yang 2006 - a method for simultaneously determining the zeta potentials of the channel surface and...

Deguang YanChun YangNam-Trung NguyenXiaoyang Huang

School of Mechanical andAerospace Engineering,Nanyang Technological University,Singapore

Received September 21, 2005Revised October 30, 2005Accepted October 31, 2005

Research Article

A method for simultaneously determining thezeta potentials of the channel surface and thetracer particles using microparticle imagevelocimetry technique

The zeta potentials of channel surfaces and tracer particles are of importance to thedesign of electrokinetic microfluidic devices, the characterization of channel materials,and the quantification of the microparticle image velocimetry (microPIV) measurementof EOFs. A method is proposed to simultaneously measure the zeta potentials of thechannel surface and the tracer particles in aqueous solutions using the microPIVtechnique. Through the measurement of the steady velocity distributions of the tracerparticles in both open- and closed-end rectangular microchannels under the samewater chemistry condition, the electrophoretic velocity of the tracer particles and theEOF field of the microchannel are determined using the expressions derived in thisstudy for the velocity distributions of charged tracer particles in the open- and closed-end rectangular microchannels. Thus, the zeta potentials of the tracer particles and thechannel surfaces are simultaneously obtained using the least-square method to fit themicroPIV measured velocity distribution of the tracer particles. Measurements werecarried out with a microPIV system to determine the zeta potentials of the channel walland the fluorescent tracer particles in deionized water and sodium chloride and boricacid solutions of various concentrations.

Keywords: Electroosmosis / Electrophoresis / Microparticle image velocimetry / Zetapotential DOI 10.1002/elps.200500713

1 Introduction

1.1 General aspects

When a solid surface is in contact with an aqueous solu-tion, the formation of an interfacial charge causes a rear-rangement of the local free ions in the solution to developa thin region of nonzero net charge density near thecharged interface. The arrangement of the charges at thesolidliquid interface and the balancing counterions in theliquid is referred to as the electric double layer (EDL). Zetapotential is an experimentally measurable electricalpotential that characterizes the EDL, and it plays animportant role in many applications such as stability ofcolloidal dispersion [1], characterization of biomedical

polymers [2], electrokinetic transport of particles [3], andCE [4], etc. In addition, electrokinetic mobilities and zetapotentials of the particles and the channel wall are crucialto the design and process control of microfluidic devices.An excellent review on the zeta potential of microfluidicsubstrates was provided by Kirby and Hasselbrink [5].

Numerous techniques based on one or more of the threeelectrokinetic effects electrophoresis, streaming poten-tial, and electroosmosis have been developed formeasuring the zeta potentials of particles and channelwalls. Using a laser-Doppler shift technique, Oka andFurusawa [6] measured the particle velocity profile in aclosed cell of 4 mm by 4 mm cross-section. Thus, theparticle electrophoretic velocity and the fluid EOF velocitywere determined using the experimental data and theo-retically derived correlations. Minor et al. [7] presented amethod for measuring the electrophoretic mobility of par-ticles by applying an alternating electric field with a cer-tain frequency, under which electroosmosis is sup-pressed, whereas the particles are still able to follow thefield according to their direct current (DC) mobility. Theprinciple was demonstrated by using a laser-Doppler

Correspondence: Professor Chun Yang, School of Mechanical andAerospace Engineering, Nanyang Technological University, NanyangAvenue 50, Singapore 639798E-mail: [email protected]: 165-67-91-1859

Abbreviations: DC, direct current; EDL, electric double layer;micro-PIV, microparticle image velocimetry; PDMS, polydimethylsiloxane

620 Electrophoresis 2006, 27, 620627

2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.electrophoresis-journal.com

Electrophoresis 2006, 27, 620627 General 621

microelectrophoretic device. This method overcomes theproblems associated with electroosmosis in locating theso-called stationary levels, but it can measure the parti-cles electrophoretic mobilities only. Yang et al. [8] meas-ured the zeta potential of microbubbles in aqueous solu-tions by developing an approach in which the bubblesmobility is determined by microelectrophoresis measure-ment on the stationary levels in a closed cell. Gu and Li [9]proposed an experimental method to measure the zetapotential of small liquid droplets dispersed in anotherimmiscible liquid. They determined the zeta potential fromthe force balance among the electrical force, the gravita-tional force, and the buoyancy force being exerted on astationary droplet.

Based on the streaming potential measurement, the zetapotential and surface conductance of polymer flat sur-faces under various aqueous solutions were character-ized [10]. Erickson et al. [11] proposed an improvedmethod for determining the zeta potential and surfaceconductance of glass microchannels. In the improvedmethod a general least-square analysis is used toaccount for measurement uncertainties. Mela et al. [12]used the streaming potential method to measure the zetapotential for characterizing the cyclo-olefin polymermicrochannels. Sze et al. [13] used the current monitoringmethod [14] to determine the zeta potentials of channelsurfaces by using the Smoluchowski equation togetherwith the measured slope of currenttime relationship inEOFs. The current monitoring method was also used byBianchi et al. [15] to measure the zeta potential of lami-nation and ablated polydimethylsiloxane (PDMS) andpolycarbonate surfaces used for microfluidic devices.

Due to the fast development of flow visualization tech-niques, microparticle image velocimetry (microPIV) tech-nique not only has been widely used to diagnose the ve-locity profiles and probe EOF characteristics in micro-fluidic channels [1618], but also is utilized as a tool formeasuring zeta potentials. It also should be noted that asmicroPIV technique utilizes tracer particles that areusually charged in aqueous liquids, the velocity fieldobtained is a combination of the electrophoretic velocityof the tracer particles which is related to the particleelectrophoretic mobility and the EOF field which is asso-ciated with the zeta potential of the channel wall. To ob-tain the EOF field, the electrophoretic component has tobe subtracted from the microPIV measured particle ve-locity so that the EOF field can be served as benchingdata for computational simulations. In addition, the zetapotential of the channel wall is an important parameter forcharacterizing the channel wall materials and modelingelectrokinetic flows [1018]. Devasenathipathy and San-tiago [16] utilized the particle tracking velocimetry (PTV)technique together with the current monitoring method to

measure the zeta potentials of the tracer particles and thechannel wall. Oddy and Santiago [17] presented a meth-od for determining the electrophoretic and electroosmoticmobilities by measuring the particle displacements inboth alternating current (AC) and DC electric fields. Toobtain the EOF velocity from themicroPIV data, MacInneset al. [18] conducted a separate experiment to measurethe electrophoretic mobilities of tracer particles at thestationary level in a closed electrophoretic cell.

In this paper, we present a novel method for simulta-neously determining the zeta potentials of both the chan-nel surfaces and the tracer particles by using the micro-PIV technique. This method combines the theories ofelectroosmosis and electrophoresis, and uses microPIVtechnique to measure the steady electrokinetic velocitydistributions of tracer particles in open- and closed-endmicrochannels.

1.2 Theory

MicroPIV technique is used to measure the steady veloc-ity of tracer particles in an electrolyte in both open- andclosed-end microchannels. Under an applied DC electricfield, the observed particle velocity up, evaluated from themicroPIV measurement, is the superposition of the elec-trophoretic velocity of the charged particle, uep, and theelectroosmotic velocity of the electrolyte, ueo

up ueo uep (1)In the following, we will provide the analytical expressionsfor uep and ueo in an open- and closed-end rectangularmicrochannel.

1.2.1 Velocity distribution of the steady EOF inopen- and closed-end microchannels slip velocity approach

Consider a rectangular microchannel having a height 2a, awidth 2b, and a length l as shown in Fig. 1. The liquid filledin the microchannel is assumed to be an incompressible,Newtonian, symmetric electrolyte of constant density r,viscosity m, and dielectric constant er. The channel wall isuniformly charged with a zeta potential zw. When anexternal electric field E is applied along the axial directionof the channel, the liquid sets into motion as a result of theinteraction between the net charge density in the EDL ofthe channel and the applied electric field. The drivingforce of EOF is present only within the EDL. The typicalthickness of an EDL is in the range of 1100 nm [19]; whilethe characteristic hydraulic diameter of microfluidicchannels is of order 10100 mm [20]. Because of suchorders of the magnitude difference, the electroosmotic


622 D. Yan et al. Electrophoresis 2006, 27, 620627

Figure 1. Geometry of the rec-tangular channel. Channel lengthis l and the size of the rectangularcross-section 2a62b.

velocity profile inside the EDL region becomes insignif-icant, and thus the EOF can be considered to be inducedby a moving wall with velocity (slip velocity) given by theSmoluchowski equation

us e0erzwEm (2)

In the literature, the fluid flow actuated by movingboundary of the wall and driven by hydrodynamic shearstresses is referred to as the Stokes second problem [21],and is specifically referred to as the slip velocity approachin EOFs. More general discussions of the applicability ofsuch slip velocity approach in electrokinetic flows havebeen provided elsewhere [22, 23]. Using the slip velocityapproach, the steady velocity field of a fully developedflow driven by an applied electric field E and a pressuregradient dp/dz is governed by the Stokes equation,expressed as [24]

q2uqx2

q2uqy2

1mdpdz

(3)

The appropriate boundary conditions applicable to Eq. (3)are

u xbj us u ya us (4)

quqx

x0

0 quqy

y0

0 (5)

Equation (3) together with its boundary conditions speci-fied by Eqs. (4), (5) can be nondimensionalized by usingthe following dimensionless parameters:

u uU

; X xDh

; Y yDh

; Z zDhRe0

; P prU2

where U is the reference velocity, Dh = 4ab/(a 1 b) is thehydraulic diameter of the rectangular channel, andRe0 = rDhU/m is the reference Reynolds number. Further,we introduce a transform

v u us (6)

Then, the governing Stokes equation and its boundaryconditions can be rewritten in dimensionless form as

q2v

qX2 q

2v

qY2 d

PdZ

(7)

with the boundary conditions

v Xb=Dh 0 v Ya=Dh 0 (8)qvqX

X 0

0 qvqY

Y 0

0 (9)

where v vU

and us usU e0erzwEmU

Using Greens function method, the solution of Eq. (7)subjected to boundary conditions given by Eqs. (8), (9)can be explicitly expressed as [25]

vX;Y limt!1

Z tt 0

dtZb=Dh

X0 0

Za=DhY0 0

GX;Y ;tjX0;Y 0; t dP

dZ

dX 0dY 0 (10)

Here, the Greens function GX;Y ;t X 0;Y 0; tj can beobtained by using the separation of variables method.The expression for GX;Y ;t X0;Y 0; tj is given by [25]GX;Y ;t X0;Y 0; tj

4D2h

ab

X1m1

X1n1

cos amX cos amX0

cos bnY cos bnY 0 eTmn t t (11)

where am 2m 12

Dhbp, bn

2n 12

Dhap, and

Tmn a2m b2nSubstituting Eq. (11) into Eq. (10) and carrying out theintegration, we obtain

v X;Y dP

dZ16p2

X1m1

X1n 1

1 mncos amX cos bnY 2m 1 2n 1 Tmn (12)

Here, two cases are considered:

1.2.1.1 Case 1: EOF field in an open-endrectangular microchannel

In this situation, dP=dZ 0, because no external pres-sure is applied (assuming that the microchannel is infi-nitely extended). Thus, Eq. (12) becomes

vX;Y ;t 0 or uX;Y ;t us (13)



Equation (13) shows that for steady, fully developed EOFin an open-end rectangular microchannel, the slip velocityapproach leads to a plug-like velocity profile, given bythe Smoluchowski equation

ueoopen ere0zwEm (14)

1.2.1.2 Case 2: EOF field in a closed-endrectangular microchannel

Due to the closed-end structure, an inner backpressuregradient dP=dZ is induced to fulfill the condition of thezero net flow rates, which mathematically is expressed as

Zb=Dhb=Dh

Za=Dha=Dh

u X;Y ;t dXdY 0 (15)

For an infinitely extended channel, dP=dZ is constantalong the axial flow direction [26]. Substituting Eqs. (6),(12) into Eq. (15), we can show that the dimensionlessinduced pressure gradient is given by

dPdZ

p4

64usP1

m1

P1n 1

12m 1 2 2n1 2Tmn

(16)

Further substituting Eq. (16) back into Eq. (12) and noti-cing v u us, we can obtain

u X;Y us p2us4

P1m1

P1n 1

1 mncos amX cos bnY 2m 1 2n1 TmnP1

m1

P1n 1

12m 1 2 2n1 2Tmn

(17)

Equation (17) gives the electroosmotic velocity distribu-tion in a closed-end rectangular microchannel.

As the microscope objective is focused on the midplaneof the channel (i.e., Y = 0) during the microPIV experiment,the dimensional electroosmotic velocity at themidplane isexpressed as

ueoclosed X;0 ueoclosed X;0 U

zwe0erEm

1 p2

4

P1m 1

P1n1

1 mncos amX 2m1 2n 1 TmnP1

m 1

P1n 1

12m 1 2 2n 1 2Tmn

2664

3775 (18)

1.2.2 Electrophoretic velocity of the tracerparticles

Under assumptions of the undisturbed EDL structure of acharged particle and the DebyeHckel approximation,the electrophoretic velocity of tracer particles, accordingto [19] can be expressed as

uep 23 f ka ere0zpE

m(19)

A simple expression for Henrys function f (ka) was pro-vided by Ohshima [27] as

fka 1 1

2 1 2:5ka1 2e ka

3 (20)

Here a is the radius of the tracer particle, and k is the

Debye parameter defined as k 2e2z2vn0ere0kT

s(where e is

the fundamental charge, zv is the valence of the sym-metric electrolyte, n0 is the ionic number concentration ofthe bulk electrolyte, k is the Boltzmann constant, and T isthe absolute temperature). It should be pointed out herethat the Henrys expression for the electrophoretic veloc-ity of tracer particles is applicable to both open- andclosed-end channels.

1.2.3 Relationships between the microPIVmeasured particle velocity and the zetapotentials of the channel surface and theparticles in open- and closed-end channels

As indicated by Eq. (1), the particle velocity measuredfrom the microPIV technique is a combination of theelectrophoretic velocity of the tracer particles which isrelated to the particle zeta potential, zp and the EOF fieldwhich is associated with the zeta potential of the channelsurface, zw. If microPIV experiments are carried out in anelectrolyte in open- and closed-end microchannels,according to Eq. (1), we can write the expressions for themicroPIV measured velocity of the tracer particles inopen- and closed-end rectangular microchannels asbelow

upopen ueoopenzw;E1 uepzp;E1 (21)

upclosed ueoclosedzw;E2 uepzp;E2 (22)

where E1 and E2 are the electric field applied across theopen- and closed-end channel, respectively.

We define the particle mobility mp measured by microPIVtechnique in an electric field E as

mp upE

(23)

Making use of the results of Eqs. (14), (18), (19), we canfurther rewrite Eqs. (21), (22) in terms of the measuredparticle mobility as

mpopen zwF zpG (24)

mpclosed zwHx zpG (25)

where the expressions for F, H, and G are given by

F ere0m

; G 23f ka e

m(26)



Hx e0erm

1 p2

4

P1m 1

P1n 1

1 mncos amx=Dh 2m 1 2n 1 TmnP1

m 1

P1n 1

12m 1 2 2n 1 2Tmn

2664

3775 (27)

In principle, Eqs. (24), (25) show that if the distributions ofthe particle mobility measured by microPIV in the open-and closed-end channels are known, the zeta potentialsof both the particles and the channel surface can bedetermined simultaneously.

2 Materials and methods

2.1 Measurement cell and materials used

The measurement cell consists of a borosilicate glassmicrochannel (VitroCom), a polymer holder, and tworeservoirs. Such microchannel has a rectangular300 mm6300 mm cross-section and is 4 cm long. Prior toexperiment, the cell was cleaned in an ultrasonic cleanerwith a NaOH base solution and then flushed with deio-nized water. For the closed-end cell, epoxy glue was usedfor sealing the two ends of the channel.

Fluorescent polystyrene particles of radius a = 465 nm(Duke Scientific) were used for tracking the flow. Suchtracer particles have the excitation and emission wave-length of 540 and 610 nm, respectively. In all experiments,the number concentration of tracer particles was ap-proximately about 26109 particles per mL.

A DC electric field was applied using platinum wire elec-trodes inserted into the two reservoirs at the ends of themicrochannel. A high-voltage power supply (PS350,Stanford Research) was used to apply 400 V potentialdifference on the two electrodes, giving rise to a 100 V/cmstrength of the applied DC field.

Three types of working fluids were used including sodiumchloride and boric acid with various concentrations (1022,1023, 1024, and 1025 M) as well as deionized water.

2.2 Experimental setup

The microPIV setup consists of four main components: anillumination system, an optical system, a CCD camera,and a control system. The control system consists of aperipheral component interface (PCI) card, and its corre-sponding software is implemented in a PC. The computercan control and synchronize all actions related to illumi-nation and image recording. The schematic of the setup isillustrated in Fig. 2.

Particles were imaged using an epifluorescent micro-scope (Nikon TE2000-S) and a 206 objective lens with anumerical aperture (NA) of 0.45. An interline transfer CCD

Figure 2. Schematic of the microPIV setup.The PC con-trols and synchronizes the lasers for illumination, CCDcamera for image recording, and high-voltage switch forturning on the high-voltage supply.

camera (Sony ICX 084) was used for recording the ima-ges. The resolution of the camera is 640 pixels6480 pix-els, with 12 bits grayscale. The active area of the CCDsensor is 6.3 mm64.8 mm. The minimum interframetransfer time, and thus the fastest time delay for the twoPIV images, is DtPIV = 500 ns. To ensure that the CCDcamera is working at its optimum temperature of 2157C,a cooling system is integrated in the CCD camera. In themode of double exposure in double frames, the camerarecords two frames of the flow fields and then digitizesthem in the same image buffer.

3 Results and discussion

3.1 MicroPIV images and particle velocity data

Focusing the objective lens on the midplane (i.e., y = 0) ofthe rectangular channel as shown in Fig. 1, we used themicroPIV to measure the particle velocity distributions inboth the open- and closed-end channels. The imagesacquired from microPIV measurements were then eval-uated with PIVview software (PivTec GmbH) to obtain theparticle velocity data. For example, the vector plots of theparticles velocity distributions in deionized water areshown in Fig. 3. Extracting the velocity data and aver-aging the values along the flowing direction, we plot theaveraged velocity values in Fig. 4.

3.2 Least-square analysis

With the experimental data, we can use the least-square analysis to determine the values of the fittedzeta potentials of both the particles and the channel



Figure 3. MicroPIV measurements of the velocity dis-tributions of the 930 nm polystyrene fluorescent tracerparticles in deionized water in (a) an open-end rectan-gular microchannel, and (b) a closed-end rectangularchannel. Channel is made of borosilicate glass and has alength of 4 cm. Both the channel width and height are300 mm (inner dimension). Electric field direction isimposed toward up and has a strength of 100 V/cm.

surface by minimizing the sum of the square of theerrors between the measured and predicted particlemobilities.

Along the lateral (x-axis) direction of the channel, weassume the measured average particles mobility at theith position in the open-end channel as mp-open,i and themeasured average particles mobility at the ith position inthe closed-end channel as mp-closed,i. Applying the least-squaremethod,we introduce the least-square function Sas

S XNi 1

mpclosed;i mpclosed 2h

mpopen;i mpopen 2 (28)

where N is the number of the measured points along thelateral direction of the midplane of the channel. Thus, thebest-fitted values of the two zeta potentials, zw and zp can

Figure 4. Plots for velocity data of the 930 nm poly-styrene fluorescent tracer particles in deionized water in(a) an open-end rectangular microchannel, and (b) aclosed-end rectangular channel. Other parameters arethe same as those specified in Fig. 3.

be obtained by minimizing the value of S. SubstitutingEqs. (24), (25) into Eq. (28), we know that the derivativesof function S with aspect to zw and zp should be equal tozero

qSqzw

XNi 1

2 mpclosed;i mpclosed H xi

2 mpopen; i mopen F 0 (29)

qSqzp

XNi 1

2 mpclosed;i mpclosed G

2 mpopen;i mopen G 0 (30)

Rearranging Eqs. (29), (30) and making use of Eqs. (24),(25), we obtain



zwXNi 1

F H xi zp 2NG

XNi 1

mpopen; i mpclosed; i

(31)

zwXNi 1

F2 H xi 2h i

zpXNi 1

G F H xi

XNi 1

Fmpopen; i H xi mpclosed; i

(32)

It is convenient to express Eqs. (31), (32) in the matrixform

PNi 1

F H xi 2NGPNi 1

F2 H xi 2h i PN

i 1G F H xi

26664

37775

zw

zp

24

35

PNi 1

mpopen;i mpclosed;i

PNi 1

Fmpopen;i H xi mpclosed;i

26664

37775 (33)

Introducing

A PNi 1

F H xi 2NGPNi 1

F2 H xi 2h i PN

i 1G F H xi

26664

37775 (34)

and

B PNi 1

mpopen;i mpclosed;i

PNi 1

Fmpopen;i H xi mpclosed;i

26664

37775 (35)

we get

zwzp

A1B (36)

With the measured data for mp-open,i and mp-closed,i, A and Bare known matrices. Using Eq. (36), we can simulta-neously determine the two zeta potentials of the channelsurface and the tracer particles in deionized water aszw = 262 6 6 mV and zp = 237 6 4 mV, respectively. Fur-thermore, we used the same method to determine thezeta potentials in the sodium chloride and boric acidsolutions with various concentrations. We plot the zetapotential data versus the electrolyte concentration andpresent it in Fig. 5. It is noted that all the zeta potentialsare negative. Furthermore, it can be observed that thehigher the electrolyte concentration, the smaller theabsolute value of zeta potentials will be. This tendency iscommon for the zeta potentials of glass or polymer sur-

Figure 5. Measured zeta potentials versus solution con-centration (mol/L) of the sodium chloride and boric acidelectrolytes for (a) the microchannel surface and (b) thetracer particles.

faces in aqueous solutions such as NaCl. Using thestreaming potential technique, Gu and Li [28] measuredthe zeta potential of glass surface in contact with differentaqueous solutions of various concentrations. For NaClsolutions, they reported the zeta potential values, rangingfrom 220 to 260 mV, which are in good agreement withour data obtained in the present work.

3.3 Measurement errors due to Brownianmotion

In microPIV measurement, the major uncertainty is due tothe Brownian motion of tracer particles. In particular, theBrownian motion plays an important role when submicrontracer particles are used in PIV experiments with flow ve-locities of less than 1 mm/s. According to Einstein [29],the Brownian motion-induced random velocity can beestimated from

uB 2DDtPIV

s(37)



Themass diffusivity of dilute tracer particles suspended inwater is given by the EinsteinStokes equation expressedas [24],

D kT6pma

(38)

Given the tracer particles of a = 465 mm, room tempera-ture T = 298 K and the PIV exposure time DtPIV = 500 ns,the Brownian velocity is estimated as 30 mm/s. As a result,the measurement error due to the Brownian motion,eB : uB/uf is about 3% when the characteristic fluid ve-locity uf is chosen as 1 mm/s.

4 Concluding remarks

Accurate measurement of the zeta potentials of tracerparticles and microchannel surfaces is crucial to under-standing the stability of colloidal suspensions and trans-port of colloidal particles, obtaining microPIV measure-ments of EOF fields, and quantifying the performance ofelectrokinetic microfluidic devices. In this study, we pro-posed a method to simultaneously determine the zetapotentials of the channel surface and the tracer particlesin aqueous solutions. The proposed method uses themicroPIV technique to measure the steady velocity dis-tributions of tracer particles in both open- and closed-endmicrochannels under the same water chemistry condi-tion. As a result, the zeta potentials of the tracer particlesand the channel surfaces can be determined using theleast-square method to fit the microPIV measured veloci-ty distributions of the tracer particles. This method wasimplemented to the open- and closed-end rectangularchannels having 300 mm6300 mm cross-section and4 cm in length under a 100 V/cm applied electric field.Measurements were carried out with a microPIV systemto determine the zeta potentials of the channel surfacesand the fluorescent tracer particles in deionized waterand sodium chloride and boric acid electrolytes of variousconcentrations. The obtained zeta potentials are in rea-sonable agreement with the data reported in the literature.Nonetheless, the proposed method avoids dealing withthe problems associated with the stationary level inmicroelectrophoretic measurements, and allows forsimultaneously determining the zeta potentials of thetracer particles and the microchannel surfaces using themicroPIV technique.

D.G.Y. is grateful for the Postgraduate Student Scholar-ship from Nanyang Technological University.

5 References

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