flow, and also the force that counteracts the PRF, very quickly giving theparticles a constant speed. The time constant for this force equilibration is on theorder of 10−7− 10−5 s in microfluidic systems. The fastness of this process enablesmeasurements of the PRF based on measurements of particle velocities using microparticle image velocimetry (PIV) [42], as done in Papers.

The last force we shall concern ourselves with here is gravity, which is a volume forceand thus often disregarded in microfluidic systems. However, when the particles in

19

a medium are heavier than the medium, as is the case with cells and polymer beadsthey will, naturally, slowly sink. It can be shown [39] that the sedimentation timeassuming terminal velocity is reached instantaneously for sedimentation a verticaldistance h is given by

τsed = 9ηh2 (ρp − ρ)R2

pg. (3.3)

For the largest particles considered here, this time will be approximately 20 seconds,meaning that for manipulations taking longer than that, a vertical ultrasonic force(“levitation”) should be employed.

Chapter 4

Alternative ContactlessManipulation Methods

This Thesis concerns the use of ultrasonic standing waves as a microparticle manip-ulation tool, a topic which will be covered in the remaining Chapters. This Chapteraims to give a brief overview of two alternative and widely used contactless methodsfor manipulating micron-sized particles or living cells in microfluidic systems; opti-cal tweezers (OTs, Section 4.1) and dielectrophoresis (DEP, Section 4.2). We shallnot herein discuss, e.g., physical microtweezers or micropipettes (not contactless),nor the use of fluid flow to move particles. The latter method is employed in muchof the work this Thesis builds on, but is then based on the Stokes’ drag force (Eq.(3.2)) and additionally perhaps not to be considered contactless. Two contactlessmethods in addition to OTs and DEP that do deserve a short mention, however,are electrophoresis and magnetic manipulation.

Electrophoresis [43] differs from electro-osmosis in that electrophoresis is the movingof charges or particles with charged surfaces (which might be very small, such asdissolved ions) in a medium, while electro-osmosis is the moving of the mediumitself. Electrophoresis has found great use in, e.g., separation techniques such ascapillary electrophoresis [44], gel electrophoresis [45], combinations thereof, andfree-flow electrophoresis [46]. Manipulation of living cells with electrophoresis is lesscommon, as the method relies on the object to be manipulated having an overallelectric charge large enough for the electrostatic force to have a significant effectcompared to other involved forces such as gravity and Stokes’ drag (Eq. (3.2)).Thus, it is a method mostly used for smaller particles such as macromolecules.

Magnetic manipulation, or magnetophoresis [47], uses magnetic fields to createforces on particles. An obvious requirement for this to work is the presence ofeither an induced or permanent magnetization in the particle to be manipulated.

21

22 CHAPTER 4. ALTERNATIVE CONTACTLESS METHODS

Biological matter, as it turns out, very seldom is magnetic. Thus, this methodbecomes indirect in that, e.g., most cells have to take up magnetic particles be-fore they can be magnetically manipulated. Biofunctionalized beads, however, areavailable loaded with magnetic nanoparticles or with magnetic cores, and the use ofmagnetophoresis in microfluidics and bio-assays is not at all uncommon [48]. Fromelectric and magnetic fields, we now turn to electromagnetic fields: The use of lightfor particle manipulation.

4.1 Optical tweezers

The use of optical fields to manipulate microparticles was pioneered in the 1960’s byAshkin et al., who in 1986 published the first paper on what today would be calleda single-beam optical tweezer (OT) [49]. The very next year, both optical trappingof single viruses [50] and optical trapping using an IR laser, greatly enhancing theviability of trapped cells [51], were demonstrated. Today, the single-beam OT isstill a useful tool, but it has been complemented by several more complex waysof creating the optical traps and manipulators. Examples include using severalbeams of light or optical fields created by spatial light modulators of differenttypes, enabling quite complex three-dimensional field geometries, multiple-particlemanipulation, and controlled rotation of trapped objects. A thorough and easy-to-read review of optical manipulation has been written by Jonáš and Zemánek.[52]

For micron-sized particles (particles of sizes comparable to or larger than the opticalwavelength), the force can in theory be evaluated using the same starting point asfor the acoustic case (cf. Section 2.4.1 and the Appendix); by evaluating the fluxof momentum through a closed surface containing the particle. However, if theparticle is of the same scale or larger than the optical wavelength, Mie scatteringtheory must be used. The calculations involved can become quite fearsome, andnumerical methods are often used. For particles much smaller than the opticalwavelength, Rayleigh scattering theory can be employed, and the general resultsapply qualitatively also to larger particles.[52] Here, we shall simply state some ofthe results without calculations.

Let us assume the particle to have a higher index of refraction than the surroundingmedium. The optical force can be split into three distinct components: The gra-dient force, the scattering force and the absorption force. In a ray-optical model,these correspond to momentum transfer by reflection, refraction and absorption,respectively.[53] We will asssume the absorption force to be negligible in compari-son to the other two. The gradient force, which is proportional to the gradient ofthe electric field squared, will be directed towards regions of high intensity, e.g., theaxis of a Gaussian beam or a focus. The scattering force will always be directedalong the direction of propagation of light. Thus, in a (Gaussian) beam of constantcross-section, a particle will be pulled towards the axis of the beam by the gradient

4.1. OPTICAL TWEEZERS 23

force and propelled along the beam by the scattering force as indicated in Fig.4.1a. In the single-beam OT, illustrated in Figs. 4.1b-c, a tightly focused beamis used. This creates high field gradients in the axial direction in the vicinity ofthe focus, enabling stable trapping of the particle at the point where the scatteringforce balances the gradient force. Note that this point will never be in the focus,but slightly displaced from it in the direction of the beam propagation as seen inFig. 4.1c. It should also be mentioned that this setup relies on the index of re-fraction of the particle to be higher than that of the medium. To trap low-indexparticles, more complex optical fields must be used, such as a beam with a centraloptical singularity [54].

Incident beam

Fgrad

Fscat

a) b) c) Incident beamIncident beam

Fgrad

Fscat

Fgrad

Fscat

Figure 4.1: Simple examples of optical manipulation: a) An incident beam of light withradially decreasing intensity impinges on a spherical particle (black ring). The gradientforce Fgrad pulls the particle towards the axis, and the scattering force Fscat pushes itin the direction of propagation. The dashed line schematically shows the path of theparticle. b-c) A single-beam OT: As in a), but the tight focus gives high field gradientsalso in the axial direction around the beam waist. The particle is trapped at a locationslightly “below” the focus, where the gradient and scattering forces balance.

By tuning the laser power, it is possible to tune the force exerted. Typical laserpowers range from a few mW up to almost 1 W, and the forces involved are inthe range of fN up to hundreds of pN.[52] Main advantages of using OTs for mi-cromanipulation compared to using ultrasound include its higher spatial precisionand the possibility to accurately manipulate considerably smaller particles (downto tens of nanometers [52]). Drawbacks include that the instrumentation needed ismore complicated, especially for the more complex manipulation, and more expen-sive (sometimes by orders of magnitude). The effect is also spatially localized inthe system which might be an advantage or a drawback depending on the targetapplication. It should also be mentioned that OTs and ultrasonic manipulation eas-ily could be employed in the same microfluidic system, with no obvious theoreticalobstacles such as too large crosstalk or interference between the two kinds of fields.

24 CHAPTER 4. ALTERNATIVE CONTACTLESS METHODS

4.2 Dielectrophoresis

Dielectrophoresis (DEP) can be defined as “the movement of a charge-neutral par-ticle in a fluid induced by an inhomogeneous electric field”.[55] Like OTs, the tech-nology was developed during the second half of the last century [56, 57] and adaptedfor manipulation of living cells in microfluidic systems during the 1990s (see e.g.,[58]). While both DC and AC fields can be used for DEP, we will here focus onlyon AC-field DEP. An advantage of using (time-harmonic) AC fields is the lack oftime-averaged effects AC fields have on charges such as ions in the solution. Addi-tionally, AC-field DEP works well on particles with non-zero electric conductivity.The (time-averaged) dielectrophoretic force FDEP on a particle of volume V arisesfrom differences in the frequency-dependent polarizability and conductivity betweenthe particle and the surrounding fluid, and can be written as [55]

FDEP = 3V ε2 Re fCM∇

(E2rms

), (4.1)

where ε is the permittivity of the fluid, “Re· · · ” means real part and the fre-quency dependence and differences in electric properties are included in the so-calledClausius-Mosotti factor fCM defined as

fCM = εp − εεp + 2ε , where εp = σp + iωεp and ε = σ + iωε. (4.2)

Here, σ is the electric conductivity, index p pertains to the particle and indexlessvariables to the fluid. Thus, fCM plays a role analogous to the acoustic contrastfactors (Eq. (2.11)). It should also be pointed out that Eq. (4.1) is valid in dipoleapproximation, i.e., higher-pole moments are considered small. We can see fromthe above equations that a prerequisite for effective DEP is high gradients in theelectric field. Basic electric field theory tells us that one way to achieve this is touse small sources, i.e., small electrodes. To realize this in a microfluidic structure,small built-in electrodes can be integrated into the chip (cf., e.g., [59]). Dependingon the sign of fCM , the particles will be attracted to or repelled from the electrodes(termed positive dielectrophoresis (pDEP) and negative dielectrophoresis (nDEP),respectively). By using nDEP and several electrodes a stable three-dimensional trapfor particles can be realised [60] (as shown in Fig. 4.2). By controlling the voltageand phase relationship between the electrodes, controlled rotation and deformationof trapped aggregates or soft particles can be achieved.

Modern microfabrication techniques also allow the creation and precise control ofarrays of electrodes, giving the possibility of manipulation along predeterminedpaths in two dimensions by sequential actuation as shown in, e.g., Refs. [61] and[62]. As the driving frequencies (a few MHz) and voltages (up to tens of volts)used for such applications are about the same as for ultrasonic manipulation inmicrofluidic systems, and the commonly used channel dimensions roughly the same,

4.2. DIELECTROPHORESIS 25

Figure 4.2: 3D-caging of a biological cell by DEP. Four of eight electrodes are visible(dark areas). Image courtesy of Magnus Jäger, Frauenhofer IBMT, Germany.

it is possible to combine the two manipulation schemes in one system.[63, 64] Theforce magnitudes are also comparable, typically in the pN range for 10-µm particles[59, 62].

An advantage of DEP over acoustic manipulation is the reachable precision andsingle-particle manipulation capabilities. However, the channels have to be madefairly shallow (20-40 µm) to generate the needed gradients in the electric field,increasing the risk of clogging, and the force is short-ranged in the sense that itdecreases very rapidly with distance from the electrodes. Furthermore, while normalcell medium shows a good electric contrast (high enough fCM ) to cells, the highconductivity means that there is significant heating of the fluid.[65] This meansthat media not suitable for long-term cell experiments must be used. In additionto this problem, there are results suggesting that electric fields at DEP-relevantfrequencies and amplitudes cause considerable stress in cells [66].

Thus, it is important to realise that contactless manipulation does not have onemethod which is simply “better” than the others, but is a vast field with differenttools suitable for different purposes. From these methods for contactless manipula-tion, we now turn to the reasearch this Thesis is built on - ultrasonic manipulation,which is the topic of the next two Chapters.

Chapter 5

Ultrasonic Standing WaveManipulation

This chapter will concern description of ultrasonic manipulation functions as wellas design considerations for, and simulations of, microfluidic systems for particleor living-cell manipulation using ultrasonic standing waves (USWs). We shall dis-cuss USW manipulation functions in one to three spatial dimensions (1D to 3D)as well as dynamic manipulation using ultrasound to transport particles along amicrochannel (Sections 5.1 and 5.2). Section 5.3 concerns the different designs thatcan be used for these manipulation puposes. In Section 5.4, the use of finite elementmethods (FEM) to simulate the radiation forces as a step in the system design andto glean deeper understanding of the transducer-chip system is discussed.

5.1 One-dimensional manipulation

The simplest chip arrangement conceivable for ultrasonic manipulation would bea long, straight channel where the USW is set up along one dimension only. Thisenables 1D focusing of particles for, e.g., concentration/sorting applications [67, 68],deposition of particles on a surface using a λ

4 -resonator [69], concentration/sequentialwashing applications [70, 71], and precise positioning of particles at the end of ofthe channel for further extraction and analysis [72–74]. In the above-mentionedmanipulation schemes, the particles are manipulated in one dimension by the PRF,and in another dimension using the Stokes’ drag (Eq. 3.2) by flowing the mediumdown the channel. Fig. 5.1 shows 1D manipulation of 10-µm polymer beads in thehorizontal (Fig. 5.1b) and vertical (Fig. 5.1c) directions compared with flowingthe beads without any ultrasound actuation (Fig. 5.1a). We note that the focusing

27

28 CHAPTER 5. ULTRASONIC STANDING WAVE MANIPULATION

field seems to have a downwards directed force component in addition to the fo-cusing force. This is further discussed in Section 5.4. The chip-transducer systemsemployed are discussed in Section 5.3.1 and also in depth in Paper IV. Of course,if this kind of 1D manipulation is desired, care should be taken when choosing thechannel dimensions so that the channel is only resonant in one direction.

a)

b)

c)

200 µm flow

Figure 5.1: 1D manipulation of 10-µm beads in a straight channel: a) The ultrasoundis off, the beads are disperserd throughout the cross-section. Note the large variations inspeed due to the zero flow velocity at the walls. b) Focusing of the beads using a singlefrequency. c) Levitation of the beads using a single but different frequency. The flow isfrom right to left in all images.

Quite often, a one-dimensional model is adopted as an approximation for the forceeverywhere in the channel in cases where the channel is straight and has constant(rectangular) cross-section. This is done in spite of the fact that it can be shown thatthe field in the channel is influenced by the chip dimensions also in the directionsalong the channel (cf. Papers IV and VII and Ref. [75]). The effect of this is furtherdiscussed in Section 5.2.3. Nevertheless, the 1D-approximation for the force is oftena good first approximation. To show why, we take from Section 2.4.1 the 1D PRF(Eq. (2.18)):

FPRF = −V β4 p20k

(f1 + 3f2

2

)sin (2kx) , (5.1)

which is, by virtue of simplicity, a good expression to use as an approximative force.The limitations hereof, especially when running a system with very low or no flows,will be discussed below. First, however, we move on to using USWs to manipulateparticles in more than one spatial dimension simultaneously.

5.2. MULTI-DIMENSIONAL MANIPULATION 29

5.2 Multi-dimensional manipulation

Multi-dimensional USW manipulation can be achieved in several different ways.Firstly, by using a single frequency signal (Section 5.2.1). This method can beemployed in, e.g., a cavity which is resonant in more than one direction, an ar-rangement using a localized vertical field (often the near field of the transducer),or by employing a focusing resonator geometry. Secondly, by using multiple fre-quencies to excite resonances in different directions (Section 5.2.2). Thirdly, byusing frequency-modulated signals (Section 5.2.3). The latter allows both for spa-tial stabilization of otherwise inhomogenous force fields and for time-dependentmanipulation in the form of flow-free transport of particles.

5.2.1 Single-frequency manipulation

In the discussion above, a single frequency was used to excite a resonance in onedirection. From here, the step is short to performing the two manipulation tasksshown in Fig. 5.1 (focusing and levitation) simultaneously by letting the channelhave a square cross-section. This would guide particles along the center line of thechannel, and is used in, e.g., Paper V. One could of course also envisage using achannel where the width and height are integer multiples of each other. A disad-vantage of these approaches is that the force fields become spatially inhomogenousthroughout the channel due to 3D resonances in the solid structure (cf. Papers IVand VII, Ref. [75] and Section 5.4), making it difficult to operate the system at lowflows rates such as fractions of µL per minute. The single-frequency approach alsomeans that it is not possible to switch the number of nodes in one direction with-out doing so in the other. These problems can be mitigated by choosing channelheight and width to be resonant at different frequencies and using dual-frequencyexcitation, as first presented in Ref. [76] and discussed in Section 5.2.2 and PaperIV.

Another example of single-frequency 2D manipulation is the arraying of particles intwo dimensions by using a chamber resonant in two directions. This chamber caneither be the channel itself (cf. Paper III), or a larger chamber built as a part of thechannel structure [34, 77]. However, results show that, as in the abovementionedcase, the arraying is significantly improved by using two different frequencies, shiftedeven by as little as 10 ppm (25 Hz) in the case of [77]. This effect is illustrated inFig. 5.2. The improvement here is due to the difference-frequency term in the totalfield increasing in frequency until the bead aggregate cannot properly “follow” thechanges in the force field. This gives the same results as time-averaging the beatingterm to zero.

The use of a localized vertical resonance, giving both levitation and retention belowor above the transducer has been employed by several authors as a simple way of


trapping cells during controlled amounts of time, as shown in Paper I and, e.g.,Refs. [78–80].

As a final example, using a focused resonator allows for trapping in 2D due tothe high pressure gradients (cf. Eq. 2.17) near the field waist either in the twohorizontal directions, as done in Paper VI (and in some sense in Papers V andVII), or in one horizontal and the vertical direction [81].

5.2.2 Multiple-fixed-frequency manipulation

As stated above, 2D manipulation becomes both more efficient and more flexi-ble if two different frequencies are used. In addition, using more than a singlefrequency opens up possibilities to design a system that performs different manip-ulation tasks in different sites in the system as well as 3D control of the particles.All Papers included in this Thesis except Paper I describe systems designed formultiple-frequency actuation. 2D arraying as described above but using two dif-ferent frequencies has been carried out in a number of settings [77, 82, 83]. Theimproved efficiency is clearly visible in Fig. 5.2.

200 µm

a) b)

Figure 5.2: 2D arraying of 10 µm polymer beads using two orthogonal sound fields: a)Using two fields of the same frequency (2.56 MHz). b) Using two fields of slightly differentfrequencies (2.56 MHz and 2.56 MHz + 25 Hz.). Images courtesy of S. Oberti, ETH Zurich(adapted from Ref. [77]).

The use of two separate fields of different frequencies to focus and levitate particlessimultaneously in a flow-through system [76], as shown in Fig. 5.3, is a powerfulmethod to avoid sample-to-wall contact causing sample contamination, channelclogging, or activation of sensitive cells. This type of 2D alignment in a channel isemployed in Papers III-VII.

The idea of separating different USW manipulation functions to different parts ofthe system is also the main topic of Paper III, where it is shown that even smalldifferences in channel width (tens of microns) can be sufficient to de-couple regions,but that the effect is more robust if larger differences are chosen. It is shown thata resonance often “leaks” into a neighbouring section of different width (with a“crossover region” of the size ∼ λ

4 ) but that the effect is negligible in flow-through


200 µm flowFigure 5.3: 2D alignment of 10 µm beads in a straight channel, using two differentfrequencies for focusing and levitation (cf also Fig. 5.1).

operation. It should also be mentioned that here, too, the frequencies should bechosen so that they are not, e.g., multiples of each other, to avoid unwanted reso-nances and cross-talk between regions of the chip.

The idea of spatial confinement of resonances also lead to the concept of ultrasonicmicrocages - a small (a few hundreds of µm long) part of the channel where particlescan be trapped in 3D and held against a fluid flow (cf. Papers V, VII and Ref. [35]).Figure 5.4 shows examples of microcage designs, simulations of force potentials, andexperimental results of particle trapping therein. FEM Simulation of the force fieldsis discussed in Section 5.4.

The top microcage in Fig. 5.4 is the main topic of Paper V. It is demonstrated that,in addition to performing 3D caging of single particles and aggregates, it is possibleto reversibly control the dimensionality of a trapped aggregate. By adjusting theamplitudes of the different fields, an aggregate can be switched from horizontal flat(2D), to compact 3D, to vertical flat (2D). It is also possible to confine a field toa larger chamber in the channel, such as the 5-mm diameter confocal resonatordescribed in Paper VI (cf. Fig. 5.11).


a)

d)

c)

b)

Figure 5.4: Simulations of force potentials (left) and expermental trapping patterns of5-µm polymer beads (right) in four different microcages. The yellow particles are fluidtracers too small to be significantly affected by the PRF. The scale bars are all 100 µm.In the simulations, blue indicates a low potential, i.e., a trapping site.


5.2.3 Frequency-modulated manipulation

As mentioned above, single-frequency actuation of a straight channel often gives aforce field which varies strongly throughout the channel. The reason for this is 3Dresonances in the solid structure of the chip. This effect can be strongly mitigatedby using frequency-modulated signals, as shown in Paper VII. Figures 5.5a-d showan example of this; four different but close single frequencies are used to actuatea straight channel with a square cross-section of 110× 110 µm2. The channel washomogeneously seeded with particles, and the ultrasound was allowed to influencethe particles for a few seconds. The experimental arrangement is described infurther detail in Paper VII. We clearly see large variations both in force magnitudeand direction. One way to remove these inhomogeneities is to sweep the signal tothe transducer over an interval of about 100 kHz around the single frequency used.This scheme gives what in principle becomes an average of the force fields at allfrequencies in the interval. Figure 5.5e shows the effect of such a modulated signal.

c)

d)e)

a) 6.85 MHz

b) 6.89 MHz6.93 MHz6.95 MHz

6.85-6.95 MHz

Figure 5.5: The effect of a 1-kHz modulated frequency sweep on the spatial force distri-bution in a straight channel: a-d) Single frequency actuation at frequencies close to thenominal λ2 -resonance, showing both areas of zero focusing force and forces pushing beadsto the walls. e) By sweeping the signal over the interval 6.85-6.95 MHz, the force fields isgreatly stabilized.

The beads are in fact focused in 2D, aligned along the center line of the channeldue to its square cross section. The same approach can be used to reduce theneed having to fine tune the system due to changes in ambient temperature, e.g.,going from room temperature to 37 . It can also be used to remove the effectof small differences in transducer mounting in systems with external replaceabletransducers such as those described in Section 5.3. Correctly applied, we believethis scheme could also improve the efficiency of acoustic-based separation methods.Using frequency-modulated signals for spatial stabilization of the force fields alsoenables use of very low flows for transport of particles down a channel, as theparticle will no longer enter regions where the levitation force is nil (or negative),or where a horizontal force would push the particle towards the wall. It also reducesthe amount of acoustic streaming in microcages.


Being able to reduce the flow speeds also has significant implications for applicationsof ultrasonic microcages for single-cell analysis, as discussed in Chapter 6. This ledto the concept of transporting particles down the channel using the ultrasound only;flow-free transport. Using frequency changes to move particles unidirectionally hadpreviously been shown in macro-scale systems [83–85], and using the phenomenonof beats between two close frequencies to produce aggregate reshaping and rotationwas investigated by Oberti et al. [77].

Figure 5.6 illustrates the method for flow-free transport described in Paper VII.The method uses 2D alignment stabilized by a quickly (1 kHz) modulated signalin the inlet channel to the microcage described in Paper V shown schematicallyin Fig. 5.6a). This is combined with a slowly (∼0.1-1 Hz) linearly sweeping sig-nal setting up a field along the channel with moving nodes. Figures 5.6c-d showsflow-free transport of aggregates of microbeads and living cells, respectively. Theprinciple behind the transport is the following: At the end of a sweep, when thefrequency drops back to the starting value for the next sweep, the particle(s) willbe closer to the starting location of the “next” node, and thus quickly move there.Transport speeds up to 200 µm/s were achieved, and (time-resolved) particle im-age velocimetry (PIV) [34, 42] measurements confirmed a more or less stationarymedium around the particles. The particles were transported into a microcage,where they were held by the 3D force field of the cage and not transported outagain.

It is important to realise that in flow-through applications such as focusing andsorting (cf. Section 6.1.1), force fields given by single frequencies and by frequency-modulated signals will have nearly the same effect. When the particles enter asection with poor focusing forces, they will simply continue in the streamline theyare in, and the parts where the force is directed towards the walls are short.

5.3 Design of USW manipulation systems

This Section concerns the design of systems for performing the USW manipula-tion functions discussed above. As the “system” in this case, we shall mean theultrasound transducer and the part of the microfluidic system that is significantlyactuated by the sound. Thus we disregard fluidic connectors, pumps, wiring to thetransducer, detection methods (most often optical microscopy), and so on. Dur-ing the last decades, many different system designs have sprung up, more or lesssimilar. These can be classified in terms of several parameters, such as:

• Medium: The fluid medium can be broadly divided into gases and liquids(e.g., water, cell medium, PBS buffer). Examples of the first include controlof aerosols [86], but the latter is by far the most common and the only onewe shall discuss below.

5.3. DESIGN OF USW MANIPULATION SYSTEMS 35

a)

100 µm

t = 3.2 st = 0.0 s

t = 7.4 st = 5.0 s

200 µm

d)

t = 1.0 s

t = 0.0 s

t = 2.0 s

b)

c)

Figure 5.6: Flow-free transport using a low modulation frequency combinded with spa-tially stabilized 2D alignment (cf. Fig. 5.5): a) The particles are aligned on the centerlineof the channel using a fast sweep. b) A standing wave is set up along the channel, causingaggregation into clumps held in 3D. c) Consecutive frames from a movie, showing flow-free transport of aggregates of 5-µm polymer beads using a slow modulation of the signaldescribed in b). d) Consecutive frames from a movie showing transport of a single HEK(human embryonal kidney) cell into a microcage followed by aggregation and caging. Thecells are fluorescently stained with the viability probe calcein.


• Particles: The particles to be manipulated can be divided into more rigid/semisolid (polymer particles, cf. Papers I, III-VII), and softer (red blood cells,cf., e.g., Ref. [87] and other cell types, cf. e.g. Papers I, V-VII). This willinfluence the magnitude of the force on the particles by virtue of the acousticcontrast factors (Eqs. (2.10) and (2.11)).

• Resonator geometry: The resonator geometry determines basic propertiesof the force field, and is thus a very central aspect of the design. Examplesinclude straight channels (Paper IV, and, e.g., Refs. [71, 80, 83]), capillaries[88, 89], straight channels of varying cross-section (Paper III), larger chambers(Papers I and VI, Refs. [34, 77]) and microcages (Papers V and VII). Inaddition, the channels may be branched/split in places, with (as in PaperIII) or without [79] the possibility to individually manipulate particles in thebranches. The acoustic field in the resonator will also be decided by choice ofmaterial and, to some extent, the fabrication methods used.

• Transducer: While the by far most common material for the actuator itselfis the piezoelectric ceramic PZT (lead zirconate titanate, another example in-cludes lithium niobate [90]), the placement of the piezo element, the couplingmethod, and the actuation scheme differ. The piezo element can be, e.g.,fixed and integrated into the system [78, 80], temporarily glued directly ontothe chip [71, 91], split into subparts by use of strip electrodes [77], or fixedonto a coupling wedge (Papers II-VII) which then together with the piezo el-ement acts as an external replaceable transducer. The above-mentioned casesall use the piezos in thickness-mode resonances, but it is also possible to usea shear-mode piezo [92] or interdigited transducer to create surface acousticwaves [90].

• Actuation: As discussed in the above Sections, the actuation can be clas-sified as single-frequency, multiple-frequency or frequency-modulated. Thereader is referred to Sections 5.1 and 5.2 for details.

The scope of the rest of this Chapter will be limited to the the system design usedin Papers II-VII. This design includes use of wedge transducers (cf. Paper IV)mounted on chips with a glass-silicon-glass sandwich structure where the channelis etched through the silicon layer.

5.3.1 Wedge transducers and microfluidic chips

This Section will deal with the basic components of the chip-transducer systemused for almost all the research this Thesis builds on. The exception is the chipused in Paper I, which was in-house built and fabricated from polydimethylsiloxane(PDMS) defining the channel structure between two glass plates. The piezo element

5.3. DESIGN OF USW MANIPULATION SYSTEMS 37

was fixed directly onto the glass surface, employing near-field trapping of cells. Thesystems described in Papers II-VII use external and replaceable wedge transducersglued onto a glass-Si-glass chip (cf. Fig. 5.7), where the channel structure has beendry-etched through the silicon. All chips have been fabricated by GeSim [93] inGermany.

Piezo

Channel

Fluidicconnection

Al wedge

[cm]

Figure 5.7: Photograph of glass-Si-glass chip with five mounted wedge transducers. Thechip was used to show spatial confinement of resonances and perform user-addressablemerging of particle streams (cf. Paper IV).

The wedge transducer itself consists of a piezo element (made from PZT) with silverelectrodes, fixed onto an aluminium wedge using silver glue. The piezo elementoperates in thickness mode, meaning that the optimal frequency of the transduceritself is mostly decided by the thickness of the PZT. However, the mass of thealuminium wedge acts as a load on the piezo, broadening and somewhat shiftingthe resonance. The transducers are glued onto the chips using a water-soluble glue,resulting in the chip itself also acting as a small load. Thus, it becomes importantto consider the entire chip-transducer system together when designing both wedgeand chip. The design of wedge tranducers is discussed in Paper IV. The mostimportant point is that the resonance that builds up is a full-system 3D resonanceprimarily determined by the solid structure, as the channel is a very small partof the total system. Doing analytical calculations, of course using much simplifiedmodels, on such a system gives only very rough approximates, and hence we turnto numerical simulations for design purposes and for better understanding of thesystem.


5.4 Numerical simulations of ultrasonic resonances

The numerical simulations of the chip-transducer systems or parts thereof were allconducted using the finite element method (FEM) software Comsol Multiphysics[94] together with Matlab [95]. Since full 3D simulations of the system provedto be beyond the capabilities of the available computer resources, all simulationswere done on 2D cross-sections of the system. It has been shown that while thismethod does not correctly predict the frequency that will create a certain forcefield, it does predict available force fields and is thus a very useful design tool (cf.,e.g., Refs. [34, 35] and Papers IV-VI). This frequency error is not unexpected whenperforming 2D simulations of 3D systems [34].

The boundary conditions of the models built are summarized in Table 5.1. TheComsol modes used were “Plane Strain” for the solid materials and “Pressure Acous-tics” for the fluids, both without damping. The reason two different modes must beused is the difference between sound propagation in fluids and solids (cf. Sections2.1-2.2). The actuation was simulated by prescribing a time-harmonic oscillationon a boundary representing the piezo element.

Comsol Mode Boundary Boundary Conditions

Pressure acoustics Fluid channel walls Normal accelerations equal (asfluid is assumed non-viscous)

Plane strain All inner solid-solidboundaries

Handled automatically

Plane strain Top surface of Al wedge Time-harmonic normal displace-ment

Plane strain Fluid channel walls Free surface with loading normalforce equal to pressure in fluid

Table 5.1: Boundary conditions used for FEM simulations.

The simulated pressure fields were then post-processed in Matlab and force po-tentials or force fields were calculated according to the equation given by Gor’kovin its pressure-dependent form (Eq. (2.17)). In the following Sections, it is impor-tant to remember that while the Figures often show cut-outs of interesting parts of

5.4. NUMERICAL SIMULATIONS OF ULTRASONIC RESONANCES 39

the chip, such as a microcage, the actual simulation was done on a cross-section ofthe entire chip to better capture resonances in the solid structure and hence, e.g.,inhomogeneities in the force field along a straight channel.

5.4.1 Straight channels

Simulations of the fields in straight channels are part of the base of Paper IV. Itis shown that as the solid structure makes up almost the entire system, the fieldin the channel at different locations becomes highly dependent on the surroundingstructure. The most common situation using single-frequency actuation is one inwhich the channel is only actuated by a displacement field giving high forces insome locations. As we saw in Fig. 5.5a-d, other locations have a zero force field, ora force pushing particles towards the walls. Top-view simulations, as shown in Fig.5.8 together with the corresponding experimental images, predict this phenomenonwell. This type of simulation is further discussed in Paper IV.

p2

F

p2

F

Figure 5.8: Top-view simulation of squared pressure field in channel (top row, blue is lowand red is high) with focusing force component (middle row, blue means “downwards” inthe image and red means “upwards”) and corresponding experimental situation (bottomrow). The left column shows “good” focusing, while the right column shows the morecommon “spotwise” focusing.

The same phenomenon applies to the levitating force throughout the channel - dur-ing single-frequency actuation, there will in general not be a homogeneous verticalforce field. A simulation of this effect is shown in Fig. 5.9. The figure has beenrescaled horizontally to fit the page, the actual length of the simulated channel is24.7 mm and the height is 110 µm, as described in Paper IV. The conclusion is thatfrequency modulation, as discussed in Section 5.2.3 should be used to alleviate thisproblem.

It should also be mentioned that in channels with a rectangular cross-section, it alsobecomes important whether the pressure field set up in one direction has gradientsin an orthogonal direction. If this is true it causes, e.g., a nominally horizontalresonance to have a force component in the vertical direction or along the channel.Simulation results as shown in Fig. 5.10 predict this, and the effect is indeed seen in


experiments. The focusing field used in Figs. 5.1 and 5.3 clearly has a downwardscomponent, as the beads sink quicker with only the focusing field on (cf. Figs.5.1a-b), and move slower in Fig. 5.3 than in Fig. 5.1c.

zy

-1

0

1Fz

Fy

Figure 5.9: Normalized components of the levitating force field calculated from pressurefield simulations in a straight channel (red corresponds to an positive force in the imageand blue to a negative force). The black contours show where the absolute value of theforce is down to 10% of its maximum. The simulated channel is 24.7 mm long and 110µm high.

x

y-1

0

1Fx

Fy

Figure 5.10: Normalized components of the focusing force field calculated from pressurefield simulations in a straight channel (red corresponds to a positive force in the imageand blue to a negative force). The black contours show where the absolute value of theforce is down to 10% of its maximum, and the white contours show locations of zero force,showing that the focusing force has a weak negative y-component in almost the entirechannel.

5.4.2 Non-straight channels

The simulation of non-straight channels is done in complete analogy with what isdescribed in the previous section. However, while a straight channel has a fixedwidth throughout, channels with microcages or larger focusing elements also hasthe added complexity of the shape and size of the non-straight part playing an im-portant role in the resonance shaping. As illustrated in Fig. 5.4, this enables design

5.4. NUMERICAL SIMULATIONS OF ULTRASONIC RESONANCES 41

of spatially confined resonances in microcages, but also investigation of modes andmode spacing in larger elements such as the 5-mm confocal element used in PaperVI. Figure 5.11 shows an overlay of experimental data on the simulated pressurefield in such a chamber. The pressure field is shown in logarithmic scale to empha-size the existance of weaker forces outside the stronger confocal mode. We now endour discussion of manipulation functions and simulations and, in the next Chapter,discuss some applications of these functions in different settings.

Figure 5.11: Pressure field simulation (logarithmic scale, red is high and blue is low)and overlaid experimental data from a large (5 mm) focusing element for cytometry ap-plications (cf. Section 6.1.1).

Chapter 6

Applications of USW Manipulationin Microfluidic Systems

This Chapter is intended as a short discussion of applications of the manipulationmethods described in Chapter 5. Generally, these are gauged towards biomedicalor cell analysis of some kind. The most common applications include handling oflarger number of particles (cf. Section 6.1). In this respect USW manipulation canbe used as a pre-analysis separation method, or in other flow-through applicationas discussed in Section 6.1.1, or an aggregating force (Section 6.1.2). It can alsobe employed as a caging force field or a transport mechanism for single-cell studies(Section 6.2). Reasons for using ultrasound for these purposes include the facts thatit is relatively gentle to living cells (cf. Paper I), it allows for precise temperaturecontrol (cf. Paper II), it is inexpensive, and it can be used both for full-systemnon-localized manipulation schemes and to create localized force fields (as shownin Papers V and VII).

6.1 Batch manipulation

Batch handling, i.e., different types of handling of larger amounts of particles si-multaneously, is a common application of USW manipulation. This stems fromthe fact that, as we saw in the previous Chapter, it is relatively easy to build upan ultrasonic force field that affects more or less the entire channel structure in amicrofluidic chip. Thus, due to the larger range of the ultrasonic forces comparedto DEP and the larger area that can be affected compared to OTs (cf. Chapter 4),it is a very attractive method for such applications.

43

44 CHAPTER 6. APPLICATIONS OF USW MANIPULATION

6.1.1 Flowthrough batch manipulation

USW-based applications operated in flow-through mode are most often based onachieving continuous separation of particles from other particles or a fluid. Theseparation can be based on size or difference in acoustic contrast with respect tothe medium (cf. Eq. (2.10)), or concentration or alignment of particles. Anotherexample is lateral control of particle position in a channel for, e.g., washing.

Examples of separation applications include separating out lipid embolii from bloodin order to give homologous transfusions during major surgery [91, 96], and size-based sequential separation [67], which also can be improved to separate, e.g., cellsof similar sizes and acoustic contrast by medium density manipulation [67]. Thelateral control of particles afforded by ultrasound has been used to perform washingusing adjacent laminar flows in a channel, yielding high selective purfication of, e.g.,phosphopeptides or bacteriophages.[71] By washing particles through up to eightfluids of different pH, it is possible to do a sequential eluation of different surface-bound molecules for further analysis using mass spectroscopy.[70]

The lateral control of particles in a fluid flow can also be used in a chip withbranched channels or flow-splitting elements to perform user-addressable mergingof adjacent particle streams, as shown in Paper III. Therein is also shown howtwo different frequencies can be used to align all the particles in a sample along asingle streamline in the center of a rectangular channel. This reduces the risk ofclogging, wall adhesion, and other effects from the walls on a delicate sample such ascontamination or activation of sensitive cells such as thrombocytes. It also reducessample dispersion in the flow as the particles travel along the same streamline, i.e.,with the same velocity. This becomes of greater importance the larger the sampleparticles are, since for small particles diffusion will somewhat mitigate this problem.Together with multiple laminar medium flows and the above-mentioned techniquesthis enables a platform of great versatility for particle washing, separation andmixing.

Alignment of particles in a channel of circular cross-section has been investigatedas a sample preparation technique for flow cytometry.[89] In Paper VI, we discussa flow cytometry system where the ultrasound can be used for selection of cells orparticles of interest followed by ultrasonic retention in the chamber shown in Fig.5.11 for further study or cultivation of cells.

6.1.2 No-flow batch manipulation

The concentration of cells and/or biofunctionalized beads into larger, often planaraggregates can be used to study, e.g., cell-cell interactions [97], or the effect ofUSWs on a batch of living cells as discussed in Paper I. It has also been shown

6.2. SINGLE-PARTICLE MANIPULATION 45

to help increase the sensitivity of certain bead-based bio-assays [81, 88] (althoughthe first of these systems is not truly microfluidic). In a 2D rectangular resonator,arraying of locomotive microorganisms has been used to investigate their motilityunder different external conditions (temperature and illumination).[83]

The USW can also be used to create a retentive force, so that while the medium isin fact flowing, particles are stopped and held against the flow. In Paper VI, thistechnique is used on small batches of particles after pre-selection as mentioned inSection 6.1. The method has also been used to sort out spermatozoa from cell lysatefor forensic analysis purposes.[79] As a last example, it is shown in Paper VII thatultrasonic forces can be used as a batch transport mechanism, transporting largeraggregates of particles down a channel without the need for medium flow (cf. Fig.5.6). The transport speed depends linearly on the modulation frequency, and thearrangement has the possibility to change direction of the transport by switchingfrom increasing to decreasing frequency sweeps.

6.2 Single-particle manipulation

The handling of very few particles using USWs is far less common than the batchhandling discussed above. While it is possible to turn a batch handling systeminto one handling single particles by simply using very low concentrations of par-ticles, few applications of this have been shown. As one example, it has beenshown that the size-dependence of the primary radiation force (cf. Eq. (2.10)) canenable enhanced separation efficiency in capillary electrophoresis by retarding oreven stopping larger particles.[68] A different example of single-particle handlingusing USWs is pre-positioning of crystals as a sample preparation step for X-raycrystallography.[98]

The ultrasonic 3D microcage described in Papers V and VII is one example ofan element designed specifically for studies of a very low number of cells and theirinteractions. The system design allows use of all kinds of optical microscopy, makingit feasible to study very small cell aggregates of, e.g., immune cells such as naturalkiller (NK) cells and their target cells, or a cell and a single bio-functionalizedbead. The spatial dimensionality control discussed in Paper V and Section 5.2.2also enables control of the number of neighbours a cell has, from two in a linear(1D) aggregate, to up to six in a flat (2D) aggregate, to twelve in a close-packed3D aggregate. When discussing this type of aggregation, it is important to realizethat there is a difference between aggregating “solid” spheres, such as functionalizedmicrospheres, and living cells, which are much more able to change their morphologyto aggregate [97]. In the first case, the final distance and forces between the particlescomes to depend not only on the ultrasound, but also on, e.g., van der Waals andelectrostatic interactions [80, 99].

46 CHAPTER 6. APPLICATIONS OF USW MANIPULATION

25 µm100 µm

a) b) c)

25 µm

Figure 6.1: Particles caged in 3D in an ultrasonic microcage: a) Verification of 3D cagingof 10-µm polymer beads using confocal microscopy. b) Transmission-light microscopy ofa linear aggregate of four human embryonal kidney cells taken with a 20× objective. c)Epifluorescence image of the same cells as in b). The cells have been stained with thegreen viability probe calcein and the red membrane probe DiD.

Figure 6.1 shows the 3D trapping of a small aggregate of fluorescent beads in amicrocage (cf. Section 5.2.2 and Fig. 5.4, top row), as well as two high-resolutionimages of caged living cells. Objectives up to 100×/1.3 have been used (cf. Pa-per V), but in that case the cells must be dropped to the bottom of the cage toaccomodate the short working distance of our objective.

As the flow-free transport scheme described in Section 5.2.3 and Paper VII alsoworks on single cells, it is possible to inject single cells one by one into a microcagewhere they then are trapped. This allows for precise studies of the interactionbetween one cell (or a small aggregate of cells) when they come into contact with anew cell. The nearly complete lack of net medium flow implies that the transportof a new cell into the cage comes without the washing away of any signal factorsor other biomolecules in the cage. By loading the system with a low concentrationof different cell types, interactions between pairs or low numbers of different cellscan be studied in a controlled fashion. The selective injection of particles in thecytometry system described in Paper VI (cf. also Fig. 5.11) also allows for injection

6.2. SINGLE-PARTICLE MANIPULATION 47

of a very low number of cells into the retention region (as shown in Fig. 6.2),especially if the injection step is built as a spatially confined region.

g)

a)

t = 0 s

500 µm

d)

t = 6 s

b)

t = 2 se)

t = 8 s

c)

t = 4 sf)

t = 20 s

Figure 6.2: Selective injection of particles followed by retention in the cytometry chipdescribed in Paper VI. White lines show channel edges, and the arrow indicates the positionof an arbitrary particle to be trapped. a) Chip in “bypass” mode. b) Switching of frequencyin the pre-alignment channel leads to injection into the retention area. c-d) Switching thefrequency back to “bypass” limits the number of injected particles. e-f) Formation of a2D aggregate levitated and retained against the medium flow. g) The aggregates formedat the location indicated by the arrow in f) resulting from six consecutive one-secondinjections.

Chapter 7

Conclusions and Outlook

Ultrasonic standing wave (USW) manipulation in microfluidic systems is still ayoung field, but one that shows great promise. We have seen in the previous Chap-ters that it is a versatile, inexpensive, and gentle manipulation method, capableof performing particle handling on different length scales and for many differentpurposes.

As discussed in Paper I, it is a gentle method when manipulating living cells. Whilemany studies remain to be done on the exact effect an ultrasonic standing wavehas on a living cell, single or in an aggregate, this will more likely open up newpossibilities than bring problems. Long-term handling in an 3D ultrasonic cage(cf. Papers V-VII) could, e.g., be used to investigate changes in behaviour in anadherent cell type when the cells are only allowed to adhere to each other andnot to a substrate. The caging provided by the ultrasound would make such asystem ideal for automated microscopic imaging. USW as a manipulation methodalso allows for precise temperature control (cf. Paper II), something that is centralto performing living-cell studies for longer periods of time. The dimensionalitycontrol afforded by the microcages also gives possibilities of studing differences incell response as a function of the number of neighboring cells. In cases of handlingsensitive cells, 2D pre-alignment (as shown in Paper IV and used in Papers V-VII)prevents the walls of the system from influencing the cells upon contact and greatlyreduces risk of clogging. In case of a small sample plug injected into the system, 2Dpre-alignment also keeps the sample from dispersing in the laminar flow profile ofthe microchannel. Frequency-modulated signals, as discussed in Paper VII, can beused to stabilize the force fields spatially, giving even better alignment and controlof particles, as well as make the system more robust with respect to changes in,e.g., temperature.

Spatially, USWs can be used both as a full-system manipulation method for manyapplications, but can also be confined to pre-defined parts of a system as shown in

49

50 CHAPTER 7. CONCLUSIONS AND OUTLOOK

Papers III and V. This opens up many possibilities for conveyor-belt type handlingin a microfluidic chip, with different downstream manipulation “stations” perform-ing sorting, user-adressable merging, retention and other manipulation functionson particles and/or cells (cf. Papers III-VII). The method of flow-free transportpresented in Paper VII could also be employed in a larger system as a whole, or inpart of the system by correct microchannel design.

On the simulation side, most work so far has been done on 2D cross-sections ofsystems, as in Papers IV-VII. One main conclusion here is that for full characteri-zation, the 3D resonances in the solid structure greatly influence the performanceof the chip. New software, better programming and better computers will enablefull-system 3D resonance simulations, work that is currently underway. This willenable the controlled design of more efficient chip systems, yielding higher forcesand even better control of, e.g., spatial confinement of the force fields.

Thus, as always in Science, much remains to be done. This Thesis, however, endshere.

Summary of Original Work

This Thesis is built upon the work presented in the Papers listed below. ThePapers are all directed towards developing tools using resonant ultrasonic fields formicromanipulation of biofunctionalized microbeads and living cells in microfluidicsystems. The author was the main responsible researcher for papers III, IV, V, andVII, and participated to various degrees in the experimental and theoretical aspectsof the other papers. This does not include development and handling of the PIVsoftware used in Paper III, or the culturing and handling of cells in Papers I andV-VII.

Paper I investigates the viability and proliferation of COS-7 cells after ultrasonictrapping for time periods up to 75 minutes in an in-house built glass-PDMS-glasschip. The proliferation rate of the cells is found to be within the normal range forthe cell type.

Paper II concerns the regulation of temperature in the microchannel, investigat-ing the possibilities to maintain a steady temperature around 37 during longerperiods of time. The Paper also investigates heating of the transducer and chip asa consequence of absorption of sound, and the possibility to use this effect as partof a temperature control system.

Paper III demonstrates spatial confinement of ultrasonic force fields to specificparts of the channel by varying the channel width and by introducing flow-splittingelements. The paper also shows operator-addressable merging of different particlestreams in the channel.

Paper IV investigates the properties of the wedge transducers and the transducer-chip system using impedance spectroscopy, numerical simulation methods, and ex-periments. The wedge angle is found to influence the force field patterns in thechannel, and the 3D resonances built up in the solid structure of the chip are foundto give rise to spatial inhomogeneities in the force field in the channel.

Paper V presents the first in-chip three-dimensional ultrasonic microcage, enablingtrapping of particles in 3D and retention against a medium flow. High-resolution

51

52 SUMMARY OF ORIGINAL WORK

imaging of caged cells is demonstrated, and the dynamics of aggregate formationduring medium flow are investigated.

Paper VI demonstrates selective injection of particles into a large (5 mm) confocalresonance cavity for cell studies or bead assays. The capability of shifting particlesbetween bypassing the trapping region and retaining the particles in the chamberis shown. The retaining forces are investigated, and live-cell imaging is shown.

Paper VII investigates the used of frequency-modulated ultrasound for manip-ulation of particles in microchips. It is shown that a proper modulation schemecan be used to greatly enhance spatial homogeneity of the ultrasonic force field ina channel. The paper also demonstrates use of frequency modulation to performflow-free transport and subsequent caging of particles.

Acknowledgments

First and foremost, I owe a great debt of gratitude to professor Hans Hertz. Firstly(as a function of time), for letting me do my MSc Thesis here at BioX. Secondly,for letting me start my PhD here (even after making me promise I would notmention doing a PhD), thirdly and more importantly, for the last 4.5 years of, timeand again, demonstrating why it is called “forskarutbildning”. I also would like toextend my warmest thanks to my supervisor Martin Wiklund for his help, support,and for keeping my ideas in check when needed. To the people here I’ve spent somany hours in the lab with, Bruno Vanherberghen and Jessica Svennebring, andlately Ida Iranmanesh, thank you for those. Someone said research is 5% inspirationand 95% perspiration - you all made them both worthwhile.

To all the members of the Biomedical and X-Ray Physics group here at KTH, boththose that I know well and not so well, thank you for making this such a wonderfulplace to work. Extra kudos to Per Takman for all the discussions during my firstyears, Ulf Lundström (during my last) and Göran Manneberg for actually trying tounderstand what the heck I mean when I try to make very strained analogies withoptics. Also to Peter Skoglund for never failing to accept a discussion on physics nomatter the time of day, location or degree of inebriation. Thanks also to my out-of-group collaborators, Hjalmar Brismar, Björn Önfelt and Bruno Vanherberghen, andout-of-country collaborators Melker Hagsäter, Henrik Bruus, Peder Skafte-Pedersenand Jörg Kutter (and Lasse Andersen, Anders Nysteen and Mikkel Settnes for helpwith that pesky density derivative in the appendix). To the guys who make things:The mechanical workshop one floor down for gadgets, gizmos and raw material,and very much to Steffen Howitz for the chips, thank you.

I’ve also done a fair amount of teaching while being here. To me, it’s one of thebest ways there is to learn. Thanks to Göran for always being willing to discussteaching and letting me play around with his courses, and to Kristina Edström andall my fellow teachers for all the good discussions. Last but not least, thanks to allthose who came, listened and learned together with me. Docendo discimus.

To my father and mother for, well, way too much to fit here, during the last 28 years.Dad for (in addition to all the above-not-listed things) always being one of my best

53

54 ACKNOWLEDGEMENTS

friends and mom for always being there - and for time and again reminding me(more or less unintentionally) that being a good human is so much more importantthan being a good physicist. To my sisters for years and years of being a familywith all that it means. Tack.

Penultimately, to all the friends who have made my life outside BioX what it hasbeen. Trying an enumeration here would be silly, so don’t feel left out. Skogis andEnar will be the only ones who get their names here, but I have a feeling the restof you know. Thank you, brothers. Lastly, to my Cecilia. . . I love you. Thank you.

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Appendix A

Appendix: Walkthrough ofGor’kov

This appendix is meant as a walkthrough of the paper “On the forces acting ona small particle in an acoustic field in an ideal fluid” by Gor’kov [5]. The papercontains an equation for the radiation force on a particle much smaller than thewavelength of the sound, placed in an arbitrary standing wave field (Eq. (2.10)).This is the equation a massive majority of the work in ultrasonic manipulationof particles in microfluidics refers to. Of course, there are certain approximationsmade to get to the equation in question. We shall here attempt to explain andmotivate these, as well as show all the intermediate steps in the calculations. Forthe theory behind the fluid mechanics in this Chapter, the reader is referred to thesomewhat theoretical but very encompassing book by Landau and Lifshitz [100],which is the book Gor’kov recommends as a fluid mechanics basis for the paper[101]. The reader should also note that the road presented herein is not in allsteps the most elegant, but rather an attempt to stay with the paper and book inquestion.

Firstly, a central approximation we make is that the fluid in which our particle isimmersed is ideal, i.e., inviscid; it deforms perfectly continuously under shear stress.Calculations for the viscous case have been presented by Doinikov [6, 7], but aremathematically very cumbersome. Secondly, a note on translation: The Englishversion of the paper has several errors in transcription of the equations. Thus, thereader is urged to check the Russian-text original for the equations and the Englishfor text (unless, of course, the reader is proficient in Russian). Thirdly, equationnumbering in this appendix is as follows: Equations appearing as numbered in thepaper are numbered as G1, G2. . . and supplementary equations (included in theappendix as intermediate steps in the derivation) are numbered A.1, A.2. . . Equa-

63

64 APPENDIX A. APPENDIX: WALKTHROUGH OF GOR’KOV

tions appearing in the paper but unnumbered are numbered by a lower-case letterfollowing the last numbered equation in the paper, e.g, “(G4 a)”.

The derivations will be done using index notation for vectors, as we shall encountersome tensor entities along the way. Occasionally, an expression will be shown invector form as well for clarity.

A.1 The first three equations from first principles

For the sake of completeness, we begin by deriving the first and third equations inthe paper (the force integral and the second-order pressure field) from more or lessfirst principles. The second equation in the paper is just a statement that the totalfield can be divided into incident and scattered field, so no derivation is provided.

A.1.1 Derivation of the momentum flux tensor

We begin by noting that we can express the force on a particle by calculating theflux of momentum through a surface enclosing the particle. If there is a positiveinflux of momentum through such surface, the explanation is that the particle gainsmomentum and thus is acted upon by a force (according to Newton’s second law,Fi = dPi

dt , where Pi is the momentum). Now, the momentum per unit volume of thefluid is ρvi, where ρ is the density and vi is the velocity. Taking the time derivativeof the momentum, we get

∂

∂t(ρvi) = ρ

∂vi∂t

+ vi∂ρ

∂t. (A.1)

Now, we use the equation of continuity, which in this case becomes a statement ofconservation of mass:

∂ρ

∂t+ ∂i (ρvi) = 0. (A.2)

We shall also need Euler’s equation, which is basically the Navier-Stokes equationwith heat conduction and viscosity removed:

∂vi∂t

+ (vk∂k) vi = −1ρ∂ip. (A.3)

where p is the pressure. Now, isolating the time-derivatives from Eq. (A.2) andEq. (A.3) and putting them into Eq. (A.1), we get as an expression for the time-derivative of the momentum that

∂

∂t(ρvi) = −∂ip− ρ (vk∂k) vi − vi∂k (ρvk) . (A.4)

A.1. THE FIRST THREE EQUATIONS FROM FIRST PRINCIPLES 65

The two last terms can be collapsed into the derivative of a product, and we get

∂

∂t(ρvi) = −∂ip− ∂k (ρvivk) . (A.5)

Now, since it would be handy to collect things into a single derivative on the right-hand side, we rewrite the gradient of p so that it gets index k using the Kroneckerdelta (∂ip = δik∂kp), and arrive at

∂

∂t(ρvi) = −∂k (δikp+ ρvivk) ≡ −∂kΠik. (A.6)

The (symmetrical by inspection) tensor Πik is the momentum flux density tensor.By integrating both sides of Eq. (A.6) over a volume and transforming the integralof the right-hand side into a surface integral, we get

∂

∂t

∫ρvidV = −

∫∂kΠikdV = −

∮ΠikdSk. (A.7)

Thus, we see that the tensor elements represent the i-th component of momentumflowing through a unit area with a normal vector in the k-th direction in unit time.If we now look again at Eq. (A.7), we note what we have here is the rate of change ofmomentum in our volume on the left-hand side, i.e., a force, and on the right-handside a nice way to calculate it using a tensor built from velocity and pressure. Thus,the time-averaged force on a particle inside the surface of integration becomes

〈Fi〉 = −∮〈Πik〉dSk = −

∮〈pδik + ρvivk〉dSk, (G0)

where the brackets 〈· · · 〉 denote time-averaging. The equation appears unnumberedin Gor’kov’s paper.

A.1.2 The second numbered equation

. . . and now for something completely different, just to follow the order of equationsin the paper. We shall do many calculations involving the velocity potential, ascalar function (as the fluid is ideal), with the property that ∂iϕ = vi. In our case,the total field will consist of an incident field and a field scattered from the particle.Using the principle of superposition on the velocity potential, we can thus write

ϕ (r, t) = ϕin (r, t) + ϕsc (r, t) . (G1)

A.1.3 Derivation of the second-order pressure field

We now aim for Eq. (G2), the expression for the acoustic pressure p′ in Gor’kov’spaper. It’s important to note that the derivation of this expression has to be done


to second order (we shall do it to second order in enthalpy), or the time-averagingwhen calculation the force according to Eq. (G0) will yield zero. This where theoft-toted expression that the acoustic radiation force is a second-order effect comesfrom. Luckily, the expression can be written using only first-order quantities, aswe shall see below. This will take some math, and a little bit of thermodynamics- we shall start by assuming the propagation of sound to be an adiabatic process,meaning in this case that the entropy S (taken per unit mass) is a constant. Weshall now rewrite Euler’s equation (A.3) into a form reflecting this fact. If we byH denote the enthalpy per unit mass of the fluid, and by V the volume per unitmass (i.e., V = ρ−1) we have

dH = T dS︸︷︷︸=0

+V dp = dp

ρ, (A.8)

which gives us that the gradients will be related as

∂iH = 1ρ∂ip. (A.9)

Thus, Euler’s equation is quite simple to rewrite into a form containing the enthalpy- just exchange the right-hand side according to Eq. (A.9):

∂vi∂t

+ (vk∂k) vi = −1ρ∂ip = −∂iH. (A.10)

Now, we are going to rid ourselves second term on the left-hand side by going overto working with the velocity potential, which will kill off some space derivatives ina nice way. We let ∂iϕ = vi, and get

∂

∂t∂iϕ+ (∂kϕ∂k) ∂iϕ = −∂iH, (A.11)

which might not look like an improvement at first, but there is a nice vector cal-culus identity we can use here (given in both index and nabla form for improvedreadability):

∂i [(∂kϕ) (∂kϕ)] = 2 (∂kϕ∂k) ∂iϕ︸︷︷︸*

+2εijk∂jϕ (εklm∂l∂mϕ)︸︷︷︸=0

∇ [(∇ϕ) · (∇ϕ)] = 2 (∇ϕ · ∇)∇ϕ︸︷︷︸*

+2∇ϕ× (∇×∇ϕ)︸︷︷︸=0

.(A.12)

The last term on the right-hand side is zero by virtue of being the rotation of agradient, and the first term on the right-hand side (marked “*”) is identical to theterm we wanted to improve on in Eq. (A.11). We now note that the left-hand sideof Eq. (A.12) is the gradient of the velocity field squared, and thus we get

∂

∂t∂iϕ+ ∂i

v2

2 = −∂iH, (A.13)

A.1. THE FIRST THREE EQUATIONS FROM FIRST PRINCIPLES 67

where v2 = vkvk. Moving everything to the left-hand side and integrating withrespect to space, we get

∂ϕ

∂t+ v2

2 +H = f (t) , (A.14)

where f (t) is an arbitrary function of time. As a remark, this is one version ofwhat is known as Bernoulli’s equation. Let us now introduce the sound field as asmall disturbance of the medium, so that we to first order in pressure and density,and second order in enthalpy have

p = p0 + p′

ρ = ρ0 + ρ′

H = H0 +H ′ +H ′′,

(A.15)

where index “0” means the unperturbed state and the primed entities are the per-turbations that constitute the sound field. Thus, we have from Eq. (A.14):

∂ϕ

∂t+ v2

2 +H0 +H ′ +H ′′ = f (t) (A.16)

Now, we absorb the constant H0 into the function f , and then absorb a spatiallyconstant term on the form

∫f (t) dt into the potential (as the velocity is the spatial

derivative of the potential, this gauge transform does not affect the physical situ-ation). Now, we expand H into second order in the pressure amplitude p′ (H is afunction of pressure by virtue of Eq. (A.9)):

0 = ∂ϕ

∂t+ v2

2 +H ′ +H ′′

0 = ∂ϕ

∂t+ v2

2 +(∂H

∂p

)S

(p− p0)︸︷︷︸=p′

+12

(∂2H

∂p2

)S

(p− p0)︸︷︷︸=p′

2.(A.17)

From Eq. (A.8), we get the derivative of H with respect to p under constantentropy, so we have(

∂H

∂p

)S

= 1ρ⇒

0 = ∂ϕ

∂t+ v2

2 + 1ρp′ + 1

2

(−1ρ2

)(∂ρ

∂p

)S

p′2

0 = ∂ϕ

∂t+ v2

2 + p′

ρ− p′2

2ρ2c2 ,

(A.18)

as the remaining derivative on the middle line by is equal to c−2, c being the speedof sound. Now, all that remains is to do a Taylor expansion of the densities ρ


(keeping only the first terms), isolate the un-squared p′, and write p′2 in terms ofvelocity potential. The first two steps are straight-forward:

0 = ∂ϕ

∂t+ v2

2 + 1ρ0

(1 + ρ′

ρ0+ . . .

)︸︷︷︸

≈1

p′ − 1ρ2

0

(1 + ρ′

ρ0+ . . .

)2

︸︷︷︸≈1

p′2

2c2 ⇒

p′ = ρ0

(−∂ϕ∂t− v2

2 + p′2

2ρ20c

2

).

(A.19)

To get the right-hand side of the equation in terms of velocity potential only, wederive a relation between ϕ and p′ valid to first order - we linearize Euler’s equation.Starting with Euler’s equation as given in Eq. (A.10) and not exchanging thepressure term for enthalpy gives, neglecting all terms of second order and higher,

0 = ∂vi∂t

+ (vk∂k) vi + 1ρ0 + ρ′

∂i (p0 + p′)

0 = ∂vi∂t

+ (vk∂k) vi︸︷︷︸second order

+ 1ρ0

(1− ρ′

ρ0+ . . .

)︸︷︷︸

≈1

∂ip0︸︷︷︸=0

+∂ip′

0 = ∂vi∂t

+ 1ρ0∂ip′.

(A.20)

From this, we deduce the very useful result that to first order

∂

∂t∂iϕ+ 1

ρ0∂ip′ = 0

∂i

(∂ϕ

∂t+ p′

ρ0

)= 0(

∂ϕ

∂t+ p′

ρ0

)= g(t)

−ρ0∂ϕ

∂t= p′,

(A.21)

where we once again absorbed a time-dependent function into the velocity potential.Using this relation together with Eq. (A.19), we now arrive at

p′ = −ρ0∂ϕ

∂t− ρ0

v2

2 + ρ0

2c2

(∂ϕ

∂t

)2. (G2)

Now, we insert this expression into the integral expression Eq. (G0) for the forceon our particle. The constant pressure p0 will not contribute to the force on theparticle, and thus we insert p′ as given above. Furthermore, assuming the time-dependence of the sound field to be harmonic (of the form eiωt), we note that the

A.2. DERIVATION OF THE SCATTERED WAVE FIELD 69

time-average of the first term of p′ will be zero, yielding

〈Fi〉 = −∮ ⟨(

−ρv2

2 + ρ

2c2

[∂ϕ

∂t

]2)δik + ρvivk

⟩dSk, (G3)

where we have dropped the index 0 on the unperturbed density, as this index willbe used to denote particle properties hereafter, following Gor’kov’s notation in thepaper.

A.2 Derivation of the scattered wave field

To continue developing the expression for the force given in Eq. (G3), we now needto consider how to express the scattered wave as a function of the incident wave.Now, at some distance away from the particle, the potential ϕ must fulfill the waveequation

∂i∂iϕ = 1c2∂2

∂t2ϕ, (A.22)

where we have omitted the subscript on the potential since indeed this is valid forboth the potentials involved. Now, we invoke the fact that the particle is muchsmaller than the wavelength of our sound field and place ourselves close to theparticle. In this region, the fluid around the particle will behave approximately asan incompressible fluid, and thus instead satisfy the Laplace equation ∂i∂iϕ = 0. Tounderstand this, consider a characteristic time tc and characteristic length lc of thefluid flow - a time and length during which the fluid velocity undergoes significantchanges. Being close to the particle, we take, e.g., the characteristic time as quarterperiod of the sound field and the characteristic length of our particle such as theradius. Now, if the time it takes for a sound signal to traverse the distance lc ismuch shorter than the time during which the fluid velocity changes significantly(tc), we interpret this as interactions on this length-scale being instantaneous, andthe fluid incompressible. Our condition, then, is of the type

tc lcc⇒

1f lc

λf⇒

λ lc,

(A.23)

which is one of our basic assumptions, and so inherently true in our case. As a note,far from the particle (in the wave zone) the characteristic length instead becomesrelated to the wavelength of the sound, giving a criterion of the type λ λ showingthat here the fluid cannot be regarded as incompressible (which we of course knowalready - if it were we would not have a sound wave here). Now, we return to the


velocity potential. We know for physical reasons that the solutions we are lookingfor must be decreasing functions of distance from the particle. Let us introducea coordinate system with the origin in the particle, so we instead can speak ofdecreasing functions of the radial coordinate r. Luckily for us, these solutions arewell-known and easy to find - they are simply r−1 and all higher space derivativesthereof, multiplied by some (spatially constant) functions of time:

ϕsc = −a (t)r

+Ai (t) ∂i1r

+ . . . (G4’)

The observant reader now notices that this is a solution to the Laplace equation asit stands (as this equation carries no time dependence), and to the wave equationif we use the retarded time τ = t − rc−1, when it becomes a multipole expansionof the wave field. She will also notice that we use a different sign convention thanGor’kov does in his paper. The reason for this is simply to get a more intuitivepicture and slightly simpler calculations in what follows. The final expressions willof course not have their signs changed with respect to the paper.

A.2.1 Derivation of the first constant a

Here, it might be beneficial for the physical understanding of the situation to havea look at the two (spatial) constants a and Ai to see what they “mean” (hence-forth, the time-dependence of these will be suppressed in notation). We begin witha. The velocity potential has dimensions of m2

s (it should yield a velocity whendifferentiated with respect to space). Thus, a carries the dimensions of volume overtime. Let us now go back to looking at our small sphere, and assume that it ispulsating, i.e,. changing its volume cyclically (emitting sound isotropically). If welook at the mass flux through a spherical surface of radius R concentric with thesphere, per unit time, we have that the flux out through this surface can be writtenas ∮

ρvidSi =∮ρ∂iϕdSi. (A.24)

Now, letting the potential be the first term in our scattered potential, the onecontaining a, and using the fact that over our spherical surface of integration, thevelocity will have a spatially constant absolute value and be parallel to the surfacenormal, we get ∮

ρ∂iϕdSi = a

R2

∮dS = 4πρa. (A.25)

Since this is the mass flux per unit time, we can interpret 4πa as the volume fluxper unit time out through our surface. We also see the reason of putting the minussign on a in Eq. (G4’) - we want a positive value of a when the velocity is directedradially outwards. For the case of an incompressible fluid, this flux has to be equal


of the time derivative of the volume V0 of the particle (from now on, index “0” willbe reserved for particle properties), hence

4πρa = ρV0

a = V0

4π

ϕ = − V0

4πr + . . .

(A.26)

where the dot notation is used for time derivatives. We now expand on the a termand see what it becomes if we let the fluid and particle be compressible. This willgive rise to the first acoustic contrast factor in the expression for the force. Themass flow per unit time through our surface of radius R will still be the total changein mass inside the volume. However, the particle will retain its mass, so the massflux out of the spherical volume will be due the oscillations of the fluid, driven bysphere which in turn is driven by the incident field. The total volume flow out ofour test surface will now be both due to the oscillations and to the compressionrelated to the compressibility of the materials. We thus split the total volume intotwo parts:

4πatot = V incomp − V comp, (A.27)

where the first term on the left-hand side is incompressible sphere case (i.e. thesphere retains its volume), and the second term is the “compressibility correction”.As we allow differences in density in the particle and the surrounding medium andthese calculations are from the beginning based on mass flux, the volume in thefirst term will be the volume of the surrounding fluid (which is what is flowingout through our test surface) which would have occupied the space of the particlewere it not there. The rate of change in mass in this volume will be V0ρ, wherewe assume the wavelength of the sound to be so large that the density is spatiallyconstant throughout our volume. This mass change corresponds to a volume changeby division with the density, so that

V incomp = V0ρ

ρ. (A.28)

For the second term of the right-hand side of Eq. (A.27), we start by noting thatwhen the pressure outside our particle changes (isentropically) by an amount dpin,the volume of the particle will change by an amount

dV0 = V0

ρ0

(∂ρ0

∂p

)S

dpin. (A.29)

Taken as a change per unit time, we get that (switching to writing the time deriva-tives out for clarity)

dV0

dt= V0

ρ0

(∂ρ0

∂p

)S

dpindt

. (A.30)


Here, we note that the partial derivative is related in a simple way to the speed ofsound, as in Eq. (A.18), and that the pressure change here can be understood asthe pressure amplitude p′. Now, using

p′in = dpin =(∂pin∂ρin

)S

dρin = c2ρ′in (A.31)

we get

dV0

dt= V0

ρ0

(∂ρ0

∂p

)S

dpindt

= V0

ρ0

1c2

0

d(c2ρ′in

)dt

= V0c2

ρ0c20

dρ′indt

.

(A.32)

Remembering that the time derivative of the density amplitude is identical to thetime derivative of the density as a whole, we get that

dV0

dt= V0

c2

ρ0c20

dρindt

(A.33)

Finally, putting together Eqs. (A.27),(A.28) and (A.33), we get

4πatot = V0

ρ

dρindt− V0

c2

ρ0c20

dρindt

4πatot = 4πR30

3ρ · dρindt

(1− ρc2

ρ0c20

)atot = R3

03ρ · ρin

(1− ρc2

ρ0c20

),

(G6’)

where R0 is the radius of our spherical particle. Note that the above expressionis the “compressibility-corrected” version of (G6) in the paper, which appears un-numbered in the English translation but numbered as (G6’) in the original.

A.2.2 Derivation of the second constant Ai

The physical meaning of the vector entity Ai from Eq. (G4’) is slightly less easyto grasp, but it is physically connected to momentum and energy of the fluid as itflows past our particle, and the effect that when the fluid oscillates back and forth,it will set our particle in a similar motion involving momentum transfer between theparticle and the fluid. Thus, this term will contain the density difference correctionsin our final equation. We shall begin by looking at how this vector is related to


momentum transfer, on our way introduce the so-called induced-mass tensor, andcalculate how the total kinetic energy of the fluid is expressed in terms of Ai.As discussed above, the flow around our particle is assumed to be incompressiblepotential flow (∂ivi = 0 from the equation of continuity (Eq. (A.2)) with constantρ). We assume the fluid to have a velocity field vi with a potential defined by∂iϕ = vi, and denote the velocity of the particle by ui. The total kinetic energy ofan incompressible fluid is

E = 12ρ∫v2dV , (A.34)

where the integral is taken over a large spherical volume of radius R, excepting thevolume occupied by the particle (i.e., “all” the fluid). Now, we shall engage in sometricks motivated by the somewhat loathsome argument that we will end up witha nice expression. We can rewrite this integral into an expression containing bothvelocities by using the obviously mathematically correct equation∫

v2dV =∫u2dV +

∫(vi + ui) (vi − ui)dV. (A.35)

Noticing that ui is independent of the coordinates, the first integral simply becomesu2 (V − V0). Continuing by rewriting the second integral, we have∫

(vi + ui) (vi − ui) dV =∫

(vi − ui) ∂i (ϕ+ ukrk) dV . (A.36)

Now, we would like to use the divergence theorem to transform this integral into asurface integral. We do this by noting that∫

(vi − ui) ∂i (ϕ+ ukrk)dV =∫∂i [(ϕ+ ukrk) (vi − ui)]dV, (A.37)

as we have that the right-hand side when expanded will contain terms that vanishas the flow vi is incompressible, and ui is independent of the coordinates:∫

∂i [(ϕ+ ukrk) (vi − ui)]dV =∫∂i (ϕvi − ϕui + ukrkvi − ukrkui)dV =∫vi∂iϕ− ui∂iϕ+ vi∂iukrk − ui∂iukrkdV =∫(vi − ui) ∂i (ϕ+ ukrk)dV.

(A.38)

Transforming this to a surface integral, we get∫v2dV = u2

(4πR3

3 − V0

)+∮

S+S0

(ϕ+ ukrk) (vi − ui)nidS, (A.39)


with ni being the outward unit normal, S the surface of our large sphere, and S0the surface of our particle. On the latter surface, the boundary condition is that thenormal components of the velocities ui and vi must be equal (the fluid is inviscid),and thus the integral over this surface is identically zero. Now it has become time,at last, to include our constant vector Ai from the potential. The (term of thetotal) potential and thus velocity field we are interested in investigating here is

ϕ = Ai∂i

(1r

)= −Ai

rir3 = −Ai

nir2

vi = ∂iϕ = (Ak∂k) ∂i(

1r

)= 3Aknkni −Ai

r3 ,

(A.40)

where we have used the fact that the outward unit normal vector of our sphere Shas everywhere the same direction as the position vector ri, and that Ai is spatiallyconstant. The last integral expression in Eq. (A.39) now becomes (noting that thesphere is a surface of constant radius R and thus r = R and ri = Rni)∮

S

(− 1R2Ajnj + ujrj

)(3Aknkni −Ai

R3 − ui)niR

2dΩ =

∮S

(−Ajnj +R3ujnj

)( (3Aknkni −Ai)R3 − ui

)nidΩ,

(A.41)

with dΩ being the solid angle element on the surface. Now, we carry out themultiplication of the first (scalar) parenthesis into the second (vector) one, andthrow away terms that vanish as we let R→∞:∮

S

(−Ajnj +R3ujnj

)( (3Aknkni −Ai)R3 − ui

)nidΩ =

∮S

(ujnj (3Aknkni −Ai) +Ajnjui −R3ujnjui

)nidΩ =

∮S

3Aknkujnjnini − ujnjAini +Ajnjuini −R3ujnjuinidΩ =

∮S

3Aknkujnj −R3ujnjuinidΩ =∮S

3 (A · n) (u · n)−R3 (u · n)2dΩ.

(A.42)

The last expression is also given on vector form for clarity. To carry out this integral,we use the fact that integrating vector fields dot-multiplied by the surface normalover all solid angles like this is equivalent to averaging the normal component andmultiplying by 4π (as the average will be the integral divided by the integral over allsolid angles, which is 4π). Now, what we want to average here are two expressionsof the type ainibknk where ai and bi are constant vectors (remember that Ai is


spatially constant, and so is ui). We now have, using over-bars to denote averagingin the mentioned sense, that

ainibknk = aibknink = aibknink = aibk13δik = 1

3aibi, (A.43)

which follows since the value of nink is zero unless i = k, and we let the indices runover i, k = (1, 2, 3) giving a mean value of one third. Our integral in Eq. (A.42)now becomes ∮

S

3Aknkujnj −R3ujnjuinidΩ = 4π(Aiui −

R3

3 uiui

)(A.44)

Inserting this in Eq. (A.39) and using Eq. (A.34) to get the energy, we end up with

E = 12ρ∫v2dV

= 12ρ

u2(

4πR3

3 − V0

)+∮

S+S0

(ϕ+ ukrk) (vi − ui)nidS

= 1

2ρ[u2(

4πR3

3 − V0

)+ 4π

(Aiui −

R3

3 u2)]

= 12ρ(4πAiui − u2V0

),

(A.45)

which is the dependence of the total energy of the fluid on the velocity of theparticle. We still have quite a bit to do before arriving at the expression for Ai inthe case of a sphere in a sound field, where both the sphere and fluid are oscillating,though. Finding the analytical expression for Ai can be done by completely solvingLaplace’s equation ∂i∂iϕ = 0 around the body in the fluid, something which is onlypossible to do analytically in a few cases. Luckily, a spherical particle is one ofthem. We have from Eq. (A.40) that vi = (3Aknkni −Ai) r−3, with the boundarycondition that the normal components of the velocities ui and vi must be equal onthe surface (a sphere with radius R0). We thus get

vini = uini

3Aknknini −AiniR3

0= uini

Ai = 12R

30ui,

(A.46)

a result we shall need fairly soon. First, we look in a more general way at themomentum transfer. Generally, Ai will be a function of ui (as seen in the exampleabove). Now, as Laplace’s equation is linear in ϕ, and the boundary conditions ofthis equation is linear in both ϕ and ui, we deduce that Ai will be a linear function


of the components in ui - if it is not, this non-linearity would “propagate” andcause, e.g., Laplace’s equation not to be linear in ϕ. Thus, we can write the energyin Eq. (A.45) as

E = 12mikuiuk, (A.47)

where the (symmetrical) tensor mik can be calculated if the dependence of Ai on uiis known. This tensor is called the “induced-mass tensor” or “added mass tensor”depending on literature, for reasons that will soon be evident. Now, knowing theexpression for the energy we can calculate an expression for the total momentumPi: If the particle is acted upon by an external force and therefore moves with avelocity ui, the momentum of the fluid will increase as the fluid is “pushed on” bythe particle. The momentum given to the fluid during time dt will be related tothis force by dPi = Fidt. Multiplying both sides of this equation by the velocity ofthe particle we get that

uidPi = uiFidt, (A.48)where the right-hand side is easily interpreted as the work done by the force Fiover a distance of uidt, thus transferring the energy dE to the fluid. Putting Eqs.(A.47) and (A.48) together, we have (since the induced mass tensor is constant -Ai depends linearly on ui, and that factor ui was “extracted” to form Eq. (A.48))

dE = 12mikuiduk + 1

2mikduiuk = dPkuk. (A.49)

Integrating this expression, we see that the momentum can be expressed (as theinduced mass tensor is symmetric) as

Pi = mikuk. (A.50)

Comparing this with Eqs. (A.45) and (A.47), we also can draw the conclusion that

Pi = 4πρAi − ρV0ui. (A.51)

As for every action there is an opposite and equal reaction, we also note that theforce on the particle from the fluid can be written as

Fi,react = −dPidt

. (A.52)

We now move on to looking at what happens if the fluid is executing a oscillatorymotion around the particle (or the particle is oscillating in the fluid, which is thesame problem). Let the wavelength of the oscillation be much larger than theparticle, as always, to ensure that we can assume the unperturbed velocity asconstant over the dimensions of the particle. The equation of motion for thissystem is found by equating the time derivative of the total momentum with thedriving force fi:

m0d

dtui + d

dtPi = fi, (A.53)


where m0 is the mass of the particle. Using Eq. (A.50), we can recast the left-handside of this equation as

m0d

dtui + d

dtPi =

m0d

dtui + d

dtmikuk =

(m0δik +mik) ddtuk.

(A.54)

Now, we let the fluid oscillate with an (instantaneous) velocity vi and see whatthe equation of motion becomes. If our particle was completely entrained by thefluid, moving with the same velocity, the force acting on it would be the same asthe force acting on a fluid particle of the same size; the momentum carried wouldbe ρV0vi and the force the time derivative of this. However, we are interested in asituation where the particle is not completely entrained, but moving with a velocityui which might be different from that of the fluid. The additional momentum fromthis difference in velocity (from the particle “pushing”/“pulling” at the fluid) willbe mik (uk − vk), i.e. Eq. (A.50) but with the relative velocity plugged in. Thismeans that there will be an additional reaction force on the body according to Eq.(A.52), and the equation of motion becomes (equating the time derivative of themomentum of the particle with the total force on it)

m0d

dtui = ρV0

d

dtvi −mik

d

dt(uk − vk) . (A.55)

Integrating this equation with respect to time and collecting the velocities on dif-ferent sides we get

m0ui = ρV0vi −mik (uk − vk)(m0δik +mik)uk = (ρV0δik +mik) vk,

(A.56)

where we have set the constant of integration to zero as we must demand that whenone of the velocities is zero, the other must also be identically zero. Also, if thedensity of the particle is equal to that of the fluid, we recover that the velocitiesare equal, which should also be true. Now, for our spherical particle we have Aifrom Eq. (A.46), which together with Eq. (A.50) gives that

Pi = mikuk = 4πρAi − ρV0ui

=(

2πρR30 − ρ

4π3 R3

0

)ui

= 2πρR30

3 ui.

(A.57)

From this, we can deduce from this that for our spherical particle we have

mik = 2πρR30

3 δik. (A.58)


Using this expression in the equation of motion (A.56) for our particle in the oscil-lating fluid we now arrive at

(m0δik +mik)uk = (ρV0δik +mik) vk(ρ0V0δik + 2πρR3

03 δik

)uk =

(ρV0δik + 2πρR3

03 δik

)vk(

ρ04πR3

03 + ρ

2πR30

3

)ui =

(ρ

4πR30

3 + ρ2πR3

03

)vi

ui = 3ρ2ρ0 + ρ

vi.

(G4 a)

This expression appears as an unnumbered equation in both the original paper andthe English translation. We are now getting very close to the end of this Section;what remains is the actual calculation of our Ai and thus our ϕ. We have from Eq.(A.40) that ϕ = −Ainir−2, and from Eq. (A.46) that Ai = 1

2R30ui. There is only

one small but important pitfall left: When we did the calculation of Ai, we usedthe velocity of the particle relative to the fluid. Thus, we must now take care tostill insert the relative velocity uk − vk:

ϕ = −Ainir2

= −R30

2r2 (ui − vi)ni

= −R30

2r2

(3ρ

2ρ0 + ρvi − vi

)ni

= −R30

2

(2 (ρ0 − ρ)2ρ0 + ρ

)∂i

(vir

).

(A.59)

Finally, combining Eqs. (G4’), (G6’), and (A.59), we get our scattered potential as

ϕsc = −a (t)r

+Ai∂i1r

= −R30ρin3ρ

(1− ρc2

ρ0c20

)1r− R3

02

(2 (ρ0 − ρ)2ρ0 + ρ

)∂i

(vir

)≡ −R

30ρin3ρr f1 −

R30

2 f2∂i

(vir

),

(G7)

where we have introduced the (now hopefully explained) contrast factors f1 and f2:

f1 = 1− ρc2

ρ0c20

f2 = 2 (ρ0 − ρ)2ρ0 + ρ

.

(G7 a)

These definitions appear unnumbered in both versions of the paper.

A.3. THE FORCE POTENTIAL IN A NON-PLANE WAVE 79

A.3 The force potential in a non-plane wave

Let us now return to our integral expression Eq. (G3) for the force. For memoryrefreshal, we have a force

〈Fi〉 = −∮ ⟨(

−ρv2

2 + ρ

2c2

(∂ϕ

∂t

)2)δik + ρvivk

⟩dSk. (A.60)

Inserting our total field (incident and scattered) into this expression yields a fairlyunwieldy equation that can easily be split into three distinct parts - one containingonly the incident field, one containing only the scattered field, and one with theinterference terms:

〈Fi〉 = −ρ∮ ⟨(

−vinm v

inm

2 + 12c2

(∂ϕin∂t

)2)δik + vini v

ink

⟩dSk+

− ρ∮ ⟨(

−vscmv

scm

2 + 12c2

(∂ϕsc∂t

)2)δik + vsci v

sck

⟩dSk+

− ρ∮ ⟨(

−vinm vscm + 1c2∂ϕin∂t

∂ϕsc∂t

)δik +

(vsci v

ink + vsck v

ini

)⟩dSk,

(A.61)

where the notation deviates in the location of the indices from the paper by Gor’kov,but should be clear. The first integral is the momentum flux density in the wavewere there no particle, and thus is no way influenced by the presence of our particle- hence, it does not influence the particle. Now, we shall skip some steps in thepaper, since we are not interested in fields similar to plane running waves. In thiscase, the result in the paper is based on calculating the momentum carried awayby the scattered wave in different directions. Since in a field similar to a planewave the time average of the incident field is spatially homogenous around theparticle, the term in Eq. (A.61) contributing to the force will be that with thescattered field only. However, Doinikov has shown [7] the result acquired by such acalculation to be incomplete, as the contributions to the actual force on the particlefrom thermal and viscous effects can become non-negligible, so let us not dwell onthis. Comparing the second and third integral we see that the second one is themomentum flux density in the scattered wave only, while the third integral has allthe interference terms. It can be shown [100] that the scattering cross-section of aspherical particle goes as

(2πλ−1R0

)4 = (kR0)4, and as λ R0, the integral withonly the scattered field will generally be small when compared to the integral withthe interference terms. Looking at the term with the velocity potentials in the thirdintegral of Eq. (A.61), with the density factor outside the integral brought in, weget that (using Eqs. (A.21) and (A.31)),

ρ

c2

⟨∂ϕin∂t

∂ϕsc∂t

⟩= ρ

c2

⟨(−p′sc

ρ

)(−p′in

ρ

)⟩= c2

ρ〈ρ′scρ′in〉 , (A.62)


And we thus get a force, using only the third integral of Eq. (A.61),

〈Fi〉 = −∮ (−ρ⟨vinm v

scm

⟩+ c2

ρ〈ρ′scρ′in〉

)δik + ρ

(⟨vsci v

ink

⟩+⟨vsck v

ini

⟩)dSk.

(G10 a)

From here, we use the divergence theorem to transform this into a volume integral,getting

〈Fi〉 = −∮ (−ρ⟨vinm v

scm

⟩+ c2

ρ〈ρ′scρ′in〉

)δik + ρ

(⟨vsci v

ink

⟩+⟨vsck v

ini

⟩)dSk

= −∫−ρ∂i

⟨vinm v

scm

⟩+ c2

ρ∂i 〈ρ′scρ′in〉+ ρ

(∂k⟨vsci v

ink

⟩+ ∂k

⟨vsck v

ini

⟩)dV

= −∫−ρ⟨(∂iv

inm

)vscm + vinm∂iv

scm

⟩+ c2

ρ〈(∂iρ′sc) ρ′in + ρ′sc∂iρ

′in〉

+ ρ(⟨

(∂kvsci ) vink + vsci ∂kvink

⟩+⟨(∂kvsck ) vini + vsck ∂kv

ini

⟩)dV

= −∫c2

ρ〈ρ′in∂iρ′sc + ρ′sc∂iρ

′in〉+ ρ

(⟨vsci ∂kv

ink

⟩+⟨vini ∂kv

sck

⟩)dV ,

(A.63)

where the equality on the last line is achieved by noticing that indices k and mare “dummy” indices to be summed over. We shall now attempt to simplify thisexpression considerably. Here it has become time to invoke the time-averaging. Wenote that while for an arbitrary periodic function the time-average is generally non-zero, the time-average of the time derivative of the function is necessarily identicallyzero. Thus, we have

0 =⟨∂

∂t

(ρ′scv

ini

)⟩=⟨ρ′sc

∂

∂tvini

⟩+⟨vini

∂

∂tρ′sc

⟩⇒⟨ρ′sc

∂

∂tvini

⟩= −

⟨vini

∂

∂tρ′sc

⟩,

(A.64)

and likewise of course for an exchange of incident and scattered fields. Furthermore,writing the linearized equation of continuity for the total field we have that

∂

∂t(ρ′sc + ρ′in) = −ρ∂i

(vsci + vini

)⇒

ρ∂ivini = − ∂

∂t(ρ′sc + ρ′in)− ρ∂ivsci .

(A.65)

Using this, we can rewrite the force expression. Taking it term by term, the firstterm becomes, using Eqs. (A.31), (A.20) and (A.64) in that order:

c2

ρ〈ρ′in∂iρ′sc〉 = c2

ρ

⟨1c2 ρ′in∂ip

′sc

⟩= −c

2

ρ

⟨ρ′in

ρ

c2∂vsci∂t

⟩=⟨vsci

∂ρ′in∂t

⟩. (A.66)


The second term becomes identical but with incoming and scattered fields ex-changed. The third term becomes, using Eq. (A.65),

ρ⟨vsci ∂kv

ink

⟩=⟨−vsci

∂

∂t(ρ′sc + ρ′in)− vsci ρ∂ivsci

⟩= −

⟨vsci

∂ρ′in∂t

⟩, (A.67)

where we have disregarded higher-order terms which are not interference terms, i.e.describe mixing of the fields (as we are calculating to first order). The fourth termwe leave intact, and thus get

〈Fi〉 = −∫c2

ρ〈ρ′in∂iρ′sc + ρ′sc∂iρ

′in〉 ρ

(⟨vsci ∂kv

ink

⟩+⟨vini ∂kv

sck

⟩)dV

= −∫ ⟨

vsci∂ρ′in∂t

⟩+⟨vini

∂ρ′sc∂t

⟩−⟨vsci

∂ρ′in∂t

⟩+ ρ

⟨vini ∂kv

sck

⟩dV

= −∫ ⟨

vini

(ρ∂kv

sck + ∂ρ′sc

∂t

)⟩dV .

(G11 line 1)

From here we re-introduce the velocity potential, using the two relations (for thesecond one, cf. Eq. (A.21))

∂kvsck = ∂k∂kϕsc

∂ρ′sc∂t

= ρ

c2∂

∂t

(c2ρ′scρ

)= ρ

c2∂

∂t

(p′scρ

)= − ρ

c2∂2ϕsc∂t2

.(A.68)

Inserting this into Eq. (G11 line 1), we recover the remainder of Eq. G11 from thepaper:

〈Fi〉 = −ρ∫ ⟨

vini

(∂k∂kϕsc −

1c2∂2ϕsc∂t2

)⟩dV . (G11 line 2)

We note that the expression in the parenthesis is actually the wave equation for thescattered field and thus an expression that is usually identically zero. In this case,however, we have the source of the field inside out volume of integration, meaningthat we will be integrating over an expression containing delta functions in space.We have from Eq. (G7) with the retarded time τ = t − rc−1 used to describe theoutgoing wave from the particle that

ϕsc = −a (τ)r

+Ai (τ) ∂i1r

= −R30

3ρ f1ρin (τ)r

− R30

2 f2∂i

(vini (τ)r

).

(A.69)

Entering this into the wave equation under the integral gives us zero everywhere ex-cept at the origin (where our very small particle is). There, we get three-dimensional


spatial delta functions according to

∂k∂kϕsc −1c2∂2ϕsc∂t2

= −R30

3ρ f1ρin (τ) · (−4πδ (r))− R30

2 f2∂i(vini (τ) · (−4πδ (r))

)= 4πR3

03ρ f1ρinδ (r) + 2πR3

0f2∂i(vini δ (r)

).

(G11 a)

Our expression for the force now becomes

〈Fi〉 = −ρ∫ ⟨

vini

(V0

ρf1ρinδ (r) + 3

2V0f2∂n(vinn δ (r)

))⟩dV , (A.70)

where V0 is the volume of the particle. The first term is quite simple to integrate,courtesy of the delta function. The second term has to be integrated by parts givingone integral over the surface of our volume and one over the volume. We thus get

〈Fi〉 = −V0f1⟨vini ρin

⟩− 3

2ρV0f2

∫ ⟨vini ∂n

(vinn δ (r)

)⟩dV

= −V0f1⟨vini ρin

⟩− 3

2ρV0f2

∫ ⟨vini δ (r) vinn

⟩dSn + 3

2ρV0f2

∫ ⟨vinn ∂nv

ini δ (r)

⟩dV .

(A.71)

The surface of integration of the first integral does not contain the origin, and thedelta function thus makes this integral identically zero. The second integral is overa volume containing the origin, and we have

〈Fi〉 = −V0

(f1

⟨vini

∂

∂tρin

⟩+ 3

2ρf2⟨vinn ∂nv

ini

⟩). (A.72)

Using the trick of Eq. (A.64) and Euler’s equation (Eq. (A.21)), the first termcan be rewritten into a function of the incident pressure field, remembering thatρin = ρ′in:

f1

⟨vini

∂

∂tρ′in

⟩= −f1

⟨ρin

∂

∂tvini

⟩= f1

⟨p′inc2

1ρ∂ip′in

⟩, (A.73)

giving a force expression of

〈Fi〉 = −V0

(f1

1ρc2 〈p

′in∂ip

′in〉+ 3

2ρf2⟨vinn ∂nv

ini

⟩). (A.74)

From here, all we need to do is notice that the brackets in the first term is half thegradient of the pressure squared, and use Eq. (A.12) on the second term to get

〈Fi〉 = −∂iV0

(f1

12ρc2

⟨p′

2in

⟩+ 3

4ρf2⟨v2in

⟩), (A.75)


which concludes this appendix, as we now have the force written as the negativegradient of a potential

U = V0

(f1

12ρc2

⟨p′2in⟩

+ 34ρf2

⟨v2in

⟩). (G12)

Ultrasound in Med. & Biol., Vol. 33, No. 1, pp. 145–151, 2007Copyright © 2006 World Federation for Ultrasound in Medicine & Biology

Printed in the USA. All rights reserved0301-5629/07/$–see front matter

doi:10.1016/j.ultrasmedbio.2006.07.024

Original Contribution

PROLIFERATION AND VIABILITY OF ADHERENT CELLSMANIPULATED BY STANDING-WAVE ULTRASOUND IN A

MICROFLUIDIC CHIP

J. HULTSTRÖM,* O. MANNEBERG,* K. DOPF,* H. M. HERTZ,* H. BRISMAR,† andM. WIKLUND*

*Department of Applied Physics, Biomedical and X-Ray Physics, KTH/Albanova, Stockholm, Sweden; and†Department of Applied Physics, Cell Physics, KTH/Albanova, Stockholm, Sweden

Abstract—Ultrasonic-standing-wave (USW) technology has potential to become a standard method for gentleand contactless cell handling in microfluidic chips. We investigate the viability of adherent cells exposed to USWsby studying the proliferation rate of recultured cells following ultrasonic trapping and aggregation of low cellnumbers in a microfluidic chip. The cells form 2-D aggregates inside the chip and the aggregates are held againsta continuous flow of cell culture medium perpendicular to the propagation direction of the standing wave. Nodeviations in the doubling time from expected values (24 to 48 h) were observed for COS-7 cells held in the trapat acoustic pressure amplitudes up to 0.85 MPa and for times ranging between 30 and 75 min. Thus, the resultsdemonstrate the potential of ultrasonic standing waves as a tool for gentle manipulation of low cell numbers inmicrofluidic systems. (E-mail: [email protected]) © 2006 World Federation for Ultrasound in
Medicine & Biology.
INTRODUCTION

Contactless handling and manipulation of cells in micro-systems are important for the development of automatedand efficient cell-based biotechnology applications. Inapplications that utilize delicate cells, it is important toavoid unwanted physical surface contact as well as in-terference with any biologic process caused by the ma-nipulation tool. Ultrasonic-standing-wave (USW) tech-nology shows promise for both efficient, as well asgentle, manipulation of cells. Here, we investigate thecell viability by studying the proliferation rate of adher-ent COS-7 cells after ultrasound exposure in a micro-chip-based USW trap.

Reported methods for contactless manipulation ofindividual cells in microchips are most often based onlaser tweezers (Enger et al. 2004) or dielectrophoresis(Müller et al. 2003). USW technology is an interestingalternative that has been introduced to microchips, e.g.,for continuous cell separation (Harris et al. 2003, Peters-son et al. 2004, Kapishnikov et al. 2006), cell washing(Hawkes et al. 2004a, Petersson et al. 2005) cell depo-sition on a surface (Hawkes et al. 2004b) and cell posi-

Address correspondence to: J. Hultström, Department of Applied
Physics, Biomedical and X-Ray Physics, KTH/Albanova, SE-106 91,Stockholm, Sweden. E-mail: [email protected]
145

tioning (Haake et al. 2005). Common for those ap-proaches is the use of MHz-frequency ultrasound inmicrochips for manipulation of large groups of cellsduring short terms. However, in contrast to optical twee-zers and dielectrophoresis, USWs have also been shownto be very suitable for long-term manipulation. This hasbeen demonstrated in macroscaled systems, e.g., for cellretention and filtering in high-density perfusion pro-cesses (Shirgaonkar et al. 2004). Here, 1000 h ofoperation is typically carried out with no significant lossin cell viability. However, to minimize the cell damage,several parameters must be carefully controlled, e.g., theacoustic pressure level, the flow properties and the tem-perature. Therefore, it is of interest to investigatewhether the results from high-density cell samples inmacrosystems also are applicable to low-density cellsamples in microchips.

In macroscaled systems (i.e., with cm- or mm-scaled resonators), the viability of USW-manipulatedcells has been measured by different methods. Mostoften, it is measured directly in connection with theexposure. Typically, the measured parameter is the in-tegrity of the cell membrane, which is determined by,e.g., the use of trypan blue dye or propidium iodide(Kilburn et al. 1989; Doblhoff-Dier et al. 1994; Pui et al.
1995; Wang et al. 2004; Bazou et al. 2005a; Khanna et
mailto:[email protected]

146 Ultrasound in Medicine and Biology Volume 33, Number 1, 2007

al. 2006). Another similar strategy is to measure therelease of intracellular components such as potassiumions or haemoglobin from red blood cells (Yasuda 2000;Cousins et al. 2000). Furthermore, early and late apopto-sis have been measured by the use of fluorescence assays(Bazou et al. 2005a). In perfusion applications, the via-bility has been measured indirectly by studying the pro-duction rate of proteins, monoclonal antibodies or vi-ruses (Zhang et al. 1998). In addition, transmission elec-tron microscopy (TEM) has been used for detailedexamination of the structure and morphology of intracel-lular components (Kobori et al. 1995; Radel et al. 2000).Besides, physical variables such as fluid flow, tempera-ture and possible cavitation around ultrasonically trappedcells have been thoroughly investigated (Bazou et al.2005b). In all these macroscale studies the cell viability,directly after exposure, is typically 95 to 99% undercontrolled conditions (i.e., at moderate pressure levels).

Another, less common, approach to measure the cellviability is to investigate the proliferation rate of reculturedcells after ultrasonic exposure. This method should be amore sensitive tool for quantification of viability, since italso takes into account any possible effects that may causedelayed damage to the cells. This hypothesis is supportedby studies of the physical factors involved in ultrasound-mediated damage of cells in standing-wave systems. Forexample, one study suggests that the structure of the cy-toskeletal elements responsible for the cell division process(e.g., spindle bodies and microtubules) may be partiallydamaged or passivated by mechanical stress from ultra-sound traps (Pui et al. 1995). Furthermore, ultrasonic expo-sure may alter the integrity of the cell vacuole in trappedyeast cells (Radel et al. 2000). Thus, proliferation is indeedan interesting parameter for sensitive viability investigation.Reports on cell proliferation after standing-wave ultrasonicexposure are, e.g., investigation of the proliferation of yeastcells fixed in a semirigid nontoxic gel matrix (Gherardini etal. 2005) and investigation of the proliferation of hybridomacells exposed to different ultrasound energies (Pui et al.1995). However, both these studies have only investigatedproliferation after short-term ultrasonic exposure (10min).

In the present paper, we study the proliferation rate ofrecultured adherent cells after both short- and long-termultrasonic standing wave exposure in a microfluidic chip. Incontrast to the long-term studies in macroscaled perfusionsystem with high cell densities, we investigate the viabilityafter individual handling of low cell numbers (102–103)and low cell densities (104 mL1) in microsystems. Thus,other effects than ultrasound that may cause stress or dam-age are also included, e.g., fluidic shear forces from pas-sages through narrow microchannels and syringe needlesand increased rate of surface contact in the high surface-to-
volume microchannels. In addition, we study the effect on
the proliferation rate of cells concentrated in 2-D aggre-gates, compared with nonconcentrated cells. The funda-mental motivation of this work is to investigate the appli-cability of chip-based USW tools for gentle and long-termhandling of individual cells within a wide range of biotech-nology applications.

MATERIALS AND METHODS

Ultrasonic microfluidic chip assemblyThe ultrasonic standing wave microfluidic chip was

fabricated in house. The chip assembly is illustrated inFig. 1. A 260 m thick polydimethylsiloxane (PDMS)layer (Sylgard 184, Dow Corning, Midland, USA) wasused as spacer between the two glass plates. The depth ofthe microchannel was close to half the ultrasonic wave-length in water (250 m) resulting in one pressurenode in the middle of the channel. The 550 m thickglass plates (21 23 mm borosilicate cover glass, Men-tzel GmbH, Braunschweig, Germany), which defined theacoustic resonator, worked both as coupling layer andquarter-wavelength reflectors. A 3-MHz circular 5-mmdiameter lead zirconate titanate (PZT) transducer (PZ26,Ferroperm, Kvistgaard, Denmark) was attached by con-ductive glue (Thermoset MD-120, Lord Chemical Prod-ucts, Manchester, UK) on the top glass plate. The chipwas designed with two separate inlets to facilitate rapidwashing during cell trapping experiments. On the inletside, a PDMS block was fabricated and attached to theside of the chip for easier and more stable connectionbetween the chip and the external fluidic system. Thelatter consisted of Teflon tubing and needles with innerdiameters of 250 m and 110 m, respectively. On theoutlet side, a free-hanging 5 5 mm thin PDMS flap ofthickness 150 m was added beneath the open end ofthe channel to allow easy ejection from the channelwithout dead volumes and sample losses.

Ultrasonic trapping forcesCells suspended in an aqueous medium are trapped in

the pressure nodes of the ultrasonic standing-wave field.Following the formalism derived by Gor’kov (1962) andassuming a plane field propagating along the vertical z-axis,the acoustic radiation force, F(z), is given by

Fz

20c03f1

3

2f2 · V · p0

2 · v · sin2z

0 ⁄ 2, (1)

where is the frequency, V is the cell volume, p0 is thepressure amplitude and 0 is the acoustic wavelength in the

medium. The dimensionless factors f1 1 0c0

2

c2 and f2

202

depend on the density and sound velocity of
0
the trapping medium (0 and c0, respectively) and the

Microfluidic chip cell manipulation J. HULTSTRÖM et al. 147

cell ( and c). Initially, the cells move within secondsalong the z-axis, due to the strong axial component of theacoustic radiation force. Once trapped in a nodal plane,the cells form 2-D aggregates due to the weaker lateralcomponent of the acoustic radiation force and the attrac-tive interaction force (Bjerknes force) working only atshort distances (m) (Wiklund and Hertz 2006). Thereare also other forces acting on the cells that influence thetrapping performance, such as the viscous drag forcefrom the flow. In our system (cf. Fig. 1), this drag force

Fig. 1. (a). Top view of the in-house glass-PDMS-glass mi-crofluidic chip with an integrated PDMS block containing twoseparate inlets with tubing and needles and the outlet with athin PDMS flap added beneath the open end of the channel. (b).Cross-section of the microfluidic chip showing the circular3-MHz PZT transducer and the three-layered structure. Thechannel height of 260 m, defined by the PDMS spacer, was closeto half the ultrasonic wavelength in water, giving one pressurenode in the middle of the channel, where the cells were trapped.The glass plates had a thickness of 550 m, corresponding ap-

proximately to a quarter wavelength for the sound in glass.

is balanced by the weaker lateral components of the

acoustic primary force, which is about 100 times lowerthan the axial force. Hence, a relatively high acousticpressure amplitude is required for stable trapping againstthe flow. In addition, at higher pressures, acousticstreaming may significantly influence the stability of thetrapped cell aggregates (Kuznetsova and Coakley 2004).

Acoustic pressure level inside chipTo estimate the acoustic pressure amplitude within

the microchannel, a gravitational escape experiment wasperformed. A single 10 m green-fluorescent latex bead(Bangs Laboratories, Fischer, USA) was trapped at atransducer driving voltage of 0.2 V (peak-to-peak) bal-ancing against the gravity force, Fg 0Vg. Thisequilibrium can be used to estimate the absolute magni-tude of the acoustic trapping force, eqn 1, and thereafterthe acoustic pressure amplitude, p0. The estimated pres-sure amplitude in the microchannel was 0.57 to 0.85MPa at a transducer driving voltage of 6 V, depending onthe exact location below the transducer.

Chip preparationBefore performing any experiment, the chip and all

other reused parts were sterilized using 70% ethanol. Thechip was then mounted on a plastic holder and placed inthe inverted epifluorescence microscope (Axiovert135M, Zeiss, Germany) equipped with 10/0.25NA ob-jective, a CCD-camera and suitable fluorescence filters.The fluidic system, consisting of Teflon tubing, needles,adaptors and glass syringes, were assembled. The lami-nar flow rate was controlled by a syringe pump(SP2101WZ, World Precision Instrument, Sarasota,USA). The cell injector (Cytocon Injector, Evotec Tech-nologies GmbH, Hamburg, Germany) was placed inclose vicinity to the chip, to minimize the tubing dis-tance. Before each experiment, a new sterile PDMS flapwas attached at the open end of the channel. A continu-ous flow of cell medium (Dulbecco’s modified eaglesmedium, Sigma-Aldrich, Stockholm, Sweden) wasstarted at a flow rate of 5 L/min (50 m/s). Theoutput from the chip was collected in the eight-well cellculture dish (Lab-Tek 8 chamber, Nunc, Rochester,USA) mounted on the chip holder in the microscope. Themicrofluidic chip and cell culture dish were kept at aconstant temperature of 37°C inside a sealed plastic hoodconnected to warm air incubation by a heating unit withregulated temperature control (Zeiss, Germany). Tem-perature and flow stabilization after closing the hoodnormally took about 30 min.

Cell preparationIn parallel with the assembly of the chip, the cell

suspension was prepared. The employed adherent COS-7
cells (purchased from ECACC no.87021302), derived


from fetal monkey kidney, were cultured in Dulbecco’smodified eagles medium containing 10% fetal bovineserum (Gibco, Invitrogen, Stockholm, Sweden), 1% pen-icillin streptomycin (Sigma-Aldrich) and 1% L-glu-tamine (Sigma-Aldrich) and incubated at 37°C in 5%CO2 atmosphere. The cells were removed from the cul-ture dish by trypsination (0.25% trypsin (trypsin-EDTA,Gibco) for 5 min at 37°C), followed by centrifugationand resuspension in new medium at a typical concentra-tion of 1.5 106 cells/mL. For use as a viability indi-cator and to make the cells visible once inside the mi-crochannel, calcein AM (500 M) (Molecular Probes,Eugene, OR, USA) was added at a concentration 2 Lper ml of cell suspension, followed by incubation for 30min in warm water bath (37°C).

Cell trapping experimentsTypically, a 15 to 20 L sample plug of cell sus-

pension was added via the cell injector (cf. Fig. 1) intothe laminar flow of cell medium (flow rate 5 L/min).The PZT transducer was operated at a voltage of 6 V(peak-to-peak) and at the channel resonance frequencyclose to 3 MHz. The cell trapping started about 1 minafter injection, when the cells reached the trapping centerbelow the transducer. Here, a few 2-D cell aggregates, asshown in Fig. 2, were formed and stably trapped againstthe continuous flow. Different USW exposure times,ranging from 30 to 75 min, were investigated with re-

Fig. 2. Image of fluorescently labeled (calcein AM) viable cellstrapped by standing wave ultrasound in the microfluidic chip.The cells formed 2-D aggregates stably trapped against the

continuous flow of cell medium.

gards to cell viability and proliferation. However, the

minimum exposure time was about 5 min, dependingboth on the volume of the sample plug and on the tubinglength between cell injector and chip. Before turning offthe ultrasonic field, images were acquired of all fluores-cently-labeled cell aggregates, for later counting. TheUSW-exposed cells were then ejected through the openchip end into a sterile eight-well cell dish by simulta-neously turning off the USW and applying manual pres-sure on the second syringe to increase the flow rate. Thethin PDMS flap allowed drops to form and fall down intoone of the wells on the cell dish, while still maintaininga constant flow inside the chip. Three drops with trappedcells were collected, giving an initial volume of 30 to 50L. The cell dish was then incubated at 37°C and 5%CO2 (Mini-Galaxy, LabRumKlimat, Stockholm, Swe-den) for 10 min, to allow the cell aggregate to sediment.The prepared cell culture medium was added (300 L)into each well before further incubation for cell cultiva-tion studies. Each experiment was performed two orthree times to obtain comparable data points.

Cell countingTraditionally, cell counting is performed indirectly

by estimation of the cell concentration from a smallaliquot of the sample (e.g., with a Bürker glass chamber).However, in the present work, we handle low cell num-bers (102–103) and low concentrations (104 cells/mL). For such cell samples, the Bürker method wouldcause significant sample losses, resulting in unreliablestatistics. Consequently, a direct cell counting methodhas been used. It is designed to suit our proliferationexperiments, assuming exponential cell growth accord-ing to

N2 N1eat, (2)

where N1 is the initial cell number and N2 is the final cellnumber after a few days of cultivation. These cell dataare used for determining the growth factor a. As a result,the cell doubling time, tdouble, can be calculated

tdouble ln2

a. (3)

Following 2 to 3 d of cell cultivation in the incubator thetotal number of cells was determined from images ac-quired in a scanning microscope. The procedure includedautomatic scanning and image acquisition of the wholecell dish area followed by cell counting. Before themicroscopy scanning, calcein AM (500 M) was addedto the cell dish (0.5 L per well) and incubated for 30min in 37°C. Calcein AM was used primarily as a cellviability indicator (monitoring the esterase activity andmembrane integrity), but also for labeling of the cells for
the fluorescence microscopy. The cell scanning proce-


dure, performed in a confocal microscope (ZeissLSM410, Zeiss, Germany), was mainly composed ofthree steps. First, the cell dish with coverslip bottom(thickness 200 m) was placed at the microscope stageand the focus and contrast settings were manually ad-justed. The next step was to define the center of thespecified well on the cell dish by first choosing the shapeof the well and then finding the outer edges of the well.Finally, the whole well was automatically scanned, col-lecting about 200 images (see Fig. 3) from a single well.The acquired images of the cultivated cells were eitherautomatically or manually counted with the free softwareImageJ (more information available at http://rsb.info.nih.gov/ij/). For time-saving purposes, an automatic cellcounting algorithm has been developed to evaluate thelarge number of cell images. This method is based on amacroprogram of predefined functions in ImageJ andworks on an image sequence containing approximately200 images originating from a single cell well. Theimage processing consists of several steps: make andfilter binary images, apply watershed and despecklefunctions and, finally, count particles. The output fromthe program gives the final number of cells in the presentwell after cell cultivation. The automatic counting cor-

Fig. 3. Confocal microscope image of recultivated COS-7 cells3 d after USW exposure. Since the cells were labeled with theviability indicator calcein AM, only living cells are visible. Tosimplify image analysis and cell counting, some high densitycell areas must be overexposed and thus saturated. (a). Cell in

division phase. (b). Low cell density. (c). High cell density.

responded well with manual counting (within 10%).

However, at very high cell densities, the difference grewto about 30%. Therefore, the presented data (see Resultssection) relies on manually counted cells, taken as anaverage of two independent operators.

The initial number of cells was estimated by thesame manual counting method, as described above, oftrapped cells in the images acquired at the end of eachtrapping experiment inside the microchip (see Fig. 2). Inaddition, the ejection step was carefully monitored in acontrol experiment where the USW trapped cells werecounted both before and after ejection. A few (about five)cells attached to either the PDMS flap or the chip duringthe ejection, but this was accounted for during the celltrapping experiments.

Control experimentsControl experiments without USW exposure were

performed with cells subjected to the same cell handlingprotocol as the USW-trapped cells. The cell suspensionwas counted in a Bürker chamber and then diluted togive a final concentration of 104 cells/mL. A smalldroplet of 10 L was placed in each of four wells in fourcell dishes and the initial numbers of cells were 1000cells. The cell dishes were incubated for 10 min and 400L culture medium was added to each well. Two of thefour cell dishes (eight wells in total) were scanned in theconfocal microscope after 1 h, to estimate the averageinitial cell number. The other two were cultivated in thesame incubator as the USW-trapped cells for 3 d beforecell counting. This gave the average final cell number forthe control cells.

RESULTS AND DISCUSSION

The purpose of our study is to measure the prolif-eration rate of adherent cells as a function of ultrasonicexposure time in a USW microfluidic chip. In all exper-iments, the ultrasonic pressure was kept constant at alevel approximately twice the minimum pressure ampli-tude needed for controlled and stable trapping perfor-mance. Typically, 500 to 2000 cells were collected andtrapped during each exposure and all measurements weredone in the same microfluidic chip.

The examination of USW-trapped cells after about3 d of cultivation showed that the cells survive andproliferate after the microfluidic USW handling. Thegrowth rates were estimated via the cell number doublingtimes, tdouble, by comparing the initial and final numbersof cells and assuming exponential growth (cf. eqn 3). Inall measurements, only viable cells were counted (by theuse of the viability indicator calcein AM). The results arepresented in the diagram in Fig. 4. First, six experimentswith 30 min exposure time were carried out. Here, cells
from two different cell preparations were used. The cells
http://rsb.info.nih.gov/ij/

http://rsb.info.nih.gov/ij/


were exposed to USWs of average pressure amplitude(0.85 MPa at an applied voltage of 6 V) for about 30 min.Cell samples were collected from each experiment andcultivated. When no effect on cell viability was observedat this exposure time, four experiments were performedat 60 to 75 min. At these longer exposure times, two cellsamples could be taken from each cell preparation (forcomparable cell handling times). Longer USW exposuretimes were not possible to measure, due to the lack ofnutrient for the cells. However, this could likely besolved by slowly perfusing the trapped cells with cellculture medium containing serum and amino-acids. Re-peated measurements for the two different exposuretimes gave similar doubling times, 35 to 47 h and 25 to62 h, respectively, and data points from the same cellpreparation also showed small variance. The error barsfor the cell doubling times depend both on uncertaintiesin the manual counting of the initial and final numbers ofcells as well as on the difference in exposure times forcells being trapped first or last, typically 3 to 11 min.

The experimental data indicate that there exist nei-ther direct nor delayed damaging effects on cells handledand trapped by ultrasonic standing waves (USWs) in amicrofluidic system. Furthermore, the proliferation rateof cells exposed to USWs up to 75 min at 0.85 MPa(cf. Fig. 4) does not deviate from typical values foradherent cells (24 to 48 h) (Freshney 2000; DSMZ2006), not even for our samples with low cell numbers(102–103) and low cell concentrations (104 mL1).

Fig. 4. Cell doubling times were estimated by comparing theinitial and final number of cells and assuming exponentialgrowth (cf. eqn 2). Two experiments with a USW exposuretime close to 30 min [filled square], [filled inverted triangle]and two experiments for USW exposure times around 60 minwere performed [open square], [open inverted triangle]. Forcomparison, eight batches of untreated cells [open circle] werealso cultivated. The average cell doubling time for the control

cells is indicated by [filled circle].

In fact, the untreated control cells (also at concentration

104 mL1) that were not exposed to ultrasound showeda significantly slower rate of proliferation. Therefore, wemay conclude that USW manipulation of cells is not onlynondamaging under controlled conditions, but also ben-eficial for the proliferation rate. We believe that this isdue to the increased local cell density obtained when theUSW-formed aggregates are transferred from the chip tothe bottom of the culture dish. This should be especiallyimportant in microchip-based applications, where smalland/or diluted cell samples are often employed. Further-more, additional chip-related factors, besides ultrasound,that may cause damage or stress to the cells do not seemto have any significance. These factors include, e.g.,fluidic shear forces and increased surface contact insidenarrow microchannels and syringe needles and the lightexposure when imaging the ultrasonically-trapped cellsbefore ejection (1 to 5 min). Finally, it should be men-tioned that the maximum pressure amplitude level usedin this work (0.85 MPa), is more than sufficient forUSW manipulation in a chip. This is especially true,since we here use the much weaker lateral force compo-nents of the USW, competing with the viscous flowforces. Thus, even lower acoustic pressure amplitudewould be needed for stable cell manipulation if thestanding wave direction is parallel with the channel.Typically, the axial USW force component is 100times higher than the lateral component in plane-parallelUSW resonators (Wiklund and Hertz, 2006). However,we have not measured the upper pressure amplitude limitfor nondamaging USW manipulation. The reason is thatthe trap is not stable under such conditions, due toacoustic streaming. Therefore, such pressure levels arenot interesting from an application point-of-view.

The general purpose of the present study is to in-vestigate the applicability of USW technology for gentlecell handling in microchips. Most of the reported bio-technology applications that utilize USW technologyhandle large sample volumes and high cell concentra-tions. On the other hand, many applications require han-dling of individual cells, e.g., for single cell character-ization. Therefore, other manipulation tools with higherspatial accuracy are often chosen, e.g., laser tweezers ordielectrophoresis. However, in terms of cell viability,both these methods have been shown to be less suitablefor long-term manipulation. An approach to solve thisproblem is to combine different manipulation technolo-gies, e.g., USW and dielectrophoretic (DEP) manipula-tion (Wiklund et al. 2006). For example, DEP can beused initially for high-precision manipulation of individ-ual cells, followed by prolonged USW retention of al-ready trapped cells. A suggested application of such acell handling device is controlled cell differentiation bysurface stimulation via artificial immobilization of mac-
romolecules on, e.g., beads. This idea is supported by,


e.g., experiments where cells are differentiated by adhe-sion to a surface coated with either immobilized cyto-kines (Leclerc et al. 2006) or immobilized extracellularmatrix molecules (Flaim et al. 2005). Here, USW tech-nology can be used for long-term trapping and position-ing of a cell-bead complex during the differentiationprocess (which is assumed to take several hours). Otherpossible biotechnology applications are live cell assaysthat require long-term manipulation, or concentration,storage and cultivation of small cell samples (i.e., lowcell numbers, small sample volumes and/or low cellconcentrations). Furthermore, USW technology can beused for automated cell preparation (e.g., washing andseparation) by replacing standard methods based on, e.g.,centrifugation and micropipetting.

Acknowledgments—The authors thank Mårten Stjernström for his con-tribution to the PDMS fabrication. This work was supported by theEuropean Community-funded CellPROM project under the 6th Frame-work Program, contract no. NMP4-CT-2004 to 500039.

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http://www.dsmz.de

http://www.dsmz.de

IOP PUBLISHING JOURNAL OF MICROMECHANICS AND MICROENGINEERING

J. Micromech. Microeng. 17 (2007) 2469–2474 doi:10.1088/0960-1317/17/12/012

Temperature regulation during ultrasonicmanipulation for long-term cell handlingin a microfluidic chipJ Svennebring, O Manneberg and M Wiklund

Biomedical and X-Ray Physics, Applied Physics, KTH/Albanova, SE-106 91 Stockholm,Sweden

E-mail: [email protected]

Received 25 April 2007, in final form 6 September 2007Published 1 November 2007Online at stacks.iop.org/JMM/17/2469

AbstractWe demonstrate simultaneous micromanipulation and temperatureregulation by the use of ultrasonic standing wave technology in amicrofluidic chip. The system is based on a microfabricated silicon structuresandwiched between two glass layers, and an external ultrasonic transducerusing a refractive wedge placed on top of the chip for efficient coupling ofultrasound into the microchannel. The chip is fully transparent andcompatible with any kind of high-resolution optical microscopy. Thetemperature regulation method uses calibration data of the temperatureincrease due to the ultrasonic actuation for determining the temperature ofthe surrounding air and microscope table, controlled by a warm-air heatingunit and a heatable mounting frame. The heating methods are independentof each other, resulting in a flexible choice of ultrasonic actuation voltageand flow rate for different cell and particle manipulation purposes. Ourresults indicate that it is possible to perform stable temperature regulationwith an accuracy of the order of ±0.1 C around any physiologicallyrelevant temperature (e.g., 37 C) with high temporal stability andrepeatability. The purpose is to use ultrasound for long-term cell and/orparticle handling in a microfluidic chip while controlling and maintainingthe biocompatibility of the system.

1. Introduction

Ultrasonic standing wave (USW) technology is a suitabletool for gentle manipulation of cells and other bioparticlesin various biotechnology applications [1]. In macro-scaledsystems (with typical active volumes >100 µl), cells canbe handled by MHz-frequency ultrasound on the time scaleof days to months without any detectable damage or loss inviability [2], and without any cavitation or acoustic-streaming-generated shear forces of significance from the surroundingfluid [3]. However, when downscaling the system dimensionsthe acoustic energy is deposited into smaller volumes, whichmay lead to an increase in temperature that is not compatiblewith careful cell-biological experiments. In the present paper,we use ultrasound for simultaneous manipulation of particlesand temperature regulation in a silicon-based microfluidic chipfor long-term gentle handling of sub-µl-volume cell samples.

Several cell-based applications in biotechnology aredependent on the development of non-intrusive tools formanipulation of cells or other bioparticles in microfluidicchips. In comparison to available techniques for contactlessmanipulation in miniaturized systems (e.g., dielectrophoresis[4] and optical tweezers [5]), USW technology is a promisingalternative for such long-term cell handling in terms offlexibility, cost-effectiveness and gentleness [6, 7]. In anUSW, suspended particles are driven to the pressure nodesfound in half-wavelength intervals, due to the primary acousticradiation force, which is proportional to the particle volume,sound frequency and pressure amplitude squared. The nodesare formed at specific frequencies fulfilling the resonancecondition of the cavity hosting the standing wave [8]. We havepreviously shown that ultrasound may be used for retention ofcells during perfusion in a relatively small (∼30 µl) PDMS-based chip for more than 1 h without any losses in cell viability

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[1]. However, when downscaling the system size even further,e.g., by the use of a microfabricated silicon chip with sub-µl-volume fluidic channels, a temperature increase in the activefluid volume cannot be avoided. Furthermore, since the fluidchannel has a high surface-to-volume ratio and only constitutes∼2% of the highly heat-conductive silicon structure, it isdifficult to regulate the fluid temperature externally (e.g., byregulating the fluid temperature outside the channel inlet ofthe chip). Therefore, the temperature in the chip itself must beregulated in order to retain a biocompatible environment.

In macro-scaled USW systems for high-power particlemanipulation, the temperature is most often controlled by aloop of cooling water close to the active chamber [9, 10].Such a cooling system is not needed for low-power acousticparticle manipulation given that the sample volume is largeenough (typically >100 µl) [3]. As an example, the estimatedtemperature increase in the latter system is at most 0.5 Cduring 30 min of operation at 0.54 MPa pressure amplitude.In silicon-chip-based USW applications, little effort has beenmade to investigate the temperature development. A possiblereason is that most of the reported USW applications in suchsystems aim for high-throughput continuous separation ofparticles or cells [11, 12]. Thus, particles are only manipulatedfor a few seconds, making temperature control less importantin terms of biocompatibility. However, in USW applicationsaiming for long-term manipulation, retention and cultivationof cells in microfluidic chips, a temperature regulation systemis necessary.

In the present paper, the origin of the heat deposition isinvestigated and the temperature increase is measured as afunction of the applied transducer voltage and manipulationtime in a miniaturized USW system operated in both non-flowing and flow-through mode. The system is basedon a glass-silicon-glass microfluidic chip and a transducerwith a refractive element for oblique coupling of ultrasoundinto the fluid channel, which has been described elsewhere[6]. The developed transducer-chip system is compatiblewith any kind of high-resolution optical microscopy andcondenser illumination, suitable for detailed characterizationof individual cells. We demonstrate a novel regulationprocedure where temperature-versus-voltage calibration datacan be used as feedback to the external temperature controlsystems (in our case a warm-air heating unit and a heatablemounting frame) for defining the temperature of the mediain contact with the transducer-chip assembly. By the useof on-line temperature monitoring, we demonstrate regulationaround an arbitrary physiological temperature with a long-termstability below ±0.1 C, independently on both transduceractuation voltage and flow rate.

2. Experimental arrangements

The temperature measurements were performed with a microthermocouple inserted into the fluid channel of the chip. Thechip (GeSim, Dresden, Germany) and its channel structureare illustrated in figure 1(a). The layer dimensions of thechip were 200/250/1000 µm (bottom glass, silicon, upperglass), respectively. The channel width of 375 µm was closeto half the wavelength at the employed ultrasonic frequencyof 2.0 MHz. The chip was excited using an obliquely coupled

(a)

(b)

(c)

(d)

Figure 1. (a) Top-view of the chip showing the channel design,access hole and transducer position. (b) Cross section of the chipshowing the obliquely coupled USW transducer (not to scale).(c) Cross section of the chip showing the T type (copper-constantan)and Teflon-insulated micro thermocouple with a total tip diameter(sensor and sheath layer) of 0.41 mm. The micro thermocouple wasthreaded down into the fluidic channel through the access hole(diameter ∼0.70 mm) in the upper glass layer approximately 3 mmdownstream from the transducer, thus measuring the localtemperature of the fluid inside the microchannel. (d) One-dimensional USW manipulation and aggregation of 10 µm beads atthe resonance frequency of 2.0 MHz.

(This figure is in colour only in the electronic version)

ultrasonic transducer (depicted in figure 1(b)) consisting ofa piezoceramic plate (PZ-26, Ferroperm, Denmark) attachedby conductive glue to an aluminum wedge with an angle, θ i,

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of 48 relative to the surface normal, in order to efficientlycouple a horizontal standing wave into the fluid channel viawave refraction (cf dotted lines in figure 1(b)). The transducerwas attached on top of the chip by a quick-drying and water-soluble electrode gel (Parker Laboratories, USA) and drivenby a function generator (Stanford DS345, Stanford, USA)coupled to a RF amplifier (75A250, Amplifier Research,USA). The fluidic system connected to the channel consistedof adapters, valves and Teflon tubing. The flow rate in thechip was controlled by a syringe pump and the chip-transducersystem was mounted on an inverted fluorescence microscope(Axiovert 135, Zeiss, Germany). 10 µm green-fluorescentpolystyrene beads (Bangs Laboratories, USA) diluted in water(106 beads per ml) were used as a cell model (i.e., havingsimilar size and acoustic properties) in the present experimentssimulating long-term manipulation of cells.

The absolute temperature measurements were performedwith a T-type (copper-constantan) and Teflon-insulated microthermocouple with a total tip diameter (sensor and sheathlayer) of 0.41 mm (IT-21, Physitemp Instruments, USA).The micro thermocouple was threaded down into the fluidicchannel through an access hole (diameter ∼0.70 mm) inthe upper glass layer approximately 3 mm downstream fromthe transducer, thus measuring the local temperature of thefluid inside the microchannel (cf figure 1(c)). The ambienttemperature outside the chip was measured by a second non-insulated micro thermocouple (MT-4, Physitemp Instruments,USA) with a tip diameter of 0.31 mm. Real-time automaticmonitoring of temperature data with an accuracy of ±0.2 Cwas performed using a thermo control unit (P655-LOG,Dostmann electronic, Germany) connected to a standard PCwhere the data were stored and further processed usingMS Excel and Matlab software. Continuous measurementsof both internal channel temperature and external roomtemperature were performed during all experiments. In thisway, any fluctuations in room temperature could be taken intoaccount. Finally, in the experiments for 37 C regulation ofthe microchannel temperature, a warm-air heating unit withtemperature control (Tempcontrol 37-2, Zeiss, Germany) wasused to connect to an in-house built plastic hood placed on topof the microscope stage combined with a heatable mountingframe (Heatable mounting frame K-H, Zeiss, Germany) indirect contact with the chip. For practical reasons, the hooddid not cover the syringe pump and the fluidic components.

In order to establish stable one-dimensional USWmanipulation and aggregation of beads, the transducer wasfirst positioned and aligned. Thereafter, the frequency wastuned into resonance by observing when stable and rapid beadaggregation occurred without flow at a transducer voltageof 10 Vpp (cf figure 1(d)). This optimum frequency was2.00 MHz, and was not changed during the experiments.Then, the ultrasound was turned off in order to let the chipreach thermal equilibrium with its surroundings before startingany measurement. The initial channel temperature withoutultrasound was logged, followed by near-continuous (2 minsample) temperature measurements during 60 min for theapplied transducer voltage. The temperature measurementseries started at 1 Vpp and was thereafter repeated for stepwiseincreasing voltages up to a maximum of 25 Vpp. During thelong-term experiments, the manipulation robustness in the chip

was visually checked in the beginning and at the end of theperiod, in order to verify that all beads in the aggregates wereretained and the aggregates were kept in their initial positionsduring the whole measurement.

To investigate possible sources of energy deposition,the surface temperatures of both the PZT element on thetransducer, and of the chip surface were measured byattaching two microthermocouples to the PZT element onthe transducer and the upper chip surface, respectively, usinga thermoconducting gel. The chip surface temperature wasrecorded at four different positions: close to the transducer(approximately 2–3 mm away) and 1 cm away in two differentand orthogonal directions. The measurements were performedat a resonance frequency of 2.00 MHz (with 10 Vpp appliedvoltage) using both the previously described transducer withan aluminum wedge and a similar transducer but with a PMMA(Polymethyl methacrylate) wedge.

3. Results

Several experimental parameters might influence the channeltemperature such as the USW exposure time, the appliedtransducer voltage, the flow rate and the surroundingtemperature. Four experiments were performed to evaluatethe effects of each of these parameters.

In the first experiment, the temperature stability andrepeatability during 12 h of particle manipulation at a constanttransducer voltage of 10 Vpp without any flow were evaluated.This voltage is typically the maximum level needed for stablemanipulation of cells in medium-ranged flows (typically a fewtens of µl min−1) [6, 7] and, thus, an approximate value ofthe upper voltage level in a future long-term cell handlingapplication. The experiment was performed with the externalheating system consisting of the sealed warm-air heating unit(above the chip) combined with the heatable mounting frame(in contact with the chip). Figure 2 shows the channeltemperature from three independent measurements, startingwith an ambient (externally regulated) temperature close to36 C. Typically, the fluid temperature inside the microchannelstabilized at a level ∼0.5–1 C below the ambient temperature,possibly due to a small non-vanishing thermal gradient acrossthe chip. As indicated in the diagram, for each of thethree measurements the temperature rises during the first fewminutes, and then remains constant with averages and standarddeviations of 36.66 ± 0.05 C, 36.20 ± 0.08 C and 36.12 ±0.07 C for the whole period, respectively. The repeatabilitycan be quantified by the average and standard deviation of thedata from all three measurements, resulting in 36.3 ± 0.3 C.

In a control experiment without any temperatureregulation the temperature in the channel was measured afterone hour of sound application for a total of 14 voltage stepsapplied to the transducer ranging from 0 to 25 Vpp. Theexperiment, presented in figure 3, was performed without flowand with an ambient (non-regulated) room temperature closeto 21 C. Here, we first note that there is an immediate increase(a ‘bias’) in temperature when the transducer is turned on at1 Vpp, which indicates that the mechanism of heat depositionin the fluid channel is of a more complex nature. However,the temperature dependence to the applied voltage above 1Vpp is near quadratic; for example, if a ‘biased’ power series

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Figure 2. The temperature stability during 12 h of particle manipulation is shown in three experiments at a constant transducer voltage of10 Vpp without any flow and with an ambient temperature of 36 C.

20

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30

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40

45

50

0 5 10 15 20 25

Voltage (V)

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tem

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)

Figure 3. The channel temperature measured as a function of anapplied transducer voltage ranging from 0 to 25 Vpp for an ambienttemperature close to 21 C (indicated by the dotted line). Thetemperature data are averaged from the three measurements at2.0 MHz and the error bars correspond to two standard deviations.

of type T = aUb + c (where T is the temperature increase, Uis the applied voltage and a, b, c are constants) is fitted tothe measured data, we obtain b ≈ 2.04 for the bias level c =2.75 C.

In order to investigate the possibilities to regulatethe channel temperature around an arbitrary physiologicaltemperature (e.g., 37 C), we performed a similar experimentas presented in figure 3 but now combined with externalheating of the chip surroundings (sealed warm-air system andheatable mounting frame system). The results are presented infigure 4, where the initial external heating was adjusted to36 C prior to ultrasonic actuation. In contrast to theexperiment without external heating (cf figure 3), we notethat there is almost no ‘bias’ level of the temperature curve infigure 4. Here, a similar power series fit gives a power b ≈2.31.

It is also of interest to investigate to what extent theflow rate influences the channel temperature. Therefore,measurements were performed at different flow rates rangingfrom 0 to 500 µl min−1 with a constant transducer voltage(7 Vpp) and with no external heating (ambient temperatureclose to 21 C). The results are presented in figure 5. Ascan be seen, there is no significant change in temperature atdifferent flow rates, although a minor decrease can be noted atthe highest measured flow rate (500 µl min−1, correspondingto a mean flow velocity ∼90 mm s−1).

20

25

30

35

40

45

50

0 5 10 15 20 25

Voltage (V)

Cha

nnel

tem

pera

ture

(°C

)

Figure 4. The channel temperature measured as a function of anapplied transducer voltage ranging from 0 to 25 Vpp for an ambienttemperature close to 36 C using the external heating system. Thetemperature data are averaged from three measurements and theerror bars correspond to two standard deviations. The dotted lineindicates the physiologically important temperature 37 C.

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26

27

0 100 200 300 400 500

Flow rate (µl/min)

Cha

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)

Figure 5. The effect on the channel temperature from the flow rateinvestigated at a transducer voltage of 7 V and with an ambienttemperature of 21 C (indicated by the dotted line). The data areaveraged from the three measurements and the error bars correspondto two standard deviations.

Finally, figure 6 presents the absolute increase in channeltemperature at three different levels of external heating whenthe transducer is turned on at constant voltage amplitudeof 10 Vpp. The investigated external heating levels were∼22 C (no heating) and 32 C and 36 C (by the use ofthe sealed warm-air system and the heatable mounting framesystem). Here, for the chosen voltage amplitude 10 Vpp, thetemperature increase is approximately 1–1.5 C for all threeinitial temperatures (reached within a few minutes and thenremains stable).

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Temperature regulation during ultrasonic manipulation for long-term cell handling in a microfluidic chip

00.4

0.8

1.2

1.6

2

20 25 30 35 40

External heat regulation (°C)

Tem

p. d

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Figure 6. The absolute increase in channel temperature evaluated atthree different levels of external heating when the transducer isturned on at a constant voltage amplitude of 10 Vpp.

4. Discussion and conclusion

In this section, we will consider temperature regulationstrategies for use with ultrasonic actuation for standing-wavemanipulation in a microfluidic chip. The purpose is touse ultrasound for long-term cell and/or particle handlingin a microfluidic chip while controlling and maintaining thebiocompatibility of the system. In addition, the origin of theultrasound-generated heat is investigated and discussed.

As seen in figure 2, the standard deviation for each ofthe three measurements over the whole time period of 12 his less than 0.1 C. This deviation is actually less than theaccuracy of the thermocouple probe (±0.2 C). Furthermore,the accuracy of the thermocouple is also comparable to thestandard deviation of the data from all three measurementsin figure 2 (0.3 C), indicating the accuracy in terms ofrepeatability. However, considering all available experimentaldata (including the measurements at different voltages andflow rates), the total accuracy is within ±1 C, especially forlow or high actuation voltages (cf figure 4).

The temperature increase due to the applied ultrasoundis at most a few C for the actuation voltages needed in cellmanipulation applications (<10 Vpp). Typically, the thresholdfor manipulation of biological cells is 2–3 Vpp in similarchip structures (with slightly varying channel layouts) [6, 7].Thus, the voltage interval 2–10 Vpp results in acoustic forcesof sufficient magnitude for retention of cells in chips operatedin flow-through mode at medium flow rates (∼5–10 µl min−1).For such flow rates, we also note that the temperature isindependent on the flow (cf figure 5). Overall, the temperatureincrease has a near quadratic relationship to the appliedtransducer voltage (and, thus, to the acoustic pressure).

To investigate possible sources of energy deposition,the surface temperatures of both the PZT element on thetransducer, and of various positions on the upper chip surfacewere measured, as described in the experimental arrangementsection. Starting with an initial temperature of 21.0 C,the PZT element on the Al-wedge transducer reaches asurface temperature of 26.1 C compared to 32.1 C for thePMMA-wedge transducer. However, for both transducersthe temperature of the upper surface of the chip stabilizes at24.4 ± 0.3 C close to the wedge, and thereafter decreaseswith increasing distance (typically 0.08 ± 0.02 C/mm).Considering these data, we conclude that the major sourceof heat deposition into the fluid channel is due to theelectromechanical losses in the PZT element (k33 = 0.68for the PZT elements). Other possible sources, such asabsorption of sound in the different layers in the chip, seem

to be of less significance. For example, the higher PZT-element temperature of the PMMA-wedge transducer canbe explained by the lower thermal conductivity of PMMA(∼0.17–0.19 W m−1 K at room temperature), compared withaluminum (235 W m−1 K at room temperature). Thus, less heatis transported away from the PZT element through the wedgedown to the chip. Furthermore, the greater sound absorptionin PMMA (relative to the absorption in aluminum) seems tobe of minor importance.

In order to incorporate the ultrasonic actuation in atemperature regulation system and take into account thebenefits from the USW-induced heating, we suggest usingthe following procedure. First, the chip is calibrated bymeasuring the temperature response as a function of theapplied transducer voltage. Then, the calibration data canbe used to define the externally regulated temperature. Forexample, the dotted line (37 C) in the diagram in figure 4reveals an actuation voltage of approximately 13 Vpp for theexternal regulation temperature 36 C. If a lower actuationvoltage is needed, the externally regulated temperature can beincreased in order to retain the channel temperature of 37 C.As seen in figure 6, the temperature increase is relativelyindependent of the initial channel temperature (within theaccuracy of the measurement), which makes it possible topredict the final temperature in the channel even when both theactuation voltage and the externally regulated temperature arechanged. If the long-term standard deviations are taken intoaccount, this procedure is suitable in applications requiringtemperature regulation accuracy of the order of ±1 C, which issufficient for most cell biological experiments [13]. However,it is possible to obtain a regulation accuracy of ±0.1 C bycontinuous monitoring of the temperature.

Besides the biological aspects, another advantage oftemperature regulation is the improved maintenance of thesystem resonance frequency. A difficulty with the long-termUSW manipulation is the drift in resonance frequency dueto shifts in temperature. This can be corrected for using anelectronic feedback loop, which has the drawback of increasedcomplexity. Our described manipulation system withtemperature control offers both improved biocompatibility andimproved resonance frequency stability.

To conclude, we have demonstrated that ultrasound-generated heating can be combined with external heating inorder to regulate the temperature in a microfluidic channelindependent of the ultrasonic actuation voltage and the flowrate, and with high temporal stability and repeatability. Theregulation temperature may be chosen arbitrarily within thephysiologically relevant interval (e.g., from 20–37 C). Oursystem is designed for ultrasonic standing wave (USW)manipulation of cells or other bio-active particles (e.g.,functionalized beads) in applications requiring stable andgentle handling of cells during long terms (hours–days). Infuture work, we aim for handling, positioning, retention, on-chip cultivation and optical characterization of delicate animalcells in a temperature-regulated chip.

Acknowledgments

The authors thank Professor H M Hertz for valuablediscussions, and MSc C Gunther, Fraunhofer Institute forBiomedical Engineering, St. Ingbert, Germany, for the

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J Svennebring et al

manufacturing of the PMMA-wedge transducers. Thiswork was supported by the European Community-fundedCellPROM project under the 6th Framework Program, contractNo. NMP4-CT-2004-500039.

References

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[2] Shirgaonkar I Z, Lanthier S and Kamen A 2004 Acoustic cellfilter: a proven cell retention technology for perfusion ofanimal cell cultures Biotechnol. Adv. 22 433–44

[3] Bazou D, Kuznetsova L A and Coakley W T 2005 Physicalenvironment of 2D animal cell aggregates formed in a shortpath length ultrasound standing wave trap Ultrasound Med.Biol. 31 423–30

[4] Muller T, Pfennig A, Klein P, Gradl G, Jager M andSchnelle T 2003 The potential of dielectrophoresis forsingle-cell experiments IEEE Eng. Med. Biol. 22 51–61

[5] Ozkan M, Wang M, Ozkan C, Flynn R and Esener S 2003Optical manipulation of objects and biological cells inmicrofluidic devices Biomed. Microdevices 5 61–7

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[7] Manneberg O, Hultstrom J, Hertz H M and Wiklund M 2007Orthogonal standing-wave fields for multi-dimensionalultrasonic manipulation in a microfluidic chip SensorsActuators A submitted

[8] Wiklund M and Hertz H M 2006 Ultrasonic enhancement ofbead-based bioaffinity assays Lab Chip 6 1279–92

[9] Doblhoff-Dier O, Gaida T, Katinger H, Burger W, Groschl Mand Benes E 1994 A novel ultrasonic resonance field devicefor the retention of animal cells Biotechnol. Prog.10 428–32

[10] Hawkes J J, Limaye M S and Coakley W T 1997 Filtration ofbacteria and yeast by ultrasound-enhanced sedimentationJ. Appl. Microbiol. 82 39–47

[11] Harris N R, Hill M, Beeby S, Shen Y, White N M, Hawkes J Jand Coakley W T 2003 A silicon microfluidic ultrasonicseparator Sensors Actuators B 95 425–34

[12] Petersson F, Nilsson H, Holm C, Jonsson H and Laurell T2004 Separation of lipids from blood utilizing ultrasonicstanding waves in microfluidic channels Analyst129 938–43

[13] Voldman J 2006 Electrical forces for microscale cellmanipulation Annu. Rev. Biomed. Eng. 8 425–54

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Ultrasonics 49 (2009) 112–119

Contents lists available at ScienceDirect

Ultrasonics

journal homepage: www.elsevier .com/locate /ul t ras

Spatial confinement of ultrasonic force fields in microfluidic channels

Otto Manneberg a, S. Melker Hagsäter b, Jessica Svennebring a, Hans M. Hertz a, Jörg P. Kutter b,Henrik Bruus b, Martin Wiklund a,*

a Biomedical and X-ray Physics, Royal Institute of Technology, KTH-AlbaNova, SE-106 91 Stockholm, Swedenb Department of Micro- and Nanotechnology, Technical University of Denmark, DTU Nanotech, Building 345 East, DK-2800 Kongens Lyngby, Denmark

a r t i c l e i n f o

Article history:Received 21 January 2008Received in revised form 9 June 2008Accepted 19 June 2008Available online 8 July 2008

PACS:43.25.Gf

Keywords:Ultrasonic manipulationAcoustic radiation forceMicrofluidic chipParticle image velocimetrySpatial confinementCell handling

0041-624X/$ - see front matter 2008 Elsevier B.V.doi:10.1016/j.ultras.2008.06.012

* Corresponding author. Tel.: +46 8 5537 8134; faxE-mail address: [email protected] (M. Wiklund).

a b s t r a c t

We demonstrate and investigate multiple localized ultrasonic manipulation functions in series in micro-fluidic chips. The manipulation functions are based on spatially separated and confined ultrasonic pri-mary radiation force fields, obtained by local matching of the resonance condition of the microfluidicchannel. The channel segments are remotely actuated by the use of frequency-specific external transduc-ers with refracting wedges placed on top of the chips. The force field in each channel segment is charac-terized by the use of micrometer-resolution particle image velocimetry (micro-PIV). The confinement ofthe ultrasonic fields during single- or dual-segment actuation, as well as the cross-talk between two adja-cent fields, is characterized and quantified. Our results show that the field confinement typically scaleswith the acoustic wavelength, and that the cross-talk is insignificant between adjacent fields. The goalis to define design strategies for implementing several spatially separated ultrasonic manipulation func-tions in series for use in advanced particle or cell handling and processing applications. One such proof-of-concept application is demonstrated, where flow-through-mode operation of a chip with flow splittingelements is used for two-dimensional pre-alignment and addressable merging of particle tracks.

2008 Elsevier B.V. All rights reserved.

1. Introduction

Ultrasonic standing wave (USW) manipulation technology inmicrofluidic chips has recently emerged as a powerful tool for,e.g., continuous alignment, separation, trapping and aggregationof micrometer-sized particles or cells [1,2]. We have previouslyshown that it is possible to generate independent standing wavefields in different directions inside a microfluidic channel, whereeach field is addressed by a specific external transducer [3]. How-ever, a remaining problem is that USW manipulation technologyhas poor spatial localization in comparison to alternative contact-less manipulation methods such as dielectrophoresis [4] and opti-cal tweezers [5]. In the present paper, we demonstrate for the firsttime multiple spatially separated and confined ultrasonic forcefields by microchannel design, with the aim of developing moreadvanced and complex lab-on-a-chip systems based on USWtechnology.

One characteristic of the present USW manipulation technology(that differs from the characteristics of dielectrophoresis and opti-cal tweezers), is the possibility to generate a uniform force field inthe entire fluid channel in a chip. For example, with USW technol-ogy it is possible to guide a particle or a cell through a microfluidic

All rights reserved.

: + 46 8 5537 8466.

chip at constant velocity and without any contact with the channelwalls [3], or to separate particles from a suspension at high flowrates [2]. On the other hand, dielectrophoresis has been used inmore complex particle or cell processing systems where severalmanipulation functions are located at different sites along the fluidchannel [4]. Here, different micro-electrode geometries define dif-ferent addressable manipulation functions, each with high spatialaccuracy in terms of both localization and confinement of the cor-responding dielectrophoretic force field. Thus, advanced single-particle handling and processing systems are realized by combin-ing several consecutive manipulation functions (such as alignment,parking, sorting, separation, etc.) and a continuous driving fluidflow. In comparison to dielectrophoresis, USW technology has amuch lower degree of instrumentation complexity [6], and alsobetter prospects for gentle and long-term handling of sensitivecells [7,8]. Therefore, it is of interest to investigate if USW technol-ogy can be used in advanced particle processing systems based oncombinations of several spatially separated and localized manipu-lation functions.

To date, several different methods have been suggested for cou-pling of ultrasound from a transducer into a well-defined standingwave in a microfluidic chip. The standard approach is based on theone-dimensional resonator that consists of a stack of plane-parallellayers: a PZT layer, a coupling layer, a fluid layer and a reflectinglayer [7,9,10], or with the reflecting layer exchanged for another


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O. Manneberg et al. / Ultrasonics 49 (2009) 112–119 113

coupling layer and PZT layer [11,12]. However, it has been shownthat in silicon/glass-based microfluidic chips, it is not of criticalimportance how the system is excited. For example, one reportedmethod is based on exciting the channel perpendicularly to theoutgoing wave from an external transducer [2]. An alternative ap-proach, developed in our lab, is based on oblique coupling via arefracting wedge on an external transducer for controlled directingof the incident wave into the fluid channel [6]. Another reportedmethod is based on bending vibrations of a glass plate in contactwith the fluid channel [13]. However, all these methods typicallyresult in a standing wave field that extends along the whole fluidchannel. Thus, it is difficult to confine an ultrasonic field in a chipby wave propagation from an external transducer only.

We note that by integrating the PZT elements in the fluid chan-nel, localization and confinement of an ultrasonic standing wavefield can be obtained [14–16]. In such devices, the extent of theultrasonic field is similar to the size of the PZT element (typically,0.5–0.8 mm wide square elements designed for operation around10 MHz). However, the generated standing wave field has a com-plicated lateral distribution due to strong near-field effects. Fur-thermore, the experimental arrangement is more complicatedand less flexible than in similar devices using external transducers(e.g., in Refs. 2,6). Another restriction with channel-integrated PZTelements is the limited optical access, which excludes trans-illumi-nation microscopy techniques. Finally, since the PZT element is indirect contact with the fluid inside the microchannel, the biocom-patibility may be reduced due to, e.g., heating (cf. Ref. 8).

In the present paper, we demonstrate for the first time spatiallocalization, separation and confinement of multiple ultrasonicstanding wave fields in optically transparent microfluidic chips uti-lizing remote actuation from external transducers. The method isbased on local matching of the channel width to the transducer fre-quency in chips with non-uniform channel cross-sections. Wepresent results from two different chip designs; one for investigat-ing the dependence of the confinement on small differences inchannel width, and one with flow splitting elements designed fortwo-dimensional alignment and addressable merging of particletracks. The ultrasonic fields are quantified by the use of microme-ter-resolution particle image velocimetry (micro-PIV) [17] duringactuation of a single channel segment, or of two adjacent channelsegments simultaneously. The results are important for the under-standing of how ultrasonic resonances are formed in microfluidicchips, as well as for developing future particle handling systemswith tailor-made, localized and confined ultrasonic resonances bymicrochannel design.

2. Theoretical background

As a basic condition for the design process, we assume that anultrasonic resonance can be localized and confined through propermatching of the width and height (relative to the acoustic wave-length) of a particular channel segment. Furthermore, we assumethat the total three-dimensional resonant field in a chip is a super-position of one-dimensional and spatially harmonic resonances inorthogonal directions, and that each such one-dimensional reso-nance can be remotely excited by an external frequency-specifictransducer. These conditions are the starting point for the theoret-ical background presented below. However, we are aware that theconditions are simplifications. In reality, the resonances in a micro-fluidic chip should be regarded as full three-dimensional fields thatextend not only in the fluid channel but rather in the whole chipstructure. Therefore, the degree of localization and confinementof the field into a particular part of the fluid channel is a functionof not only the channel geometry, but also the acoustic impedancesand geometries of all supporting layers to the channel structure,

including the whole fluid channel itself [18]. The validity of oursimplified conditions below is further discussed in Section 5.

2.1. Ultrasonic standing wave manipulation

It has long been known that particles in an ultrasonic standingwave will be subjected to a primary radiation force FPR, which at-tracts suspended particles to the nodes or antinodes of the stand-ing wave depending on the acoustic properties of the particlesrelative to the surrounding medium [19]. Gor’kov has shown thatthe force on a particle of volume V in an arbitrary acoustic fieldis given by [20]

FPR ¼ Vr f1hp2i2qc 3

2qf2hv2i

2

ð1Þ

where the brackets denote time-averaging and q and c are the den-sity and speed of sound in the medium. f1 and f2 are contrast factorswhich depend on the speed of sound and the density of the mediumand particle according to

f1 ¼ 1 qc2

qpc2p

and f 2 ¼ 2qp q 2qp þ q

ð2Þ

where the index p indicates ‘‘particle”. In the simple case of a one-dimensional spatially sinusoidal standing wave in the x direction,Eq. (1) reduces to [20]

FPRðxÞ ¼Vp2

0k4qc2 f1 þ

32

f2

sinð2kxÞ ð3Þ

where k is the wavenumber, defined as k = 2p/k where k is theacoustic wavelength. As mentioned above, a microchip containinga microchannel is a complex resonator. However, to a first approx-imation, the forces in such a channel can be obtained by simplesuperposition of plane-parallel resonators in perpendicular direc-tions, each with a force field given by Eq. (3) [21]. This approxima-tion (i.e., assuming no coupling between the orthogonal fields) issufficiently accurate if the superposed fields do not operate at fre-quencies that are multiples of each other [22].

2.2. Force field quantification by micro-PIV

In the present work, the primary radiation force field FPR isquantified in two dimensions (x and z, cf. Fig. 1) using the micro-PIV technique, in which the motion of tracer particles in the formof velocity vector fields is acquired from consecutive image frames[17]. FPR is proportional to the bead velocity given that no otherforces or flows are present, and that the time after activating atransducer is well above the time constant sp for reaching forceequilibrium between FPR and the viscous Stokes drag. The timeconstant sp is given by [23]

sp ¼ 2qpr2p=9g ð4Þ

where rp is the radius of the particle and g is the viscosity of the li-quid medium. When representing the relative force fields withvelocity fields, possible sources of error are, e.g., acoustic streaming[24] and sedimentation by gravity. Acoustic streaming will, throughviscous drag, influence the particles with a force proportional to theparticle radius r. As FPR is proportional to r3, the streaming will typ-ically dominate when the particles are small (r 0.5 lm) whereasFPR will typically dominate when the particles are larger (r 5 lm),as in our experiments. The time constant ssed for sedimentation a(vertical) distance h in a fluid channel is given by

ssed ¼h

vsed¼ 9gh

2ðqp qÞr2pg

ð5Þ

Fig. 1. Photograph (a) and schematic (not to scale) of cross-section (b) of the ‘‘SplitChip” with mounted transducers. The ruler scale is in millimeter. In (b), the dashedlines represent wavefronts incident at an angle typical for manipulation in the xdirection.

Fig. 2. Schematics (not to scale) top-view of the two employed chips; the ‘‘StepChip” (a) and the ‘‘Split Chip” (b). The horizontal lines in the channels indicate thepressure node pattern, i.e., the lines to which particles are focused. The thin dashedlines in (b) mark the boundaries of the spatially confined resonances in eachchannel segment. The levitator transducers operating at 7.1 MHz is not shown, butis placed to the far right in experiments.

114 O. Manneberg et al. / Ultrasonics 49 (2009) 112–119

where vsed is the sedimentation speed and g is the acceleration ofgravity. A typical value of ssed in our microchannels is 1 minute(for 5-lm-diam. polyamide beads in water, and choosing h as halfthe channel height), and is therefore of little importance.

2.3. Combined ultrasonic standing wave manipulation and flow

At the employed flow level (0.1 lL/s) in our flow-throughexperiments (cf. Section 4.2), the flow is laminar in the wholechannel structure (e.g., the Reynolds number is 1). This meansthat once the force from the ultrasonic field has positioned a par-ticle in a streamline, it will stay in that streamline until subjectedto an external force. In our experiments, we distinguish between astreamline (path of a fluid element) and a particle track (path of asuspended particle).

3. Experimental arrangement

In our experiments, we used two different chip designs (de-scribed in detail in the next paragraph). Fig. 1a is a photographof one of the chips used with mounted transducers and Fig. 1billustrates the principles of the oblique coupling method (describedin Refs. [3,6]). Both chips are fabricated from 51.4 22 mm2 glass-

silicon-glass stacks with the microchannel plasma etched into thesilicon layer (GeSim, Germany). The bottom glass plate of bothchips is 200 lm thick, i.e., close to standard microscope coverslipthickness. This allows investigation of the channel using any kindof high-resolution optical microscopy, including both trans- andepi-illumination techniques. The transducers were fabricated bygluing planar PZT elements (Pz26, Ferroperm, Denmark) to alumi-num wedges (cf. Fig. 1a) with a cross-section of 5 5 mm2, anddriven at peak-to-peak voltages up to 13 V by separate functiongenerators operating at different frequencies within the range1.5–7 MHz. The aluminum wedges were attached to the chip (cf.Fig. 1a) using a quick-drying and water-soluble adhesive gel (Ten-sive, Parker Laboratories, USA).

The channel designs in the two investigated chips are schemat-ically illustrated in Fig. 2. In both designs, the channel height is110 lm and the widths are specifically designed to spatially con-fine resonances to a certain part of the channel by matching ofwidth and frequency as to fulfill the simplified resonance condition

L ¼ m2 k ¼ m

2 c

fð6Þ

where L is the channel width in the relevant direction, m is a posi-tive integer, k is the acoustic wavelength in the fluid, c is the speedof sound in the fluid and f is the acoustic frequency. The first chip(the ‘‘Step Chip”, cf. Fig. 2a) has a straight channel with three 15-mm long sections of different width (643 lm, 600 lm and500 lm). This chip is designed to utilize the fields from four differ-ent transducers, three of which act to focus particles in the x direc-tion in each of the segments and one to levitate them in the ydirection against the force of gravity. The second chip (the ‘‘SplitChip”) has a more complex channel structure including two flowsplitting elements, as illustrated in Fig. 2b. This chip is designedto use the fields from five different transducers operating at differ-ent frequencies to excite resonances in different parts of the chip, asindicated in Fig. 2b. Four of these can perform focusing of the par-ticles in the x direction, and one is used to levitate the beads inthe y direction. Thus, the operator can choose between merging par-ticle tracks 1 + 2, tracks 2 + 3 or all tracks (cf. Fig. 2b). This principle

Fig. 3. Characterization of the primary radiation force field FPR in the ‘‘Step Chip”(cf. Fig. 2a), measured by micrometer-resolution particle image velocimetry (micro-PIV). Actuation at 2.62 MHz of the left channel segment (a), at 3.51 MHz of the rightchannel segment (b), and at 2.62 and 3.51 MHz of both channel segmentssimultaneously (c). White arrows indicate the relative sizes and directions of theforces immediately after actuation is initialized. Dark regions indicate the beadpattern after 10 s of actuation. The length of the coordinate arrows in (a)corresponds to a velocity of 10 lm/s.

Fig. 4. Characterization of the primary radiation force field FPR in the ‘‘Split Chip”(cf. Fig. 2b), measured by micrometer-resolution particle image velocimetry (micro-PIV). Actuation at 2.94 MHz of the lower right channel segment (a), at 2.10 MHz ofthe left channel segment (b), and at 2.94 and 2.10 MHz of both channel segmentssimultaneously (c). White arrows indicate the relative sizes and directions of theforces immediately after actuation is initialized. Dark regions indicate the beadpattern after 10 s of actuation. The length of the coordinate arrows in (a)corresponds to a velocity of 10 lm/s.


could easily be expanded, and more in- or outlets added, to accom-modate to the needs of a specific application (cf. Section 5).

Each resonance frequency was identified by tuning the appliedtransducer frequency in small steps around the expected frequency(according to Eq. 6) and observing the particle manipulation re-sponse in the corresponding channel segment. The operating fre-

quency was then manually selected via the optimal ability toposition particles quickly and uniformly into the nodes. Micro-PIV measurements were performed at all sites where the channelschange width. To investigate the degree of spatial confinement,measurements were made with operation of either of the two orboth transducers corresponding to actuation of the channel seg-ments on each sides of the change in channel width (cf. Section

Fig. 5. Quantification of the field confinement and cross-talk in the ‘‘Split Chip” (cf.Fig. 4). The diagrams present the x components (cf. coordinate system in Fig. 4) ofthe velocity vectors along 31 z-axes equally spaced in the x direction. (a) Shows thex component of the sum of the velocity fields acquired when actuating the twochannel segments separately (cf. Fig. 4a and b). (b) Shows the x component of thevelocity field acquired when actuating both channel segments simultaneously (cf.Fig. 4c).

Fig. 6. Demonstration of addressable merging of particle tracks in the ‘‘Split Chip”.Panels (a) and (b) show the particle tracks without and with actuation of the upperleft channel segment, respectively. Panel (c) shows merging of the two lowerparticle tracks by actuation of the lower left channel segment. The chip site in (a)and (b) is located at the 2.5-MHz transducer, and the chip site in (c) is located at the3.0-MHz transducer (cf. Fig. 2b).

1 ‘‘Immediately” means approximately a few tenths of a second after turning on theansducer(s). This is well above the time constant, s, for reaching equilibriumetween the radiation force and the viscous drag (s 1 ms, cf. Section 2.2), and well

below the time to reach a static bead distribution in the channel (10 s).


4). We also demonstrate flow-through-mode operation with theSplit Chip operated with up to four independent transducerssimultaneously.

Two different kinds of particles were employed in the experi-ments;10.4 lm green-fluorescent polystyrene beads (Bangs Labs,USA) for the flow-through experiments and 5 lm polyamide beads(Danish Phantom Design, Denmark) for the micro-PIV investiga-tions. The beads were chosen for their resemblance to cells in bothvolume and acoustic properties. The beads were diluted in phos-phate-buffered saline (PBS), pH 7.4, with 0.05% Tween-20 andintroduced into the system by use of a syringe pump and Teflon(FEP) tubing.

In the flow-through-mode experiments (cf. Fig. 6), imaging wasperformed using an inverted microscope (AxioVert 135 M, Zeiss,Germany) with a 2.5 /0.075 NA objective and a CCD camera (Axi-oCam HSc, Zeiss, Germany). In order to visualize both the beadsand the microchannel, epi-flourescence and low-level trans-illumi-nation were used simultaneously. For the micro-PIV measure-ments performed without flow (cf. Figs. 3 and 4), image frames

were recorded in pairs with a CCD camera (HiSense MkII, DantecDynamics, Denmark) mounted on an inverted microscope (Axio-Vert 100, Zeiss, Germany) with a 10 /0.25 NA objective. The sam-ple was illuminated in back-lit mode by a light emitting diode (K2,Lumileds, USA) [25]. The velocity vector fields were generatedusing essentially the same protocol as described by Hagsäteret al. [18]. Before each new micro-PIV measurement, the channelwas flushed and re-seeded to give a homogenous starting distribu-tion of beads.

4. Results

In this section, we report on micro-PIV results when the twochips (the ‘‘Step Chip” and the ‘‘Split Chip”) are operated withoutflow during ultrasonic actuation of one or several channel seg-ments. The micro-PIV results are analyzed in order to quantifythe spatial separation and confinement of the force fields, and pos-sible cross-talk between two adjacent channel segments. Further-more, we demonstrate flow-through operation of the Split Chip,which is designed for two-dimensional alignment and addressablemerging of particle tracks.

4.1. Micro-PIV measurements

Micro-PIV measurements were made at all sites where thechannels change width, both in the Step Chip and in the Split Chip(cf. Fig. 2). However, in order to minimize the number of figures wehave chosen to present results from one representative site in eachchip, which is sufficient for the important conclusions. The resultsare presented as plots of the velocity vector fields (white arrows)superimposed with images of beads (dark regions) in the micro-channels (bright regions) (cf. Figs. 3 and 4). Typically, the vectorfield plots are averages of 10–15 data sets. The micro-PIV imageframes were recorded immediately1 after turning on the trans-

trb


ducer(s), thus representing the initial and transient motion of beads.In contrast, the bead images were acquired after a few seconds, thusrepresenting the (near-)steady-state distribution of manipulatedbeads. Finally, in order to investigate and compare the radiationforce fields produced by individual transducers, no levitation (inthe y direction) was performed during the micro-PIV measurements.

4.1.1. Micro-PIV measurements in the Step ChipIn Fig. 3, the results are presented from measurements at the

transition region from a 600 lm wide channel (left side) to a643 lm wide channel (right side) in the Step Chip. In Fig. 3a the600-lm-wide segment is actuated at 2.62 MHz, in Fig. 3b the643-lm-wide segment is actuated at 3.51 MHz and in Fig. 3c bothsegments are actuated simultaneously at 2.62 and 3.51 MHz,respectively. Ideally, each force field should be confined to its cor-responding channel segment (cf. Eq. 6). However, in Fig. 3a we seethat the resonance ‘‘leaks” over to the adjacent channel segment.Although the forces are larger in the left segment, they are still sig-nificant in the right segment (i.e., on average a few times smaller tothe right than to the left). Thus, a 7%-change in channel width ishere not enough for fully confining the resonance to the proposedchannel segment. On the other hand, the performance in Fig. 3b ismuch better in terms of confinement. Here, the forces in the leftchannel segment are insignificant in comparison to the right seg-ment, and the transition region (defined as the approximately dis-tance from maximum to insignificant forces in the z direction) is ofthe order of k/4. Finally, Fig. 3c shows the results when both chan-nel segments are actuated simultaneously. Interestingly, we seehere that the ‘‘resonance-leakage” into the right segment originat-ing from actuation of the left segment (cf. Fig. 3a) is quenched bythe actuation of the right segment. We also note that the vectorfield in Fig. 3c is not equal to the sum of the vector fields inFig. 3a and b. For example, the periodic variation of the force alongthe z direction in the right channel segment in Fig. 3c can not bederived from the vector fields in Fig. 3a and b.

4.1.2. Micro-PIV measurements in the Split ChipIn Fig. 4, the results from measurements at one site in the Split

Chip are presented. The sub-figures show actuation at 2.94 MHz ofthe lower right channel segment (Fig. 4a), actuation at 2.10 MHz ofthe left channel segment (Fig. 4b), and actuation at 2.94 MHz and2.10 MHz of both segments simultaneously (Fig. 4c). Here, wesee almost no ‘‘resonance-leakage” (as seen in Fig. 3a). Instead,the fields are well-confined and independent, and with a transitionregion along the z-axis (cf. Section 4.1.1) of the order of k/2. InFig. 4c, we also note the occurrence of areas having velocity fieldsof rotational character. Such vortices, produced by acoustic stream-ing, may influence the particle movement in areas with low radia-tion forces (e.g., in the transition region between two adjacentchannel segments).

In order to quantify more accurately the degree of spatial con-finement, we have plotted the lateral velocity components (i.e.,in the x direction in Fig. 4 where the radiation force is strongest)at different x-coordinates across the channel width, as a functionof the z-position (i.e., along the channel direction). In Fig. 5a, thelateral velocities during single-segment actuation are plotted (i.e.,the x components of the fields shown in both Fig. 4a and b). InFig. 5b, the lateral velocities during dual-segment actuation areplotted (i.e., the x components of the field shown in Fig. 4c). Inter-estingly, we note that the forces are weaker in the central region(i.e., 300 lm < z < 600 lm) of the diagram in Fig. 5b, comparedto the corresponding region of the diagram in Fig. 5a. Thus, a mu-tual force-quenching-effect is present in the transition region be-tween the two channel segments during dual-segment actuation.This effect is even more distinct for the Step Chip, where it is di-rectly visible in Fig. 3. Thus, for both chips, the cross-talk between

two adjacent channel segments actuated simultaneously seems tohave a character of destructive interference and is limited to a re-gion of typical length k/2.

4.2. Flow-through operation of the Split Chip

In Fig. 6, we demonstrate flow-through-mode operation at0.1 lL/s of the Split Chip by the use of up to four simultaneouslydriven transducers. This chip is designed for two-dimensionalalignment and addressable merging of particle tracks. In contrastto the micro-PIV experiments (cf. Sections 4.1 and 4.2), the levita-tor transducer (cf. the uppermost transducer in Fig. 1a) was oper-ated in all flow-through experiments, resulting in vertical (ydirection) centering of the particles in the whole channel system.Together with operation of the pre-alignment transducer (cf.Fig. 2), the result is two-dimensional alignment (i.e., simultaneousfocusing of particles in both the x and y directions), and thus con-trolled transport of particles in terms of both spatial position anduniform velocity [3]. In the present proof-of-concept chip design,all particles are injected through the one and only inlet for easierfluidic operation. However, depending on the needs from a futureapplication, splitting of the main channel endpoints in several in-lets and outlets is straightforward.

Fig. 6a and b shows the effect of actuating the upper left channelsegment in flow-through-mode. In Fig. 6a, only the levitator andpre-alignment transducers are activated, and all aligned particlescontinue in their respective streamline (also in the upper rightun-actuated channel segment). In Fig. 6b, the upper left channelsegment is actuated, resulting in localized merging of the particletracks 1 and 2 (cf. denotation in Fig. 2). The images are taken witha long exposure time, making the particles appear as streaks to bet-ter visualize their direction of movement. We clearly see that theparticle tracks 1 and 2 merge at a distance longer than the k/2-distance after which the force in a channel segment was found toreach its full value (cf. Section 4.1). This is the result of the fluidflow giving the particles a considerable velocity component inthe z direction relative the radiation-force-induced velocity com-ponent in the x direction. Fig. 6c shows merging of particle tracks2 and 3 further down the channel by actuation of the lower leftchannel segment (cf. Fig. 2). This experiment was performed with-out any preceding merging of particle tracks 1 and 2. Finally, allparticle tracks (two or three, depending on whether any of theabove merging steps is performed) can be merged by actuationof the final channel segment (cf. Fig. 2).

5. Discussion and conclusions

In this section, we will consider channel design strategies forimplementing several localized manipulation functions in seriesalong a microchannel by the use of ultrasonic standing wave(USW) technology in a microfluidic chip. Ideally, each manipula-tion function should be represented by a localized and spatiallyconfined force field that can be independently addressed by a fre-quency-specific external transducer. Furthermore, the overlap orcross-talk between the force fields of two adjacent manipulationfunctions should be minimized. Below we outline design criteriafor advanced particle handling and processing chips based on ourexperimental observations.

When actuating a single-channel segment in both the Step Chipand the Split Chip, we may conclude that each primary radiationforce field FPR is localized to its corresponding segment (cf. Figs.3 and 4). At the beginning and the end of each segment, there isan intermediate area of force field gradient (from insignificant tofull value of the forces) with typical length k/4 – k/2 (where k isthe acoustic wavelength in the fluid). However, one exception to


this degree of confinement is seen in Fig. 3a, where the force fieldgradient in the z direction outside the actuated channel segment isvery small. The result is a resonance that ‘‘leaks” out into the rest ofthe fluid channel. We believe that one reason for this poor confine-ment could be bad matching between the transducer resonanceand the channel resonance. As a comparison, for a conventionallydesigned one-dimensional layered resonator (where the trans-ducer is an active part of the resonator), the forces are typicallyhalved if the driving frequency is changed with only 0.5% from aresonance peak [26]. In Fig. 3, the change in channel width corre-sponds to a change in resonance frequency of 7%. Thus, given asimilar performance in our chip as in Ref. [26], we would not ex-pect any forces of significance outside the actuated channel seg-ment. On the other hand, if the channel segments are consideredseparately it is also possible that the wider channel segment inFig. 3a is wide enough to be close to another resonance peak thanthe peak in the thinner segment. For example, when tuning theactuation frequency for a certain channel segment there are typi-cally several resonance frequencies separated with similar (rela-tive) steps as the relative change in channel width in Fig. 3. Thus,we believe that similar resonances would be found if we could‘‘tune” the channel segment width at a fixed frequency (cf. e.g.,Ref. [27]). One simple design strategy to avoid resonance leakageis to employ much larger steps in channel width, as demonstratedin the Split Chip.

When two adjacent channel segments are actuated simulta-neously by the use of two transducers operating at different fre-quencies, we conclude that no cross-talk of significance (for theperformance of each manipulation function) occurs in neither ofthe two chips. Typically, there is a near-force-free transition regionbetween the manipulation functions of length k/4 in the StepChip (cf. Fig. 3c), and k/2 in the Split Chip (cf. Figs. 4c and 5).The reason for the longer transition region in the Split Chip isdue to the gradually (and not stepwise) increasing channel widthin that chip. However, it is important to note that the sum of theforce fields during single-segment actuation is not equal the forcefield during dual-segment actuation. Minor field coupling effectsare visible in Figs. 3 and 4, e.g., periodic force variations in the zdirection (along the channel), acoustic-streaming-induced vorticesin low-force regions, and mutual quenching of ‘‘leaky” resonancesin the intermediate area between the segments. Neither of theseeffects causes any reduction in performance of significance of aparticle handling/processing chip based on several spatially sepa-rated manipulation functions (as demonstrated in e.g., Fig. 6).

Finally, it should be noted that the radiation forces are not con-stant throughout the segment (i.e., along the z-axis) to which it isconfined. There will be periodically recurring areas where thefocusing component of the force is very weak, or indeed is almostequal to zero. Actually, this is a general effect that is visible duringboth single- and multi-segment actuation. The reason is that we donot solely have a simple standing wave in the channel, but rather athree-dimensional resonance which exists in the whole chip struc-ture, including all supporting layers to the fluid channel (such asthe silicon layer, the glass layers, the external transducers, andeven the microscope chip holder). While it is possible to designthe system so that the force field is considerably confined, the restof the chip will still influence the actual shape of the confined field.Finite-element simulations on our chips (data not shown) usingthe method described in Ref. [18] predict the existence of suchareas, which are confirmed in our experiments (cf. e.g., Fig. 3c)but also in other reports (see e.g., Refs. 18,22,28). The influenceof the entire chip (in terms of material choices and geometry) onthe resonance shape is the underlying reason for this phenomenon.For example, a simple and straight half-wavelength channel doesnot focus particles into a straight line, but rather into slightlycurved lines and at some places not at all under static (no-flow)

conditions. However, this effect is often not visible in flow-throughapplications for several reasons. Firstly, the laminar flow profilewill cause a particle to simply follow its streamline through areaswhere the forces are low. Secondly, any effect on the bead move-ment due to the force asymmetry around curved nodes is typicallycancelled out in flow-through-mode. In our suggested flow-through application (cf. Section 4.2), these effects will be of littleor no importance for the performance of the chip. However, for achip designed for no or very low flow, or designed for retentionof particles in a flow, the effects must be considered as a part ofthe design process.

Acknowledgements

The authors would like to thank Peder Skafte-Pedersen at MIC/DTU for his simulations of resonances in the chip. This paper wasgenerated in the context of the CellPROM project, funded underthe 6th Framework Program of the European Community (ContractNo.: NMP4-CT-2004-500039). The work was also supported by theSwedish Research Council for Engineering Sciences.

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[7] J. Hultström, O. Manneberg, K. Dopf, H.M. Hertz, H. Brismar, M. Wiklund,Proliferation and viability of adherent cells manipulated by standing-waveultrasound in a microfluidic chip, Ultrasound Med. Biol. 33 (2007) 145–151.

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IOP PUBLISHING JOURNAL OF MICROMECHANICS AND MICROENGINEERING

J. Micromech. Microeng. 18 (2008) 095025 (9pp) doi:10.1088/0960-1317/18/9/095025

Wedge transducer design fortwo-dimensional ultrasonic manipulationin a microfluidic chipO Manneberg, J Svennebring, H M Hertz and M Wiklund

Biomedical & X-Ray Physics, Department of Applied Physics, Royal Institute of Technology,KTH/AlbaNova, SE-10691 Stockholm, Sweden

Received 21 May 2008, in final form 22 July 2008Published 14 August 2008Online at stacks.iop.org/JMM/18/095025

AbstractWe analyze and optimize the design of wedge transducers used for the excitation of resonancesin the channel of a microfluidic chip in order to efficiently manipulate particles or cells in morethan one dimension. The design procedure is based on (1) theoretical modeling of acousticresonances in the transducer–chip system and calculation of the force fields in the fluidchannel, (2) full-system resonance characterization by impedance spectroscopy and (3) imageanalysis of the particle distribution after ultrasonic manipulation. We optimize the transducerdesign in terms of actuation frequency, wedge angle and placement on top of the chip, and wecharacterize and compare the coupling effects in orthogonal directions between single- anddual-frequency ultrasonic actuation. The design results are verified by demonstrating arrayingand alignment of particles in two dimensions. Since the device is compatible withhigh-resolution optical microscopy, the target application is dynamic cell characterizationcombined with improved microfluidic sample transport.

1. Introduction

Ultrasonic particle manipulation in microfluidic chips is anemerging tool in lab-on-a-chip systems with applicationssuch as washing [1, 2], separation [3, 4], positioning [5],aggregation [6, 7] and assaying [8, 9] of bio-functionalizedparticles or cells. Most of the previously reportedmicro-machined systems employ single-frequency, near-one-dimensional (1D) ultrasonic fields for focusing particles intovertically oriented pressure node planes of the standing wave[5, 10, 11]. However, a less desired effect with thisarrangement is that the particles settle to the lower surface ofthe microchannel due to gravity [10, 12]. In pressure-drivenflows with near-parabolic flow profiles, the result is a largevariation in particle speeds and a significantly increased risk ofadhesion of particles or cells to the channel surfaces that maycause problems such as sample loss, sample contaminationand channel clogging. In order to solve this problem, wehave previously demonstrated preliminary results on two-dimensional (2D) continuous alignment of particles based oncombining (horizontal) focusing and (vertical) levitation ofparticles in a microfluidic chip [13]. In the present paper,we provide a detailed analysis and design optimization of our

wedge-transducer-based actuation method, and verification ofthis design by demonstration of both arraying and alignmentin 2D of micro-particles or cells in microfluidic chips.

Different strategies have been suggested for achieving 2Dultrasonic resonances in microfluidic chips. These includetransducer-based methods [9, 14], channel-geometry-basedmethods [15, 16] or a combination of both [17]. However, allthese devices operate on a single frequency [9, 14–16] or ontwo near-identical frequencies [17]. Therefore, the orthogonalcomponents of the generated 2D field are strongly coupledand the result is an unpredictable and/or complicated patternof the manipulated particles.

We have previously demonstrated ultrasonic manipulationin microfluidic chips based on oblique coupling of ultrasoundfrom external transducers combined with refractive wedges[10, 18, 19]. Important advantages of this coupling methodare compatibility with high-resolution optical microscopy, andthe flexibility and small size of the transducers. Furthermore,we have demonstrated multi-frequency operation by use ofseveral wedge transducers simultaneously [13, 19]. To a firstapproximation, one could believe that the direction of theincident wave into the fluid channel can be derived by simplyusing Snell’s law of wave refraction on a plane incident wave in

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J. Micromech. Microeng. 18 (2008) 095025 O Manneberg et al

the wedge. However, this simplified model is not applicableto a transducer-microfluidic chip system where most of itsdimensions are comparable to the acoustic wavelength. Thus,in order to optimize the coupling and control the properties ofthe generated acoustic field in the channel, it is necessary toanalyze the full transducer–chip system.

In the present paper, we investigate and optimize thedesign of wedge transducers for 2D ultrasonic manipulationof particles or cells in a microfluidic chip. The couplingmechanism and the corresponding force field in the channelare investigated with (1) theoretical modeling of the acousticfield and (2) impedance measurements of the transducer–chipsystem, and with (3) image analysis of the particle distributionafter ultrasonic actuation. In particular, we investigatethe dependence of the wedge angle on the manipulationperformance, as well as to what extent it is possible to achieveindependent 1D standing-wave fields in orthogonal directionsinside the channel of a microfluidic chip by remote actuationfrom external wedge transducers. Finally, we verify our designby demonstrating 2D centering and alignment as well as 2Dmicro-aggregation and arraying of particles. In the future, ouraim is to use the device in cell and bead assays for gentle cellcharacterization and/or medical diagnosis.

2. Theoretical background

2.1. The ultrasonic radiation force

The theory of ultrasonic radiation forces is well understood[20]. Suspended particles in an ultrasonic standing wave aresubjected to a primary radiation force FPR, which attracts themto the nodes or antinodes of the standing wave depending on theacoustic properties of the particles relative to the surroundingmedium [21]. Gor’kov has shown that the force on a particleof volume V in an acoustic field not similar to a plane wave isgiven by

FPR = −V ∇(

f1〈p2〉2ρc

− 3

2ρf2

〈v2〉2

), (1)

where the brackets denote time-averaging, p is the acousticpressure, v is the acoustic particle velocity and ρ and c arethe density and speed of sound in the medium.f1 and f2 arecontrast factors which depend on the speed of sound and thedensity of the medium and particle according to

f1 = 1 − ρc2

ρpc2p

and f2 = 2(ρp − ρ)

2ρp + ρ, (2)

where the index ‘p’ indicates ‘particle’.Within the applicability range of equation (1) [20], we

are in particular interested in resonant (stationary) acousticfields. This gives us the possibility of separating the time andspace dependence of the field and rewriting the force FPR asa function of known parameters and the pressure field only.In this way, we may perform numerical calculations of forcefields from simulated pressure fields (cf section 2.2).

We begin by assuming a velocity potential such thatv(r, t) = ∇(r, t), where r is the position vector and tthe time, for the acoustic field which factors according to

(r, t) = ϕ(r) cos(ωt), where ω is the angular frequency.This yields pressure and velocity fields

P(r, t) = −ρ∂

∂t(r, t) = −ρωϕ(r)︸︷︷︸

p(r)

(−sin(ωt))

v(r, t) = ∇ = −∇ 1

ρ

∫P(r, t) dt (3)

= − 1

ρ∇p(r)

∫−sin(ωt) dt = − 1

ρ

cos(ωt)

ω∇p(r).

Substituting these expressions into equation (1) andcarrying out the time-averaging now yields

FPR = −V

[f1

2ρc2∇

(1

2p2(r)

)

− 3

4ρf2∇

(1

2ρ2ω2(∇p(r))2

) ], (4)

which, after some algebraic manipulation, can be written as

FPR = −Vβ

2

[f1p∇p − 3f2

2k2(∇p · ∇)∇p

], (5)

where β is the compressibility and k = ω/c is the wavenumber, both in the medium.

Finally, it should be mentioned that when several particlesare present, each particle will also be subjected to a secondaryradiation force, known as the secondary Bjerknes force, whichis due to the field scattered from other nearby particles [22].This attractive secondary force contributes to the formation ofclosely packed aggregates of particles in the pressure nodes.

2.2. Numerical modeling and calculations

Numerical modeling of the acoustic field in the chip wascarried out using the FEM software Comsol Multiphysics[23]. Postprocessing of the calculated pressure field inthe microchannel into the primary radiation force field(cf equation (5)) was carried out in MATLAB [24]. Allpressure field simulations were performed in 2D cross-sectionsof the system, as a full 3D-model of the transducer–chip-channel system would demand enormous amounts of computerpower. The modeled cross-section planes are marked infigure 1(d) by the dotted line (xy plane), the dashed line (yzplane) and the plane of the paper (zx plane in the middle ofthe silicon layer). The outer boundaries of the solid structuresof the transducer–chip system were set to be free (without anyload). Mesh element limits were first set to be the smallest ofeither λ

5 or the criterion that a layer should contain at least fivemesh points in its ‘thin’ direction. The mesh was then refinedto the limits of the available computer power. The simulationsdo not take into account scattered pressure fields in the channel,and thus only the primary radiation force is simulated. Neitheris streaming or heating effects included, since they are ofminor importance in our system and for the particle sizes used[15, 18].

2


Figure 1. Photograph of the transducer–chip system (a) andschematics of a standing wave along the x-axis (b) and y-axis (c).Pressure nodal planes in (b) and (c) are indicated by the dashed lines;(d) shows a top-view schematic of the silicon layer of the chip, withtransducer positions from (a) shown as gray squares. The dashedand dotted lines in (d) are cross-sections discussed in section 4.1.1.

(This figure is in colour only in the electronic version)

3. Device

Figure 1 shows a photograph (a) of the transducer–chipsystem and schematics (b)–(c) demonstrating the idea of two-dimensional (2D) manipulation by orthogonal standing-wavefields. The detailed geometry of the silicon structure is shownin figure 1(d). The H-shaped fluid channel is chosen forflexibility reasons, but the multiple inlets and outlets are notof importance for the work presented in this paper. Each fieldis generated by a transducer resonantly tuned to a channeldimension. As illustrated in figures 1(b)–(c), the channeldimensions and operating transducer frequencies are matchedto fulfill the simplified resonance condition L = mλ/2, whereL is the extent of the channel in the relevant direction, m is apositive integer and λ is the acoustic wavelength in the fluid.This simple design criterion was used in the manufacturingprocess of the chip, and for selecting the nominal resonancefrequencies of the transducers. Air pockets were includedin the chip design for defining air-backed quarter-wavelengthsilicon reflectors in the x-direction.

The chip is made of a 22 × 34 mm2 glass–silicon–glass stack with layer thicknesses 0.20 mm, 0.11 mm and1.0 mm, respectively (GeSim, Germany). A 375 × 110 µm2

(cross-sectional width × height) channel was etched throughthe whole silicon layer, creating a fully transparent chip.Ultrasound was coupled into the fluid channel by one or twowedge transducers attached on top of the chip (cf figure 1(a))by a quick-drying and water-soluble adhesive gel (‘Tensive’,Parker Laboratories, USA). The transducers were made ofPZT (lead zirconate titanate) piezoceramic plates (Pz-26,Ferroperm, Denmark) with nominal fundamental thickness

resonances of 6.89, 2.04 and 4.12 MHz, respectively, whichwere glued to (5 × 5 mm2 cross-section) aluminum wedgeswith angles of incidence (between the chip surface and thepiezoceramic plate) ranging from θi = 0 to θi = 50. Thetransducers were labeled X, Y and Z, indicating the primarydirection (x, y and z, respectively) of the resonance. Effortswere made to make the device fully compatible with anykind of high-resolution optical microscopy, including bothepi-fluorescence and trans-illumination techniques. Here,important properties are the coverslip-thickness bottom glasslayer, full optical transparency both above and below thechannel, and the transducer placement close to the chip edgesallowing trans-illumination condenser light (cf figure 1(a)).

Three kinds of beads were employed in the experiments:10.4 µm green-fluorescent polystyrene beads (Bangs Labs,USA), 5 µm non-fluorescent polyamide beads (Orgasol,Danish Phantom Design, Denmark) and 1.8 µm red-fluorescent polystyrene beads (Polysciences Inc., USA). The10.4 µm beads were chosen for their resemblance to cells inboth volume and acoustic properties. The beads were diluted inphosphate-buffered saline (PBS), pH 7.4, with 0.01% Tween-20 and introduced into the chip by use of a syringe pump andTeflon (FEP) tubing.

The mechanism and efficiency of coupling ultrasoundvia a wedge into the fluid channel were investigated bydifferent methods. Besides the theoretical modeling (cfsection 2.2), the coupling was experimentally analyzed byimpedance spectroscopy, and the manipulation performance inthe channel was characterized by image analysis of sonicatedbeads. For the impedance spectroscopy, the resonances of thefree transducers, and of the transducer–chip assembly withand without a fluid-filled channel, were characterized by animpedance analyzer (Z-check 16777k, Sonosep Technologies,Austria). The analyzer scanned the frequency from 1.8 MHz to2.1 MHz in steps of 10 kHz on transducers with wedge anglesbetween 0 and 50 (in steps of 10). The image analysisprocedure is described in detail in section 4.1.3.

4. Results and discussion

4.1. Wedge transducer design

4.1.1. Modeling results. Figure 2 shows selected resultsof modeling the ultrasound field in a transducer–chip systemaccording to the procedure described in section 2.2. Thecoordinate system is chosen so that the z-axis points inthe channel direction (cf figure 1(a)). Figure 2(a) depictsthe resulting displacement amplitude in an xy cross-section(vertical plane across the channel, illustrated by a dotted grayline in figure 1(d)) of the transducer and chip when the topsurface of the aluminum wedge (where the PZT element isattached; cf section 3) is forced to vibrate at 1.97 MHz.This models the actuation of the X transducer in figures 1(a)and (d), used for creating a standing wave similar to theillustration in figure 1(b). The simulation also yields thepressure field in the channel, which is used for the calculationof the force field according to equation (5). The blow-upinset in figure 2(a) shows the x (upper diagram) and y (lower

3


Figure 2. Modeling of acoustic fields in the transducer–chip system in two vertical planes: xy (a) and yz (b) planes. These planescorrespond to the dotted and dashed gray lines in figure 1(d), respectively. Figure 2(a) shows the normalized displacement amplitude in anxy cross-section (across the channel) when the source is actuated at 1.97 MHz. The blow-up insets show the x (upper diagram) and y (lowerdiagram) components of the primary radiation force in the channel. The black contours represent lines where the absolute force is 10% of itsmaximum value. Figure 2(b) shows the normalized displacement amplitude in a yz cross-section (along the channel) when the source isactuated at 6.851 MHz. The blow-up shows the z (upper diagram) and y (lower diagram) components of the force field in the channel. Thenormalization is different in figures 2(a) and (b).

diagram) components of the normalized force field in thechannel (from which the dashed lines emanate) at 1.97 MHz.The figure is to scale, and hence the channel itself is hard toresolve with the naked eye. Comprehensive frequency scanshave been carried out (typically ±15% around the nominaltransducer frequency), and we note that there are severalactuation frequencies for a given angle of incidence that resultin near-1D force fields such as the one depicted in figure 2(a)(i.e., with primarily an x component). However, other resonantfrequencies within the investigated interval also include asignificant y component of the field that would either levitate orsink particles in the channel (simultaneously with the particlefocusing in the x-direction). This predicted phenomenon isexperimentally verified and further discussed in section 4.2.2.We note that in no cases do we get a displacement field thatcould be explained by a simple model such as plane-wavepropagation in the wedge and refraction according to Snell’slaw at surfaces. The reason is that the sizes of all of theinvolved structures are of the same order of magnitude as theacoustic wavelength λ. In the case of the silicon spacer, oursimulations show that the layer is so thin that the field leaksthrough it in an evanescent fashion.

Figure 2(b) shows the displacement amplitude in a yzcross-section (the vertical plane along the channel, illustratedby a dashed gray line in figure 1(d)) when the Y transducer(cf figures 1(a) and (d)) is actuated at 6.851 MHz. The blow-up inset shows the z (upper diagram) and y (lower diagram)components of the resulting normalized force field in thechannel. Above the microchannel, the top glass plate ofthe chip is designed to function as a reflection layer closeto this frequency, and we note that we get a distinct resonantbehavior in the y-direction in the glass. More interestingly,a periodic variation in the z-direction both in displacement(in the solid structure) and y component of the force (in thefluid) is predicted at the simulated frequency in figure 2(b).In fact, a similar striated pattern is predicted for all of thefound resonance frequencies within the simulated interval(∼6.85 MHz ±15%). Such phenomena are associated withacoustic cavities having large lateral dimensions compared tothe axial dimension and to the wavelength, and have previouslybeen observed by, e.g., Townsend et al [16].

When comparing the full system resonances infigures 2(a) and (b), we note an interesting difference. In

figure 2(a), the resonance is distributed throughout the fulltransducer–chip system. In particular, much energy seemsto be stored in the wedge, where a complex resonant patternis observed. On the other hand, we do not find a similarbehavior in figure 2(b). Here, most of the energy stored in thesolid structures seems to be confined within the glass layersabove and below the fluid channel, and not in the wedge.We believe that the reason is the near-1D character of theresonance in figure 2(b), where the glass layer thicknesses areselected as odd multiples of λ/4. Although we have includedair pockets in the silicon layer at 5 × λ/4 distances fromthe fluid channel (cf figure 1(a)), we do not obtain a similarsimple near-1D resonance in figure 2(a). Instead, we note‘local resonances’ below these air pockets (hardly resolved infigure 2(a)). A general explanation for the resonancedistribution in both figures is that the glass layers are theprimary hosts for the resonance in the solid structure. Forall actuation frequencies (∼2–7 MHz), the silicon layer is thincompared to the wavelength (<0.1 × λ) and does not influencethe full system resonance to any noticeable extent. One methodto improve the chip design in the future is to match the widthof the full glass–silicon–glass stack (and not only the channeland silicon widths) with the wavelength.

4.1.2. Impedance spectroscopy. The dependence ofthe wedge angle and actuation frequency on the coupledtransducer–chip resonance was experimentally characterizedby impedance spectroscopy. Here, the X transducers with2.04-MHz PZT elements were chosen for wedge angleoptimization. The PZT elements used in these experimentswere all circular with a diameter of 10 mm. Figure 3(a)shows the conductances measured over a transducer mountedon a chip with water-filled channel as a function of wedgeangle (ranging from 0 to 50) and frequency (between1.7 MHz and 2.3 MHz). We note that the strongest resonancepeaks are found for the wedge angles 0 and 30, where the30-resonance is close to the nominal resonance frequency ofthe transducer (2.03 MHz) while the 0-resonance frequency isshifted to 1.97 MHz. Figures 3(b) and (c) show a more detailedinvestigation of the 30-transducer, where the free (unattached)transducer is compared with the transducer mounted on a chipwith either a water-filled or an empty (air-filled) channel. As

4


Figure 3. Impedance spectroscopy of the transducer–chip system.Figure 3(a) shows the conductances of five transducers of differentwedge angles as functions of the frequency. All values below 10 mShave been cut for clarity. Figure 3(b) shows the conductance of theunattached 30-transducer in air (‘free’), the transducer mounted ona chip with air-filled channel (‘air’) and on a chip with water-filledchannel (‘water’). Figure 3(c) shows the differences between thecurves in figure 3(b).

illustrated in figure 3(c) (which plots the differences betweenthe conductances in figure 3(b)), the dependence of the channelmedium on the resonance of the transducer–chip system isnegligible. This is in contrast to conventional 1D layeredresonators, where the fluid layer has a clear dependence on thesystem resonance [25].

In summary, by choosing an angled wedge transducerwe significantly lower the coupling between the channelresonance and transducer resonance. Thus, our simplifieddesign criterion (L = mλ/2) defined in section 3 is adequatefor angled wedges, as opposed to a 1D layered resonatorwith a plane-parallel coupling layer. Furthermore, we mayposition the transducer close to an edge of the chip, whichis a great advantage for the compatibility of our device withhigh-performance optical microscopy.

4.1.3. Experimental manipulation performance. In thissection, we investigate the dependence of the wedge angle(0–50) and actuation frequency (1.8–2.1 MHz) on theparticle manipulation performance in the x-direction, usingthe same X transducers as in section 4.1.2. The manipulationperformance is quantified by an image-analysis-based figureof merit (FOM), which is a measure of the average (alongthe channel) particle concentration into the vicinity of thepressure node after 15 s of particle focusing (in the x-direction,cf figure 1(b)), relative to the concentration outside the node.Note that the FOM by its definition below is related to the half-wavelength resonance condition, but could easily be adjustedto accommodate another desired pattern.

Each measurement was performed by seeding the channelwith a homogenous distribution of 5 µm polyamide beadsat a high concentration, stopping the flow, switching on thetransducer for 15 s at a low voltage (3 V peak-to-peak) andacquiring a micrograph. Figure 4(a) shows a typical exampleof such a micrograph where the areas used for calculatingthe FOM are indicated with colored lines. The yellow linesshow the boundaries of the channel as found by automatedimage analysis (edge detection), and the green lines showthe mid-15% of the channel, where the beads end up if themanipulation performance is good. Since the dark regionsare beads, we define the FOM as the mean pixel value outsidethe middle strip divided by the mean pixel value inside themiddle strip (after adjusting all images to the same brightnessrange). Thus, a high FOM corresponds to a high local beadconcentration in the center of the channel.

Figure 4(b) presents the results of these measurements,with all FOMs below 1.65 cut out for clarity. Mostimportant, we only obtain a high FOM for the30-transducer. Furthermore, we note a clear differencebetween the manipulation performance shown in figure 4(b)and the impedance spectroscopy results shown in figure 3(a).While impedance spectroscopy predicted the strongestresonances for both the 0- and 30-transducers, we note thatthe 0-transducer (i.e., with a plane-parallel coupling layer)is not efficient for particle manipulation in the channel. Inthe impedance measurements, the resonances are typicallydefined by the solid structure, and do not say anything aboutthe manipulation performance. In order to obtain a high FOM(cf figure 4(b)), the resonances in the solid structure mustalso create a resonance in the fluid. Therefore, the results infigure 4 are more complex, without any clear interrelationbetween, e.g., wedge angles.

Finally, we have also investigated the dependence onthe transducer position on top of the chip for the 0- and30-transducers, respectively. Two different positions wereinvestigated: close to a chip edge (the same position as usedin figure 4(b) and in the simulation in figure 2(a)), and closeto the chip center (directly above the channel). Although wecould not perform comparative image analysis in the lattercase (due to the broken optical path caused by the transducerplaced over the channel), manual inspection indicated a similaror slightly lower manipulation performance if the transducerswere placed directly above the channel compared to close toan edge. A related conclusion is presented by Neild et al [26],

5


Figure 4. Experimental manipulation performance for differentwedge transducer angles and frequencies. Figure 4(a) shows atypical micrograph of manipulated beads in the channel. Thecolored lines illustrate the areas of interest for the figure-of-merit(FOM) calculation used for quantifying the manipulationperformance. Yellow lines indicate the channel walls, and greenlines indicate the mid-15% of the channel. In figure 4(b), the FOMis presented for transducer angles ranging from 0 to 50 andfrequencies from 1.8 to 2.1 MHz. Values below 1.65 have been cutfor clarity. Figure 4(c) shows the local (i.e., not z-averaged)normalized FOM for the 30-transducer as a function of the positionalong the channel (z-direction) and of frequency. Thus, figure 3(c)quantifies the periodicity in the FOM at certain frequencies.

who used asymmetric excitation via a strip electrode close tothe edge of the piezoelectric element.

It should be noted, however, that our definition of theFOM used in figure 4(b) only gives an estimate of the averagemanipulation performance in the area photographed. As canbe seen both experimentally in figure 4(a) and theoreticallyin figure 2(b), the performance often varies with locationalong the channel. Thus, a possible source of error in ourquantification of the manipulation performance is if suchperiodic variations are present but with a period larger thanthe area photographed. Figure 4(c) shows a characterizationof the manipulation performance along the channel for thetransducer with the highest FOM (with the 30-wedge).

We note that at the frequency giving the highest FOM(1.97 MHz) the particle focusing along the channel is fairlyuniform, but also that a periodic pattern such as at 2.00 MHz(cf figure 4(c)) can result in a FOM above the cut at 1.65 infigure 4(b). Such a periodic manipulation performancephenomenon is often negligible and invisible when the chip isoperated in a flow-through mode. On the other hand, if the flowin the channel is very low or under no-flow conditions, sucheffects become very important. We demonstrate an applicationof a periodic resonance in section 4.2.1 (2D arraying).

4.2. Verification of design

4.2.1. Single-frequency and no-flow operation: 2D arraying.Figure 5 illustrates commonly observed distributions ofmanipulated beads in a microchannel for different frequenciesclose to the nominal X transducer frequency (∼2 MHz, aimedfor focusing in the x-direction, cf figure 1(b)), and comparesthe experimental distributions (micrographs) with modeledforce fields. The simulation graphs (below each micrographin figure 5) are selected areas from numerical modelingin two dimensions (xz plane, a ‘top view’) of the entirechip, which means that the comparison is semi-quantitative(in terms of, e.g., absolute frequency matching) [15]. The‘straight’ node shown in figure 5(a) is actually less commonthan the ‘wobbly’ node (figure 5(b)) or the ‘periodic’ node(figure 5(c)). This fact is reflected in previous observationsof similar node shapes in microchips (e.g., in [10, 16, 19,26]). As seen in the modeling results in figures 5(b), (c),the ‘wobbly’ or ‘periodic’ shapes are predicted in theory ifthe resonance of the whole transducer–chip system is takeninto account. Thus, the phenomenon is typically associatedwith ultrasonic manipulation in microfluidic chips, where themicrochannel serves as a closed cavity of very small volumerelative the whole chip volume. The result is complex 3Denclosure modes of the solid structure, which are coupled withthe microchannel resonance. It should be noted, however,that in flow-through applications, e.g., continuous particleseparation [4], the effects of ‘wobbly’ or periodic’ nodes areoften averaged out and therefore not even visible. Still, theeffects must be considered in no-flow applications as discussedhere. Finally, it should also be noted that while the model canpredict the shape of the observed force field distributions, it isvery difficult to predict the corresponding actuation frequencywith high accuracy. One reason is the uncertainty in the soundspeed in the modeled materials.

We will now demonstrate an example of the use of the‘wobbly’ and ‘periodic’ effects in single-frequency fields inmicrochannels. Figures 6(a) and (b) illustrate a selectedarea of the full simulated field at 3.98 MHz (i.e., a full-wavelength resonance across the x-direction of the channel),where the actuation frequency is chosen in order to achieve x(figures 6(a)) and z (figure 6(b)) force components in thechannel of similar magnitudes. Figure 6(c) displays predictedtrapping sites (dark spots), based on the intersections betweenthe predicted potential wells of each force component x andz in figures 6(a), (b), respectively. For this purpose, we have

6


Figure 5. Comparison between experimental manipulationperformance (micrographs) and modeled normalized forces(x components only, red is positive and blue negative) in threecharacteristic cases: the ‘straight’ node (a), the ‘wobbly’ node (b)and the ‘periodic’ node (c). The contour lines correspond to theabsolute forces being equal to 10% of the maximum value. Thenormalization is different in the three simulations. The scalebar in(a) applies to all images. The micrographs are acquired from thefrequency scans discussed in section 4.1.3. The frequencies used inthe micrographs were (a) 1.88 MHz, (b) 1.98 MHz and (c)2.03 MHz, and in the simulations (a) 1.86 MHz, (b)1.92 MHz and(c) 1.87 MHz.

Figure 6. Two-dimensional (2D) arraying of particles in a straightchannel. Figures 6(a) and (b) show modeling of the x and zcomponents, respectively, of the force during single-frequencyactuation (at 3.98 MHz). The contour lines are forces 10% of themaximum value. Figure 6(c) illustrates the results of calculations onprobable trapping sites based on the results shown in figures 6(a)and (b). Figure 6(d) demonstrates a corresponding experiment,where 2.8 µm beads are arranged in a 2D array of small beadaggregates at 4.00 MHz actuation.

defined a point rwell to be in the potential wells in figures 6(a)and (b) by the condition that

|FPR(rwell)| < 0.1 · |FPR|max and(6)

∇FPR,i (rwell) < −0.02 · |∇FPR,i |max,

where the symbol ||max means the maximum of the absolutevalue, and the second condition must hold for the gradient ofboth components of FPR, i.e., i = x and i = y.

Thus, simulation predicts that it is possible to arrangeparticles in a 2D array of small aggregates by single-frequencyactuation of a simple straight microchannel. The predictionis experimentally confirmed in figure 6(d), where 2.8 µmfluorescent polystyrene beads were actuated for 5 min at4.00 MHz and 8 Vpp by a 48-wedge Z transducer1.Interestingly, both theory and experiments indicate an irregularand complex force distribution resulting in, e.g., ‘missing’nodes, ‘out-of-place’ (compared to a symmetric grid) nodes

1 The result that the 30-wedge transducer is optimal is valid when the targetapplication was uniform focusing, which is not the case here.

Figure 7. Two-dimensional (2D) alignment of 10.8 µm beads inflow-through operation using two independent transducers.Figure 7(a) shows the distribution of beads in the channel withoutany acoustic fields. Figures 7(b) shows the effect of focusing ofbeads towards a vertical plane in the middle of the channel.Figure 7(c) shows the effect of levitation of beads towards ahorizontal plane near the middle of the channel. Both figures 7(b)and (c) are 1D manipulation functions corresponding to the modeledforce fields in figures 2(a) and (b), respectively. Figure 7(d) shows2D alignment of the beads into the centerline of the channel bydual-frequency actuation. This is a combination of the focusing andlevitation functions in figures 7(b) and (c).

and elongated shape of some nodes (cf figures 6(c) and (d)).This is a typical effect of strong mode coupling in orthogonaldirections during single-frequency actuation.

4.2.2. Dual-frequency and flow-through operation: 2Dalignment. We will now demonstrate an important flow-through application of two different-frequency, uncoupled,near-1D, orthogonal fields used for 2D particle alignment.Figure 7 shows images acquired with 19 ms exposuretime, demonstrating 1D focusing (figure 7(b)), 1D levitation(figure 7(c)) and 2D alignment (figure 7(d)) of fluorescent10.4 µm beads pumped through the channel at 5 µl s−1,and compared with the initial no-field operation (figure 7(a)).In the experiment, the system is excited at either 1.97 MHz/5.0 Vpp by a 30-wedge X transducer (figures 7(b) and (d)),and/or at 6.90 MHz/5.0 Vpp by a 20-wedge Y transducer(figures 7(c) and (d)). Thus, focusing (figure 7(b)) andlevitation (figure 7(c)) are single-frequency manipulationfunctions, while alignment (figure 7(d)) is a dual-frequencymanipulation function.

Without any ultrasonic actuation (cf figure 7(a)), a typicaland general microfluidic effect is a wide distribution in speedsof the beads due to the wide distribution of beads in thecross-section (in both x- and y-directions) in combinationwith the laminar flow and no-slip boundary conditions ofthe medium. In particular, beads that settle by gravity tothe bottom surface of the microchannel are partly retained(‘stuck’) by the surface interaction, resulting in very lowand irregular, or no speed. The latter effect is still presentin figure 7(b), where a significant majority of the focusedparticles move close to the bottom surface at low speed. Infact, we believe that the difference in the relative amount ofbeads close to the bottom surface in figures 7(a) and (b) iscaused by the pseudo-1D resonance in the x-direction, having

7


a small but not negligible (negative) y component pushingthe beads towards the bottom of the channel. Such lateralcomponents are predicted in theory (e.g., the inset in figure 2(a)shows a positive y component, but simulations at other nearbyfrequencies confirm the existence of negative y components).

Streak length measurements of the imaged beads infigure 7 can be used for the quantification of the bead speeddistribution. For example, our measurements demonstratethat the standard deviation of the speeds is lowered by morethan a factor of 2 if the levitation function (figure 7(c))is compared with no-field operation (figure 7(a)). Finally,figure 7(d) shows alignment of the beads into the centerlineof the channel by actuating both transducers simultaneously.The beads are now centered both vertically (levitated) andhorizontally (focused), i.e., aligned and centered in twodimensions in the channel with trajectories parallel to thechannel walls. In agreement with the observation madefor the focusing function (figure 7(b)), we also note thatthe actual bead speeds in figure 7(d) are lower than infigure 7(c). A reasonable explanation is that the verticalposition of beads is primarily defined by the equilibriumbetween the lateral (negative, y-directed) component of thefocusing (x-directed) field and the (positive, y-directed)levitating field. Furthermore, the standard deviation of thevelocity distribution is now almost negligible, since all beadsfollow the same fluid streamline. Thus, figure 7(d) shows thatwith our system it is possible to guide suspended particlesor cells through a microfluidic channel at constant speed andconstant cross-sectional position, without any contact withthe channel walls. Direct benefits are reduced sample lossor contamination, a retained spatial confinement of particlesalong the channel in an injected sample volume, and improvedcompatibility with high-resolution microscopy-based opticalmonitoring of particles and cells (by matching the optical focalplane with the levitation plane).

5. Summary and conclusion

Analysis of the coupling method with wedge transducersclearly shows that it is advantageous to use an angled wedgecompared to a simple plane-parallel coupling layer (referredto as a 0-wedge in section 4). In our coupling analysisfor the focusing manipulation function, we conclude thatthe X transducer with a 30-wedge is the optimal choice.It is also noted that the optimal position of the 30-wedgetransducer is close to a chip edge, and not directly above thechannel (close to the chip center). Such asymmetric transducerplacement is not only advantageous for the coupling, but alsofully compatible with trans-illumination-based high-resolutionoptical microscopy. A future design improvement is to matchnot only the height, but also the width of the whole chip(including all three layers) with the wavelength.

Concerning the manipulation characteristics, we note thatone-dimensional (1D) resonances excited at single frequenciesdo not exist in microchannels or microchips. Any resonanceranges from a complex 3D resonance with strong couplingeffects, to a pseudo-1D resonance with only minor lateralforce components, or variations in the axial component

along the lateral direction. Typical effects of pseudo-1Dresonances in a fluid channel are ‘wobbly’ and ‘periodic’ nodes(cf figure 5). Under certain circumstances the forces paralleland perpendicular to the channel are of equal magnitudes,which can give rise to an array of isolated trapping sites(cf figure 6). This is one strategy to obtain a 2D manipulationfunction by single-frequency actuation. Another strategy is tosuperpose pseudo-1D resonances by dual-frequency actuation(cf figure 7). While strong coupling effects have been observedand theoretically predicted in the case of two frequencies ofvery small difference [17], we have not observed any couplingeffects in our measurements performed at two frequencies oflarger difference (cf figure 7). A general multi-frequencystrategy to minimize coupling effects is to avoid frequenciesthat are close to multiples of each other.

In the future, our device can be used for high-resolutionoptical monitoring of 2D aligned particles or cells, or ofcells positioned in an array of small aggregates for long-term,dynamic optical characterization.

Acknowledgments

This paper was generated in the context of the CellPROMproject, funded under the 6th Framework Program ofthe European Community (Contract No NMP4-CT-2004-500039). The work was also supported by the SwedishResearch Council for Engineering Sciences.

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A three-dimensional ultrasonic cage for characterization of individual cellsOtto Manneberg,1 Bruno Vanherberghen,1 Jessica Svennebring,1 Hans M. Hertz,1

Björn Önfelt,1,2 and Martin Wiklund1,a

1Department of Applied Physics, Royal Institute of Technology, KTH-AlbaNova, SE-106 91 Stockholm,Sweden2Department of Microbiology, Tumor and Cell Biology, Karolinska Institutet, SE-171 77 Stockholm, Sweden

Received 10 June 2008; accepted 26 July 2008; published online 14 August 2008

We demonstrate enrichment, controlled aggregation, and manipulation of microparticles and cells byan ultrasonic cage integrated in a microfluidic chip compatible with high-resolution opticalmicroscopy. The cage is designed as a dual-frequency resonant filleted square box integrated in thefluid channel. Individual particles may be trapped three dimensionally, and the dimensionality ofone-dimensional to three-dimensional aggregates can be controlled. We investigate the dependenceof the shape and position of a microparticle aggregate on the actuation voltages and aggregate size,and demonstrate optical monitoring of individually trapped live cells with submicrometerresolution. © 2008 American Institute of Physics. DOI: 10.1063/1.2971030

Microfluidic systems for three-dimensional 3D con-tactless manipulation of individual cells or other micropar-ticles are classically based on either dielectrophoresis1 or op-tical tweezers.2 In dielectrophoresis-based systems octopolefield cages have long been used for 3D trapping and charac-terization of single cells,3 but also for 3D formation andstructuring of particle aggregates.4 Single-beam optical twee-zers have been used for 3D trapping and accurate positioningof individual cells.5 Multiple-beam or holographic opticaltweezers have been employed to create 3D structures, linesor arrays of particles.6,7 Both dielectrophoretic field cagesand optical tweezers have been implemented into lab-on-a-chip devices compatible with high-resolution opticalmicroscopy,1,2,5 and are therefore useful in, e.g., cell charac-terization applications. However, both techniques require ex-pensive or complicated instrumentation, and suffer fromlimitations in the long-term 30min biocompatibility.1,8

In contrast, manipulation devices based on ultrasoundhave been used for 1h cell retention in microfluidic chan-nels without any loss in viability,9 and have the potential ofbeing biocompatible for up to several days of operation.10,11

Even small living animals have been manipulated by ultra-sound without evidently changing their state of health.12

Furthermore, ultrasonic manipulation is a simple, inexpen-sive, and straightforward method for cell and particle han-dling. Demonstrated microfluidic-based applications includeparticle or cell separation, washing, aggregation, and bio-sensing.13–15

In addition to full-channel-actuation systems,14 semi-closed multiwavelength-size fluidic chambers have beenused for multidimensional ultrasonic manipulation of largeparticle ensembles in microfluidic chips.16–19 However, noreported ultrasound-based microfluidic device to date is com-patible with controlled 3D manipulation of individual micro-particles.

In this letter, we demonstrate 3D manipulation of indi-vidual microparticles and cells by an ultrasonic cage inte-grated in a microfluidic chip. The system is compatible withhigh-resolution optical microscopy allowing on-line observa-

tion of intracellular parameters. The ultrasonic cage is de-signed as a 3D resonant box, which is simultaneously excitedat two different frequencies corresponding to half-wave reso-nances in three orthogonal directions. By tuning the relativeactuation voltages at the two frequencies we show 3D par-ticle positioning and enrichment in the center of the cage,and reversible dimensional shape transformation of aggre-gates containing up to 100 particles. Finally, we demonstratesubmicrometer-resolution confocal fluorescence and trans-mission light microscopy imaging of trapped human immuneand kidney cells.

The experimentally observed acoustic properties of thecage are compared with two-dimensional 2D modeling ofthe horizontal top-view pressure field frequency responsein the cage. The pressure field was obtained by numericalsimulations using COMSOL MULTIPHYSICS Ref. 20 with MAT-

LAB Ref. 21 postprocessing. The acoustic radiation forceFPR is calculated according to22

FPR = −V

2c21 −c2

pcp2p p

−3p −

k22p + p · p , 1

where p is the acoustic pressure, V is the particle volume, kis the wave number, and and c are the density and speed ofsound in the medium no index and particle index p, re-spectively.

Figure 1a shows the chip-transducer system. The chipis made of a 14.7550 mm2 glass-silicon-glass stack withlayer thicknesses of 0.20, 0.11, and 1.0 mm, with the micro-channel dry etched in the silicon layer. The cage dimensionis 0.300.300.11 mm3. The inlet channel cross section is0.110.11 mm2 cf. Figs. 1c and 1d. The cage was ex-cited by two wedge transducers22 with nominal resonancefrequencies of 2.50 and 6.89 MHz, respectively, which wereattached on top of the chip cf. Fig. 1a by an adhesive gel.All driving voltages were maximum 10 Vp.p.. The chip de-sign, combined with the transducer placement, allows forhigh-resolution transillumination microscopy, as well as con-focal or epifluorescence microscopy. In the manipulation ex-aElectronic mail: [email protected].

APPLIED PHYSICS LETTERS 93, 063901 2008

0003-6951/2008/936/063901/3/$23.00 © 2008 American Institute of Physics93, 063901-1

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http://dx.doi.org/10.1063/1.2971030

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periments, we used green-fluorescent 10.4 m and non-fluorescent 5.0 m polymer beads, immune cells from ahuman B cell line 721.221 Ref. 23 labeled withcalcein-AM and DiD Invitrogen, and human embryonickidney cells HEK 293 T.

Figure 1b shows simulations of the normalized x and zcomponents of FPR cf., Eq. 1 for the actuation frequency2.51 MHz. This frequency is optimized for focusing and re-tention of particles in the x and z directions, respectively. Themodeling results were compared to flow-through dual-frequency experimental operation at 2.57 and 6.81 MHz. InFig. 1c 10 m beads are trapped, lined up, and retainedclose to the center of the cage slightly displaced down-stream due to the viscous fluid drag. Note that the incomingbeads enter the cage along the central streamline of the inletchannel due to the additional “funneling” 2D-prealignmentfunction22 of the levitation field at 6.81 MHz, which is alsoresonant in the x direction in the square-cross-section inlet.The measured trapping efficiency was found to be 100% forenrichment of up to 100 beads at the measured flow speed1 mm/s generating 10−11 N viscous forces on a trapped10 m bead. The loading capacity of the cage was investi-gated by long-term overnight enrichment of 5 m beads,without considering the trapping efficiency. Figure 1dshows the final aggregate containing 104 beads. Here, wesee that such a large aggregate cannot be fully caged in 3D.Beads in the lower right corner are driven to the cage wall,marked with a dotted line in Fig. 1d. This effect is alsopredicted in the simulations cf., corresponding area in Fig.1b. However, for smaller aggregates up to a few hundredparticles this effect can be completely avoided by funnelingincoming particles by the levitation field cf., Fig. 1c.

The position and shape of a caged aggregate of 10 mbeads was characterized in 3D with confocal microscopy.Figure 2 shows two orthogonal 2D-cut images of an10-bead aggregate from a full-cage volume scan. Imagesare shown for four different combinations of actuation volt-ages of the levitation 6.81 MHz and focusing/retention2.57 MHz modes. At 7 Vp.p. and 2.57 MHz operation only,a 2D aggregate is “standing” vertically i.e., occupying theyz plane on the bottom of the cage Fig. 2a. Figures2b–2d show dual-frequency operation with different rela-tive actuation voltages, where the aggregate is transformedbetween standing 2D Fig. 2b, 3D Fig. 2c, and “lying”2D i.e., occupying the horizontal xz plane Fig. 2d, re-

spectively. Comparing single-frequency actuation Fig. 2awith dual-frequency actuation Figs. 2b and 2d, we notethat the levitation field 6.81 MHz lifts the aggregate40 m above the channel bottom in Figs. 2b–2d,which corresponds to 3D positioning approximately one celldiameter below the center of the cage. The blurring of theimages looking down the x axis in Fig. 2 left panels isattributable to a combination of the lack of depth resolution,and a slight motion blur caused by the particles movingslightly between consecutive scans of different xz planes.

The packaging and structuring of beads during continu-ous enrichment and aggregation are quantified in the diagramin Fig. 3a. This is a dynamic study of the experimentshown in Fig. 1c. The diagram displays the top-view out-line and estimated depth of the developing aggregate as a

FIG. 1. Color a Photograph of chip-transducer system. b Modeling ofthe z retention and x focusing components of the normalized acousticradiation force at 2.51 MHz. In the color plot, red is positive, blue is nega-tive, and green is zero. 3D caging of c 10 m beads and d 5 m beadsat simultaneous 2.57 and 6.81 MHz actuation 10 Vp.p. for both.

FIG. 2. Demonstration of 3D caging and transformation between a vertical2D a and b, 3D c, and horizontal 2D d bead aggregate positionedwith b and d or without a a levitation field. For the two actuationfrequencies 2.57 and 6.81 MHz, the applied voltages are a 7 and 0 Vp.p.,b 7 and 10 Vp.p., c 4 and 10 Vp.p., and d 3 and 10 Vp.p., respectively.The images are orthogonal 2D cuts extracted from a 3D full-cage confocalmicroscopy scan. The dotted lines indicate the top and bottom of the chan-nel. The axes refer to the coordinate system in Fig. 1.

FIG. 3. Color a Top-view outline black contours and average numberof layers red curve of a developing bead aggregate vs bead number ag-gregate size, in green during flow-through enrichment. Micrograph of acompact 3D b and a 2D monolayer c aggregate of 50 beads trapped inthe center of the cage. d 1D aggregate of four caged HEK cells. e andf High-resolution imaging of a single focused and retained B cell labeledwith calcein-AM and DiD, dropped to the bottom of the cage. The scale barsare 25 m in b–d, and 10 m in e and f.

063901-2 Manneberg et al. Appl. Phys. Lett. 93, 063901 2008


function of the number of trapped beads, with the aggregatelength and depth on the left and right vertical axes, respec-tively. The outlines are extracted from image analysis of se-lected frames from a 30 s video sequence. Care was takento select frames of the aggregate in steady state. The aggre-gate depth is estimated without taking differences in packingdensity into account. We note that the aggregate undergoes arestructuring into a more compact shape i.e., shorter andthicker at certain sizes e.g., around 25, 38, and 65 beads inFig. 3a. These critical sizes depend on the actuation volt-ages relative to the flow rate. Typically, for 100 bead ag-gregates the thickness-to-length ratio i.e., the “compact-ness” increases as aggregate size and flow rate increase.

When an adequate number of beads or cells have beencollected and aggregated it is possible to reversibly trans-form the aggregate between a compact 3D structure as inFig. 3b and a lying 2D monolayer as in Fig. 3c. Thisexperiment is performed with 50 caged beads at no-flowconditions by decreasing the 2.57 MHz focusing/retentionvoltage from 10 to 3 Vp.p., while keeping the 6.81 MHzlevitation voltage constant at 10 Vp.p..

Caged cells may be characterized by high-resolution op-tical microscopy. Figure 3d shows four caged HEK cellsduring medium perfusion. As seen in the image, it is possibleto form a one-dimensional 1D aggregate when the cellnumber is low enough approximately 10. More advancedimaging can be performed by dropping the cells to the bot-tom of the cage i.e., by turning off the 6.81 MHz levitationfield. Figures 3e and 3f show high-resolution bright-fieldand confocal fluorescence microscopy imaging, respectively,of a single focused and retained B cell at 2.57 MHz actua-tion. The micrographs are obtained with a 100 /1.3 NAoil-immersion objective. The cell is labeled with the green-fluorescent viability indicator calcein-AM, and the red-fluorescent membrane probe DiD. The orange part in thecenter of the cell indicates an internal membrane, possiblythe Golgi apparatus.

To conclude, we have demonstrated 3D caging, enrich-ment, and shape-specific aggregation, combined with high-resolution imaging of cells or beads in an ultrasonically ac-tuated microfluidic chip. The cage dimension is optimizedfor individual particle or cell handling, or handling of aggre-gates containing up to a few hundred particles or cells. Sincethe cage is simultaneously actuated at two frequencies, it ispossible to structure the trapped particles as either a 2Dmonolayer or a compact 3D aggregate. Monolayer position-ing is particularly useful for characterization by nonconfo-cal high-resolution optical microscopy. Transformation be-tween monolayer and multilayer structures is interesting for,e.g., investigation of cell-cell interaction with control of thenumber of neighbors for each cell.24 Furthermore, the cage

can be used for cell or particle enrichment of very dilutedsamples due to its 100% trapping efficiency combined withthe sample-to-wall preventing funneling prealignmentfunction. Future applications include long-term high-resolution monitoring of interactions between individualcells, e.g., the immune synapse,25 and ultrasensitive bead-based bioanalytics.13

The authors gratefully acknowledge the financial supportof the Swedish Research Council, the Swedish Foundationfor Strategic Research, and the CellPROM project within the6th Framework Program of the European Community GrantNo. NMP4-CT-2004–500039.

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11J. Svennebring, O. Manneberg, and M. Wiklund, J. Micromech. Microeng.17, 2469 2007.

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13M. Wiklund and H. M. Hertz, Lab Chip 6, 1279 2006.14T. Laurell, F. Petersson, and A. Nilsson, Chem. Soc. Rev. 36, 492 2007.15L. A. Kuznetsova and W. T. Coakley, Biosens. Bioelectron. 22, 1567

2007.16A. Haake and J. Dual, J. Acoust. Soc. Am. 117, 2752 2005.17S. Oberti, A. Nield, and J. Dual, J. Acoust. Soc. Am. 121, 778 2007.18S. M. Hagsäter, T. Glasdam Jensen, H. Bruus, and J. P. Kutter, Lab Chip

7, 1336 2007.19J. Svennebring, O. Manneberg, P. Skafte-Pedersen, H. Bruus, and M. Wik-

lund unpublished.20See http://www.comsol.com/products/multiphysics/21See http://www.mathworks.com/22O. Manneberg, J. Svennebring, H. M. Hertz, and M. Wiklund, “Wedge

transducer design for two-dimensional ultrasonic manipulation in a micro-fluidic chip,” J. Micromech. Microeng. to be published.

23Y. Shimizu and R. DeMars, J. Immunol. 142, 3320 1989.24P. J. Lee, P. J. Hung, R. Shaw, L. Jan, and L. P. Lee, Appl. Phys. Lett. 86,

223902 2005.25D. M. Davis and M. L. Dustin, Trends Immunol. 25, 323 2004.

063901-3 Manneberg et al. Appl. Phys. Lett. 93, 063901 2008


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http://dx.doi.org/10.1063/1.1938253

ARTICLE

Selective Bioparticle Retention andCharacterization in a Chip-IntegratedConfocal Ultrasonic Cavity

J. Svennebring,1 O. Manneberg,1 P. Skafte-Pedersen,2 H. Bruus,2 M. Wiklund1

1Biomedical & X-Ray Physics, Department of Applied Physics,

Royal Institute of Technology, SE-106 91 Stockholm, Sweden;

telephone: þ46-8-5537-8134; fax: þ46-8-5537-8466; e-mail: [email protected] of Micro- and Nanotechnology, Technical University of Denmark,

Kongens Lyngby, Denmark

Received 3 August 2008; revision received 2 November 2008; accepted 30 December 2008

Published online 6 January 2009 in Wiley InterScience (www.interscience.wiley.com)
. DOI 10.1002/bit.22255
ABSTRACT: We demonstrate selective retention and posi-tioning of cells or other bioparticles by ultrasonic manip-ulation in a microfluidic expansion chamber duringmicrofluidic perfusion. The chamber is designed as a con-focal ultrasonic resonator for maximum confinement of theultrasonic force field at the chamber center, where the cellsare trapped. We investigate the resonant modes in theexpansion chamber and its connecting inlet channel bytheoretical modeling and experimental verification duringno-flow conditions. Furthermore, by triple-frequency ultra-sonic actuation during continuous microfluidic samplefeeding, a set of several manipulation functions performedin series is demonstrated: sample bypass—injection—aggregation and retention—positioning. Finally, wedemonstrate transillumination microscopy imaging of ultra-sonically trapped COS-7 cell aggregates.

Biotechnol. Bioeng. 2009;103: 323–328.

2009 Wiley Periodicals, Inc.

KEYWORDS: ultrasonic manipulation; cell characterization;microfluidic chip

Introduction

Ultrasonic manipulation technology has recently emerged asa powerful tool for handling micrometer-sized biomaterials(such as cells and bio-functionalized beads) in microfluidicchips (Laurell et al., 2007; Wiklund and Hertz, 2006a), withapplication examples such as separation and fractionation

Correspondence to: M. Wiklund

Contract grant sponsor: 6th Framework Program of the European Community

Contract grant number: NMP4-CT-2004-500039

Contract grant sponsor: Swedish Research Council for Engineering Sciences

Contract grant sponsor: Goran Gustavsson Foundation

2009 Wiley Periodicals, Inc.

(Harris et al., 2003; Nilsson et al., 2004; Petersson et al.,2007), washing (Hawkes et al., 2004; Petersson et al., 2005),positioning (Haake et al., 2005), and aggregation andretention (Evander et al., 2007; Hultstrom et al., 2007;Lilliehorn et al., 2005). Although efficient and compatiblewith high-throughput operation, the current ultrasonicmanipulation technology in chips is typically limited toperform a single manipulation function, which is most oftendistributed along the whole microchannel. However,Manneberg et al. (2009) have recently demonstrated howto spatially separate and localize several independentlyaddressable manipulation functions in series by geome-trically varying the ultrasonic resonance conditions alongthe microchannel. In the present study, we extend thisconcept by introducing a chip-integrated confocal ultra-sonic cavity designed for selective bioparticle retention andcharacterization.

Resonant ultrasonic actuation of a microchannel ofconstant cross-section typically results in transverse acousticradiation forces (see Fig. 1) that focus the particles in well-defined separated bands along the channel. Favorableacoustic resonance conditions occur when actuating chipsof small channel heights at frequencies close to those beingmultiples of half the acoustic wavelength across the channelwidth (Hagsater et al., 2008; Manneberg et al., 2008a). Fortrapping and retention purposes, however, axial gradients(see Fig. 1b) in the sound field are needed. Such gradientscreate axial acoustic radiation forces capable of balancing theviscous drag from the fluid flow. Suggested approaches inchips for axial confinement and localization of the ultrasonicforces are based on either confinement of the channelresonance conditions via variations of the channel geometry(Hagsater et al., 2007; Manneberg et al., 2008b), or con-finement of the incident acoustic field via near-field effectsfrom the transducer (Hultstrom et al., 2007; Lilliehorn et al.,

Biotechnology and Bioengineering, Vol. 103, No. 2, June 1, 2009 323

Figure 1. a: Photograph of the transducer-chip system. b: Illustration of the

resonator design: the confocal ultrasonic cavity (in red), and the plane-parallel pre-

alignment channel (in blue). The red and blue solid lines indicate the primary reflecting

walls of the resonators. The red and blue dashed lines indicate the approximate

boundaries of the generated force fields. c: Schematic of the available manipulation

functions during sample flow: (1) bypass, (2) injection/selection, (3) retention/position-

ing. The particle paths are defined by the pressure nodes in the pre-alignment channel.

2004). The latter method has been used for sequentialtrapping of beads above three channel-integrated ultrasonictransducers (Lilliehorn et al., 2005). However, currentultrasonic retention devices cannot be used for the selectionof a discrete subpopulation from a continuous sample flow.

Confocal or hemispherical ultrasonic cavities are focusedstanding-wave resonators based on curved reflector ele-ments. Such resonator designs have previously beenemployed in macro-scale systems for trapping of millimetersize objects in air (Brandt, 1989; Xie and Wei, 2001), and ofmicrometer size objects in fluid suspensions (Hertz, 1995;Wiklund et al., 2001, 2004). The curved reflector elements

324 Biotechnology and Bioengineering, Vol. 103, No. 2, June 1, 2009

create a focused resonant acoustic field with a highlyconfined force field, which makes it possible to accuratelyposition objects three-dimensionally (3D) (Hertz, 1995).However, confocal ultrasonic cavities have not yet beeninvestigated in microfluidic chips.

In the present study, we demonstrate and investigate anintegrated confocal ultrasonic cavity in a microfluidic chipfor selective retention and optical characterization of cells orother bioparticles (Fig. 1). The ultrasound is coupled to thechip by external wedge transducers (Manneberg et al.,2008a; Wiklund et al., 2006b) that are fully compatible withany kind of high-resolution optical microscopy (Manneberget al., 2008b). In the present work, we investigate theresonant modes in the confocal cavity by theoreticalmodeling and experimental verification during no-flowconditions. Furthermore, we demonstrate the flow-throughoperational modes (the manipulation functions) of ourdevice based on triple-transducer actuation, which are (1)pre-alignment and bypassing of cells, (2) selective injectionof cell by pre-alignment frequency shift, (3) trapping,retention, and positioning of cells in the center of theexpansion chamber, and finally (4) label-free transillumina-tion optical microscopy of a monolayer aggregate of retainedcells. The purpose of our design is to select, retain, andposition a discrete subpopulation of up to100 cells from acontinuous feeding sample flow for dynamic opticalcharacterization.

Device

The device (Fig. 1a) consists of a dry-etched silicon structuresandwiched between two glass layers (GeSim, Dresden,Germany), and three external transducers with refractiveelements (Manneberg et al., 2008a) placed on top of the chipfor efficient coupling of ultrasound into the channel. Thelayer dimensions of the chip were 200/110/1,100 mm(bottom glass, silicon, upper glass), respectively. Theresonator elements are illustrated in Figure 1b. The328 mm wide inlet channel was used as a plane-parallelresonator (indicated with blue solid lines in Fig. 1b) forparticle pre-alignment, bypassing and selection, and wasoperated in either dual-node (at 4.6 MHz) or single-node(at 2.1 MHz) mode (see blue dashed and solid lines,respectively, in Fig. 1c). The expansion chamber, intendedfor sample retention and positioning, was designed as aresonant confocal cavity with two cylindrical segmentsseparated by twice their radius of curvature 2R¼ 4.92 mm(indicated with red solid lines in Fig. 1b), for maximum axialfocusing of the standing wave (indicated with red dashedlines in Fig. 1b). The chamber width was chosen as 15 thewidth of the pre-alignment channel, which results inapproximately the same factor of reduction in the viscousdrag on a trapped particle without reducing the flow rate.The chamber was actuated at a frequency close to 6.9 MHz,which also matched with a half wavelength along the channelheight for vertical centering (levitation) in the whole chip atthis frequency. All actuation voltages were 10 Vpp.

The endpoints of the main channel were branched intothree inlets and three outlets (see Fig. 1a), although only oneinlet and one outlet were used in this work. The flow rate inthe chip was controlled by a syringe pump. The chip-transducer system was mounted on an inverted microscope(Axiovert 135; Zeiss, Jena, Germany) for optical monitoringof manipulated particles or cells. Due to the thin bottomglass (200 mm), the fully transparent chip is compatible withboth fluorescence (cf. Manneberg et al., 2008b) andtransillumination high-resolution optical microscopy(shown in Fig. 5). Five micrometer non-fluorescentpolyamide beads (Danish Phantom Design, Jyllinge,Denmark) were used to visualize the acoustic force fieldsin the expansion chamber, and 10 mm green-fluorescentpolystyrene beads (Bangs Laboratories, Fishers, IN) wereused as a cell model (i.e., having similar size and acousticproperties) in the experiments simulating manipulation ofcells. Finally, COS-7 cells derived from fetal monkey kidneywere cultivated and prepared according to the proceduredescribed in Hultstrom et al. (2007). The cells were used fordemonstrating label-free transillumination imaging techni-ques of a retained cell aggregate.

Figure 2. a: Theoretical modeling of the acoustic pressure field in the expansion

chamber at 6.92 MHz. The arrows mark the observed trapping sites in Figure 3. b: No-

flow experimental verification at 7.07 MHz. The micrograph shows the distribution of

5 mm beads (dark pattern) after 10 s of ultrasonic actuation without fluid flow. The

acoustic forces are proportional to the square of the pressure field and tend to drive

particles to the pressure nodes (green areas, in between yellow/red and turquoise/

blue areas, in Fig. 2a). c: Flow-through experimental verification with COS-7 cells at

Simulations

Two-dimensional (2D) simulations of the acoustic pressurefield for determination of the eigenmodes and eigenfre-quencies were made using the COMSOL eigenvalue solversearching for solutions around 6.9 MHz. Three differentmodels with different degrees of geometry simplificationswere applied: simulations with the entire channel system(including the branched inlet/outlet), only the straightcenter channel, and the expansion chamber alone (seeFig. 1a). Except for the first model, the channel ends havebeen set to acoustically soft ends (open ends kept at ambientpressure) and the remaining boundaries to hard, perfectlyreflecting walls. All simulations were performed for amaximum mesh size of 20 mm. This corresponds toapproximately 10 mesh points per wavelength at theinvestigated frequencies in an aqueous medium.

7.20 MHz. Contour lines from the simulated pressure field in (a) are superimposed to

the micrograph.

Results

Resonance Characterization in the Expansion Chamber

The simulated and experimental particle responses toactuation of the expansion chamber during no-flowconditions are shown in Figure 2a and b, respectively. InFigure 2a, the simulated acoustic pressure field is shown forthe eigenfrequency 6.92 MHz. The top-view, linear-scale,color plot displays high-pressure areas (red and blue inFig. 2a) focused in the center of the chamber. The log-scalecolor plot (inset in Fig. 2a) reveals a non-zero fine structureon the upstream and downstream sides of the chambercenter. The simulated field is verified in Figure 2b, where5 mm polyamide beads are manipulated at 7.07 MHz during

10 s without fluid flow. The dark bead pattern displays areaswith zero forces, proportional to the square of the acousticpressure amplitude (Groschl, 1998). The thin near-horizontal lines of packed beads above, below, and in thecenter of the chamber appear within less than 1 s andcorrespond well with the simulated linear-scale pressurepattern in Figure 2a. The more complex pattern outside theregion of lines appears within 10 s and corresponds well withthe simulated log-scale pattern in Figure 2a.

Figure 2c demonstrates flow-through operation of thechip at 7.20 MHz with a sample flow from right to leftcontaining COS-7 cells. Here, contour lines from the

Svennebring et al.: Selective Retention and Positioning of Cells 325

Biotechnology and Bioengineering

Figure 3. Characterization of the retention sites in the expansion chamber during fluid flow and 7.07 MHz actuation. The upper panels show manipulation of 5 mm beads, and

the lower panels show manipulation of 10 mm fluorescent beads. The flow rates are 50 mL/min (a) and 2.5 mL/min (b). The arrows pointing up indicate the location of maximum

retention forces where a 3D aggregate is trapped. The arrows pointing down indicate the location where a 2D aggregate is positioned and retained. The dashed rectangles indicate

the scale and position of the micrographs in the lower panels relative to the micrographs in the upper panel.

Figure 4. Demonstration of selective retention and positioning from a contin-

uous sample flow (5 mL/min) containing 10 mm fluorescent beads: sample bypass (a),

sample injection (b), sample bypass (c), and sample aggregation and retention (d–f).

The actuation frequencies are 4.60 and 7.07 MHz in (a) and (c–f), and 2.13 and 7.07 MHz

in (b). g: The retention result of six consecutive 1-s long injections.

modeled field in Figure 2a are superimposed on themicrograph. In the fit, the node-to-node distance of 120 mmwas chosen. As seen in the image, the axial acoustic forces inthe five central pressure nodes (marked with ‘‘retentionregion’’ in Figure 2c) are balanced with the viscouscompeting drag. The result is localized retention of theincoming COS-7 cells distributed within an area of size0.5 mm 0.2 mm, while bypassing all other incoming cellsin the peripheral nodes outside this retention region. At thepresent flow rate (1 mL/min), the axial retention force in thecenter of the chamber is approximately 10 pN for the COS-7cells.

The retention performance is investigated in more detailin Figure 3. Here, the chamber is actuated at 7.07 MHz whileslowly decreasing the flow rate. The upper panels showmanipulation of 5 mm beads within a region correspondingto the black rectangle in Figure 2a, and the lower panelsshow manipulation of 10 mm fluorescent beads within aregion corresponding to the dashed white boxes in the upperpanels. The trapping and retention first start at the beadvelocity of 3.0 mm/s at the location marked with an arrowpointing up in Figure 3a. Here, a 3D aggregate is formed veryclose to the mid-point of the chamber. The retention forceon the first trapped 10 mm bead is 280 pN, and thecorresponding fluid flow rate is 50 mL/min. When the beadvelocity is decreased to 0.15 mm/s another trapping location(marked with an arrow pointing down in Fig. 3b) appearsapproximately 0.7 mm in the upstream direction fromthe first location. Here, a 2D aggregate is formed andlevitated approximately 50 mm from the channel bottom.The retention force on the first trapped 10 mm bead is now14 pN, and the corresponding fluid flow rate is 2.5 mL/min.The locations for 3D and 2D retention are also marked in theinset in Figure 2a with arrows pointing up and down,respectively. Thus, the levitation function, causing 2Daggregation, is restrained at the chamber center due to thedominating transverse (horizontal) forces. However, asdemonstrated in Figure 3b, 2D retention can be accom-plished at slightly lower flow rates and will be investigated inmore detail in the next section.

Finally, it should be noted that while the theoreticalsimulations can be used to predict the overall shape of the


force field in the microfluidic system (cf. Fig. 2), it is moredifficult to accurately predict the resonance frequency.Frequency difference between experimental and simulatedmodes has previously been observed and discussed(Hagsater et al., 2007, 2008; Manneberg et al., 2008a),and is an artifact from the simplified boundary conditions ofthe model that only take into account the fluid channel andnot its supporting solid structures of the chip. In practice,several experimental chamber resonances similar to themodeled resonance in Figure 2a exist, for example, at 6.87,7.07 (in Figs. 3 and 4), 7.20 (in Fig. 2c), and 7.84 MHz. Inour present setup, the 7.07-MHz resonance seems togenerate the strongest forces.

Figure 5. Label-free transillumination imaging of positioned and retained COS-7

cells in the expansion chamber, visualized by phase-contrast (top panel) and dark-field

(bottom panel) microscopy. [Color figure can be seen in the online version of this

article, available at www.interscience.wiley.com.]

Sample Selection, Retention, and Positioning

In this section, we will demonstrate how to select, retain, andposition a discrete subpopulation of cells or particles from acontinuous sample flow, according to the scheme presentedin Figure 1c. Here, the chip is actuated by three transducersoperating around 2.1, 4.6, and 6.9 MHz (cf. Fig. 1a).

Figures 4a–f are frames from a video sequence when thechip is operated at a constant sample flow rate of 5 mL/min.The dashed vertical line indicates the end of pre-alignmentchannel (right side) and the beginning of the expansionchamber (left side). The sample is 10 mm fluorescent beadssuspended in water to a concentration of 105 mL1.During the whole sequence, the expansion chamber iscontinuously actuated at 7.07 MHz. The process begins withpre-alignment of particles (on the right side of the verticaldashed line) into two nodes at 4.60 MHz actuation, resultingin bypassing of particles through peripheral streamlines inthe expansion chamber (cf. Fig. 4a). Then, by switching to2.13 MHz actuation, particles in the pre-alignment channelare aligned into a single node, which is used for injectionof particles into a streamline crossing the center of theexpansion chamber (cf. Fig. 4b). When switching back to4.60 MHz actuation, all particles still present in the pre-alignment channel are bypassed when they enter theexpansion chamber (cf. Fig. 4c). Thus, only the particlespassing the vertical dashed line in Figure 4 during the 3-slong time interval between switching from 4.60 to 2.13 andback to 4.60 MHz are injected towards the retention region.Finally, the injected particles are trapped, aggregated, andretained close to the center of the expansion chamber(cf. Fig. 4d–f).

The white arrows in Figure 4b–f track a single particlethrough the selection and trapping process. For this choiceof flow rate and particle concentration, the time scale for thewhole process is less than 10 s. The 3-s long injection inFigure 4b resulted in 31 selected and positioned beads. Theresult of repeated 1-s injections are displayed in Figure 4g. Asseen in the micrographs, the beads are closely packed inhorizontal monolayers, which are levitated and positionedin between the channel floor and roof. For the six injections,the number of collected and retained beads is 16.5 6.0(average and standard deviation). If we assume that theindividual bead injection events are uncorrelated, we wouldexpect a Poisson distribution of the counting statistics, thatis, N

ffiffiffiffiNp

. The observed counting statistics is in agreementwith this hypothesis. Single-particle injection accuracy canin principle be obtained at low particle concentrations andflow rates, followed by manual switching between the pre-alignment frequencies. However, under such circumstancesthe collection efficiency is of the order of a few particles perminute. It should also be noted that a retained aggregatewith 10 or more particles or cells can be retained in thechamber for several hours during constant-flow mediumperfusion. The only observed perturbation source causingunwanted release of trapped particles is the occurrence of airbubbles in the fluid channel. Such problems are typically

related to the external pump and tubing system connected tothe chip.

Optical Characterization of Cells

Since the retained cell aggregate can be positioned andarranged as a horizontal monolayer (cf. Fig. 4g), we mayperform cell characterization based on high-resolutionmicroscopic monitoring, as previously demonstrated withfluorescent labels in Manneberg et al. (2008b). In Figure 5,we demonstrate examples of label-free imaging of anultrasonically retained aggregate containing 100 COS-7cells using transillumination techniques: phase-contrast anddark-field microscopy. Thus, the device is compatible withboth functionality studies based on, for example, fluorescentprobes, as well as with label-free studies, for example, themorphology or topology of cells.

Discussion

In this section, we exemplify and discuss different targetapplications that our device is designed for. We haveidentified two different potential bio-applications, where thechip will be operated in slightly different functional modes:(I) Ultrasensitive bead-based biomolecular detection and(II) serial screening and/or long-term characterization ofcells. The presented results in the former section are proof ofconcepts of the below applications.

In the first application (I), the chip can be used for ultra-sonic enhancement of bead-based immunoassays (Wiklundet al., 2004) incubated at ambient analyte conditions (Ekins,1989). Basically, the trick to obtain high sensitivity is toincubate the sample with extremely diluted bead-based

Svennebring et al.: Selective Retention and Positioning of Cells 327

Biotechnology and Bioengineering

reagents (Wiklund and Hertz, 2006a). The ultrasound isthen used for bead enrichment and positioning followed byconfocal fluorescence detection. While the current device isbuilt on a 96-well plate platform and suffers from limitationsin both the optical detection performance and theenrichment efficiency (Wiklund et al., 2004), our chip-based platform presented in this study has potential tosignificantly improve both these factors. Since the aim is toenrich and position all incoming beads in a monolayer inthe detection zone (the center of the expansion chamber),we only need the manipulation functions pre-alignment/injection and retention/positioning, and not the selection/bypassing functions (see Fig. 4).

In the second application (II), the set of manipulationfunctions demonstrated in Figure 4 (i.e., bypass—injection—retention—positioning—bypass) can be usedrepeatedly for real-time investigation of the cellular responseto variations in a particular parameter of interest (e.g.,concentration of a chemical compound or biomolecule).With our presented device, it is possible to assemble andposition a small aggregate of 10–100 cells within 10 s,followed by optical monitoring while bypassing excess cellsfrom a continuously feeding sample flow. Thus, after a cellaggregate has been assembled and positioned, the bypassfunction prevents delayed addition of cells to the aggregate.This is important for defining a starting time valid for allcells in the aggregate when monitoring time-dependentbiological processes. Furthermore, since ultrasonic cellhandling is a gentle and biocompatible method (Bazouet al., 2005; Evander et al., 2007; Hultstrom et al., 2007;Svennebring et al., 2007), it is also possible to study thedynamics of a cellular parameter during long terms(hours to days). Examples of such ‘‘slow’’ parameters aremonitoring of activation, differentiation and proliferationprocesses of individual cells. Future planned applicationsinclude dynamic monitoring of immunological synapses forstudying immune cell interactions (Davis and Dustin, 2004).

The authors gratefully thank Prof. Hans M. Hertz for valuable

discussions. This study was generated in the context of the CellPROM

project, funded under the 6th Framework Program of the European

Community (Contract No. NMP4-CT-2004-500039). The work was

also supported by the Swedish Research Council for Engineering

Sciences and the Goran Gustavsson Foundation.

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Flow-free transport of cells in microchannels by frequency-modulatedultrasound†

O. Manneberg,a B. Vanherberghen,a B. €Onfeltab and M. Wiklund*a

Received 13th October 2008, Accepted 9th January 2009

First published as an Advance Article on the web 2nd February 2009

DOI: 10.1039/b816675g

We demonstrate flow-free transport of cells and particles by the use of frequency-modulated ultrasonic

actuation of a microfluidic chip. Two different modulation schemes are combined: A rapid (1 kHz)

linear frequency sweep around 6.9 MHz is used for two-dimensional spatial stabilization of the force

field over a 5 mm long inlet channel of constant cross section, and a slow (0.2–0.7 Hz) linear frequency

sweep around 2.6 MHz is used for flow-free ultrasonic transport and positioning of cells or particles.

The method is used for controlling the motion and position of cells monitored with high-resolution

optical microscopy, but can also be used more generally for improving the robustness and performance

of ultrasonic manipulation micro-devices.

Introduction

Flow-free transport and positioning of cells in microfluidic

systems is important for studies of processes such as cellular

release of signaling molecules, intercellular communication and

cell proliferation.1 Available methods for controlled translation

of cells relative to the fluid medium in a microchannel are, e.g.,

dielectrophoresis2 and optoelectronic tweezers.3 However, these

methods are either bulky, expensive or complex, and they suffer

from limited biocompatibility. In the present paper we present

a simple method for flow-free cell transport in a microchannel

based on frequency-modulated ultrasonic actuation.

Forces generated by resonant acoustic fields can be used for

manipulation of cells or other micrometer-sized particles in

microfluidic chips. In particular, the method has shown to be

attractive and efficient in flow-through-operation applications

such as continuous alignment, separation and enrichment of

cells4 and bio-functionalized beads.5 On the other hand,

frequency-modulated ultrasonic actuation has previously been

employed in flow-free macro-scale (>1 mm) chambers for

transportation and positioning of suspended particles. Examples

include simultaneous actuation at two slightly different

frequencies for either translation6,7 or confinement8 of trapped

particles. Furthermore, different schemes for sweeping or

changing a single actuation frequency have been used for

translation or merging of particle aggregates.9,10 However, it is

not straightforward to implement frequency-modulation

methods in microfluidic chips. In order to realize flow-free

particle transport by ultrasound in a chip, the spatial distribution

of the generated force field must be pre-controlled along the

whole microchannel. In contrast, recent evaluations have shown

that the commonly employed design for ultrasonic manipulation

in a chip (the half-wavelength-wide channel) does not focus

particles uniformly along the length of the channel.11,12 Instead,

the focusing forces along the channel typically vary between

being positive (alignment), zero (no effect) and negative (de-

alignment). Since an acoustic particle separator4 operated with

a significant fluid flow is only dependent on the net effect along

the full channel, this problem has previously not been considered

or known. For flow-free transport purposes, however, spatial

stabilization of the pre-alignment forces is crucial.

In the present paper we demonstrate flow-free transport of

cells and other particles in a microfluidic chip by the use of

frequency-modulated ultrasonic actuation. We combine two

modulation strategies: Rapid frequency sweeping for stabilized

particle alignment in two dimensions; and slow frequency

sweeping for flow-free particle transport along a microchannel.

The method is used for controlled transport, merging and optical

characterization of ultrasonically caged13 human immune and

kidney cells. We conclude that rapid frequency sweeping is

a simple approach for improving the robustness of an ultra-

sound-actuated microfluidic chip, with benefits such as reduced

temperature dependence and less need for trimming/controlling

the actuation frequency. Furthermore, rapid frequency sweeping

is also a prerequisite for accurate particle transport over several

millimeters, which here is realized by a combined rapid and slow

frequency sweeping approach.

Methods

Fig. 1 shows the experimental arrangement. It is similar to the

one in Ref. 13, but with the modification that the two excitation

signals (around 2.6 and 6.9 MHz) were modulated by

a sawtooth-shaped frequency sweep. In brief, the chip includes

a 5 0.11 0.11 mm3 inlet channel for two-dimensional (2D)

alignment, arraying11 and transport of particles or cells, and

a 0.30 0.30 0.11 mm3 filleted square box for three-dimen-

sional (3D) caging13 of particles or cells. The wedge transducers

employed were designed and fabricated according to the

aDepartment of Applied Physics, Royal Institute of Technology, AlbaNovaUniversity Center, SE-106 91 Stockholm, Sweden. E-mail: [email protected] of Microbiology, Tumor and Cell Biology, KarolinskaInstitutet, SE-171 77 Stockholm, Sweden

† Electronic supplementary information (ESI) available: Real-timevideos of ultrasound-mediated transport of cells and particles, andtime-resolved particle image velocimetry (PIV) of the fluid motionduring particle transport. See DOI: 10.1039/b816675g

This journal is ª The Royal Society of Chemistry 2009 Lab Chip, 2009, 9, 833–837 | 833

TECHNICAL NOTE www.rsc.org/loc | Lab on a Chip

procedure described in Ref. 11, and operated at 10 Vpp. For

stabilization of the 2D alignment in the inlet channel, the

6.9 MHz transducer was driven in linear sweeps from 6.85 to 6.95

MHz at a rate of 1 kHz (rapid modulation). For particle trans-

port, the 2.6 MHz transducer was driven in linear sweeps from

2.60 to 2.64 MHz at a rate of 0.2, 0.5 or 0.7 Hz (slow modula-

tion), while the 6.9 MHz transducer was driven in linear sweeps

from 6.90 to 7.00 MHz at a rate of 1 kHz (rapid modulation). In

the experiments, 1 and 5 mm polymer beads were used for visu-

alizing the fluid flow and the acoustic force fields, respectively,

and 10 mm polymer beads, human embryonic kidney (HEK

293T) cells and natural killer (NK) cells isolated from peripheral

blood were used for proof-of-concept demonstration of the

target application of our device. The fluid motion during trans-

port was characterized by the particle image velocimetry (PIV)

package ‘‘MPIV’’14 executed on consecutive frame pairs

from a video captured during several periods of the frequency

modulation.

Results

Fig. 2 demonstrates the effect of stabilizing the 2D alignment

function by use of rapid modulation of the 6.9 MHz transducer.

Initially, the 5 mm long inlet channel is seeded with a uniform

distribution of 5 mm beads, and each image is acquired after 5 s of

ultrasonic actuation without any fluid flow. In Fig. 2a–f, the

result is shown for six single (non-modulated) frequencies within

the investigated interval 6.85–6.95 MHz. We note that all single-

frequency patterns contain several ‘‘blind spots’’ of different

sizes, which are characterized by weak forces unable to align the

beads within the 5 s (cf. e.g. at the white arrow in Fig. 2c).

Interestingly, while all investigated frequencies can align the

beads very efficiently at some locations, the relative total length

of the blind spots over the full inlet channel still varies between

approximately 20% (Fig. 2c) and 60% (Fig. 2e). Furthermore,

certain frequencies also have areas where the beads are driven

towards, and not away from the channel walls (‘‘de-alignment’’,

cf. e.g. at the yellow arrow in Fig. 2c).

In Fig. 2g, the actuation frequency is swept linearly from 6.85

to 6.95 MHz at a rate of 1 kHz. We see that the result of this

rapid modulation is uniform alignment of the beads into the

vicinity of the midpoint of the channel cross section over the

entire inlet channel. It is noted that up to 5% of the inlet

channel still has slightly weaker forces causing incomplete

alignment. However, if the actuation time is increased to 10 s, all

beads can be aligned during no-flow conditions (data not

shown).

In Fig. 3a, we demonstrate flow-free transport of aggregates of

5 mm beads simultaneously with stabilized 2D alignment. (The

micrographs in Fig. 3a are selected frames from the first ESI video

clip.)† Here, the 2D alignment is performed by rapid modulation

(6.90–7.00 MHz; rate 1 kHz), and the particle transport is realized

by slow modulation (2.60–2.64 MHz; rate 0.5 Hz). Fig. 3b

quantifies the distance d traveled along the channel as a function

of time t for one aggregate at three different sweep rates (0.2, 0.5

and 0.7 Hz). As can be seen in the inset in Fig. 3b, the transport

speed scales linearly with the modulation frequency. The

maximum modulation frequency for achieving effective transport

of the aggregates shown in Fig. 3a turned out to be 0.7 Hz, which

corresponds to a transport speed of 0.2 mm s1. Finally, in Fig. 3c

we demonstrate controlled transport and caging of individual

HEK cells (first three panels), and a fluorescence image of a single

Fig. 1 (a): A photo of the chip (further described in Ref. 13) with

mounted wedge transducers (further described in Ref. 11); a 6.9 MHz

transducer for particle alignment, and a 2.6 MHz transducer for particle

transport and caging. (b): A micrograph showing part of the 5 mm long

inlet channel for alignment and transport of particles (to the right), and

the cage for trapping and positioning of particles (to the left).

Fig. 2 Fixed-frequency operation (a–f) compared with modulated-frequency operation (g) of the 6.9 MHz transducer when the inlet channel is filled

with 5 mm beads (10 Vpp actuation during 5 s without fluid flow). The white arrow marks a ‘‘blind spot’’ having insignificant forces, and the yellow arrow

marks an area of ‘‘de-alignment’’ where the particles are driven to the channel walls.

834 | Lab Chip, 2009, 9, 833–837 This journal is ª The Royal Society of Chemistry 2009

HEK cell (green) caged and merged with NK cells (red) that have

been ultrasonically transported into the cage (last panel). Both

the green and red fluorescence are viability indicators (calcein-

AM). Single cell transport is demonstrated in the second ESI

video clip.†

The positioning accuracy of particles in the cage during

frequency modulation is characterized in Fig. 4a–b. (The

micrographs in Fig. 4a–b are selected frames from the third ESI

video clip.)† Here, 5 mm beads (green) are transported (cf. dashed

arrows) and positioned (cf. solid arrows) by ultrasound, while 1

mm beads (yellow) are used as fluid trackers as they are small

enough for the viscous drag to dominate over the acoustic

forces.15 The caged aggregate is repeatedly transformed between

spheroid-shaped (Fig. 4a) and elongated (Fig. 4b). Simulta-

neously, the center of gravity of the aggregate oscillates with

amplitude 20–30 mm and period 5 s (i.e. the period of the 0.2 Hz

modulation frequency), while the maximum displacement of an

individual bead in the aggregate is 80 mm. Similar position

oscillations as for the center of gravity are seen for individual

cells in the cage. (Single cell transport is demonstrated in the

second ESI video clip.)†

The fluid motion caused by the ultrasound-mediated trans-

port was characterized by time-resolved particle image veloc-

imetry (PIV) on the same video sequence as seen in Fig. 4a–b,

but on the full 30 s interval. The PIV calculations were per-

formed on processed images suppressing anything but yellow

pixel values (which display the 1 mm beads). Fig. 4c shows the

time-averaged velocities of the fluid flow over six cycles of

0.2 Hz modulation within the same imaged area as seen in

Fig. 4a–b. (Time-resolved PIV results are provided in the

fourth ESI video clip.)†

Fig. 3 (a): Three frames from a video clip (provided as ESI)† demon-

strating ultrasound-mediated arraying and transport of aggregates of 5

mm beads without fluid flow (sweep rate 0.5 Hz). The dotted line indicates

corresponding aggregates between the frames. (b): Quantification of the

distance d traveled along the channel for the aggregates in (a) as a func-

tion of time t for different sweep rates. The inset plots the slope of a linear

fit to each distance-versus-time curve (i.e., the velocity v) as a function of

the sweep rate f. (c): Demonstration of ultrasound-mediated transport for

individual cell injection into the ultrasonic cage. The first three panels

show sequential merging and positioning of three HEK cells without fluid

flow (also provided as ESI),† and the last panel shows a caged HEK/NK-

cell conjugate monitored by fluorescence microscopy. The HEK cells and

NK cells are labeled with green- and red-fluorescent viability indicators

calcein-AM, respectively.

Fig. 4 (a–b): Position and shape of a caged aggregate of 5 mm green

beads (marked with solid arrows) during ultrasound-mediated injection

of a new aggregate (marked with dashed arrows). The images illustrate

the two turning points of the oscillating displacement and shape trans-

formation of the caged aggregate. (c): Average during 30 s (6 modulation

cycles) of the fluid velocity field measured by time-resolved particle image

velocimetry (PIV). All data in (a–c) are extracted from the third video

sequence provided as ESI.†


Discussion and conclusion

Spatial stabilization of ultrasonic alignment forces in micro-

fluidic chips is important in applications requiring accurate

transport of particles or cells at low or moderate speeds (<1 mm

s1). The principle is based on averaging the force fields obtained

from different fixed actuation frequencies. For example, fixed-

frequency operation may cause an aligned cell entering a ‘‘blind

spot’’ (cf. Fig. 2) to settle by gravity and adhere to the channel

bottom. Such settlement of HEK or NK cells typically has

a sedimentation time of 10 s in our system.15 Furthermore,

areas of ‘‘de-alignment’’ (cf. Fig. 2) may drive the cells to the

channel wall within less than one second. Thus, at flow (and/or

transport) velocities up to 0.1 mm s1 there is a significant risk

of particle-to-wall contact during fixed-frequency ultrasonic

alignment, leading to, e.g., contamination, clogging or loss of

sample. We have also noted that the ultrasonic resonances are

sensitive to how the transducer is placed on the chip. Small

changes in transducer position and orientation also change the

force field pattern, which, in turn, requires manual selection of

the best operating frequency from one experiment to another.

Furthermore, similar experiments as presented in Fig. 2 show

that the alignment performance changes with temperature. For

example, the relative length of the blind spots changed from 58 to

45% when the temperature of the microscope stage was increased

from 23 to 37 C (data not shown). All these limitations associ-

ated with fixed-frequency ultrasonic actuation can be eliminated

with a properly chosen frequency modulation scheme.

Ultrasound-mediated transport in microchannels is an

attractive and simple approach for flow-free control of the

motion and position of individual particles or cells. The principle

is based on ultrasonic arraying11 of particles (i.e. grouping

particles along the channel in a 1D array) followed by translation

of the trapping sites in the array by a slow frequency sweep

within a suitably selected frequency interval. The frequency

sweep interval must be chosen so that, at the end of a sweep, the

position of a trapping site is closer to the ‘‘next’’ site of the

starting frequency than it is to the one where the particle(s) were

at the beginning of the sweep. Our demonstrated method shows

promise for high flexibility and precision: The particle speed is

controlled by the modulation frequency (cf. inset in Fig. 3b), and

the direction of motion can be reversed by switching the sweep

direction (i.e., from positive to negative slope of the sawtooth-

shaped frequency sweep). (Demonstration of reversed transport

is provided in the first ESI video clip.)† By simultaneously per-

forming rapid modulation (for alignment stabilization) and slow

modulation (for transport), it is possible to move the particles

along the full channel length of 5 mm, away from the channel

boundaries and within the focal plane of the microscope. In

addition, by avoiding particle transport based on fluid pumping,

common problems such as unwanted transient flows after

a pump is started or stopped are eliminated. On the other hand,

there is also a possibility to move particles or cells and the fluid at

different speeds independently of each other by the use of

combined ultrasound- and pump-mediated transport. One

observed limitation of the method arises when transporting high-

concentration samples of particles or cells (cf. Fig. 3a). Under

such circumstances some particles may ‘‘leak’’ from one aggre-

gate to an adjacent aggregate. (This effect can be seen in the first

ESI video clip.)† One possible reason for this effect is the limited

size of the trapping sites in the 1D array, limiting the maximum

number of particles in each aggregate that can be transported.

This hypothesis is supported when studying single-cell transport,

where the effect is not present. (Provided in the second ESI video

clip.)†

In the future we aim for utilizing the device for monitoring

intercellular interactions between NK or T cells and their target

cells (such as HEK or B cells). A proof-of-concept experiment for

this application is provided in Fig. 3c. For example, a controlled

number of target cells may be injected into the cage one-by-one

by the slow-frequency-modulation method, and merged with

a pre-injected NK cell. Here, dynamic studies of the intercellular

interactions may be performed, and correlated with, e.g., the

number of neighbors for each cell in the aggregate,13 or with

stimuli from various soluble agents provided via microfluidic

perfusion. Additionally, the flow-free transport approach also

makes it possible to inject a cell into the cage without consider-

ably diluting or removing any molecules diffusing in the cage

compartment (such as signaling molecules produced by another

pre-injected cell). However, as indicated in Fig. 4 the positioning

performance during slow frequency modulation is not as accu-

rate as for fixed-frequency actuation.13 Although there is no net

displacement of caged cells, the maximum temporary displace-

ment of individual cells is typically 50 mm (cf. Fig. 4a–b).

Furthermore, local fluid flows exist with average velocities up to

20 mm s1 (cf. red areas in Fig. 4c). The local flows originate

partly from acoustic streaming vortices12 and partly from fluid

dragged along with a transported aggregate. (This effect can be

seen in the fourth ESI video clip.)† However, around the center

of the cage where cells are positioned, the average velocity of the

fluid flow is less than 10 mm s1. This is one order of magnitude

below the ultrasound-mediated transport speed, and of the same

order as the molecular diffusion speed in a fluid at room

temperature. In applications where true zero-flow or high posi-

tioning accuracy are important, the frequency modulation

should be stopped when the transport and injection of cells into

the cage are completed.

In this context, it should also be noted that ultrasonic

manipulation in microfluidic systems has proven to be

a biocompatible method allowing long-term (>1 h) monitoring

of trapped cells.16,17 In a larger perspective, we believe that

ultrasound-actuated microsystems in the future could serve as

simple and gentle multi-purpose tools applicable to a wide

variety of cell handling tasks.

Acknowledgements

The authors thank Prof. H. M. Hertz for valuable discussions

and for contributions to the original idea of this work. Financial

support is gratefully acknowledged from the Swedish Research

Council and the G€oran Gustavsson Foundation.

References

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Otto Manneberg PhD Thesis: Multidimensional Ultrasonic Standing Wave Manipulation in Microfluidic...

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