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Trapping of micrometre and sub-micrometre particles by high-frequency electric fields and hydrodynamic forces This content has been downloaded from IOPscience. Please scroll down to see the full text. Download details: IP Address: 129.171.178.62 This content was downloaded on 28/09/2013 at 10:15 Please note that terms and conditions apply. 1996 J. Phys. D: Appl. Phys. 29 340 (http://iopscience.iop.org/0022-3727/29/2/010) View the table of contents for this issue, or go to the journal homepage for more Home Search Collections Journals About Contact us My IOPscience

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Page 1: Trapping of micrometre and sub-micrometre particles by high-frequency electric fields and hydrodynamic forces

Trapping of micrometre and sub-micrometre particles by high-frequency electric fields and

hydrodynamic forces

This content has been downloaded from IOPscience. Please scroll down to see the full text.

Download details:

IP Address: 129.171.178.62

This content was downloaded on 28/09/2013 at 10:15

Please note that terms and conditions apply.

1996 J. Phys. D: Appl. Phys. 29 340

(http://iopscience.iop.org/0022-3727/29/2/010)

View the table of contents for this issue, or go to the journal homepage for more

Home Search Collections Journals About Contact us My IOPscience

Page 2: Trapping of micrometre and sub-micrometre particles by high-frequency electric fields and hydrodynamic forces

J. Phys. D: Appl. Phys. 29 (1996) 340–349. Printed in the UK

Trapping of micrometre andsub-micrometre particles byhigh-frequency electric fields andhydrodynamic forces

Torsten M uller †, Annamaria Gerardino ‡, Thomas Schnelle †,Stephen G Shirley †, Franco Bordoni ‡, Giovanni De Gasperis ‡,R Leoni § and Gunter Fuhr †† Humboldt-Universitat zu Berlin, Institut fur Biologie, Invalidenstrasse 42,10115 Berlin, Germany‡ Universita degli Studi di L’Aquila, Dipartimento Ingegneria Elettrica, L’Aquila, Italy§ IESS, Istituto di Elettronica dello Stato Solido, CNR, Rome, Italy

Received 22 September 1995

Abstract. We demonstrate that micrometre and sub-micrometre particles can betrapped, aggregated and concentrated in planar quadrupole electrodeconfigurations by positive and negative dielectrophoresis. For particles less than1 µm in diameter, concentration is driven by thermal gradients, hydrodynamiceffects and sedimentation forces. Liquid streaming is induced by the AC field itselfvia local heating and results, under special conditions, in vortices which improvethe trapping efficiency. Microstructures were fabricated by electron-beamlithography and modified by UV laser ablation. They had typical gap dimensionsbetween 500 nm and several micrometres. The theoretical and experimentalresults illustrate the basic principles of particle behaviour in ultra-miniaturized fieldtraps filled with aqueous solutions. The smallest single particle that we could stablytrap was a Latex bead of 650 nm. The smallest particles which were concentratedin the central part of the field trap were 14 nm in diameter. At high frequencies (inthe megahertz range), field strengths up to 56 MV m−1 can be applied in thenarrow gaps of 500 nm. Further perspectives for microparticle and macromoleculartrapping are discussed.

1. Introduction

High-frequency electric field cages for trapping singleliving cells and microparticles were recently introduced intothe fields of biotechnology and biomedical research [1–3]. Cells and microparticles are stably trapped in fluids byelectrode devices of cellular dimensions which can only befabricated by semiconductor structuration techniques. Thedamping effect of the surrounding fluid allows trappingwithout obligatory spin application, in contrast to theelectromagnetic field cages used in atomic and elementaryparticle physics [4, 5]. However, torque induced by rotatingelectric fields can be used to manipulate and characterizeindividual particles or cells [1, 2, 6].

The forces leading to particle levitation and motion aredielectric polarization forces, the so-called dielectrophoreticforces [7]. We have to distinguish between positive dielec-trophoresis (p-DEP, attracting cells toward the electrodes)and negative dielectrophoresis (n-DEP, repelling them) andalso between trapping of particles (confinement withoutelectrode contact) and simple immobilization (where par-

ticles are attracted to and collect on an electrode). In abroad frequency range, p-DEP occurs with cells and par-ticles and, therefore, this phenomenon has been investi-gated in some detail [7–13]. Trapping of cells and mi-crobeads by p-DEP requires a minimum of two electrodesbut feedback-controlled field application is necessary [8].Particle trapping by p-DEP forces alone, without feedbackcontrol, seemed impossible since particles collected on thesurface of the electrodes [7–9]. However, in this paperwe show that stable trapping in planar quadrupole elec-trode structures is possible if some special conditions arefulfilled.

Repelling forces (n-DEP) are better suited for particletrapping. Microbeads or cells move toward regions oflower field strength. The basic laws of electrodynamicsallow such field minima to be created easily, far from theelectrodes.

n-DEP or p-DEP occurs according to the complexpermittivity of the particle and the surrounding liquid (ε =σ + iωεεvacuum, whereε is the relative permittivity,σ is theconductivity andω is the frequency of the field in radians).

0022-3727/96/020340+10$19.50 c© 1996 IOP Publishing Ltd

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Trapping of micrometre and sub-micrometre particles

Figure 1. (a) The arrangement of four planar gold electrodes (thickness 100 nm titanium covered by 50 nm gold) on a quartzsubstrate. The shape of the electrodes in the central part is hyperbolic and the distance between diametrically oppositeelectrodes is 2 µm. The width of the gaps is between 500 nm and 2 µm. Application of AC electric signals with frequenciesin the kilohertz or megahertz range produces a quadrupole field in the central part and strong field gradients above the gaps(the bar is 15 µm long). (b) Laser-beam-modified electrodes. The electrode area was decreased and additional field minimawere created. The central part of the hyperbolic electrode shape is unchanged (the bar is 15 µm long). (c) A scanningelectron microscope view of an electron-beam-fabricated multi-electrode structure on silicon. Four electrode lines are coiledas a meander system ending in a quadrupole field trap (upper right-hand corner). (d ) A magnified section of (c) showing thecentral part of the meander. The electrode thickness is 500 nm, the width is 500 nm and the electrode lines are spaced by500 nm.

If both the conductivity and permittivity of the particleare lower than those of the solution n-DEP occurs at allfrequencies.

For most artificial beads, like Latex or Sephadex, n-DEP is found at high frequencies (in the megahertz range)and in conductive electrolyte solutions (> 1 mS m−1,[7, 9]). Most living cells show n-DEP at all frequencieswhen the conductivity of the medium is greater than0.5 S m−1. As shown in previous work [14] withsuch conductive solutions, ultra-microelectrodes allow theapplication of electric fields strong enough for particle andcell manipulation (kV m−1 to MV m−1).

n-DEP trapping needs no feedback control andelectrode devices can be scaled down into the micrometreor sub-micrometre range, which enables trapping ofsub-micrometre particles [14]. Also, the nonlinearitiesassociated with small electrodes allow the application ofmuch stronger fields than in macroscopic devices [15].Strong fields and steep field gradients lead to local heatproduction and conductivity gradients [16], hence liquidstreaming can occur.

Hydrodynamic effects have previously been assumedto be counter-productive for particle trapping. The aimof this paper is to show that high-frequency electric

fields and hydrodynamic forces can be combined andused to direct particle motion and produce stable trapping.In the experiments presented here, field strengths upto 56 MV m−1 were applied. Under such high-fieldconditions, connective streaming cannot be avoided.

2. Materials and methods

2.1. Microstructures

The microelectrodes were fabricated on quartz glass orsilicon by electron beam lithography [3, 12]. The basicarrangements of four planar electrodes are shown infigures 1(a), (c) and (d). To investigate the influence ofthe electrode geometry on particle behaviour, parts of theelectrode areas shown in figure 1(a) were ablated by anUV laser microfabrication system (EXITECH EX-PS-750,Long Hanborough, Oxford, UK). An example of a modifiedstructure is given in figure 1(b).

The structures were electrically connected by wirebonding. The whole chip surface was wetted with a dropletof a particle suspension and covered by a plate. Thedistance between the cover plate and the electrodes wasin the range 20–40µm.

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Figure 2. The dielectrophoretic force (DEP) of a single Latex bead as a function of the frequency (f ) of the field and theexternal conductivity (σe , in S m−1). The broken line marks the zero plane of DEP (the cross over frequency, f0). At externalconductivities greater than 1 mS m−1 and at frequencies above 800 kHz n-DEP always occurs. Under these conditionsparticles are polarized so that they are repelled from the electrodes. At low external conductivities and low frequencies,p-DEP attracts particles toward the electrodes. The parameter set is εparticle = 3.5, εsolution = 80, σparticle = 9 mS m−1 and radius0.5 µm.

2.2. Field generation

AC (HP-8116A, Hewlett-Packard, USA) or rotating electricfields (HP-8131A, Hewlett-Packard, USA) were appliedas described in [1]. The frequency could be variedbetween 1 kHz and 200 MHz at amplitudes between 1and 14 V (square pulses). Particle behaviour was recordedby a microscope–video system and with a confocal laserscanning microscope (CLSM Leica, Germany).

2.3. Microparticles and media

Commercially available Latex particles, Standard DowLatex from 0.1 to 10µm (Serva, Heidelberg, Germany) andLatex Fluospheres, carboxylate-modified, 9.9, 1, 0.093 and0.014µm in size (Molecular Probes, Inc, Eugene, Oregon,USA) were diluted in aqueous solutions, sonicated for 5 minprior to use and solution conductivity was adjusted byaddition of KCl.

3. Theory

As explained in previous papers (see [1]), the understandingof the behaviour of particles in a field trap requires both(i) calculation of the force acting on a probe sphereof similar dimensions and dielectric composition to theparticles used (figure 2) and (ii) knowledge of the three-dimensional field distribution (even in the case in whichonly a chip with planar electrodes is used (figure 3)).

Since the problem is three-dimensional, the completevisualization of the force distribution requires differentplots. We have used the plots of〈E2〉t (which isproportional to the heating, figures 3(a) and (b)) and

the vertical component of the dielectrophoretic force(figure 3(c)). Due to the planar electrode arrangement,these plots are similar to each other and to the (notpresented) diagram showing the surface where〈E2〉t isconstant and hence the direction of force.

If only AC fields are applied, the dielectrophoreticforce increases with the gradient of the mean square valueof the electric field,E, and can be expressed in dipoleapproximation for a particle of volumeV [7] as

FDEP = 1.5V εlεvacuum Re(fCM)∇E2rms (1)

where fCM is the Clausius–Mosotti factor. For ahomogeneous particle it is

fCM = εp − εl

εp + 2εl

(2)

where the indexl refers to the liquid andp to the particle.Normally, therefore, the electrodes should be designed in amanner that produces strong field non-uniformities [1, 7].

Since we have applied very high field strengths (up toseveral MV m−1) in conductive liquids (up to 1 S m−1)there are also strong hydrodynamic forces. Due to theohmic heating (q = σE2, which is of the order of109 W m−3) the liquid becomes highly inhomogeneouswith respect to density, temperature, thermal and ohmicconductivity as well as permittivity. This results in thermalforces (convection) and also in electro-hydrodynamic ones[16, 17]. The latter arise because an electric field canproduce bulk charges in an inhomogeneous dielectricmedium [18].

It is to be expected in planar electrode arrangements(the subject of this paper) that heating, streaming and

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Trapping of micrometre and sub-micrometre particles

Figure 3. (a) A plot of 〈E 2〉t near the electrode plane illustrating the distribution of the field in the central part of the structureshown in figure 1(a) with AC driving of the electrodes. Between the gaps, heat production is maximal (proportional to〈E 2σe〉t ) and drives four centrally directed liquid streams (long arrows). Due to the planar arrangement and geometry of theelectrodes, the gradient of 〈E 2〉t which is proportional to the dielectrophoretic force is large in these regions. In the centralpart of the device, a dielectrophoretic field funnel is produced. Large particles or aggregates cannot overcome the front wallof force at the gaps and circulate in a stable whirl. Particles trapped in the field funnel can escape from the central part at thetop. However, sedimentation forces and the cover plate (here shown as the top plane of the cube) prevent this. (b) A surfaceplot for the meander coiled electrodes (figure 1(c)). The situation is more complex; however, the strong outside gradientshave been eliminated. (c) Cross sections through the central part of the surface plot of the vertical component of thedielectrophoretic force {FDEP }z for the meander coiled electrodes (figure 1(c)). Whereas the field funnel in (a) is thin anddeep, the meander structure (b) and (c) forms a flatter and more extended field minimum.

particle collection are mainly determined by the areaenclosed by an electrode rather than by its geometric area(see also figure 3). Therefore, removing inner regions ofan electrode (without altering its outline) should change the

behaviour only slightly. However, for three-dimensionalelectrode arrangements (field cages), the whole electrodearea contributes to the field distribution and, to reduce heatproduction, that area has to been minimized.

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T Muller et al

Figure 3. Continued

4. Results

4.1. Particle concentration by p-DEP

All types of Latex beads were attracted toward theelectrodes in aqueous solutions of conductivities less then1 mS m−1 and at kilohertz frequencies (see figure 2).1 µm Latex beads were deflected to the electrode gapsfrom distances of several tens of micrometres. They firstfilled the gaps and later occupied parts of the electrodes,building planar aggregates of high packing density. Thestructures shown in figure 1(a) and (b) allow the applicationof signals up to 28 Vptp. In the narrow gaps of 500 nmthis corresponds to 56 MV m−1. Under such intenseelectric field gradients, strong forces press particles ontothe electrodes (figures 4(a) and (b)).

As the number of particles increased, there wasaggregation in the central region. Fluid motion started atamplitudes greater then 10 Vptp and aggregates tumbled upand down due to upward streaming of the fluid. This specialcase demonstrates that particle trapping without feedbackcontrol can be achieved under p-DEP. At lower amplitudesno noticeable streaming could be observed and all particlesstayed on the chip surface.

4.2. Particle trapping by n-DEP

Stable trapping of single beads or aggregates normallyoccurs in three-dimensional arrangements of electrodes [1].The situation in the case of planar electrode structures isdifferent. No field cage is created, only a field funnel (seefigure 3(a) and (b)). If the sedimentation force is too weak,particles can escape from the funnel, but the effect can bereduced by closing the system with a cover slip at a heightof several tens of micrometres.

Particle levitation and aggregation occurred in aqueoussolutions of conductivities greater than 1 mS m−1. Asshown in figures 4(c) and (d), the aggregate shape dependedon the geometry of the electrodes. Under n-DEP, particlescould be trapped at amplitudes below 10 Vptp. In contrastto p-DEP, the levitated aggregate tumbled only slightly.However, at higher amplitudes, single beads continuallychanged their position within an aggregate. As shown infigure 5, single beads of 10 down to 1µm could also bestably trapped.

Best trapping of particles was obtained near the crossover frequency(f0). At much higher frequencies, thefields needed to induce flow and transport particles to thetrap also produce an increased repelling, dielectrophoreticforce and prevent particle entry. Near the electrode plane,particles were not only levitated but also rapidly centred.Near the cover slip, the particle behaviour is influenced byhydrodynamic effects (see also figure 3(a)).

In the case of the quadrupole electrode structures(figures 1(a) and (b)), particles were transported into thefield funnel by four centrally directed liquid streams (seealso figure 3(a)). Liquid streaming was upward above thegaps where the most intense fields were created. Althoughthe strongest repulsion forces acted above the gaps, thetrajectories of particle motion followed the streaming. Onlylarge particles (> 1 µm) or aggregates were deflected at thebeginning of the narrow gaps and could not overcome thebarrier. Due to the input of particles, the central aggregategrew, in several minutes, up to the cover plate, 20µmabove the electrode plane. Near the glass plate, the fieldfunnel was so flat that the particle aggregate expanded to30 µm in diameter or more. Increasing the amplituderesulted in the release of beads on trajectories directedoutwards and lying above the electrodes.

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Trapping of micrometre and sub-micrometre particles

Figure 4. (a) Latex beads of 1 µm size attracted toward the electrodes by p-DEP (frequency 500 kHz, amplitude 6 Vptp andσe = 0.4 mS m−1; the dimensions of the structure are as in figure 1(a) and (b)). (b) A collection of 1 µm beads in thelaser-beam-modified chamber. The enlarged gaps are completely filled with particles. At the terminal electrodes ‘pearlchains’ of beads are oriented in the direction of the field lines (the same conditions as given in (a)). (c) The formation of aparticle aggregate (marked by the symbol) levitated and trapped above the central part of the electrodes by n-DEP. Theshape of the aggregate is rectangular (frequency 4 MHz, amplitude 6 Vptp and σe = 0.4 mS m−1). (d ) The same situation inthe chamber shown in figure 1(b). The aggregate of Latex beads is stably trapped in the force funnel but more rounded (fieldconditions as in (c)).

Figure 5. (a) A 9.9 µm Fluospheres Latex particle trapped and levitated in the structure shown in figure 1(a) (frequency3 MHz, amplitude 0.8 Vptp and conductivity 11 mS m−1; the bar is 10 µm long). (b) A single 1 µm bead stably trapped in thequadrupole system shown in figure 1(a) (frequency 5 MHz, amplitude 5 Vptp and conductivity 0.6 mS m−1; the bar is 3 µmlong). (c) A single 1 µm Latex particle trapped in the meander-electrode system shown in figure 1(c) (frequency 5 MHz,amplitude 6 Vptp and conductivity 0.6 mS m−1; the bar is 5 µm long). All photographs are computer-processed and madewith a confocal laser scanning microscope.

4.3. Measurements of the particle properties

Some particle properties can be estimated withoutassumption or calculation of the actual field distribution. Agood parameter is the cross over frequency (from negativeto positive dielectrophoresis). For the limit value of zeroexternal conductivity a cross over frequency for Latexaggregates (see also figure 2) of 1.6 MHz was found.This value corresponds to an effective conductivity of the

particle aggregates of about 9 mS m−1 (the cross overfrequency can be calculated from Re(fCM) = 0, seeequation (2)). The experimental data could only be fittedby using a much higher effective conductivity than that ofindividual Latex spheres (in [19] the conductivity of Latexspheres was determined to be less than 0.7 mS m−1). Thisis a strong hint that a dense particle aggregate was build inour structure (typically, an increase of conductivity is to beexpected [20] on aggregation).

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T Muller et al

Figure 6. (a) A fluorescence image of 100 nm Fluospheres beads focused by p-DEP into the gaps between the electrodesin the structure shown in figure 1(a) (frequency 2 MHz, amplitude 6 Vptp and conductivity 3 mS m−1). (b) The same type ofLatex beads under the n-DEP regime. A condensed cloud of particles was levitated and trapped in the central part(frequency 8 MHz, amplitude 6 Vptp and conductivity 3 mS m−1). (c) The concentration of 14 nm Fluospheres beads byp-DEP (frequency 2 MHz, amplitude 8 Vptp and conductivity 2.5 mS m−1). (d ) Levitated and trapped aggregate (diameterapproximately 2 µm) of 14 nm Latex beads in the central field funnel (frequency 10 MHz, amplitude 10 Vptp and conductivity2.5 mS m−1).

4.4. Collection of particles smaller than 200 nm

Of special interest was the collection, levitation andtrapping of sub-micrometre particles. Down to 200 nm,particle behaviour was the same as for larger Latex beads.However, surprisingly, we were able to collect particles of100 and even 14 nm size by p-DEP and n-DEP (figure 6).

Collection of 100 and 14 nm beads occurred withinseconds at amplitudes of several volts. After the fieldhad been switched off, the intensely fluorescing cloudsdispersed within some milliseconds.

4.5. Streaming and behaviour of particles outside thefield funnel

Interesting trajectories of motion were shown by beadsabove and outside the electrodes as well as by those inthe field funnel The fields in the narrow gaps producedthe largest amounts of heat, especially in the structuresof figure 1(a) and (b). The symmetric arrangement ofthe four gaps was reflected in the streaming of the fluid.Under both p-DEP and n-DEP conditions and AC fieldapplication, streaming was upwards above each electrodegap and downwards at a distance of about 100µm fromthe centre. In the central part of the funnel only weakupwardly directed fluid motion occurred. This pattern wasobserved with or without a cover plate. However, closing

the structure with a cover slip improved and stabilized fluidstreaming.

The liquid streaming transported particles into the fieldtrap. Particle aggregates could also form outside theelectrodes, in front of the gaps. These could not overcomethe force barrier and circulated in the liquid stream.

Note that the stability of the fluid whirls depends onthe field conditions (amplitude and frequency) and thesymmetry of the chamber. In our structure streamingstarts at voltages of about 6 Vptp and shows a frequency-dependence typical for ion relaxation in water [16] which ischaracteristic for electrohydrodynamic pumps (EHD) [18].

A complex streaming behaviour became visible ifrotating instead of AC fields were applied. A sequenceafter an abrupt change in the direction of field rotation isshown in figure 7. Both for rotating and for AC fields athigh amplitudes (> 15 Vptp) streaming became turbulentso that no further particle trapping was possible.

5. Discussion

Field traps and three-dimensional cages scaled in themicrometre range lead to complex microparticle motion.High field strengths can be applied (up to severalMV m−1) and hydrodynamic effects are superimposed onthe polarization forces.

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Trapping of micrometre and sub-micrometre particles

Figure 7. The particle distribution after changing the direction of a rotating field (frequency 1.6 MHz and amplitude 6 Vptp)under n-DEP conditions. Before the change in field direction there was one central, rotating (several revolutions per second)particle aggregate (1 µm Latex beads). (a) This aggregate divided into rotating clusters and started long-range circularstreaming. (b)–(h) The particle distribution at intervals of several seconds. Two circulating streams were induced, rotatingslowly around the field funnel. At the beginning, the collected particles seemed to disperse completely. However, after someseconds they came back to the central electrode space over distances of more than 100 µm and were again condensed.

Stable streaming of the fluid in electrode devices can

improve trapping and concentration of particles (especially

of small particles) under p-DEP and n-DEP conditions. The

induced, centrally directed streams transport material into

the field funnel, overcoming the problem that extremely

small traps may initially contain only a few or no particles.

Liquid streaming is induced by a combination of thermal

and dielectrophoretic effects. Liquid in the electrode

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T Muller et al

gaps will be heated, changing its permittivity (by about−0.4% per degree [21]) and the electrical conductivity (byabout 2% per degree [21]). Under our conditions (liquidconductivity greater than 0.4 mS m−1 and frequency greaterthan 500 kHz) cold water tends to replace warm water fromthe regions of high field strength. According to equation (2)this will happen for frequencies greater than

fc = 1

2πε0

(−σ1σ/1T

ε1ε/1T

)1/2

.

For a conductivity of 0.4 mS m−1 the critical frequencyis about 200 kHz. Experimentally no streaming wasobserved below this value. The direction of fluid motion isdetermined by the thermal convection.

Best trapping was obtained at frequencies of somemegahertz, a little above the cross over frequency fromp-DEP to n-DEP, and a detailed description of particlemotion requires not only consideration of dielectrophoreticand hydrodynamic forces but also the effect of multipoleinteractions between the trapped particles. The electrodegeometry and particle size determine how large the fieldbarrier is and which types of particles can enter the centralregion. However, particles inside the trap can aggregateand the dielectrophoretic forces vary with the cube of theaggregate radius whereas the hydrodynamic forces varyonly with the first power. In addition, aggregates canbe more effectively polarized than the sum of the singleparticle moments indicates and there will be a shift of thecharacteristic frequencies. Therefore, we could trap smallerparticles (600, 200, 100 and 14 nm) as aggregates and largerparticles as single beads (diameter 9.9 and 0.65µm).

Hydrodynamic forces also allow particles to be trappedby p-DEP without feedback control. To avoid particle–electrode contact a well-balanced force is needed inthe opposite direction to the p-DEP to substitute forthe feedback regulation. The upwardly directed liquidstreaming in the central part of the structure can fulfil thisrole. Both the electric and the hydrodynamic effects mustact symmetrically (in our case in a quadrupolar manner).This occurs in the basic structure shown in figure 1(a)because the field itself drives the liquid streaming. Ina limited frequency and field strength range, four stablewhirls can stabilize particle trapping. p-DEP and particle–particle interactions focus particles to the central part, wherean aggregate tumbles up and down. However, this isonly the case within a very small interval of conductivity,frequency and amplitude. More commonly, particles areattracted into the gaps between the electrodes.

The superposition of different effects is reflected bythe high field strengths that we had to apply in the caseof p-DEP. Below 2 Vptp no trapping could be achieved.The reason for this threshold value is the development ofthe thermal component and the starting of local streaming.In the case of n-DEP, such a threshold could not beidentified. Here, single particles were trapped at low fieldstrength with no noticeable motion and stable levitationwas observed as the result of the equilibrium betweenpolarization, sedimentation and hydrodynamic forces. Thisagrees well with data obtained in field cages of 20 or several

hundred micrometres [1]. However, with increased fieldstrength (as under p-DEP conditions), particle tumblingoccurs up to the point at which microbeads escape fromthe field funnel.

As a result of our experiments some questions arise.

(i) The collection of 14 nm beads cannot be theresult of polarization forces alone. Interactions betweenparticles and random aggregation due to thermal collisionsare important. There are collective effects and multipole–multipole particle interactions which should investigatedtheoretically and experimentally. What is the effectivediameter of a sub-micrometre particle?

(ii) What role do thermal gradients play? Theyalways result in conductivity and permittivity gradients inthe bulk, since both quantities are temperature-dependent.Anisotropic media exhibit space charges which lead toadditional forces, such as accelerated fluid streaming[16, 18].

(iii) What is the minimum size of particles that canbe stably trapped or concentrated? The range of particlesize that we have trapped makes us optimistic abouttrapping and concentrating bacteria, viruses and some typesof macromolecules in ultra-microelectrode systems. Inour opinion, these devices are the first preliminary butstimulating steps in this new field of research.

Acknowledgments

We thank Dr B Wagner, C Dell, K Reimer and T Lisecfrom the Fraunhofer Institute for Silicon Technology (ISiT,Berlin) for fabrication of the structure shown in figure 1(c).This work was supported by grant 0310260A of the BMFT(Germany).

References

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