4th Micro and Nano Flows Conference
UCL, London, UK, 7-10 September 2014

Dielectrophoretic Manipulation of Particles and Lymphocytes
Using Rail-type Electrodes
Kazuya TATSUMI 1,2,*, Haruka OKUI1, Koki KAWANO1, Kazuyoshi NAKABE1,2* Corresponding author: Tel.: ++81 (75)383 3606; Fax: ++81 (75)383 3608;
Email: tatsumi@me.kyoto-u.ac.jp
1 Department of Mechanical Engineering and Science, Kyoto University, JAPAN
2 Advanced Research Institute of Fluid Science and Engineering, Kyoto University, JAPAN
Abstract A particle manipulation and sorting device using the dielectrophoretic (DEP) force is described inthis study. The device consists of “ladder-type”, “flip-type” and “oblique rail-type” electrode regions. The
ladder-type and rail-type electrodes can generate a DEP force distribution that captures the particles, the DEP
force of which is “negative” (repulsion force), in the area located at the center of the electrodes. The particles
can then be guided individually along the electrode. In addition to this, the ladder-type electrode can alignthe particles with equal spacing in the streamwise direction. Using the “flip-type” electrode, which pushes
the particles away, in combination with these electrodes, the direction of the particle can be selected withhigh accuracy, reliability and response. In the first half of this paper, numerical simulation was carried out tocalculate the particle motion and evaluate the performance of the ladder-type electrode. Several models werevalidated to investigate the influences of the non-uniformity of the electric field and the electric interactionof the surface charges and polarizations. Measurement using the high-speed camera was then carried out toinvestigate the motions of the particles and sorting reliability. The trajectories and the probability density
functions of the particles at the inlet and outlet of the electrode region showed that by using these electrodes
the particles can be aligned, sorted and guided accurately.
Keywords: Micro Flow, Dielectrophoretic Force, Sorting, Manipulation, Micro-particles and Cells

1. Introduction
The technologies for manipulating andsorting cells and microparticles in the
microchannel flow have been studied
intensively in the last decade. Those using
DEP force has been one of the promising tools
because it can produce a driving force to theparticles or cells without changing or
modifying them or the fluid properties (Chenet al. 2008, Gagnon 2011, Yi et al. 2006,
Zhang et al. 2010). Although many types ofelectrodes and channels have been proposed inother studies, substantial issues remain to besolved for satisfying the demands of theapplications, such as accuracy, sorting rate,
response and applicability under various
conditions. One such problem is because the
DEP force, FDEP, is mainly produced by theelectric field gradient, it decays markedly withthe distance from the electrode. Other
problems are the fact that in many cases, a(a) schematic of the microchannel and electrodes(b) principle of the alignment, sorting and guiding
Fig. 1: (a) Schematics of the microchannel and electrodesin the present micro-device, and (b) the schematic
showing the concept of the alignment and sorting, andparticle motions in the present device.

negative FDEP, namely a repulsion force-1-4th Micro and Nano Flows Conference
UCL, London, UK, 7-10 September 2014

against the electrode works on the particle orcell, and that the distance between the particles
flowing in the channel are random and notaligned. It is, therefore, difficult to precisely
control the particle position. In order toovercome these problems, an electrodepatterns, which are not only effective but also
fundamental and versatile, is developed in thisstudy.
The Schematic of the electrode patterns areshown in Fig. 1. The manipulation and sorting
device consists of the ladder-type electrode,the flip-type electrode and the oblique rail-type
electrode regions (Tatsumi et al. 2013). Theseelectrodes are attached to the channel bottom
wall, and the top wall is an electrodeconnected to the ground. The ladder-type willproduce FDEP which work on the particles tomake them align not only at the centerline but
also in equal spacing. The flip-type operating
as a gate electrode will lift the particle whennecessary and exclude it from the electroderegion. The remaining particles will be guided
along the oblique rail-type electrodes and canbe collected.

Table 1: Physical properties of the nucleated cell.
dne[m]Rcell[m]dcm[m]

4.9

0.04

6

0.007

’np

np[1/m]’nene[1/m]

52

1.35

28

610-3

’cp

cp[1/m]’cm

cm[1/m]

60

0.32

6.8

110-3

Table 2: Physical properties of PBS and PS particle.
’PBS

PBS[1/m]

’PS

PS[1/m]

78.3

1.55

2.65

0

membrane, cytoplasm, nuclear envelope, andnucleoplasm are simplified on the basis of theof model presented by Asami et al (1989) andHanai et al (1992).
The model using the CM function applies
the 1st order approximation for the external
electric field. However, the electric potential inthemicrochannelshowsastrongnon-uniformity, and the electric potential may
not be calculated correctly under thisapproximation. Therefore, the second model
employed in the present study is the one
considering the multi-pole. The FDEP in thiscase can be written as Eq. (3).

2. Methods
2.1 Numerical methods
To calculate the dielectrophoretic force,
Calusius-Mossotti (CM) function (Cetin and
Li 2011), Multipole (Washizu ad Jones 1994,
Jones and Washizu 1996), and Force density
methods were first applied and evaluated inorder to validate the numerical scheme applied
to the present computation. The means ofcomputation using the CM function can be
defined as Eq. (1).
2
(1)
FDEP  2 0 1 ' R 3 Re[ K CM ]Erms
K CM 

Rnc[m]

FDEP   F (n)

(3)



 

2
2 0 1 ' R 3
( n)
n 1
Re[ Kn ]   E0 rms(n  1)!(2n  1)!!
 2  1(n)K (n  1) 1  n 2

F (n)  E 
n 1

0 rms





1
n E 0 n E 0 *2When calculating the multi-layer structure of
the lymphocyte, the following equation
defining the equivalent complex relative
dielectric constant is applied to calculate K(n).

 2  1，    0 ' i 2f 2  2 1

where, 0 is the dielectric constant of vacuum，
’ is the relative dielectric constant,  is thecomplex dielectric constant, and  is theelectric conductivity. f is the frequency of thealternate current, KCM is the CM function. The
underline indicates the complex value, and thesubscripts shows the values of fluid and solid.
Since the lymphocyte has a shell structure,
the layers with different properties of the cell    a2,eq n2

2 n 1 (n  1) K

a 2 n1  n K

(n)

(n)

(4)

The third model is the force density
method. Time mean value of the FDEP of aparticle with arbitrary shape can be calculatedusing the following equation.

-2-

4th Micro and Nano Flows Conference
UCL, London, UK, 7-10 September 2014

 

 

1
 E *0  P eff  E *0 dV
2 all freePeff (r )  ( (r )   1 ) E ind
FDEP 

(6)
DEP forces free is the density of the free charge, P eff isTrapping zone

the effective polarization. E 0 is the external
electric field, and E ind is the electric field
induced by the presence of the particle. FDEP
calculated by each model are referred to as
FCM, FMP and FFD.
The electric field was calculated using the
COMSOL multyphysics ver. 4.3a by solving
the Poisson equation. In the case of FFD, notonly the external electric field but also theelectric field considering the electricinteraction between the fluid and particle or
lymphocyte parts. We will need to calculate
the electric field in the areas of cell membrane,
cytoplasm, nuclear envelope, and nucleoplasm.
Since the thickness of the cell membrane andnuclear envelope are significantly small,directly generating mesh in this area requires
serious computational cost. Therefore, theboundary condition shown by Eq. (7) isapplied to each boundary in the present study.
This model calculates the potential drop at thelayer of the membrane directly and reduce thecomputational cost.
J n 



mem



'
Vout  Vin 
 i 2f 0 mem
t mem

Flow

Particles and cells

Fig. 2: Schematics of motion of the particle trappedand guided by the rail-type electrodes.
0.0

0.4

0.8

1.2

FCM,z [nN]

1.6

50

40

40

30

30

z [m]z [m]

FCM,y [nN]
50

20
10

-1.2

-0.8

-0.4

0.0

60

80

100

20
10

0

0
0

20

40

60

80

100

0

20

40

y [m]y [m](a) FCM,y distribution(b) FCM,z distribution

FMLT,2,z [nN]
50

-1.6

-1.2

-0.8

-0.4

FMLT,3,z [nN]

0.0

50

40

40

30

30

z [m]z [m]

-1.6

20
10

-1.6

-1.2

-0.8

-0.4

0.0

60

80

100

20
10

0

0
0

20

40

60

80

0

100

20

40

y [m]y [m](c) FMP,2,z distribution(d) FMP,3,z distribution

Fig. 3: The distributions of the DEP forces FCM and
FMP working on the Jurkat cell in the case ofrail-type electrode at the cross-sectional plane. FMP,2
and FMP,3 present the force of the multi-pole model
considering 2nd and 3rd order term, respectively.

(7)
0.0

J is the current density, n is the normal vectorof surface. Vout and Vin are the potential at the'
inner and outer side of the boundary.  mem,
 mem and t mem the relative dielectric constantof the membrane, conductivity, and membranethickness. The properties applied to the cell in
the computation are summarized in Table 1
reffering the results of Asami et al. (1989).
These are the values for lymphocyte of amouse. The radius of the nucleus was obtainedon the basis of the ratio of the nucleus and cellradii, which the value 55% is used in this study(Shmid-Schonbein, 1990). Subscripts cm, cp,
ne, and np presents the values of cell
membrane, cytoplasm, nuclear envelope, andnucleoplasm, respectively. The diameters of
the particle and cell are 6m. The properties ofthe fluid and polystyrene particle are shown in

FDEP,z [nN]

-0.1
-0.2
-0.3
-0.4

FCM

FMLT,3

FQ

FP

FFD

-0.5
6

8

10

12

14

zp [m]16

Fig. 4: The influence of the z positions on the DEP
force working on the Jurkat cell. Comparison ismade among computation applying the three models.

Table 2.
2.2 Experimental methods
Micro-device was fabricated using top andbottom walls made of glass substrates with Pt
electrode pattern bonded with SU-8 (Micro-3-

4th Micro and Nano Flows Conference
UCL, London, UK, 7-10 September 2014(a) zp=6.1m

Fig. 6: Composite stroboscopic photo of the particle
in the case of Vp-p=20V and Um=4.94mm/s.

(b) zp=8.0m
20

10

FCM ,z [nN]-0.8z [m]

15

8

-0.6

10

up [mm/s]

-0.4
-0.2

5

0.0

0
40

(c) zp=12m

45

50

y [m]

55

60(d) FCM,z distribution

642

experimental
FCM (Vrail=10.5Vpp)
FMLT (Vrail=11Vpp)
FFD (Vrail=11Vpp)

Fig. 5: (a)(c) Distributions of the force density of theJurkat cell located at different z positions using theforce density model, and (d) the distributions of
FCM,z. The circles shown in (d) displays the surfacesof the cell at different heights.

0
-60

-40

-20

0

20

40

60

t-tUm [ms]Fig. 7: Relationship between up and t of experiment,
and computation using FCM, FMP and FFD.

Chem Co.). The microchannel shown in Fig. 1(a) was patterned in the SU-8 layer. The
channel width and height are 200 and 50 m,
respectively.
Sheath flow was supplied from the
upstream using three inlet flows. The particles
and lymphocytes were supplied from thecenter inlet, and the spanwise position was
roughly controlled.
Two electrode patterns were employed in
the experiment. One is the combination ofrail-type, ladder-type and flip-type electrodes
illustrated in Fig. 1. The present ladder-type
electrode is able to trap and guide the particles
at certain height and spanwise positions, andmoreover, with even streamwise spacing ofeach particle. The flip-electrode will push theparticles in the height direction and exclude
them when the voltage is supplied to theelectrode and activated. The rail-type electrodelocated downstream will trap the particles
passing the flip-type electrode (when not
activated), guide them in the spanwise
direction, and can be collected from anotherreservoir
locateddownstream.
Detailexplanation on the function of the ladder-type
electrode will be discussed shortly.
The other electrode is the simple rail-type

electrode shown in Fig. 2. This electrode isused to verify the model and numerical
scheme of the present computation.
Peak to peak voltage of 20V was supplied
to the rail-type electrode at the frequency of
10MHz. In the case of ladder-type electrode,the voltage of 10MHz to generate DEP force
was additionally oscillated with periods of low
frequency in order to align the particles in thestreamwise direction.
Polystyrene (PS) particles of nominal
diameter 6m (Thermofisher scientific,
4112A) were used as micro-particles. Jurkat
cells (ATCC: CRL2570) were used as
lymphocytes. These were suspended inphosphate buffered saline (PBS). In the case of
PS particles, sodium lauryl sulfate was added
to the solution with 0.1wt% to prevent theparticle attach to the channel wall.

3. Results and Discussion
3.1 Numerical verification
Particle were supplied to the rail-type
electrode with the flow rate of Q =3.2L/min
and Um=4.94mm/s. The particle motion wasrecorded by a high-speed video camera and the-4-4th Micro and Nano Flows Conference
UCL, London, UK, 7-10 September 2014

position and velocity of the particle wasmeasured.
Figures 3 (a) and (b) show the distributionsof the y and z components of the FCM on theyz plane. (c) and (d) show the z component of
FDEP in the case of MP model. (c) and (d)shows the results when the 2nd and 3rd orderterms are considered, respectively.
FDEP generated by the rail-type electrode
moves the particles toward the channel
centerline and close to the bottom wall. By this,the particle position can be controlled, andallows us to guide the particle in the channel
with high accuracy.
The minimum value of FCM is FCM,z =42nN in Fig. (b). However, in the case of
FMP,2 shown in (c), the value is 0.4nN and islarger than that of FCM. The 1st order term Fz(1)is proportional to the z gradient of Erms2 . Fz(2)is proportional to the z gradient of E :E *.
These values are positive and negative in thearea adjacent to the channel bottom wall. Thus,
FMP,2 slightly increases compared with FCM.
The third term showing the influence of E
rms appears to be small in the rail-type
electrode case.
Figure 4 shows the FDEP distribution
against the height position in the case of Jurkat
cell. The Coulomb force working on themembrane surface FQ and the force related tothe polarization FP, both composing the FFD,
are shown in the figure. In Fig. 5, thedistributions of the force density at different z
locations are shown. For comparison, the FCM
distribution is shown in Fig. (d).
In Fig. 4, the values of FQ and FP arenearly equal. Although not shown here, in thecase of PS particles, FP was dominant and FQ
was nearly zero due to the fact that PS particle
could be considered as a conductive body. On
the other hand, in the lymphocyte case, thecharges on the membrane and nuclear
envelope increases, and the influence of the
Coulomb force becomes noticeable.
In Fig. 5, the distribution of FFD and FCM
shows similar value in the nucleoplasm. The
distribution in the area of nucleoplasm shows
similar trend. On the other hand, in cytoplasm
a large difference can be observed where FFDof large value is observed in the z axis. In theFig. 8: DEP force working on the particle foralignment(a) relative positions of the particles converging tocertain positions with equally spaced(b)~(e) The streamwise components of FDEP and thestreamwise velocity of the particle up in relation to
the streamwise position xp.
Fig. 9: (a) The relative positions of the particles
initially located at xp,0=0 and 10m at t=0s and theapplied low frequency oscillation, and (b) & (c) the
FDEP applied to the particles in these two cases, and(d) & (e) their streamwise velocities (particle
velocity=11.6mm/s).

case of nucleoplasm, the influence of the
non-uniformity of the electric field is dominant,and at the cytoplasm, effect of the interactionof the polarization and charges additionallybecomes noticeable.
As for the influence of the height positionzp, one can see in Fig. 4 that FCM, FMLT,3 andFFD, differs equally at zp showing that the
influences of the electric field non-uniformity
and electric interaction exist similarly.
However, as zp increases, FCM approaches to
FMLT,3 indicating that the effect of the
non-uniformity decreases as the lymphocyte
distance itself from the electrode. However,-5-

4th Micro and Nano Flows Conference
UCL, London, UK, 7-10 September 2014

experimental results. The figure shows the
distribution of the particle streamwise velocity
up. The abscissa axis presents the time, and tUm
is the period when the cell reaches the bottom
wall and the velocity becomes constant. The
error bars shows the 95% uncertainty on thebasis of the ASME standard.
Comparing the three models, the results
using the fluid density model agrees well theexperimental data. The results of the CM
function and the multi-pole model, on theother hand, show deviation by 70% and 20%.
This concludes that in the case of
microchannel flows, the FDEP calculated using
the CM function may not be correct due to the
non-uniformity of the electric field, andmoreover, to the electric interaction due to thepresence of the nucleus.

Fig. 10: Snapshots of the particles aligned equally
spaced as they flow along the ladder-type
electrodes.

3.2 Numerical evaluation of particle
motions for ladder-type electrodes
The numerical model and scheme
evaluated in Section 3.1 was used to calculate
the particle motions in ladder-type electrode.
The ladder-type electrode shown in Fig. 1
consists of two streamwise parallel electrodes
and numbers of traverse electrodes. As
described in Section 2.2, low-frequency, fladder,fluctuation of square wave is added to the highfrequency fluctuation of 10MHz. When thevoltage is applied to the electrode (activated),
FDEP the distribution of which is shown in Fig.
8, will work on the particle. This force will
work in the direction not only toward thechannel bottom wall but also in the streamwise
direction if the particle is not located at thestreamwise center of the traverse electrodes.
Figure 9 (a) shows the schematic of theapplied voltage pattern and the relationshipbetween the relative streamwise position of theparticle to the center of the traverse electrodes,xp’, and time, t. Figure 9 (b) shows thestreamwise component of FDEP and particle
velocity up distributions against xp.
The initial position of the particles are
xp’=0 and 10m which is the relative position
at t=0. The mean flow velocity is 11.6mm/s,
and fladder=100Hz.
The FDEP,x and up distributions shown in
Fig. 9 indicate that the force is working on the(a) fladder oscillation non-activated(b) activatedFig. 11: Probability density distributions of thedeviation of the particles  from the synchronizedtime of the oscillation (Measured at the outlet of theladder-type electrodes).

the interaction effect still exists strongly evenat zp=15 showing that we need to employ thefluid density model in order to calculate the
FDEP correctly in the case of nuclear cell.
Figure 6 shows the snapshots of a particle
flowing above the rail-type electrodes. The
photograph is a superposition of images
recorded with an interval of 5ms. One can seethat the distance between the particles
decreases and converges to a constant value as
the particle flow downstream. This indicatesthat the particle is trapped by the FDEP andmoves toward the channel bottom wall, andeventually flow with a constant velocity.
Figure 7 compares the numerical and-6-4th Micro and Nano Flows Conference
UCL, London, UK, 7-10 September 2014

depending on its initial position.
3.3 Experimental results of the sorting
systemFigure 10 shows a photograph of theparticle flowing in the ladder-type electrodes.
The particles are located at the same position
relative to the traverse electrodes. The timeinterval of each particle measured by thehigh-speed camera were exactly 7ts and 4ts,
where ts is 1/fladder which is the period of the
low frequency fluctuation.
Figure 11 shows the probability density
distributions of the deviation of the particle
from the synchronized time of the low
frequency oscillation of the applied voltage. is the deviation and is normalized by ts. (a) isthe case when only high frequency voltage isapplied to generate the FDEP, and (b) shows theresults when the electrode is activated. Bothcases were measured at the outlet of theladder-type electrode. In Fig. (a), P is scatteredacross the /ts region indicating that theparticles flowing from the electrode region are
not aligned and randomly distributed. On theother hand, a peak is observed near the regionof /ts=0 showing that the particle are aligned
to match the period of the low frequency
fluctuation.
These results show that by flowing along
the ladder electrodes, the particle positions arealigned equally spaced.
Figure 12 shows the probability density
distributions of the particle spanwise positionat the locations of the outlets of the ladder-type
electrode and the sorting region. The
flip-electrode shown in Fig. 1 is activated(voltage is applied to the electrode) only at the
moment when the particle is expected to flow
above the electrode. Namely, the flip-electrodeis activated at the timing synchronized with tsof the ladder-type electrode.
Figure (a) shows the non-activated caseand (b) is for the case of activated one. In thecases of (a) and (b), the spanwise position arecontrolled to be as yp=0m. In Fig. (a), the Pof yp distributes in the range of 0<yp<40 and
yp=90. The former group is for the particle
excluded by the flip-electrode and flowing
downstream. The distribution has a broad(a) FDEP with fladder oscillation non-activated(b) FDEP with fladder oscillation activatedFig. 12: Probability density distributions of theparticle spanwise positions yp at the outlets of theladder-type electrodes and the sorting region. All
particles are synchronized accurately and flipped
when activated.

particle in the positive and negative directions
depending on the deviation of position. As thetime elapse, FDEP,x converges to zero, and up
approaches to a velocity which is related to theheight position of the particle. Therefore, xp’
also converges and remains constant in thedownstream region at a relative position-7-

4th Micro and Nano Flows Conference
UCL, London, UK, 7-10 September 2014

ACKNOWLEDGEMENT

range indicating that at the period when the
flip-electrode is activated the relative positionof the particle against the electrode varies.
This means that even though the particles are
excluded there is a mismatch with the timing.
The latter group in the distribution depicts
those which passed the flip-electrode without
any interference, and captured by the obliquerail-type electrodes. This should not occur if
the flip-type electrode is operated correctly.
On the other hand, a clear peak isobserved at yp=10m in Fig. (b). This showsthat all the particles are excluded at an exact
timing when the low frequency fluctuation at
the ladder-type electrode is activated.
These results show that by aligning theparticles in the streamwise direction with theladder-type electrode, the particles can be
excluded in a precise timing. This confirmsthat the particles which are excluded andcollected by the oblique-type electrodes can besorted in high accuracy which leads toenhancing the sorting performance.

This work was partially supported by
JSPS KAKENHI from the ministry ofeducation, culture, sports, science andtechnology, Japan.

REFERENCES

Chen, P., Feng, X., Du, W., and Liu, B.-F.,
2008. Microfluidic Chips for Cell Sorting,
Frontiers in Bioscience 13, 2464.
Gagnon,
Z.
R.,
2011.
CellularDielectrophoresis: Applications to theCharacterization, Manipulation, Separation
and Patterning of Cells, Electrophoresis 32,
2466.
Tatsumi, K., Shintani, H., Katsumoto, Y., andNakabe, K., 2013. Dielectrophoretic sorting of
microparticles and lymphocytes using rail-type
electrodes, micro-TAS2013.
Yi, C., Li, C., Ji, S., and Yang., M, 2006.
Microfluidics technology for manipulation andanalysis of biological cells, Analytica Chimica
Acta 560, .1-23.
Zhang, C., Khoshmanesh, K., Mitchell, A.,andKalantar-Zadeh,
K.,
2010.
Dielectrophoresis
formanipulationofmicro/nanoparticles in microfluidic systems,
Analytical and Bioanalytical Chemistry 396,
401-420.
Cetin, B., and Li, D., 2011. Dielectrophoresis
in microfluidics technology, Electrophoresis
32, 2410-2427.
Washizu, M., and Jones, T.B., 1994.
Multipolar dielectrophoretic force calculation,
Journal of Electrostatics 33, 187-198.
Jones, T.B., and Washizu, M., 1996.
Multipolar
dielectrophoreticandelectrorotation theory, J. of Electrostatics 7,
121-134.
Asami, K., Takahashi, Y., and Takashima, S.,
1989. Dielectric properties of mouse
lymphocytes and erythrocytes, Biochimica etBiophysica Acta, 49-55.
Hanai, T., 1968. Electric properties of
emulsions, in Emulsion Science (Ed.: Sherman,
P.) Academic Press, London, 353-478.
Shmid-Schonbein, G.W., 1990. Leukocyte
Biophysics, Cell Biophysics, 107-135.

4. CONCLUSIONS
Numerical
computationandmeasurements were conducted to evaluate theperformance of the micro-device for sortingand manipulation using the ladder-type,flip-type and oblique-rail-type electrodes.
Computations using the CM function,
multi-pole model, and fluid density model
were carried out. The electric charge on themembrane and nuclear envelope, and thepolarization in cytoplasm and nucleus showeda large effect on the FDEP working on thelymphocyte. Comparing the numerical resultswith the experiment, the fluid density model
showed the highest accuracy, while the CM
function and multi-pole showed 70% and 20%
deviation in the particle velocity distributions.
The simulation showed that theladder-type electrode can control the particles
positions and align them with even spacing inthe streamwise direction. Measurement
showed that by this particle alignment, theperformance of the sorting using the flip-type
electrode enhanced markedly. The probability
function of the particle position confirmed theaccuracy of the present sorting micro-device.
-8-