Electrokinetic effects on motion of submicron particles in microchannel

Fluid Dynamics Research 38 (2006) 787–802

Electrokinetic effects on motion of submicron particles inmicrochannel

Yohei Sato∗, Koichi Hishida

Department of System Design Engineering, Faculty of Science and Technology, Keio University, 3–14–1 Hiyoshi, Kohoku-ku,Yokohama 223-8522, Japan

Received 18 October 2004; received in revised form 16 March 2006; accepted 18 April 2006

Communicated by Y. Matsumoto

Abstract

Two-fluid mixing utilizing electrokinetically driven flow in a micro-channel is investigated by micron-resolutionparticle image velocimetry and an image processing technique. Submicron particles are transported and mixed withdeionized water by electrophoresis. The particle electrophoretic velocity that is proportional to an applied electricfield is measured in a closed cell, which is used to calculate the electroosmotic flow velocity. At a constant electricfield, addition of pressure-driven flow to electrokinetically driven flow in a T -shaped micro-channel enhancestwo-fluid mixing because the momentum flux is increased. On the other hand, on application of an alternativesinusoidal electric field, the velocity difference between pressure-driven and electroosmotic flows has a significanteffect on increasing the length of interface formed between two fluids. It is concluded from the present experimentsthat the transport and mixing process in the micro-channel will be enhanced by accurate flow-rate control of bothpressure-driven and electroosmotic flows.© 2006 The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved.

Keywords: Micro-channel; Electroosmotic flow; Electrophoresis; Micro-PIV; Submicron particles

1. Introduction

Micro-technology will be expected to miniaturize the present large electrochemical analysis equip-ments, bringing about drastic changes in total analysis systems in laboratory. This technology will be

∗ Corresponding author. Tel.: +81 45 566 1740; fax: +81 45 566 1720.E-mail address: [email protected] (Y. Sato).

0169-5983/$30.00 © 2006 The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved.doi:10.1016/j.fluiddyn.2006.04.003

mailto:[email protected]

788 Y. Sato, K. Hishida / Fluid Dynamics Research 38 (2006) 787–802

based upon the development of a micro-scale multiphase flow system that is composed of liquids ascontinuous phase, and submicron particles and molecules as dispersed phase. In this system, analyzingchemical reaction, migration (Devasenathipathy et al., 2003), mixing (Johnson et al., 2001) and separation(Giddings, 1989; Andrew et al., 1999) will be innovatively synthesized. Small fluid sample volumes arehandled by a force on the liquid, which is generally exerted by an external electric field. This transportmechanism is well known as electrokinetically driven flow, that is, particles transported by electrophoresisand electroosmotic flow are induced by the motion of ions. Quantitative measurements of electrokineti-cally driven flow structure will advance our understanding. The accurate control of electrophoresis andelectroosmotic flow is a key issue of development of miniaturized and integrated system. Experimentalefforts using caged fluorescent dye (Paul et al., 1998; Ross et al., 2001) show the velocity distributionof electroosmotic flow in capillaries and micro-channels, but the influence of charged dye on velocitymeasurements has been vaguely discussed.

The advantage of applying electrokinetically driven flow to the transport and mixing process in micro-fluidic devices is that the electrophoretic and electroosmotic flow velocities are proportional to the electricfield. Thus, one can control two-fluid mixing by changing the magnitude of electric field. However, onlya few experiments have been carried out for quantitative measurements of electrophoretic and electroos-motic flow velocities separately (Sato et al., 2002). When micron-resolution particle image velocimetry(micro-PIV, Devasenathipathy et al., 2002) is utilized to measure electrokinetically driven flow in amicro-channel, the measured velocity represents the summation of electrophoretic and electroosmoticflow velocities, implying that it is impossible to distinguish these velocities. For further developmentin the understanding of the transport and mixing process using micro-fluidic devices, the electrokineticeffect on motion of submicron particles should be quantitatively examined.

The objective of the present study is to investigate the influence of electrokinetic phenomena on two-fluid mixing in a micro-channel by using micro-PIV and an image processing technique. When dielectricparticles are injected into electrokinetically driven flow, the surface of particles is negatively charged,so that particles cannot be tracer particles of fluid. The observed velocity of submicron particles in aclosed cell is measured by micro-PIV (Ichiyanagi et al., 2004) in order to calculate the electrophoreticvelocity. Using this electrophoretic velocity, it is possible to obtain the electroosmotic flow velocity in anI -shaped micro-channel and to investigate two-fluid mixing in a T -shaped micro-channel by applying aconstant or an alternative electric field. Deionized water seeded with submicron particles is injected intoopposite inlets of the T -shaped mirochannel and moved toward the junction area by electrokineticallydriven flow that is generated by the constant or the alternative sinusoidal electric field to enhance mixing.The interface length between two fluids is extracted by image processing. Results obtained in the presentstudy will enable us to develop the assaying process in micro-fluidic devices by changing the flow-rateratio of electrokinetically driven flow to pressure-driven flow.

2. Experimental setup

A schematic of the present optical measurement system is illustrated in Fig. 1. A 12-bit Peltier-cooledCCD camera (Hamamatsu Photonics, K.K., C4880-80) with a 656×494 array is mounted on a microscope(Nikon Corp., E800). Illumination is provided by a continuous mercury lamp, which is then routedthrough a bandpass filter (450–490 nm) and a dichroic mirror transmitting wavelengths above 505 nmonto the micro-channel. Fluorescence from the submicron particles are collected through an objective lens

Y. Sato, K. Hishida / Fluid Dynamics Research 38 (2006) 787–802 789

Fig. 1. Schematic of the measurement system.

Table 1Properties of fluorescent particles

Number mean diameter (nm) 400 1000Stan. dev. of diameter (%) < 5 < 5Density (g/cm3) 1.05 1.05Absorption wavelength (nm) 468 468Emission wavelength (nm) 508 508Concentration (−/ml) 2.6 × 1011 1.8 × 1010

Measurement deptha (�m) 1.9 4.5

aThe measurement depth was calculated from the equation given by Meinhart et al. (2000) in which n = 1.515, � = 508 andNA = 1.4.

(Nikon Corp., CFI60 Plan Fluor) and an emission filter transmitting wavelengths longer than 520 nmonto the CCD pixel sheet. Images are captured with a frame grabber (Coreco Inc., IC-PIC) for furtherpostprocessing and analysis. A thermally controlled stage maintains a constant temperature of 293 K toremove temperature effects on measurement results.

Soft lithography (Hosokawa and Maeda, 2001) is used to fabricate micro-channels with the widthrange from 100 to 400 �m for the current experiments. The channel structure is fabricated from a]50 mm diameter poly(dimethylsiloxane) (PDMS) chip and sealed with a 170 �m thickness glass coverslip.

Properties of tracer particles (Duke Scientific Co.) used for the reported experiments are compiled inTable 1. Submicron diameter particles are selected to achieve high spatial resolution. Fluorescent particlesare chosen to remove scattered light from the walls and substrate, which is a much bigger problem incapturing images by the CCD camera. The fluorescent particles allow selective acquisition of signal,which is important for the increase in signal-to-noise ratio of captured images. The measurement depth


is calculated from (Meinhart et al., 2000)

�z = 3n�

NA2+ 2.16dp

tan �+ dp, (1)

where n is the refractive index of the fluid between the objective lens and the micro-channel, � is thewavelength of light, NA is the numerical aperture of the objective lens and dp is the diameter of particles.

It is noted that all the experiments are carried out using deionized water containing particles and 0.2–2%surfactant (SDS, Triton X-100, Tween 80, etc.) from an original bottle provided by Duke Scientific Co.in order to avoid particle aggregation.

Micro-PIV was developed based upon a cross-correlation technique by Abe et al. (1998), while aGaussian peak-fit method (Westerweel, 1997) was employed to interpolate the subpixel displacement.Because the background noise from out-of-focus particles near the wall is contained in the images andreduces visibility of in-focus particles, the noise influence is removed by subtracting the backgroundintensity from captured images. The effect of Brownian motion of submicron particles upon velocitydetection is not neglected. A noisy vector field is obtained for the laminar flow field as expected due tothe influence of Brownian motion. Brownian motion is statistically random and is unbiased spatially andtemporally, so that the ensemble average over several measurements substantially reduces the unbiasednoise due to Brownian motion (Santiago et al., 1998). In the present study, the ensemble-averaging methodusing 100 instantaneous images is performed to obtain velocity-vector fields.

3. Results and discussion

3.1. Quantitative measurements of electrokinetically driven flow

When micro-PIV is applied to electrokinetically driven flow, the measured velocity, Uobs, is expressedas

Uobs = UEP + UEOF, (2)

where UEP and UEOF are the particle electrophoretic and electroosmotic flow velocities, respectively. Inthe present study, UEP is obtained first in the closed cell, and then UEOF in the I -shaped micro-channelis calculated by subtracting UEP from Uobs (Ichiyanagi et al., 2004).

Fig. 2 shows a schematic diagram of closed cell consisting a ]50 mm diameter ×170 �m thicknessglass plate and a 5 mm PDMS chip (Shin-Etsu Chemical Co., Ltd., EK119). The aspect ratio of the widthto the depth is chosen to be 38.5 to neglect an influence of side walls on measurement results. Deinonizedwater containing 400 nm fluorescent particles is injected into the closed cell. An electric field of 10 V/cmis applied via platinum electrodes that are sputtered on the cover glass.

A schematic of electrokinetically driven flow in the closed cell is illustrated in Fig. 3. In a steady state,a circulation flow is observed, which is induced by electroosmotic flow. As the surface of particles is neg-atively charged, the velocity profile is shifted to the anode. The integration of flow rate of electroosmoticflow in the positive and negative X-direction has a same value, so that the net flow rate of electroosmoticflow becomes zero in the closed cell. This means that the measured velocity by micro-PIV represents thevelocity of submicron particles affected by electrophoresis.


X

Y

Pt electrode 20 mm Pt electrode

1 m

m

(a)

PDMS

X

Z

Cover glass

170

�m26

�m

(b)

Fig. 2. (a) Top and (b) cross-sectional views of the closed cell.

Wall

Wall Velocity = 0

− +

Power supply

X

Z

Buffer

Electrophoresis

Particle

Electroosmotic flow

Observed velocity

Fig. 3. Schematic of electrokinetically driven flow in the closed cell.

Velocity measurements are performed at 11 planes in the depth-wise direction by using a 60× mag-nification, oil-immersion objective lens (Nikon Corp., CFI60 Plan Fluor) with a numerical aperture of1.4. The size of the CCD pixel sheet along with the objective lens corresponds to a measurement area of


U [�m/s]-40 -20 0 20 40 60 80

z [�

m]

0

5

10

15

20

25

30

Micro-PIV

UEP

PDMS

Glass

Fig. 4. Velocity profile of 400 nm diameter particles in the closed cell on application of 10 V/cm. The electrophoretic velocity ofparticles, UEP, was calculated to be 36.2 �m/s toward the anode.

109 �m × 82.3 �m in the object plane. The exposure time and frame interval of the CCD camera are 5.72and 37 ms, respectively. A parabolic velocity profile shown in Fig. 4 is obtained by time averaging 100instantaneous measurements in order to eliminate the effect of Brownian motion of particles on velocitydetection. The spatial resolution is 8.3 �m × 8.3 �m (50 × 50 pixels) × 1.9 �m, based upon the size ofthe first interrogation window and the measurement depth. It is found that the velocity at each wall hasa different value due to the difference in the zeta potential that is defined as the electric potential at theshear plane between the solid and diffusive layer of ion.

Using the velocity profile in Fig. 4, UEP is calculated based upon equations proposed by Mori andOkamoto (1980). The measured velocity U is normalized as

U∗ = U

Ub + Ut, (3)

where Ub and Ut are the velocities near the bottom and top walls, respectively. The z coordinate in Fig.3 is nondimensionalized by using the cell depth 2D as

z∗ = z − D

D. (4)

The quadratic curve of velocity profile in Fig. 4 is determined by the least-squares method, which takesthe form

U∗ = c2z∗2 + c1z

∗ + c0, (5)

with c2 = 2.5312, c1 = −0.214 and c0 = −2.0309. UEP is calculated as

UEP = c0 +(

1

3+ 0.420166

R

)c2, (6)

where R is the aspect ratio of width to depth of the closed cell. UEP is determined to be 36.2 �m/s towardthe anode by substituting c0, c2 and R = 38.5 into Eq. (6).


X

YPDMS

Y

Z

35 mm

Pt electrode

Cover glass100 �m

30 �

m17

0 �m

(a)

(b)

Fig. 5. (a) Top and (b) cross-sectional views of the I -shaped micro-channel.

UEOF [�m/s]0 50 100

y [�

m]

0

20

40

60

80

100

UEOF [�m/s]0 50 100

y [�

m]

0

20

40

60

80

100

UEOF [�m/s]0 50 100

y [�

m]

0

20

40

60

80

100

(a) (b) (c)

Fig. 6. Velocity profile of electroosmotic flow on application of 10 V/cm in the Z-direction: (a) near the glass wall (z = 1 �m),(b) at the depth-midpoint (z = 15 �m) and (c) near the PDMS wall (z = 29 �m). • mean velocity.

Velocity measurements of electroosmotic flow are carried out by using the micro-channel depictedin Fig. 5. The micro-channel is composed of PDMS and a glass cover slip that are the same mate-rials as the closed cell. An applied field and fluorescent particles are identical to those used in theclosed cell.

Velocities are measured on three planes in the depth-wise direction; that is, near the cover glass wall(z = 1 �m), at the depth-wise midpoint (z = 15 �m) and near the PDMS wall (z = 29 �m). Fig. 6 showsvelocity profiles of electroosmotic flow on these planes. The measurement uncertainties for electroos-motic flow velocities depend on those for the particle electrophoretic velocity, whose maximum value is6.8 �m/s. The error bar is calculated by the root-mean-square value of measured velocity. The velocityprofile at glass wall shows a plug flow (Fig. 6(a)), while the that at the depth-wise midpoint representsa reverse parabola (Fig. 6(b)), which is mainly due to a rise in the water head of cathode-side inlet.


InletInlet

Pt electrode5 mm distance

Outlet

X

Y

200

�m

5 mm

PDMS

Cover glass

400 �m

100

�m17

0 �m

400 �m

(a)

(b)

Fig. 7. (a) Top and (b) cross-sectional views of the T -shaped micro-channel.

These results are consistent with the past experimental results using fluorescence imaging (Paul et al.,1998; Ross et al., 2001).

3.2. Two-fluid mixing by constant electric field

Mixing process is realized in the cross-, T - or Y -shaped micro-channel under an external force. Thepresent study focuses on two-fluid mixing by the electric field in a T -shaped micro-channel, which isshown in Fig. 7. The depth of the channel is 100 �m. The widths of the horizontal and the vertical channellengths are 200 and 400 �m, respectively. The hydraulic diameter of the channel for the vertical armsection is 160 �m. Two platinum electrodes are fabricated by a sputtering machine to generate a constantelectric field of 20 V/cm. Deionized water seeded with 1 �m diameter particles is injected into the oppositeinlets. The measurement depth is calculated to be 11 �m by using a 10× magnification objective lens(Nikon Corp., CFI S Fluor) with a numerical aperture of 0.5. The size of the CCD pixel sheet along withthe objective lens corresponds to a measurement area of 640 �m × 480 �m in the object plane. The frameinterval of the CCD camera in this experiment is 100 ms.

By the measurement method described in the previous section, the electrophoretic velocity UEP of1 �m diameter fluorescent particles is calculated to be 85.0 �m/s toward the anode on application of a10 V/m electric field. The electrophoretic velocity of particles is estimated from the balance between theelectric force and the Stokes drag acting on the particle (Probstein, 1994) as

UEP = 2

3

ε�pE

�f

(dp

�D

), (7)

where ε is the permittivity of liquid, �p is the zeta potential around a particle, E is the electric field, � isthe viscosity of liquid, f is the Henry function which defines that the electric double layer is sphericallysymmetric around a particle, and �D is the thickness of electric double layer around a particle. The ratioof dp/�D is assumed to be large in the present study (dp = 1.0 �m and �D ≈ 10 nm) in comparison with


Fig. 8. Time evolution of particle image in the T -shaped micro-channel on application of 20 V/cm at (a) t = t0, (b) t = t0 + 2 sand (c) t = t0 + 4 s.

the thick electric double layer, so that f (dp/�D) takes a value of 32 (Probstein, 1994). The electrophoretic

mobility uEP of particles is defined by (Probstein, 1994)

uEP = UEP

E= ε�p

�, (8)

which is independent of the electric field. The electrophoretic mobility of 1 �m particles is calculated tobe 8.50 × 10−4 cm/(V s).

Fig. 8 shows the time evolution of particle image in the junction area. Fluorescent particles are injectedonly into the left-hand side inlet in order to visualize particle motion affected by the electric field. At t=t0,fluorescent particles move downstream by pressure-driven flow, which is generated by the difference inheight of water surface between the inlets and outlet, without mixing with deionized water from theright inlet (Fig. 8(a)). When an electric field of 20 V/cm is applied, the particles move toward the rightregion of the junction area (Figs. 8(b) and (c)). The electrophoretic velocity of particles is calculated tobe 170 �m/s.

Fig. 9(a) shows a time-averaged velocity-vector map when deionized water containing particles isinjected into both inlets, i.e., pressure-driven flow. This map was obtained by taking ensemble averageover 20 instantaneous measurements. The Reynolds number based on a channel equivalent diameter of160 �m and a bulk velocity of 180 �m/s is 3.35 × 10−2.


Fig. 9. Time-average velocity-vector map of (a) pressure-driven flow, (b) electrokinetically driven flow and (c) electrokineticallydriven flow plus pressure-driven flow. Applied field of 20 V/cm.

Fig. 9(b) illustrates a velocity-vector map of electrokinetically driven flow, which is generated byapplying a 20 V/cm electric field, just after the velocity of pressure-driven flow becomes zero. Themeasured velocity at y = 100 �m indicates 60 �m/s. By using the particle electrophoretic velocity of170 �m/s, the electroosmotic flow velocity at y = 100 �m is evaluated to be 110 �m/s, which means thatthe particles are transported from left to right by electrophoresis, while electroosmotic flow moves fromright to left.

When the particles are moved by pressure-driven flow from both inlets, the electric field of 20 V/cm isapplied. A vector map of the sum of velocity fields of electrokinetically driven flow and pressure-drivenflow is shown in Fig. 9(c). In order to investigate two-fluid mixing in the junction area, the momentumflux is calculated by using the velocity information obtained by micro-PIV. The momentum flux Mx inthe X-direction is defined by

Mx = 12CD�U2

reldp × N , (9)

where CD is the drag coefficient of particle, � is the fluid density, Urel is the relative velocity betweenfluid and particles, dp is the particle diameter and N is the number density of particles. The drag force


x [�m]0 100 200 300 400

Mx

[g/s

2 ]

-60

-40

-20

0

20

40

60

Fig. 10. Profile of momentum flux in the X-direction. • electrokinetically driven flow plus pressure-driven flow, � electrokinet-ically driven flow. Applied field of 20 V/cm.

acting on a particle induced by electrophoresis is composed of the Stokes drag and the force associatedwith the drift of ions within the electric double layer around a particle (Morrison, 1970; Anderson, 1989).In the present study the ratio of the particle diameter to the thickness of electric double layer is assumedto be large (Probstein, 1994), therefore the drag coefficient is calculated based on only the Stokes drag.The particle Reynolds number Rep of 1 �m diameter particles is assumed to be less than 0.1 (Clift et al.,1978). The number of particles is assumed to be equal to the particle concentration in Table 1 and the fluiddensity to be equal to that of pure water. On the other hand, it is difficult to measure the relative velocityin this experiment, thus Urel is evaluated by using the fluid velocity in Fig. 9(a) and the electroosmoticflow velocity calculated from Fig. 9(b).

In Fig. 10 we compare the profile of momentum flux by electrokinetically driven flow plus pressure-driven flow with that only by electrokinetically driven flow in the junction area. It is found that themomentum flux by both flows has positive values over the two-third of the micro-channel, while onlyelectrokinetically driven flow has little influence on the momentum flux distribution. This implies thatmixing enhancement can be expected by a combination of electrokinetically driven flow and pressure-driven flow.

3.3. Two-fluid mixing by alternative sinusoidal electric field

Pressure-driven flow plays a significant role in mixing enhancement by using electrokinetic phenomena.In this subsection, mixing between fluid and particles in the T -shaped micro-channel by an alternativesinusoidal electric field is investigated by using an image processing technique. A schematic of the T -shaped micro-channel is shown in Fig. 11. The depth of the channel is 26 �m. The width of the horizontaland the vertical channel lengths are 60 and 120 �m, respectively. The hydraulic diameter of the channelfor the vertical arm section is 42 �m. Two platinum electrodes are submerged into two inlets to generate120–480 V/cm (peak to peak) operating at 0.5–2 Hz. 1 �m diameter particles are injected only into theleft-hand side inlet. The measurement depth is calculated to be 11 �m by using a 10× magnification


InletInlet

Electrode

Outlet

X

Y

120 �m60

�m

35 mm

PDMS

170

�m26

�m

120 �mY

Cover glass

Z

(a)

(b)

Fig. 11. (a) Top and (b) cross-sectional views of the T -shaped micro-channel.

Fig. 12. Time evolution of particle image on application of an alternative electric field of 480 V/cm operating at 0.5 Hz at (a)t = t0, (b) t = t0 + 1.5 s and (c) t = t0 + 2.5 s.

objective lens (Nikon Corp., CFI S Fluor) with a numerical aperture of 0.5. The size of the CCD pixelsheet along with the objective lens corresponds to a measurement area of 640 �m × 480 �m in the objectplane. The frame interval of the CCD camera in this experiment is 50 ms.

Fig. 12 depicts the time evolution of particle image on application of 480 V/cm operating at 0.5 Hz.Before the alternative electric field is applied, deionized water and particles are moved by pressure-drivenflow. The channel Reynolds number based on a vertical channel width of 120 �m and a centerline velocityof 310 �m/s is 2.46 × 10−2. When the electric field is applied, the interface between deionized watercontaining particles from the left inlet and deionized water from the right inlet shows a wavy motion.


f [Hz]0.0 0.5 1.0 1.5 2.0

U0/� i

[1/

s]

0

1

2

3

Fig. 13. The ratio of pressure-driven flow velocity to interface wavelength against the applied frequency. • 120 V/cm, � 240 V/cm,� 360 V/cm, ♦ 480 V/cm.

Time [s]0 1 2 3 4 5 6

Rl [

%]

0

2

4

6

8

Fig. 14. Temporal variation of the increasing ratio of interface length operating at 1 Hz. —– 240 V/cm, - - - - - 360 V/cm,· · · · · · · · · · · · 480V/cm.

The wavelength �i is determined as the length between two peaks of the interface wave. The ratio of thecenterline velocity U0 of pressure-driven flow to the interface wavelength is plotted against the appliedfrequency f in Fig. 13. It is found that this ratio is proportional to the frequency, implying that there isno influence of electric field on the interface wavelength.

The length l(t) along the interface is extracted by the edge-extraction filter that is based upon theluminance value of each pixel. Fig. 14 illustrates the temporal variation of the increasing rate

Rl = l(t) − l(0)

l(0)× 100 (10)


E [V/cm]60 120 180 240 300 360 420 480 540

Rl [

%]

0

2

4

6

8

Fig. 15. Increase in the interface length against the alternative electric field. • 120 V/cm, � 240 V/cm, � 360 V/cm, ♦ 480 V/cm.

of interface length operating at 1 Hz, where l(0) is the interface length of pressure-driven flow as shownin Fig. 12(a). The time interval between peak values for each case is 0.5 s that is twice a sinusoidalfrequency of 1 Hz. This is mainly attributed to the effect of velocity difference between pressure-drivenflow and electroosmotic flow in the junction area in the downstream region. From the experimental resultsof the previous sections, the electroosmotic and electrophoretic flow velocity are evaluated as 1.32 and0.868 mm/s, respectively, in the junction area on application of 240 V/cm. This means that electroosmoticflow contributes to an increase in the interface length.

The mean maximum value of the increasing rate is calculated by taking phase average of the increasingrate in Fig. 14 and plotted against the electric field in Fig. 15. It is found that the increasing rate of theinterface length is augmented with increasing the electric field operating at 0.5 and 1 Hz. However, thisrate is decreased at 480 V/cm at operating frequency more than 1 Hz. It may be seen that the velocitydifference between pressure-driven flow and electroosmotic flow has a significant effect on increasingthe interface length, whereas submicron particles are unable to respond to the higher frequency due toparticle inertia, inducing a decrease in the interface length.

The effect of electric field on the interface is examined by using the nondimensionalized numbers, whichis shown in Fig. 16. The abscissa shows the Reynolds number based on the velocity UPDF of pressure-driven flow, the electroosmotic flow velocity UEOF, and the hydraulic diameter Deq of the horizontal armwhich is defined by

(UPDF + UEOF)Deq

�, (11)

while the ordinate represents the Strouhal number

lmaxf

UEOF, (12)

where lmax is the applied frequency. It is found that the Strouhal number is decreased and tends to anasymptotic value with increase in the Reynolds number, implying that the interface length is controlled bychanging the electroosmotic flow velocity. It is concluded from these results that the flow-rate control of


0 5 10 150.0

0.1

0.2

0.3

0.4

0.5

0.6

l max

f

UE

OF

(UPDF + UEOF) Deqx 10−2

v

Fig. 16. The relationship between nondimensionalized numbers based upon the electroosmotic flow velocity and the maximuminterface length. • 0.5 Hz, � 1 Hz, � 1.5 Hz.

both pressure-driven and electroosmotic flows yields a significant increase in the interface length, whichcan be contributed to enhancement of transport and mixing.

4. Conclusions

An experimental study was performed to investigate two-fluid mixing using electrokinetically drivenflow in a micro-channel. A micro-PIV technique and an image processing using the edge-extractionfilter were applied to measure the electrokinetic effect on submicron particles’ motion and the interfacelength between two fluids. The particle electrophoretic velocity that is proportional to an electric fieldwas obtained by micro-PIV. The important conclusions obtained from this work are summarized asfollows. First, the electroosmotic flow velocity in an I -shaped micro-channel was measured by micro-PIV, which enables us to investigate quantitatively a micro-channel flow affected by the electrokineticphenomena. Secondly, two-fluid mixing in a T -shaped micro-channel is enhanced by a combination ofelectrokinetically and pressure-driven flows, which was confirmed by the fact that an addition of pressure-driven flow to electrokinetically driven flow increases the momentum flux in the junction area. Thirdly, thevelocity difference between pressure-driven and electroosmotic flows induced by an alternative sinusoidalelectric field increases the interface length between two fluids in the downstream region. It is notedthat quantitative control of the relationship between electroosmotic and pressure-driven flows should beinvestigated for further development of the transport and mixing process in micro-fluidic devices.

Acknowledgments

The authors would like to thank Messrs. S. Inaba, G. Irisawa and N. Nakajima at Keio University forperforming their experiments. This work was subsidized by the Grant-in-Aid for Scientific Research ofMinistry of Education, Culture, Sports, Science and Technology (No. 14702030 and 15206024).


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Electrokinetic effects on motion of submicron particles in microchannel