1. Introduction:

Flow phenomena are of great importance in the study of biological systems, both natural

organisms as well as biomedical devices. Recent strides in micrometer- and nanometer-scale

diagnostic techniques have allowed exploration of flow phenomena at length scales comparable

to single cells, and even smaller. New fabrication tools have enabled therapeutic and analytical

biomedical devices to be constructed which interact with biological components on their intrinsic

length scale. One of the most useful means of manipulating fluids and suspended species such as

cells, DNA, viruses, etc., is with electric fields. Electrokinetic phenomena are important at

micron length scales, and can be used to manipulate fluid and particle motion in microfluidic

devices. Electrokinetics can be broadly classified into DC and AC electrokinetics, as shown in

Table 1. DC electrokinetic phenomena include electrophoresis and electroosmosis.

Electrophoresis has been widely used in capillary gel electrophoresis for fractionation of DNA,

and capillary zone electrophoresis for separation of chemical species (Thormann, 01). Nanogen,

Inc. (San Diego, CA) uses DC electrophoresis from individually addressable electrodes to

Table 1. Classification of AC and DC electrokinetic phenomena

Type of Force AC Electrokinetics DC Electrokinetics

Body Force on Fluid Electrothermal

Surface Force on Fluid AC Electroosmosis Electroosmosis

Force on Suspended

Particles

Dielectrophoresis Electrophoresis

control motion of DNA molecules – first concentrating and separating target particles from the

sample, then combining with target oglionucleotides at a specific location in an array of spot

electrodes (Forster, 01).

Electroosmotic flow is generated when microchannels with glass walls, filled with aqueous

solutions naturally produce electric double layers (Probstein, 1994). In the presence of an

external electric field, the electrical charge in the double layers exhibit a Coulomb force causing

the ions to migrate parallel to the channel wall. The movement of the ions induces fluid motion

in the channel, creating electroosmotic flow. Electroosmosis is widely used for sample injection

and transport in microchannels in commercial systems manufactured by companies such as

Aclara and Caliper (Chien, 02; Bousse, 00).

2. DC Electrokinetics

Electro-Osmosis

Electro-osmosis is a good place to begin discussions of electrokinetic effects because the

geometries involved can be idealized to considering a liquid in contact with a planar wall. When

a polar liquid, such as water, and a solid surface are brought into contact, the surface acquires an

electric charge. The surface charge attracts oppositely charged ionic species in the liquid which

are strongly drawn toward the surface, forming a very thin tightly bound layer of ions called the

Stern layer in which the ions in the liquid are paired one for one with the charges on the surface.

Thermal energy prevents the ions from completely neutralizing the surface charge. The surface

charge not neutralized by the Stern layer then influences the charge distribution deeper in the

fluid creating a thicker layer of excess charges of the same sign as those in the Stern layer called

the diffuse or Gouy-Chapman layer. Together these two layers are called the electric double

layer, or EDL. Because of the proximity of charges, the Stern layer is fixed in place while the

diffuse layer can be moved. In particular, the diffuse layer has a net charge and can be moved

with an electric field. Consequently the boundary between the Stern layer and the diffuse layer is

called the shear surface because of the relative motion across it. The potential at the wall is

called the wall potential φw and the potential at the shear plane is called the zeta potential ζ. This

situation is shown in Figure 1 and is typical of the charge distributions observed in many

microfluidic devices. Both glass (Hunter, 1981) and polymer-based (Roberts, 1986) microfluidic

devices tend to have negatively charged or deprotonated surface chemistries which means that

the EDL is positively charged.

The governing equation for the electric potential φ is found to be the Poisson-Boltzmann

equation

φ

ε=

φ ∞

KTzFFzc

dyd sinh2

2

2

(1)

where c∞ is the concentration of ions far from the surface, z is the charge number (valence) of

each ion, ε = εrε0 is the dielectric constant of the liquid, is the electric potential, T is the absolute

Potential φδ

Stern layerDiffuse layer

0

φw

ζ

λD

(a) (b)

Figure 1. Sketch of the electric double layer showing (a) the Stern layer and the diffuse layer

and (b) the resulting potential.

temperature, K is Boltzmann’s constant and F is Faraday’s constant. This equation is clearly

nonlinear and difficult to solve. However, the relative thickness of the EDL is usually small

enough in micron-sized systems, that the hyperbolic sine term can be replaced by the first term in

its Taylor series–just its argument. This approximation is called the Debye-Hückel limit of thin

EDLs and it greatly simplifies Eq. 1 to

2D

2

2

λφ

=φ

dyd where 2

D 2 22KT

z F cελ

∞

= (2)

where λD is called the Debye length of the electrolyte. The solution to this ordinary differential

equation is quite straightforward and found to be

λ

−φ=φD

w exp y

(3)

Hence, the Debye length represents the 1/e decay distance for the potential as well as the electric

field at low potentials.

This potential can be added into the governing equations of fluid mechanics, namely the

Navier-Stokes equation, to calculate the flow produced by the electro-osmotic effect. Consider

Electric Double Layer

Negatively charged wall

y

x

Eel

vepλD

Figure 2. Schematic representation of electro-osmosis (left) and electrophoresis (right).

the geometry shown in Figure 2 where electro-osmotic flow is established in a long chamber of

constant cross section. Combining the appropriate form of the Navier-Stokes equation with the

potential distribution in Equation 3 we get

η

ζε= el

eofEu (4)

where the component of the flow due to electro-osmosis is denoted ueof., the dynamic viscosity of

the liquid is η, and ζ is the zeta potential, or potential at the location of the shear plane just

outside the Stern layer. This equation is known as the Helmholtz-Smoluchowski equation and is

accurate when the Debye layer is thin relative to the channel dimension. Because of the typical

low Reynolds number behavior of electrokinetic flows, the velocity field can be directly added to

that obtained by imposing a pressure gradient on the flow to find the combined result of the two

forces. Obtaining solutions for the flow when the Debye length is large generally requires

resorting to numerical solutions because the Debye-Hückel approximation is not valid when the

Debye layer is an appreciable fraction of the channel size.

For the purpose of comparing the effectiveness of several different electro-osmotic

channel/solution combinations, the electro-osmotic mobility µeo is defined as

el

eofeo E

u=µ . (5)

The electro-osmotic mobility is a useful, empirical quantity that aids in predicting flow velocities

expected for different imposed electrical fields. In the absence of appreciable Joule heating, the

proportionality is very good.

Electrophoresis

This phenomenon is closely related to the electro-osmosis phenomenon discussed above and

relies on the interaction of the EDL with an electric field to manipulate particles. The analysis of

particles moving in fluids necessarily includes some drag model to account for the effect of the

fluid drag on the particle. Because the electrophoretically manipulated particles tend to be small

and slow moving, inertia is not important to the particle’s motion and a very simple Stokes drag

model is used to approximate the fluid drag on the particle. Further, the particle is assumed to be

nonconducting which is reasonable because even materials that would normally be conducting

tend to become polarized by the applied field and behave as nonconductors.

There are two cases of importance in electrophoresis, when the Debye length is small

compared to the radius of the particle and when it is large. The electrophoretic motion of

molecules oftentimes meets the limit of Debye length large compared to the effective size of the

molecule simply because molecules can be very small. In addition, with the emergence of gold

and titania nanoparticles, and fullerenes, this limit becomes a very important one for

nanotechnology. The expression for the electrophoretic velocity uep becomes:

η

εζ=

πη= el

0

elsep 3

26

Er

Equ

(6)

where the first form of the equation is well suited to molecules in which the total charge q = qs of

the molecule may be known (valence number) rather than some distributed surface charge. The

second form of the equation is more appropriate for very small particles for which the zeta

potential ζ might be known. This form of the equation is called the Hückel equation.

The limit of small Debye length compared to particle radius is an appropriate limit to

consider for particles in excess of 100 nm. Examples of these types of particles include

polystyrene latex spheres used to “tag” biomolecules as well as single-cell organisms, which tend

to have diameters measured in microns. When the Debye length is small compared to particle

radius, the EDL dynamics are approximately reduced to the flat plate scenario discussed in the

case of electro-osmosis. Hence, the equation of motion becomes:

η

εζ= el

epEu (7)

which is simply the Helmholtz-Smoluchowski equation from the electro-osmosis phenomenon.

One interesting thing to note about Equations 6 and 7 is that even though they are developed for

opposite limiting cases, they differ only by the constant factor 2/3. When the Debye length is

neither large nor small relative to the particle radius, the dynamics of the particle motion are

significantly more difficult to calculate. However, even in these cases Equation 7 is still a

reasonable estimate of particle velocity.

As with the electro-osmosis case, the effectiveness of electrophoresis is quantified using an

electrophoretic mobility parameter defined as:

el

epep E

u=µ (8)

where µep can be thought of as motion produced per unit field.

Applications:

Because the negative charge associated with DNA molecules, electrophoresis can be used to

manipulate DNA molecules. A classic example is capillary gel electrophoresis, where an

electrical field is used to pull tagged-DNA molecules through a gel matrix. The gel effectively

filters the DNA molecules according to size, since the shorter DNA segments can travel through

the gel much quicker than the longer segments.

Nanogen’s biochip (Gurtner, et al.., 2002) is an example of using electrophoresis enhance

hydridization of DNA in a microfluidic chip (see Fig. 3). The electrodes have a positive

potential, thereby inducing the DNA molecules towards specific hybridization sites. The

microfluidic chip shown in Fig. 3 (Gurtner, et al., 2002), contains 100 microlocation test sites,

which are approximately 80 µm in size.

Figure 3. Active microelectronic DNA chip device and DNA transport. (a) Basic structure of an active microelectronic array, which contains 100 microlocation test sites. (b) Basic scheme for electrophoretic transport of charged molecules (DNA, RNA) on the active microelectronic array test sites. Taken from Gurtner et al. (2002).

3. AC Electrokinetics

AC electrokinetics has received limited attention in the microfluidics community, compared to

its DC counterpart. AC electrokinetics refers to induced particle and/or fluid motion resulting

from externally applied AC electric fields. A primary advantage of AC electrokinetics is that the

alternating fields significantly reduce electrolysis at the electrodes. In addition, the characteristic

voltages are typically of order tens of volts, which are typically much smaller than DC

electrokinetics. AC electrokinetics can be classified into three broad areas: dielectrophoresis

(DEP), electrothermal forces and ac electro-osmosis (Ramos et al., 1998).

3.1 Dielectrophoresis (DEP)

Dielectrophoresis, or DEP, is a force on particles in a non-uniform electric field arising from

differences in dielectric properties between the particles and the suspending fluid. The time-

averaged force on a homogeneous sphere of radius rp can be approximated as

3 22 Re( )DEP m p rmsF r K Eπε= ∇ . (9)

Here Re(K) is called the dielectrophoretic mobility and is the real part of K, the Clausius-Mosotti

factor,

2

p m

p m

Kε ε

ε ε−

=+

. (10)

The Clausius-Mosotti factor depends upon the complex permittivity of particle and medium.

Complex permittivity is

* jε ε σ ω= − , (11)

where 1−=j , ε is the electrical permittivity, σ is the electrical conductivity, and ω is the

angular field frequency. In this way, the DEP force depends not only on the dielectric properties

of the particle and medium, but also on the frequency of the applied field. For a sphere, the real

part of K is bounded between 0.5 Re( ) 1.0K− < < . Positive DEP occurs for Re{K} > 0, where

the force is toward the high electric field, and the particles collect at the electrode edges. The

converse of this is negative DEP, which occurs when Re(K) < 0, where the force is in the

direction of decreasing field strength, and the particles are repelled away from the electrode

edge. Since the dielectrophoretic force scales with the cube of particle size, it is effective for

manipulating particles of order one micron or larger. DEP has been used to separate blood cells

and to capture DNA molecules (Miles et al., 1999; Wang et al. 1998).

DEP has limited effectiveness for manipulating proteins that are of order 10 – 100 nm (Deval,

2002). However, for these small particles, DEP force may be both augmented and dominated by

the particle’s electrical double layer, particularly for low conductivity solutions (Gascoyne &

Vykoukal, 02).

DEP has been used to manipulate macromolecules and cells in microchannels. For example,

Miles et al. (99) used DEP to capture DNA molecules in microchannel flow. Gascoyne &

Vykoukal (02) presents a review of DEP with emphasis on manipulation of bioparticles. An

example of a cancer cell separation device is shown in Fig. 4. Here, interdigitated DEP

electrodes are fabricated on the surface of a microchannel. Cells are transported through the

channel using pressure-driven flow. Negative DEP forces levitate the cells in the microchannel at

varying heights, depending upon the electrical properties of the cell. Since the velocity profile in

the microchannel is parabolic, cells that are levitated in the center of the channel advect

downstream faster than cells near the microchannel surface. Therefore, cancerous and non-

cancerous cells can be separated distinguished based upon their electrical properties. This

separation technique is known as flow field fractionation (FFF). A schematic of this separation

technique is shown in Fig. 4 (taken from Gascoyne & Vykoukal, 2002).

Figure 4. Schematic of Field Flow Fractionation. DEP electrodes on the bottom microchannel surface create a non-uniform electric field. The cells are levitated from negative DEP force. The cells levitated in the center of the channel are advected faster than cells near the channel walls. This provides a mechanism for separating cells based upon their electrical properties. Taken from Gascoyne and J. Vykoukal Electrophoresis 2002, 23, 1973–1983.

The combination of DEP & Electrothermal flow and AC electroosmosis is discussed in detail by

Green et al. (98), who demonstrated how, in the absence of pressure-driven flow, different sized

particles can be separated based on the balance of DEP force and fluid drag force from

electrothermally generated flow. Figure 5 depicts how particles can be separated by varying sizes

under the influence of DEP and electrothermal flow. By varying the frequency (up to 500 kHz)

and the voltage (up to 10 V peak-to-peak), the stable position of the larger beads can be moved

from the electrode edges to position A, to position B.

Figure 5. Size-selective movement of sub-

micron beads based on the balance of

electrothermal force and DEP (Taken from

Green,et al., 98)

DEP has also been demonstrated by Huang (2001) Nanogen, Inc., San Diego, CA to concentrate

a dilute sample of e. coli cells by 20-fold, and to separate e. coli cells from b. globigii cells. A

picture of the microfabricated electrode structure and captured bacteria is shown in Fig. 6.

Figure 6. (A) Images representing the microscale separation of B. globigii spores and heat-killed E. coli bacteria on the 5 _ 5 array. The electrodes in the array were addressed with an ac voltage at 50 kHz and 5 V(p-p). The spores and bacteria were suspended in a 280 mM mannitol solution having a conductivity of 20 ÌS/cm. (B) Expanded view showing that the spores were collected on the electrodes and the bacteria were repelled from the electrodes. Taken from Huang et al. (2001)

3.2 Electrothermally-Driven Flow

Electrothermal body forces are created by non-uniform Joule heating of the medium. The Joule

heating is a source term in the temperature equation, and creates spatial variations in

conductivity and permittivity, which in turn create Coulomb and dielectric body forces in the

presence of an externally applied electric field. The resulting fluid motion can be determined by

solving the Navier-Stokes equation with the electrothermal body force. Electrothermally-driven

flow can be simulated by solving the quasi-static electric field for a specific geometry. The non-

uniform electric field, gives rise to non-uniform temperature fields through Joule heating.

Ignoring unsteady effects and convection, and balancing thermal diffusion with Joule heating

yields

2 2 0k T Eσ∇ + = , (12)

where T is temperature and 2E is the magnitude squared of the electric field, given by

E V= −∇ , where k and σ are the thermal and electrical conductivity.

Gradients in temperature produce gradients in permittivity and conductivity in the fluid. For

water (1/σ) (∂σ/∂T) = +2% and (1/ε) (∂ε/∂T) =-0.4% per degree Kelvin. These variations in

electric properties produce gradients in charge density and perturb the electric field. Assuming

the perturbed electric field is much smaller than the applied electric field, and that advection of

electric charge is small compared to conduction, the time-averaged electrothermal force per unit

volume for a non-dispersive fluid can be written as (Ramos et al., 1998)

( )

2

20.5 0.51

rmsET rms rms

EF E Eεσ ε εσ ε ωτ

∇ ∇ = − − + ∇ +

, (13)

where τ ε σ= is the charge relaxation time of the fluid medium and the incremental

temperature-dependent changes are

, T TT Tε σε σ∂ ∂ ∇ = ∇ ∇ = ∇ ∂ ∂

. (14)

The first term on the right hand side of Eq. 13 is the Coulombic force, and is dominant at low

frequencies. The second term is the dielectric force, and is dominant at high frequencies. The

crossover frequency scales inversely with the charge relaxation time of the fluid, and typically

occurs at around several MHz.

The electrothermal force shown in Eq. 13 is a body force on the fluid. The motion of the fluid

can determined by solving the Stokes’ equation for zero Reynolds number fluid flow, such that

20 ETP u Fµ= −∇ + ∇ + , (15)

where u is the fluid velocity, P is the pressure in the fluid, and µ is the dynamic viscosity of the

fluid.

3.3 AC Electroosmosis

AC Electroosmosis arises when the tangential component of the electric field interacts with a

double layer along a surface. It becomes less important with increasing electric field frequency.

For example, in an aqueous saline solution with an electrical conductivity of, σ = 2 X 10-3 S/m, it

is predicted that AC electroosmosis is not important above 100 kHz (Ramos, 02).

3.4 Numerical Simulations of Electrothermal Flow

AC electrokinetics can be used to manipulate fluid motion, and enhance sensitivity of certain

biosensors (Sigurdson et al., 2002). The finite element package CFD-ACE+ (CFD Research

Corp, Huntsville, AL) was used to simulate electrothermally-induced flow and subsequent

enhanced binding in the cavity. First, the quasi-static potential field for two long electrodes along

the cavity wall is calculated (Fig. 7a). The Joule heating of the fluid from this electric field

produces local changes in temperature. Figure 7b shows the temperature field resulting from

Joule heating. From this temperature field, electrothermal force, ETF , can be estimated from

Eq.’s 13 & 14. The fluid motion can be calculated using the Stokes’ equation, Eq. 15. Figure 7c

shows the resulting velocity field. The velocity of the ETF is of order 500 µm/s, and

characterized by a pair of counter rotating vortices. This fluid motion will effectively stir the

analyte, and move it towards the immobilized antibodies.

(a) Potential Field

(b) Temperature Field

V max=7 V rms V min= -7 V rms

Tmin=300 K

Tmax ≈304 K

(c) Velocity Field

Figure 7. Simulation of ETF in 2000µm long × 40 µm cavity: (a) Quasi-static electric

potential field, calculated from two electrodes with potentials of +/- 7Vrms (10V peak-

peak). (b) Temperature field resulting from a balance of Joule heating and thermal

diffusion The fluid has an increase in temperature between the electrodes; electrodes

conduct heat to the environment. (c) Velocity vectors from 2-D simulation of

electrothermally generated fluid motion.

The convective scalar equation can be used to calculate the effect of electrothermally-induced

fluid motion on the concentration of analyte in the cavity and the binding of analyte on a cavity

wall

2C u C D Ct

∂+ ⋅∇ = ∇

∂, (16)

where C is the concentration of antigen in the outer flow, u is the fluid velocity, D is the

diffusivity of the antigen, and t is the time. Following the model given by Myszka et al. (98), the

rate of association is ( )a Tk C R B− , where ak is the association constant, C is the concentration of

antigen at the surface, and TR B− is the available antibody concentration. The rate of

dissociation is dk B , where dk is the dissociation constant, and B is the concentration of bound

antigen. The time rate of change of antigen bound to the immobilized antibodies is equal to the

rate of association minus the rate of dissociation

Velocity ~ 500µm/s

( )a T dB k C R B k Bt

∂= − −

∂. (17)

The rate of antigen binding to immobilized antigen, B t∂ ∂ , must be balanced by the diffusive

flux of antigen at the binding surface, 0y = , such that

0y

B CDt y =

∂ ∂=

∂ ∂. (18)

Equations 16, 17 & 18 are solved with an initial antigen concentration 0 0.1 nMC = , and an

immobilized antibody concentration RT = 1.7 nM cm (i.e. one molecule per 100 nm2). The

binding rates for three conditions, 0V, 7V and 14 V root-mean-square voltage, are shown in Fig.

8. The 0V case corresponds to the passive case, which is the result of pure diffusion. This is the

standard mode of most immobilized assays, such as ELISA. The 7V and 14V curves correspond

to the result of electrothermally-driven flow enhancing the transport of antigen to the

immobilized antibodies. The curves in Fig. 8 show that a factor of up to 8 (800%) improvement

in sensitivity (or response) is obtained by using AC electrokinetics.

Figure 8. Numerical simulation of dimensionless binding curves for non-enhanced (0 V) and

enhanced (7V, 14V) transport. The differences in the two curves show an increase in binding rate

0

1

2

3

0 20 40 60 80 100t (s)

B/RT

x 10-3

0 V

7 V

14 V

8X increase in bound antigen

4X increase in bound antigen

which yields a factor of 4 higher binding for 7 V and a factor of 8 higher binding after 30 seconds

for 14 V applied root-mean square potential. The binding improvement for the 14 V case

decreases to around 6 X after 100 seconds: the binding is no longer completely transport-limited.

4. Experimental Measurements of Electrokinetics

Two examples of using electrokinetics to manipulate small particles will be given here. Since

both examples use the µPIV technique to quantify the response of the small particles to the

electrically-induced forces, a brief introduction to the technique will be given here. The first

example electrokinetic flow illustrates the electrothermal effect while the second illustrates the

dielectrophoretic effect.

4.1 Micro Particle Image Velocimetry (µPIV)

µPIV is a technique that has been developed recently to measure the velocity of small scale

flows in a spatially resolved manner (Santiago, et al., 1998). Figure 9 shows the typical layout of

a µPIV system. The flow is illuminated by either a broad wavelength continuous light source,

such as a mercury vapor lamp, or a pulsed laser, such as a frequency doubled Nd:YAG.

Normally µPIV is used to measure the velocity of small scale flows by measuring the motion of

small tracer particles either naturally present in the flow or artificially added to the flow. In the

following examples however, the motion of the fluid is not primary subject of study, but rather

the motion of the suspended particles in response to an electrically-applied force. Regardless of

whether the fluid motion or particle motion is being studied, the technique is the same. The

small particles are observed with a microscope. Typically the particles are coated with a

fluorescing dye to enable epifluorescent imaging. Images are captured with a precise time delay

from one image to the next. A consecutive pair images is divided into many small interrogation

regions. The corresponding interrogation regions from each of the two original images are cross-

correlated to determine the most likely relative displacement of the particles in the interrogation

regions in the form of a cross-correlation peak. Repeating this procedure thousands of times

produces the spatially-resolved measurements of fluid or particle motion seen in the following

sections.

Figure 9: Diagram of typical µPIV system.

4.1 Electrothermal Effect

Micro-PIV experiments using polystyrene spheres in an optically accessible flow cell with

wedge-shaped electrodes have been conducted. The trajectories of 1-µm diameter polystyrene

particles suspended in sugar solution were measured in a device consisting of two brass electrodes

sandwiched between two glass wafers. An AC potential of 10 Vrms at 10 kHz was applied to the

Laser

Microscope Objective

Epi-Flourescent Filter Cube

Beam Expander

12 bit CCD Camera (1280 x 1024 pixels)

Focal Plane

Exciter 532 nm

Emitter

Cover Slip

Fluorescent Microspheres

electrodes. The particle-velocity field is measured quantitatively using micro-PIV following

Meinhart et al. (99), and is shown in Fig. 10a.

The experimental results compare well to numerical solutions of electrothermally-driven flow:

fluid motion is simulated by solving the Stokes equation, subject to an electrothermal force (Eq.

13). The velocity of suspended 1-µm particles relative to the fluid medium can be estimated by

balancing the two dominate particle forces, Stokes’ drag force and DEP force. The numerically

simulated particle velocity field is shown in Fig. 10b. For these parameters, according to model

results, the DEP was negligible in comparison with motion generated through electrothermal

flow. The results are described in detail by Meinhart et al. (02). The agreement between

simulations and experiments may indicate that electrothermal forces are important in the

microfluidic devices tested. However, in these numerical simulations, the effect of AC

electroosmosis is not modeled.

(a) Measured Particle Velocity field (b) Model of ETF

4.2 Dielectrophoretic Effect

The second set of experiments were designed to isolate the effects of dielectrophoresis from

electrothermal motion. A channel measuring 350 µm wide by 12 µm deep is shown in Figure 11.

Flow proceeds from right to left in this image. The bright regions in the image are platinum

electrodes while the dark regions are areas without platinum, or electrode gaps. The entire

imaged region is covered by a thin layer of silicon dioxide which insulates the electrodes from

the fluid medium to suppress the Joule heating that typically causes electrothermal effects. The

electrodes are arranged in interdigitated pairs so that in Figure 11 the first and third electrodes

are always at the same potential as each other. The second and fourth electrodes are also at the

same potential as each other but can be at a different potential than the first and third electrodes.

An alternating electric potential is applied to the interdigitated electrodes to create an

electromagnetic field with steep spatial gradients. Particle motion through the resulting electric

field gradients causes polarization of the microspheres, resulting in the DEP body force that

repels particle motion into increasing field gradients.

Figure 10. AC electrokinetically-driven particle motion: (a) Experimentally measured particle

velocity field using micro-PIV, and (b) Numerically simulated particle velocity arising from

electrothermal fluid motion and viscous drag. This suggests that for this regime, ETF is dominant

compared to DEP.

Figure 11. Dielectrophoretic device (Courtesy of Bashir and Li, Purdue University).

Six sets of experiments were performed, each using a different voltage. All experiments used the

same flow rate of 0.42 µl/hr (equivalent to a Reynolds number of 3.3×10-4) and the same AC

frequency of 580 kHz. The voltages were chosen between zero and 4 V. Charge neutral

fluorescent polystyrene particles measuring 0.69 µm in diameter (Duke Scientific) were

suspended in the flow. Sets of images 800 images each were acquired using a Photometrics

CoolSNAP HQ interline monochrome CCD camera from Roper Scientific. This camera is

capable of 65% quantum efficiency around the 610 nm wavelength, which is the emission

wavelength of the red fluorescing microspheres. Images were captured at a speed of 20 frames

per second. The microscope used in these experiments was an epifluorescent Nikon E600 with a

Nikon “CFI W FLUOR 60X” water immersion objective lens having a numerical aperture of

1.00. Epifluorescent imaging was used because the silicon base of the device is highly reflective,

resulting in strong background noise. The broad spectrum Mercury vapor light source is

bandpass filtered to admit wavelengths of approximately 540 nm. This wavelength excites the

red dye on the latex microspheres which emit light at approximately 610 nm. The epifluorescent

filter cube then bandpass filters the light directed to the camera to admit wavelengths of

approximately 610nm. Thus the 540nm light reflected by background features which do not

fluoresce is removed.

A particle velocity increase can bee seen from 0.5 volts to 2.0 volts, and a velocity decrease is

seen from 2.0 volts to 4.0 volts. In the 2.5 volt case, low velocity regions between electrodes are

first noticeable. In the 3.5 volt and 4.0 volt cases, large numbers of trapped particles result in

near zero velocities. Figure 12 shows the experimental results with a plot of the particle velocity

as a function of position within the device for each of the six voltage cases measured. The three

lowest voltages share a trend of decreasing particle velocity in the downstream direction. The

simplest explanation for this behavior is that with each electrode a particle encounters, it lags the

fluid velocity a little more. The cumulative effect of encountering a series of electrodes is a

gradual slowing of the particles.

Another interesting result apparent from Figure 12 is that initially the average particle velocity

increases as the voltage increases from 0.5 volts to 2.0 volts. This phenomenon is explained by

particles being pushed away from the channel bottom (where the electrodes are located) into the

faster areas of the fluid flow near the center of the channel. For the higher voltage

measurements, the effect of particles being hindered by field gradients is compounded by

particles being pushed beyond the high speed portion of the flow profile and toward the low

speed upper wall of the device. It can be qualitatively confirmed that particles are pushed to the

upper wall of the channel by observing the particle shapes from the higher voltage cases. Many

different particle shapes are evident in Figure 13a in which the voltage is 0.5 volts. These many

shapes represent how the particle images change with distance from the focal plane, which is

focused on the electrodes. Particles in focus appear as small round dots while particles out of

focus (near the upper wall of the device) appear less bright and have rings around them from the

diffraction pattern. Figure 13b shows the particle images for a voltage of 4.0 volts. Two

phenomena are obvious here. First, the particles tend to cluster at the edges of the electrodes,

and second, that almost all the particle images are out of focus, indicating that nearly all the

particles are found near the top wall of the device, remote from the electrodes.

0 20 40 60 80 100 120 1400

5

10

15

20

25

30

35

40

Axial Position (microns)

Ave

rage

Axi

al V

eloc

ity (m

icro

ns/s

ec)

0.5V1.0V2.0V2.5V3.5V4.0V

Figure 12: Average axial velocity results from PIV results for all voltage cases. Note: flow is

from right to left in this figure, opposite that in Figure 11.

(a) (b)

Figure 13: Raw particle images for the case of 0.5 volts (a) and 4.0 volts (b).

4.4 Summary

The results from Sections 4.2 and 4.3 show that the motion of suspended particles in response to

applied electric fields can be quite complicated. Experiments and modeling are often needed to

determine not only the dominant phenomenon (DEP vs. ETF) but also how the particles are

distributed within the flow. Particle distribution is of great importance in biological systems.

Sometimes they need to be trapped near a wall for analysis and sometimes they need to be kept

away from walls to reduce fouling of a device.

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