A Bubble-Free AC Electrokinetic Micropump Using the Asymmetric Capacitance-Modulated Microelectrode Array for Microfluidic Flow Control

38 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 18, NO. 1, FEBRUARY 2009

A Bubble-Free AC Electrokinetic Micropump Usingthe Asymmetric Capacitance-Modulated

Microelectrode Array for Microfluidic Flow ControlChing-Te Kuo and Cheng-Hsien Liu, Member, IEEE, Member, ASME

Abstract—A novel ac electrokinetic micropumping devicebased on ac electro-osmotic flow induced by asymmetricallycapacitance/chemistry-modulated microelectrode arrays has beensuccessfully developed and demonstrated. Asymmetric capaci-tance modulation is made of comb electrode arrays and parts ofindividual electrode surfaces are modulated/deposited with a SiO2

dielectric layer. This proposed design can be utilized to shift theoptimal operation frequency of maximum velocity from tens ofkilohertz to megahertz to minimize electrolytic bubble generationand enhance micropumping performance. The pumping velocity,described in this paper, is measured via the tracing of microbeadsand is a function of applied potential, signal frequency, bufferconcentration, and dielectric layer thickness. A maximum pump-ing velocity up to 290 μm · s−1 in 5-mM buffer solution with theapplied potential of 10 Vpp is observed in our prototype device,and the estimated maximum flow rate is up to 26.1 μl · h−1. Thisis the first successful demonstration regarding bubble-free ac elec-trokinetic micropumping via such an asymmetrically capacitance-modulated electrode arrays. Design, simulation, microfabrication,experimental result, and theoretical model are described in thispaper to characterize and exhibit the performance of proposednovel bubble-free ac electrokinetic micropump. [2008-0030]

Index Terms—Microelectrodes, microelectromechanical de-vices, micropumps, pumps.

I. INTRODUCTION

THE micropump is one of the most important microflu-idic components for the applications of microbiological

and microchemical analysis systems to precisely control thebio/chemical samples in both spatiality and temporality. Anumber of micropumps using different actuation mechanismsand various MEMS technologies have been proposed [1], [2].These proposed micropumps can be divided into two cate-gories: membrane-displacement-based micropumps and field-induced-flow-based micropumps. Compared to membrane-typemicropumps, field-induced-type micropumps have several ad-vantages, including the simple design without the demand of

Manuscript received February 6, 2008; revised August 11, 2008. Firstpublished December 16, 2008; current version published February 4, 2009. Thiswork was supported in part by the National Science Council under Grant NSC-93-2218-E-007-021 and in part by the Nano-technology Research Program ofthe University System of Taiwan. Subject Editor C. Mastrangelo.

C.-T. Kuo is with the Research Center for Applied Sciences, AcademiaSinica, Taipei 30043, Taiwan.

C.-H. Liu is with the Department of Power Mechanical Engineering and theInstitute of Microelectromechanical Systems, National Tsing Hua University,Hsinchu 30043, Taiwan (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JMEMS.2008.2008627

Fig. 1. Depiction of traditional electro-osmotic flow.

moving mechanical parts and the simple fabrication processeswhich allow them to be easily integrated with other microflu-idic components. Besides, most field-induced micropumps canpump the liquids at a wide range of flow rate. Furthermore, incontrast with other types of field-induced micropumps, electro-osmotic micropumps can pump the fluids with a rather widerange of conductivity [3]. However, traditional electro-osmoticmicropumps, shown in Fig. 1, typically require the use ofhigh potential (sometimes > 1 kV) [4] and/or complex channelstructures [5], [6].

In previous research, Ajdari [7] had suggested that an acelectro-osmotic flow (ac EOF) can be driven at a low acpotential without breaking the symmetrical electrode structures.Similarly, the pumping of fluid flow via asymmetric 2-D or 3-Delectrode arrays subjected to low-potential alternating electricfields had been reported with experimental demonstrations[8]–[12]. The pumping mechanism, so-called ac EOF, can beexplained by the interaction of nonuniform electric field withthe ions induced in the electric double layer (EDL) providinga net flow along the electrode surfaces. The advantages of acEOF micropumps include low-potential requirement (an ac po-tential of less than 5 Vrms) [10], simple channel structures, andordinary supporting power system. One practical application ofthe ac EOF micropumps is the on-chip circular chromatographywith the function of separating each biological/chemical samplein a close-loop separation column [13].

When an electric current is sent through the two adjacentmetal electrodes in electrolyte, electrolysis takes place at theinterface between the electrode and electrolyte once the overpotential at the electrodes exceeds 1.23 V for aqueous solution[14]. If the gas molecules produced by electrolysis reach asufficient concentration, bubble nucleation will occur on theelectrode. This usually occurs over a period of several secondsdepending on pH value of liquid and applied current. Hence,

1057-7157/$25.00 © 2008 IEEE

KUO AND LIU: MICROPUMP USING THE ASYMMETRIC CAPACITANCE-MODULATED MICROELECTRODE ARRAY 39

optimal operation frequency of maximum velocity should beshifted to a higher value to overcome the bubble nucleation.Besides ac EOF micropumps described above [8]–[12], othertype of EOF micropumps have also been proposed based onasymmetric electrical signal that can be designed specifically toachieve zero net current flow without gas evolution [15], [16].

In this paper, we focus on the development of a bubble-free ac electrokinetic micropump via the asymmetricallycapacitance-modulated microelectrode arrays. Asymmetric ca-pacitance modulation (ACM) design can enhance the desiredtangential electric field to control the local fluid and drivethe micro-objects. Capacitance modulation is achieved by de-positing SiO2 dielectric layer onto the aluminum microelec-trode arrays, and it helps to decrease the electrolytic bubblegeneration. Experimental results successfully demonstrate theconcept of our proposed novel bubble-free ac electrokineticmicropump. The equivalent circuit model involving the double-layer relaxation effect [17] is exploited to explain the pumpingmechanism. With our proposed designs, this bubble-free acelectrokinetic micropumping device can be precisely integratedwith other microfluidic components on a monolithic chip,leading to great feasibility and functionality for lab-on-a-chipapproach.

II. PRINCIPLE, DESIGN, AND SIMULATION

A. AC EOF

Recent work has shown that the application of an ac potentialto a pair of coplanar microelectrodes generates a steady fluidflow with a velocity depending on both applied potential andfrequency [8]–[10]. The phenomenon is called ac EOF. Thedriving force is the Coulomb force induced by the tangentialcomponent of electric field exerting on the induced charges.Therefore, the EOF velocity can be written as

VEOF =λDρDLEt

η(1)

where λD is the Debye length, ρDL is the induced charges inthe double layer per unit area, Et is the tangential componentof electric field, and η is the viscosity of the liquid. While theproperties of the suspending liquid are homogeneous in thechannel, the value of λDρDL/η in (1) is the same through thischannel. Hence, the EOF velocity can be simplified as

VEOF ∝ Et. (2)

By applying ac potential to the coplanar microelectrodes, thetime-averaged ac EOF velocity using a simple circuit model isgiven by [18], [19]

VacEOF = ΛεLΨ2

0

8ηr

Ω2

(1 + Ω2)2(3)

with the nondimensional frequency Ω given by

Ω =ωCπr

2σ. (4)

Here, εL is the permittivity of the liquid, Ψ0 is the magnitudeof the applied potential, r is the characteristic length of the

electrodes, ω is the applied ac frequency, C is the surfacecapacitance of the double layer, and σ is the conductivity ofthe liquid. The capacitance C is given by ΛCD, where CD

is the surface capacitance of the diffusion double layer. Theparameter Λ is a constant which accounts for the ratio ofvoltage drop across the diffusion layer to that across the totaldouble layer (diffuse plus compact or Stern layers). Thus, theparameter Λ is then given by CS/(CS + CD), where CS is thesurface capacitance of the Stern layer. A bell-shaped profile forthe frequency-dependent velocity is given by (3). The velocityapproaches to zero at both high- and low-frequency limits,and it has a maximum value at an intermediate characteristicfrequency.

Depositing dielectric layers onto the electrode surfaces canbe utilized to shift the optimal operation frequency of maximumac EOF velocity to a higher value [20]. The current–voltagecharacteristics can be approximated to be linear as either the ap-plied potential is small (< 100 mV) or the applied frequency ishigh (> 100 Hz) [16]. In other words, the dielectric modulationonto the electrode surface can be utilized to minimize the gasbubble evolution on the electrode. Based on the considerationaddressed above, the generation of ac EOF via the anisotropicshape of electrode has been presented [8]–[12]. In this paper,it is demonstrated, for the first time, that the asymmetriccapacitance-modulated microelectrode arrays has successfullygiven rise to a net fluidic flow. Through our proposed ACMdesign, not only the optimal frequency of maximum velocitymay be shifted, the tangential electric field can also be enhancedto increase the efficiency of the micropumping.

B. Design Concept and Operational Principle

The ac EOF force, which is generated via the design ofasymmetric capacitance-modulated microelectrode array andhas the features of low actuation voltage and bubble-free pump-ing, is used and developed in this research. The schematicdiagram and chip design are illustrated, as shown in Fig. 2. Themicropumping chip is composed of planar electrodes fabricatedon a silicon substrate. These interdigitated planar electrodes arealso called “comb electrode arrays.” Fig. 2(b) shows a cross-sectional view of one pair of comb electrodes. The width ofelectrode is 100 μm, and the gap between adjacent electrodesis 50 μm. A half of electrode surface is coated with dielec-tric layer, which is called “asymmetrical capacitance/chemistrymodulation.” This modulation can enhance the device perfor-mance by increasing the ac EOF force. This effect results fromthe enhancement of the electric field due to the fact that ACMcannot only enhance but also provide local maximum tangentsof electric fields to drive the fluids via the ac EOF force. Byemploying carefully designed micropumping electrodes, thefield-induced ac EOF force can transport the micro-objects inreal time.

Fig. 3 shows the operation principle of our proposed bubble-free ac electrokinetic micropump. The plus/minus signs on theelectrodes represent positive/negative potentials on the individ-ual electrode. Moreover, the plus/minus signs at both electrodesurfaces and dielectric layers indicate positive/negative ions in-duced in the EDL, respectively. Two out-of-phase ac potentials


Fig. 2. Illustration and design concept of our ac electrokinetic micropumping. (a) Illustrated configuration of the micropumping device. (b) Cross-sectional viewof the electrode structure from A–A′ plotted in (a).

Fig. 3. Schematic diagrams of microelectrode structure and operational principles. These diagrams illustrate the mechanism of ac EOF due to the modulationsof the asymmetric dielectric layer. The plus/minus signs on the electrodes represent the positive/negative applied potential on the individual electrode. Theplus/minus signs at both the electrode surfaces and dielectric layers represent the positive/negative ions induced in the EDL. (a) shows the electric field and chargedistributions due to the applied ac potential. (b) shows the equivalent circuit model. (c) Interaction between the induced charges and the tangential electric fieldscauses a unidirectional net fluid flow. Here, xL = (L + G)/2, and xG = G/2. L and G are the width of the electrode arrays and the gap between the electrodearrays, respectively. R(x), R(xL), and R(xG) are the resistances of the fluid bulk. CL and CR are the capacitances. VL and VR are the voltage drops across theCL and CR, respectively. Et,L and Et,R are the tangential electric fields.

are applied to the adjacent electrode. During the operation,time-varying electric fields are created and liquid becomespolarized in the nonuniform electric fields. Hence, a volume-charge density corresponding to the negative divergence of thepolarization is created. If the distortion of the electric field linesat the edges of electrode is ignored, the electric field lines areapproximately semicircular. As shown in Fig. 3(a), the inducedcharge distribution forms a double layer near the surfaces of thepositive/negative electrodes and dielectric layers. Correspond-

ing to Fig. 3(a), Fig. 3(b) shows an equivalent circuit modelwith capacitance modulation. The characteristic length of theelectrode structure is much longer than the dielectric layerthickness, L/tdie � 1, so the dielectric layer can be consideredas a “thin” layer which can be approximated as a capacitor inseries with the double layer. The EDL and dielectric layer areelectrically equivalent to two capacitors, while the bulk fluid isequivalent to a resistor. The Stern layer within the double layeris neglected here but it could be easily included. The voltage


drop across the equivalent capacitor is a function of positionon the electrode. This variation will give rise to a tangentialelectric field above the EDL. For our proposed ACM design,the apparent voltage drop across the modulated capacitor CR

is larger than that across the unmodulated capacitor CL, i.e.,VR > VL. Consequently, the tangential electric field above theEDL on modulated electrode (Et,R) is larger than the tangentialelectric field above the EDL on unmodulated electrode (Et,L)according to Et = −∇V , where V is the voltage drop. Thecharge density in the EDL on modulated and unmodulated elec-trodes is assumed to be the same due to the same voltage dropacross the capacitor CEDL. Since the EOF velocity dependson the interaction between tangential electric field and inducedcharge density, the instantaneous fluid velocity on modulatedelectrode is larger than that on unmodulated electrode, as shownin Fig. 3(c). In this way, it is implied from the asymmetry ofcapacitance modulation on the electrode array that the timeaverage of the resulting fluid flow is biased in a particulardirection.

There will be an ion current flow parallel to the dielectric andexposed electrode surfaces due to convection. The tangentialconvective current along the modulated electrode surface islarger than that along the unmodulated electrode surface in thesame unit electrode cell due to the voltage difference. The ratiobetween tangential convective and normal ohmic conductioncurrents is on the order of vε/σλD [19]. If the slip velocity vis much smaller than, typically, 10 cm · s−1, this ratio will bemuch smaller than unity [19]. The experimentally measuredmaximum velocity is 290 μm · s−1 for our device (all the detailswill be described later), which is much smaller than 10 cm · s−1.Therefore, the normal ohmic conduction current into the doublelayer is equal to the increase in the stored charges. In otherwords, the double layer forms much more quickly than thetime period for the ion transportation between adjacent unitelectrode cells due to the convection. Hence, we can neglect theion current flow parallel to the dielectric and exposed electrodesurfaces.

The frequency-dependent pumping velocity can be explainedby the equivalent circuit model, as shown in Fig. 3(b). At lowapplied ac frequencies, the capacitors behave like open circuitand the electric field in the fluid bulk approaches zero. At highfrequencies, the capacitors are shorted and whole voltage dropis almost entirely across the fluid bulk to make few inducedcharges. In this way, the pumping velocity will be approxi-mately zero at both low and high frequencies. The characteristicfrequency of maximum EOF velocity can be estimated by theequivalent resistance-capacitance (RC) relaxation frequency ofthe microfluidic driver. The RC relaxation frequency of themicropump with ACM will be larger than that modulated onlyby the capacitance Cdie. Hence, the characteristic frequencyof our microfluidic pump may be tuned to the high frequency(from several hundreds to several MHz). In other words, theelectrolytic bubble due to shifted operation frequency of ourmicrofluidic pump can thus be prevented.

The net fluid flow is dominated by the amplitude of appliedpotential, concentration of fluid bulk, and thickness of dielectriclayer. All related details with experimental results will bedescribed and explained later in this paper.

C. Numerical Simulations

For the feasibility verification of our proposed design, thecommercial finite-element package (FEMLAB) is utilized tosimulate the standard model equations for induced-chargeelectro-osmotic flows in weak electric fields with thin doublelayers [12]. We assume symmetry transverse to the flow direc-tion and thus only simulate 2-D model. The height of the modelis set as 100 μm according to our experimental condition. Weemploy periodic boundary conditions in the pumping direction,so the in-series hydrodynamic resistance outside the channelcan be neglected. First, the electrochemical equivalent-circuitmodel is solved. The bulk fluid is modeled as an Ohmic resis-tance. The double layer and the dielectric layer are modeledas two thin linear capacitors. Once the electrochemical prob-lem is solved, the Helmholtz–Smoluchowski formula is uti-lized to derive the slip velocity, which drives a Stokes flow.Finally, we simulate for the time-averaged flow profiles andflow velocities.

Fig. 4(a) and (b) shows the simulated fluid streamlines ofmicroelectrodes without and with ACM design, respectively. Asshown in Fig. 4(a), the time-averaged fluid streamlines exhibitwell-known counterrotating vortices [18] and a net fluid flowcannot be generated. Fig. 4(b) and (c) shows the simulatedresults with the ACM design of 0.8 μm. The tangential electricfield is nonuniform on the electrode surfaces, thus generate a netfluid flow, driving the micro-objects in a particular direction.The simulation result [Fig. 4(d)] shows that the distributionof Et can be enhanced by our proposed ACM design. Forexample, for the 0.8-μm capacitance modulation, Et on themodulated electrode surface is much larger than that on theexposed electrode surface. Fig. 4(e) shows the potential dropsacross the double layers on the electrodes. The nonuniformpotential drops are due to the nonuniform electric field inducedby the applied ac potential. The potential drop across the doublelayer on the modulated electrode surface is approximatelyequal to that on the unmodulated electrode surface. In otherwords, the surface charge density on the modulated electrodeis approximately equal to that on the unmodulated electrodeaccording to ρDL = CDΔΨ, where ΔΨ is the potential dropacross the double layer. Here, the double layer capacitance,CD = εL/λD, on the modulated electrodes and unmodulatedelectrodes are assumed to be the same. From (2), the EOFvelocity is proportional to tangential electric field. In otherwords, from Figs. 3 and 4, proposed ACM design cannot onlycause a net fluid flow, but also enhance the efficiency of themicrofluidic pump.

III. THEORETICAL ANALYSIS AND MODELING

To further understand the pumping mechanism due to theinteraction of the induced charges and the tangential elec-tric fields, we develop a theoretical model and apply theDebye–Hückel approximation for simplifying the model to geta physical intuition. The following assumptions are made in ourmodel derivation: 1) The microelectrodes are assumed to beideally polarized and the free charges that flow from the elec-trodes to the liquid are neglected. 2) The Debye length (λD),


Fig. 4. Numerical simulations of ac EOF induced by applying the potential of 10 Vpp at 4.5 MHz. (a) shows the simulated time-averaged fluid streamlineswithout any ACM. (b) shows the simulated time-averaged fluid streamlines with the ACM of 0.8 μm. (c) shows the simulated electric fields (gray scale) and flowvelocity vectors (arrow) from (b). (d) Numerical comparison plotted from (a) and (b) on the double layer, respectively, for the magnitude of the tangential electricfield (Et) versus the distance from the electrode structure. (e) shows the potential drop across the double layer versus the distance from the electrode structurefrom (b).

the thickness of the EDL, is much smaller than the electrodedimension. 3) The convection current is assumed to be muchsmaller than the conduction current induced by the applied elec-tric field [21]. 4) The fixed surface potential of the electrodesand the applied ac potential are assumed to be very small.Therefore, we could apply the linear approximation to modelour ac electrokinetic micropump.

In this section, we discuss the frequency-dependent Debyelength first. Then, the equivalent capacitance model for thecapacitance-modulated electrode structure is derived. Finally,we use an equivalent circuit model to analyze our ac electro-kinetic micropump.

A. Frequency-Dependent Debye Length

Due to the ACM design, the shifted characteristic frequencyof maximum velocity may exceed or be in the range of thecharge relaxation frequency. In this condition, the double-layerstructure does not have enough time to build up. The chargerelaxation frequency is defined as the frequency ω with ωτ = 1,where τ = εL/σ is the charge relaxation time. To study the ef-fect of double-layer relaxation and the latter theoretical model,this section starts with introducing the frequency-dependentDebye length.

The electrokinetic equations are a set of partial differentialequations that contain electric potential, ion densities, and fluidvelocity in liquids [17], [21], [22]. The electric potential φ isrelated to the positive and negative ion densities, n+ and n−,by Poisson’s equation

∇2φ =ze(n− − n+)

εL(5)

where z is the valence of ions and e is the electric charge. Thestrong symmetric electrolyte that includes only positive andnegative ions is assumed. The conservation equations for twoion numbers are given by

∂n±

∂t+ ∇ · J± = 0. (6)

The ion density currents J± are

J± = −D

(±zen±

kBT∇φ + ∇n±

)+ n±u (7)

where t is the time, kB is the Boltzmann’s constant, T is theabsolute temperature, D is the diffusion coefficient of ions,and u is the liquid velocity. The diffusion coefficient D isapproximated to 1/κ2τ , where κ is the inverse of Debye length.


Fig. 5. Frequency-dependent Debye length λD(ω) versus nondimensional frequency ωτ . (a) and (b) show the magnitude and phase angle of the frequency-dependent Debye length, respectively, in different buffer concentrations.

The ionic currents, (7), consist of three terms: electric drift,diffusion, and the drift due to the fluidic motion. The lastterm of (7) is the convection current which is neglected forthe following derivation, because the electric Reynolds numberis much smaller than unity. The electric Reynolds number,Rel = εv/lσ, is the ratio of the characteristic times for doublelayer relaxation and for ion transport due to convection [19].For our case, this ratio is much smaller than unity, allowing usto neglect the charge convection term from (7). To describe thelocal ion density variation with frequency, we set the ion densityfunctions as

n±(x, y, t) = n∞ + δn±(x, y, t) (8)

where n∞ is the bulk concentration of ions and δn± is a smallperturbation of liquid concentration due to the applied ac poten-tial. The x/y-directions are defined as the tangential/normal tothe liquid-dielectric layer interface. At a low applied potential,δn+ and δn− have the equal amplitude but 180◦ out of phase,and |δn+ − δn−| < 2n∞ [17]. It also means that δn+ + δn−

may be considered negligible. From (6)–(8), we can obtainthe following equations by utilizing the Fourier transform andallow these to be viewed in the frequency domain:

iωδn+ = D

[∇2δn++

ze

kBT((n∞+δn+)∇2φ+∇δn+ ·∇φ

)](9)

iωδn−= D

[∇2δn−− ze

kBT((n∞+δn−)∇2φ+∇δn−·∇φ

)].

(10)

By introducing the parameter n = δn+ − δn−, (9) and (10) canbe simplified as

iωn = D

[∇2n +

2zen∞kBT

∇2φ

](11)

where we neglect the term of δn+ + δn−. By plugging thePoisson’s equation, (5), into (11), we have

∂2n

∂y2+ Δ2 ∂2n

∂x2= κ2n(1 + iωτ). (12)

The parameter Δ is defined as the ratio of the system’s char-acteristic length and the Debye length, and it is also definedas another notation in Gonzalez et al. [21] research work. This

allows the thin double-layer approximation Δ � 1 to be used[21]. The inverse of Debye length κ is given by [22]

κ2 =2z2e2n∞εLkBT

. (13)

The following simplification is valid if Δ � 1:

∂2n

∂y2= k2n(1 + iωτ). (14)

The boundary conditions are n = 0 and ∂n/∂y = 0 as y → ∞.The solution of (14) is

n = Ae−κ(ω)y (15)

where A is the integration constant and the inverse offrequency-dependent Debye length κ(ω) is a function of fre-quency, which is described as

κ(ω) = κ√

1 + iωτ . (16)

Consequently, the frequency-dependent Debye length is thengiven by

λD(ω) =1

κ(ω)=

λD√1 + iωτ

. (17)

In Fig. 5, the frequency-dependent Debye length λD(ω) isshown as functions of nondimensional frequency ωτ withdifferent buffer concentrations. The parameters that are usedin (17) for the simulation shown in Fig. 5, are z = 1, e =1.602 × 10−19 C, εL = 40 ε0, ε0 = 8.85 × 10−12 F · m−1,kB = 1.38 × 10−23 N · m · K−1, and T = 300 K. The increaseof buffer concentration results in a decrease on the magnitudeof the frequency-dependent Debye length but has no effecton the phase angle. As shown in Fig. 5, when ω � τ , theeffect of double-layer relaxation could be neglected and themagnitude of Debye length keeps constant, i.e., λD(ω) ≈ λD,which agrees with the static double layer structure.

B. Equivalent Capacitance Model Involving theDouble-Layer Relaxation

Fig. 6(a) shows a capacitance-modulated electrode structurewith notation definition. The capacitance outside the EDL ismuch small, and we neglect it in this model. The relationship


Fig. 6. Capacitance-modulated/SiO2-deposited electrode structure with nota-tion definition.

between the potential drop across the system and the accumu-lated charges in the liquid is modeled as

∞∫0

ze(n+ − n−)dy ≡ CEDL [φ(x, 0) − φ(x,∞)]

≡ Csum [φ(x,−tdie) − φ(x,∞)] (18)

where Csum is the equivalent surface capacitance across theEDL and the dielectric layer, and tdie is the thickness of di-electric layer. It is not clear so far how the capacitances of Sternlayer and diffusion layer in the EDL might combine. Besides,there is no model that satisfactorily predicts the nature of Sternlayer as it depends on the ion species, electrode material andapplied potential [8]. In the following derivation, we assumethat all the ions in EDL are mobile, and we neglect the Sternlayer to simplify our theoretical analysis. For a symmetric andbinary electrolyte, the classical Gouy–Chapman theory yieldsa simple form for the charge-potential model of EDL [23]. Bydifferentiating this form, the capacitance of EDL is given by

CEDL(ζ) =εL

λD(ω)cosh

(zeζ

2kBT

)(19)

where ζ is the potential drop across the double layer inthermal equilibrium. According to Debye–Hückel limit, i.e.,ζ � kBT/ze, the surface capacitance of double layer can beapproximated as

CEDL =εL

λD(ω). (20)

As y → ∞, the electric field vanishes, i.e., φ(x,∞) → 0. Thus,by plugging (15) into (18), the potential φ(x,−tdie) can berepresented as

φ(x,−tdie) =1

Csum

zeA

κ(ω). (21)

Since the charge injection is neglected, the normal componentsof the ion density currents vanish at the interface between theliquid and the dielectric layer, i.e., at y = 0, and they can berepresented as

n · J±|y=0 = ∓zen±

kBT∂φ

∂y

∣∣∣∣y=0

− ∂n±

∂y

∣∣∣∣y=0

= 0. (22)

From (8), (15), and (22), we can obtain the following equation:

∂φ(x, 0)∂y

=zeA

κ2εLκ(ω). (23)

According to Gauss’s law, the electric displacement D above(D⊥

L) and below (D⊥die) the liquid-dielectric layer interface are

equal if there are no real charges at the interface [24]

D⊥L − D⊥

die = εLE⊥L − εdieE

⊥die = 0 (24)

where εdie is the permittivity of the dielectric layer. Accordingto (23), (24) can be reduced to

εLzeA

κ2εLκ(ω) = εdie

[φ(x,−tdie) − φ(x, 0)]tdie

. (25)

By rearranging (25), we have

φ(x, 0) = φ(x,−tdie) −zeA

κ2

tdie

εdieκ(ω). (26)

From (18), (21), and (26), the inverse of equivalent capacitanceC−1

sum can be represented as

C−1sum = C−1

EDL + (1 + iωτ)C−1die (27)

where Cdie is given by Cdie = εdie/tdie. When the double-layerrelaxation is much faster than the applied ac frequency, i.e.,ω � τ , the effect of double-layer relaxation can be neglectedand the equivalent capacitance is approximated to the in-seriescapacitance of both the EDL and the dielectric layer.

C. Equivalent Circuit Model

Fig. 3(a) shows one unit cell of our ac electrokinetic micro-pump for the model analysis. When an ac potential is appliedto the electrodes, an electric field will be induced in the liquid.Above the surfaces of electrode and dielectric layer, the EDL iselectrically equivalent to a capacitor. If the distortion of electricfield lines at the edges of electrodes is ignored, the electricfield lines are approximately semicircular. In our equivalentcircuit model, we also neglect the capacitance between theadjacent electrodes because of the smaller value compared withother equivalent capacitors. Besides, indeed, the time-averagedinteraction forces on the dielectric gap approximate to zeroand can be neglected. If we model the buffer solution as anindividual electric channel [with the resistance R(x)] in parallelto the electric field, the lumped equivalent circuit model of ourac electrokinetic micropumping is shown in Fig. 3(b).

The equivalent resistance R(x) is approximated as R(x) ≈πx/σ. As shown in Fig. 3(b), two capacitors (CEDL and Cdie)are in series and notated as CR. The in-series capacitance CR,relating the double-layer relaxation has been addressed as(27). Along the unmodulated electrode surface, the capaci-tance is dominated by CEDL. With the applied potential Ψ =Ψ0 exp(iωt), the voltage drop across the EDL above the un-modulated electrode surface VL is given by

VL = Ψ − IR − I

iωCR

= ΨλD(ω)

[2 + δD(ω)] λD(ω) + iωτπx(28)


where δD(ω) = δD(1 + iωτ)3/2 and δD = εLtdie/εdieλD. Ψ0

is the amplitude of applied potential, and I is the electric currentthrough the individual electric channel. The voltage drop acrossthe modulated capacitance CR, VR, is given by

VR = Ψ − IR − I

iωCL

= Ψ[1 + δD(ω)] λD(ω)

[2 + δD(ω)] λD(ω) + iωτπx. (29)

The tangential electric field Et,L and Et,R are given, respec-tively, by

Et,L = − dVL

dx= Φ

iωτπλD(ω){[2 + δD(ω)] λD(ω) + iωτπx}2 (30)

Et,R = − dVR

dx= Φ

iωτπ [1 + δD(ω)] λD(ω){[2 + δD(ω)] λD(ω) + iωτπx}2 . (31)

The slip velocity v is determined based on the condition that theviscous drag across the double layer is equal to the electrostaticforce and is given by

vL,R =λD(ω)σ±

DEtL,R

η. (32)

Here, the surface charge density σ±D is given by σ±

D =±εLΦEDL/λD(ω). If the properties of buffer solution areconsistent during the pumping operation, the surface chargedensity is proportional to VL. In other words, the surface chargedensity is assumed the same on the modulated and unmodulatedelectrode surfaces to simplify the theoretical derivation. Thus,the time-averaged ac EOF velocities, denoted as 〈v〉L and 〈v〉R,are given by

〈v〉L =12Re

{λD(ω)σ−

DE∗t,L

η

}

= − εLΨ20

2η

(ωτ)2 |λD(ω)|2 (πλD + π2x)|[2 + δD(ω)] λD(ω) + iωτπx|4

(33)

〈v〉R =12Re

{λD(ω)σ+

DE∗t,R

η

}

=εLΨ2

0

2η

(ωτ)2 |λD(ω)|2 (πλD + π2x)Re [1 + δD(ω)]|[2 + δD(ω)] λD(ω) + iωτπx|4

.

(34)

The notation “∗” represents the complex conjugate. Accordingto our assumption described before, the Debye length is muchsmaller than the electrode dimension, i.e., π2x � πλD, (33)and (34) can be simplified as

〈v〉L = − εLΨ20

2ηx

(ωτπx)2 |λD(ω)|2

|[2 + δD(ω)] λD(ω) + iωτπx|4(35)

〈v〉R =εLΨ2

0

2ηx

(ωτπx)2 |λD(ω)|2 Re [1 + δD(ω)]|[2 + δD(ω)] λD(ω) + iωτπx|4

. (36)

If we neglect the double-layer relaxation and there is no ca-pacitance modulation on the electrode surface, i.e., ω � τ andδD = 0, (35) and (36) can be simplified as

〈v〉L,R = ∓εLΨ20

8ηx

(ωτπx/2λD)2[1 + (ωτπx/2λD)2

]2 (37)

which agrees with the result reported by Ramos et al. [18].The total net slip velocity can be obtained by integrating the

time-averaged ac EOF velocities along the electrode surfaces,and it is given by

〈v〉total =

∫ xL

−xL(〈v〉L + 〈v〉R) dx

2xL

=

∫ −xG

−xL(〈v〉L) dx +

∫ xL

xG(〈v〉R) dx

2xL

=εLΨ2

0

8ηxL

f21

(xL

xG− xG

xL

)|λD(ω)|2 Re [δD(ω)]∣∣∣ f2

xL+ i · f1

∣∣∣2 ∣∣∣ f2xG

+ i · f1

∣∣∣2 (38)

where f1 = ωτπ√

xLxG and f2 = [2 + δD(ω)]λD(ω)√

xLxG.In principle, (38) can be modified and is compatible with theequation derived by Brown et al. [8] by neglecting the double-layer relaxation, i.e., λD(ω) ≈ λD and δD(ω) ≈ δD. Anotherimportant approach is the pumping flow rate. From Fig. 4(b)and (c), there are vortexes above the electrode surfaces, whichhave smaller velocity comparing with the slip velocity. Ne-glecting the flow profile in the double layer and the influenceof vortexes, the flow induced by ac EOF can be consideredequivalent to the Couette flow [25] driven by the average slipvelocity on the bottom wall. Assuming that the back pressure isnegligible, the mean pumping flow rate can be given by Qm =〈v〉totalWH/2, where W and H are the width and height of thechannel, respectively.

Fig. 7(a) and (b) shows the simulated results which are basedon (38) with different electrode dimensions. The pumpingvelocity has a maximum value at the frequency ωc = (2 +δD)λD/τπ

√xLxG when we neglect the double-layer relax-

ation. Fig. 7(a) and (b) shows that the larger electrode dimen-sions lead the characteristic frequency to be much smaller thanthe double-layer relaxation frequency. The double-layer relax-ation gets more dominant when the micropumping electrodesget more miniaturized. Similarly, Fig. 7(c) and (d) shows thatthe two curves converge when the permittivity of dielectriclayer gets increased. This is equivalent to increase the capac-itance of dielectric layer, to reduce the magnitude of δD orto reduce the thickness of dielectric layer. The characteristicfrequency of (38) that involves the double-layer relaxationnever exceeds the double-layer relaxation frequency. As shownin Fig. 7, these curves converge as ωcτ � 1. If the conditionωcτ � 1 is not fulfilled, the double-layer relaxation will pre-dominate our pumping performance. In other words, (38) whichinvolves the double-layer relaxation can be more appropriateto describe the pumping mechanism like our proposed micro-pumping design for the general case.


Fig. 7. Simulated ac EOF velocity versus the nondimensional frequency ωτ , which is based on our theoretical model as summarized in (38). (a) and(b) show the simulated results in different electrode dimensions. These parameters used for the simulations are the following: εL = 80 ε0, εdie = 4 ε0, ε0 =8.85 × 10−12 F · m−1, η = 10−3 kg · m−1 · s−1, Ψ0 = 4 Vpp, tdie = 0.8 μm, λD = 70 nm, and σ = 0.073 S · m−1. (c) and (d) show the simulated resultsfor different dielectric materials. These parameters used for the simulations are the following: L = 10 μm, G = 5 μm, εL = 40 ε0, ε0 = 8.85 × 10−12 F · m−1,η = 10−3 kg · m−1 · s−1, Ψ0 = 4 Vpp, tdie = 0.8 μm, λD = 70 nm, and σ = 0.073 S · m−1.

Fig. 8. Microfabrication process of our ac electrokinetic micropumping de-vice and the finally fabricated microelectrodes. (a) SU-8 negative photoresist isused to define microchannel (100-μm height and 500-μm width). (b) PDMSis micromolded to serve as a transparent top cover. (c) PDMS top coveris drilled to obtain the access holes for the fluidic inlet/outlet connections.(d) Comb electrode arrays are microfabricated on the silicon substrate. (e) SiO2

dielectric layer is asymmetrically deposited onto the electrode surfaces as thesurface modulation. (f) Plasma treatment is applied on the PDMS mold. Thesilicon substrate is bonded to the PDMS top cover. (g) Picture of the finallyfabricated comb electrode arrays.

IV. MICROFABRICATION AND MATERIAL PREPARATION

A. Microfabrication Process

As shown in Fig. 8, the proposed microfluidic pump is im-plemented on our micromachined prototype chip, using MEMSmicrofabrication technology. Silicon substrate was first pre-pared by utilizing piranha clean technique. The microchannel

with 100-μm height and 500-μm width was defined by usingSU-8 negative photoresist [Fig. 8(a)]. After elastomer base andcuring agent of Polydimethylsiloxane (PDMS, sylgard 184,Dow Corning, MI) were mixed together (10 : 1), the mixturewas then poured onto the silicon-PR mold prior to a degassingstep and later cured at 90 ◦C for 1 h [Fig. 8(b)]. Afterward,holes of 1 mm were mechanically drilled through the curedand detached PDMS top cover, acting as fluidic inlet/outletconnections [Fig. 8(c)]. Thermal oxide was grown onto a siliconsubstrate as an insulator to prevent ac potential from crosstalk.The micropumping electrodes were then microfabricated on thesilicon substrate using metal evaporation and lift-off processes[Fig. 8(d)]. The ACM is first achieved by plasma-enhancedchemical vapor deposition process to deposit SiO2 dielectriclayer onto electrode surfaces, then by reactive ion etchingprocess to define the asymmetric pattern [Fig. 8(e)]. After oxy-gen plasma treatment on both silicon substrate and PDMS topcover, two parts were aligned and bonded together [Fig. 8(f)].Last, plastic tubes were connected to the sample inlet andoutlet from drilled holes. Micropumping electrodes were finallyfabricated, as shown in Fig. 8(g).

B. Sample Preparation

Regarded as representative tracing targets, latex beads of1-μm diameter were utilized to demonstrate the ac electroki-netic microfluidic pumping. The latex beads used were polysty-rene monodisperse microspheres (Polysciences, Warringgton,


Fig. 9. Schematic diagram of the experimental setup and the comb microelec-trode arrays. Microparticles of 1 μm are placed in the testing liquid to help thevisualized flow velocity measurements.

PA, USA). These beads were suspended in the aqueous solu-tion, where its concentration was adjusted to 5, 10, and 20 mM,respectively, in accordance with the varied sodium phosphatebuffer (NaH2PO4, pH = 3.6).

C. Experimental Setup

The experimental setup to characterize our micropumpingperformance is schematically shown in Fig. 9. The microelec-trodes were driven by using a waveform generator (Aglient33120A) which provides the sinusoidal wave excitation up to15 MHz and 10 V peak to peak. An oscilloscope (54624A,4-channel, 100 MHz Oscilloscope, Aglient Technologies) wasutilized to verify the input signal. Both motions and displace-ments of Latex beads were monitored using microscope (20X,NA = 0.4, M Plan Apo Series, Mitutoyo Corporation) withhigh-magnification zoom lens (Zoom 6000, Navitar Inc.). Afterfocusing onto the dielectric layer surface, only beads within thedepth of field, less than 1 μm, can be observed. The images andmovies were captured and recorded by a digital charge-coupleddevice camera connected to a computer. The averaged pumpingvelocity was calculated by measuring the total distance threebeads has traveled as tracked from the digital movie and divid-ing it by the number of beads and the time interval betweendigital movie frames.

V. RESULTS AND DISCUSSION

A. Experimental Results

When an ac potential is applied to the microelectrodes, theflow direction of tracing microbeads is observed from modu-lated electrode surface to unmodulated electrode surface. Thisobserved result is in agreement with our theoretical predictionas shown in Fig. 3. Several sequential images about the move-ment of microbeads are recoded. Fig. 10 shows two sequentialpictures taken in the period of 6 s, and the microbeads aremarked in the pictures for the purpose of easy visualization.The applied ac potential is 8 Vpp at 3 MHz in a 10-mM buffersolution. The averaged pumping velocity is estimated around10.3 μm · s−1 in this case. To further verify the accuracy ofour proposed theoretical prediction and the driving mechanism

Fig. 10. Two sequential pictures taken in 6 s are used to trace the microbeadswith a potential of 8 Vpp at an excitation frequency of 3 MHz in a 10-mMbuffer solution.

Fig. 11. Consecutive pictures snapped form the video showing the experimen-tal results for the fluid motion demonstration. The applied potential is 10 Vppat an excitation frequency of 5 MHz in a 20-mM buffer solution.

of the bead’s transportation in our device, the following ex-periments and observation are performed. A test micropumpchip with nonperfect parallel electrodes was utilized to observewhether the dielectrophoresis (DEP) force or the ac electroki-netic force dominates the transportation of microbeads. Fig. 11shows the six sequential pictures taken in 16 s. The individualtracing microbeads are moved from the upstream section, wherethe influence of electric-field-induced DEP force is much small,to the downstream active pumping section. If the driving forceresults from DEP force, the microbeads should be either trappedat the highest electric-field-gradient section (positive DEP) orrepelled to the lowest electric-field-gradient section (negativeDEP). The experimental results prove that the DEP force isnot the driving force for the transportation of microbeads.Besides, as the beads are charged, they will experience theelectrophoresis force. However, as long as the experimentaltime is long enough compared with the period of the appliedpotential, this net electrophoresis force will average to zeroand have no net driving effect under an ac driving potential.


Fig. 12. Micropumping velocity measurements. (a) and (b) show the fluidicvelocity versus the applied ac potential varying from 1 to 10 MHz at differentapplied potential amplitudes (4, 6, 8, and 10 Vpp). The pumping liquid isNaH2PO4 buffer solution with concentrations of 10 mM [(a)] and 5 mM [(b)],respectively. The thickness of modulated layer (SiO2) above the electrodes is0.8 μm.

Therefore, we conclude that the microbeads are driven by theac electrokinetic micropump instead of either DEP or electro-phoresis. We assume that the microbeads move with the fluid torepresent the velocity of the fluid motion.

A series of similar experiments are carried out as well to mea-sure the frequency-dependent pumping velocity under differentpotential magnitudes and buffer concentrations. The pumpingliquids are NaH2PO4 buffer solutions with concentrations of10 mM [Fig. 12(a)] and 5 mM [Fig. 12(b)], and the character-ized conductivities are 0.145 and 0.073 S · m−1, respectively.Fig. 12(a) and (b) shows that the pumping velocity approximatezero at low-and high-frequency limits. The maximum pumpingvelocity, which depends on the buffer concentration and thepeak-to-peak ac applied potential, will appear at the character-istic frequency. For this case, the buffer solution with a lowermolal concentration has a higher pumping velocity. For eachbuffer solution, there is no obvious trend for the characteristicfrequency of maximum pumping velocity versus peak-to-peakac applied potential in these experimental observations. Themaximum observed pumping velocity is up to 290 μm · s−1 at10 Vpp 4.5 MHz in 5-mM buffer solution, and the estimatedmaximum flow rate is up to 26.1 μl · h−1.

Fig. 13 shows the measurement result for the micropumpingvelocity with different thickness of dielectric layer (0.8 and1.2 μm). The applied signal frequency is varied from 10 kHzto 15 MHz with the applied potential of 8 Vpp. The buffer

Fig. 13. Measurements for the ac EOF velocity with different thicknessesof dielectric layer (0.8 and 1.2 μm). The pumping liquid is NaH2PO4 buffersolution with a concentration of 20 mM.

Fig. 14. Experimental results for the pumping velocity versus the frequencyat the applied potential of 10 Vpp in the buffer solutions of 10 and 5 mM areplotted as -�- and -•-, respectively. The simulated curves are plotted from (38)for (black line) 10-mM buffer solution and (gray line) 5-mM buffer solution,respectively.

concentration is 20 mM (with a characterized conductivity of0.29 S · m−1). As shown in Fig. 13, the characteristic frequencyof maximum velocity is varied with the thickness of dielectriclayer. Measured characteristic frequencies of maximum veloc-ity with the dielectric-layer thickness of 0.8 and 1.2 μm are6 and 7.5 MHz, respectively. Larger thickness of dielectric layerresults in higher characteristic frequency but lower pumpingvelocity.

B. Theoretical Prediction and Experimental Result

Fig. 14 shows the comparison of the theoretical model [(38)]with the experimental result [Fig. 12] at an applied potentialof 10 Vpp. The parameters used for the theoretical modelare based on our device design and experimental material asfollows: εL = 80ε0, εdie = 3.8ε0, ε0 = 8.85 × 10−12 F · m−1,η = 10−3 kg · m−1 · s−1, Ψ0 = 10 Vpp, tdie = 0.8 μm, L =100 μm, and G = 50 μm. As shown in Fig. 14, the trends aresimilar but do not exactly match between the simulated and theexperimental results. Both simulated and experimental resultsshow that the buffer concentration increases with increasingoptimal frequency of maximum velocity but with decreasingpumping velocity, and they tend to have a minimum value atthe highest and lowest frequency limits.


TABLE ITHEORETICAL PREDICTION AND EXPERIMENTAL RESULT

Table I shows the comparison of theoretical predictions andexperimental results from Fig. 14. As shown in Table I, thereare some differences between theoretical predictions and exper-imental results. The buffer solution of the lowest concentrationhas a frequency of maximum velocity closer to the doublelayer relaxation frequency (σ/εL). As the buffer concentrationincreases, the experimentally measured frequency of maximumvelocity will approach to frequency predicted by theory, whiledistant from double layer relaxation frequency. The frequen-cies of measured maximum velocity are higher than predictedvalues, and the difference between experimental and predictedvalues gets smaller as the buffer concentration increases. Thesimilar phenomena have also been observed and reported byother research groups [26]. This discrepancy of conductivity ata high applied potential may be an important factor. Practically,the salt concentration near the electrode surface may be sig-nificantly higher than that in the bulk fluid under high appliedpotential. In other words, the conductivity above electrodesurface may be higher than the measured bulk conductivity,and the variation in surface conductivity tends to increase withdecreasing ionic concentration [26]. This conductivity discrep-ancy will lead to lower measured pumping velocity, which islower than the predicted value; however, optimal frequency ofmaximum velocity is higher than the predicted value. Moreover,the discrepancy of conductivity also greatly affects DEP [27].

The tangential ohmic current flux along the double layeron the unmodulated electrodes is negligible because it is ofthe order of λD/l times the normal current flux, where l is atypical distance of the system [19]. For the experimental setupdescribed in this paper, l is approximately 1000 times greaterthan λD. If the ohmic current induced by the system is denotedas I , the tangential ohmic current It_un along the double layeron the unmodulated electrode from calculation is about 10−3Iand the normal ohmic current In_un is approximately equal toI . The ratio between It_un and In_un is much smaller thanunity. Therefore, the current into an element of the doublelayer on the unmodulated electrode is equal to the increase inthe stored charges. Along the double layer on the modulatedelectrodes, a similar condition holds; however, in this case,the tangential ohmic current It is approximated to δDIt_un ≈0.2286I , and the normal ohmic current In is calculated as0.9735I . The ratio between It and In is not much smaller thanunity. Hence, the current into the double layer of the modulatedelectrode is not equal to the increase in the stored charges.However, it contributes a larger tangential electric field on themodulated electrode than that on the unmodulated electrode inan adjacent electrode cell. Therefore, the “loss” stored chargesin the double layer on the modulated electrodes may account

for some discrepancy between the experimental result and thetheoretical prediction.

In addition, the deviation between the experimental resultand theoretical prediction also results from the following prac-tical implementations. First, our PDMS microchannel consistsof a passive section (inlet/outlet static section) in series with anactive section (the “flow generator”). A simple analysis in termsof equivalent circuits is shown that the mean pumping velocityis equal to the intrinsic pumping velocity multiplying the ratioof active hydraulic resistance to total hydraulic resistance ofthe microchannel. For our experimental device, the ratio isestimated to be 67%, which is in a reasonable range comparingto the predicted and measured results from Table I. Second,the tracing Latex microbeads of 1 μm may distort the electricfield induced by the applied ac potential, and the transporta-tion of microbeads induced by the ac EOF may be sloweddown due to DEP force. The ratio of ac EOF to DEP veloc-ity mentioned here could be represented by (VEOF/VDEP) =3.33 Λ(r/a)2[1/(1 + Ω2)], where a is the radius of tracingparticles [19]. The maximum ac EOF velocity is obtainedat Ω = 1. Therefore, the ratio of maximum ac EOF to DEPvelocity could be given by (VEOF/VDEP) ≈ 1.67 Λ(r/a)2. Forour experimental case, the ratios are about 33.87 for 5-mMbuffer solution and 24 for 10-mM buffer solution. From Table I,the estimated maximum DEP velocities are 13.79 μm · s−1 for5-mM buffer solution and 13.89 μm · s−1 for 10-mM buffersolution. In this condition, relatively small-sized beads can bechosen to minimize the effect of DEP on these experiments.Third, the electric field line is, in fact, not a perfect semicirclebecause the enhancement of electric field occurs at the edgeof electrodes, resulting in the distortion of the applied electricfield. Fourth, the measurements presented in this paper areperformed close to the surface-liquid interface, and the beadmovement is observed within 1-μm depth of field; hence, thevariation of fluid flow in the vertical direction can accountfor some of the discrepancy. In this condition, the microscopewith larger numerical aperture can be applied to decrease thediscrepancy. All of these actions make it difficult for theoreticalprediction to fully match the experimental result. However, theorder between predicted and experimental results is within areasonable agreement and it is also sufficient for theoreticalprediction to fully explain the operational mechanism for ourac electrokinetic microfluidic pump.

Fig. 15 shows the maximum pumping velocity versus thefactors δD and L/G, respectively. The solution concentration ischosen as 20 mM. The maximum velocity appears at δD = 3.06[Fig. 15(a)] and at L/G = 1.7 and 1.9 [Fig. 15(b)]. In otherwords, the maximum pumping velocity can be approachedby the proper design with the optimal factors δD and L/G.The increase of δD is equivalent to increase the thickness ordecrease the permittivity of dielectric layer. Thus, the measuredpumping velocity, as shown in Fig. 13, confirms the predictionin Fig. 15(a) that the pumping velocity decreases when δD >3.06 and the thickness of dielectric layer increases.

The fluid flow described in this paper cannot be explainedin terms of the electrothermal effect resulting from heatingof the fluid by the electric field [28]. The magnitude of theelectrothermal velocity should increase with conductivity or


Fig. 15. Simulated maximum pumping velocities are plotted in (a) and (b) versus the factor δD, where δD = εLtdie/εdieλD, and the factor L/G, respec-tively. These parameters used for the two simulations are the following: εL = 80 ε0, εdie = 3.8 ε0, ε0 = 8.85 × 10−12 F · m−1, η = 10−3 kg · m−1 · s−1,Ψ0 = 8 Vpp, buffer concentration = 20 mM, σ = 0.29 S · m−1. L = 100 μm, G = 50 μm, and tdie = 0 ∼ 1.2 μm are chosen in (a). L/G = 0 ∼ 6 arechosen in (b).

molal concentration; however, the observed fluid flow velocitydecreases instead. The frequency at which the relaxation occursdepends on two mechanisms [17], [26]. First, as shown inFig. 3(b), there is an RC relaxation due to the resistanceof the fluid bulk between in-series capacitance of the EDLand the dielectric layer. This relaxation results in an increasein the magnitude of tangential electric field at high frequen-cies. Therefore, a fluid flow at high frequencies is introduced.Second, the EDL has a charge relaxation time τ = εL/σ. TheEDL relaxation implies that the induced charges do not haveenough time to build up the EDL structure as the appliedfrequency approaches this relaxation frequency. The EDL re-laxation should only be taken into account if the RC relaxationfrequency is greater than the EDL relaxation frequency or ofthe same order with it. As shown in Table I, measured optimalfrequencies of maximum velocity are lower than the estimatedEDL relaxation frequencies. Consequently, the EDL relaxationeffect on our device could be ignored. For our experimentalconditions, ωcτ is equal to 0.274 and 0.169 for 5- and 10-mMbuffer solutions, respectively. In our prototype device, ωcτ isnot much larger than one. However, the double-layer relax-ation still has a dominant influence when we optimize themicropumping design by miniaturizing the electrode dimensionor reducing the thickness of dielectric layer. Therefore, thetheoretical model involving double-layer relaxation is sufficientto explain the micropumping mechanism for our proposed acelectrokinetic microfluidic pump case by case.

In order to improve our device, we propose the followingmodifications to enhance the micropumping performance:

1) decreasing the gap between the adjacent electrodes;2) adding a second electrode array on the top cover;3) decreasing the width of electrode;4) either decreasing the thickness of dielectric layer or in-

creasing the permittivity of dielectric layer to approachδD = 3.06;

5) changing the electrode material. For an example, golddoes not form an oxide layer in the buffer solution thatwill increase the surface capacitance [8] and decreasethe voltage drop across the solution to reduce the micro-pumping velocity.

C. Electrolysis

In our experimental results, no electrolytic bubble is ob-served at the characteristic frequency of maximum pumpingvelocity under the applied potential even up to 10 Vpp. Ourmeasured characteristic frequency of maximum pumping ve-locity in 5-mM buffer solution is 4.5 MHz, which is highenough to prevent electrolytic gas bubbles from occurrence.When the applied frequency is decreased to about 1 kHz, thebubbles will be generated rapidly and deteriorate the fluid flow.In several kilohertz frequency range, the electrolytic bubblestend to occur in other ac electrokinetic micropumps [13]. Basedon theoretical prediction and experimental observation, ourproposed ac electrokinetic microfluidic pump via the asymmet-rically capacitance-modulated microelectrodes can effectivelyprevent the occurrence of electrolytic bubble.

VI. CONCLUSION

We have successfully demonstrated the feasibility of pro-posed ac electrokinetic microfluidic pump via the asym-metrically capacitance-modulated microelectrode arrays. Themaximum pumping velocity at the applied potential of 10 Vppin 5-mM buffer solution can reach 290 μm · s−1, and theestimated flow rate is up to 26.1 μl · h−1. The phenomenon ofelectrolytic gas bubble does not appear at the characteristic fre-quency of maximum velocity during long-term observation. Anequivalent circuit model involving the double-layer relaxationeffect mentioned in this paper offers a good insight on the op-erational mechanism of our microfluidic pump. The deviationsbetween theoretical predictions and experimental results maybe resulted from nonlinear effects, experimental uncertainties,and device variations. In this paper, some improvements areproposed to counter against this discrepancy. It should alsobe noted that the charge injection from the electrodes andthe nonlinear double layer structure should be considered at ahigher applied potential. Furthermore, other coupling effects,such as electrothermal flow induced by Joule heating, may alsobe taken into consideration. Our proposed bubble-free ac elec-trokinetic microfluidic pump has the advantages of simple in-tegration and low required applied potential. The phenomenon


of electrolysis can be effectively prevented by particular ACMdesign. The micropumping efficiency also increases with deviceminiaturization but has an upper limit constraint by double-layer relaxation. The micropumping prototype presented inthis paper is not optimally design but a suited prototype fordemonstrating the micropumping mechanism. This proposedmicrofluidic pump is suitable for the applications of lab-on-a-chip and can easily be integrated with other microfluidiccomponents for a feasible micrototal analysis system.

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Ching-Te Kuo received the B.S. degree in mechani-cal and electromechanical engineering from NationalSun Yat-sen University, Kaohsiung, Taiwan, in 2003,and the M.S. degree in power mechanical engineer-ing from National Tsing Hua University, Hsinchu,Taiwan, in 2005. He is currently working toward thePh.D. degree at National Taiwan University, Taipei,Taiwan.

He was a Research Assistant with the ResearchCenter for Applied Sciences, Academia Sinica,Taipei. His research interests include electrokinetics,

microfluidic MEMS, and system control engineering.

Cheng-Hsien Liu (M’02) received the B.S. degreein power mechanical engineering from NationalTsing-Hua University, Hsinchu, Taiwan, in 1987,the M.S. degree in mechanical engineering fromLehigh University, Bethlehem, PA, in 1992, andthe M.S. degree in electrical engineering andthe Ph.D. degree in mechanical engineering fromStanford University, Stanford, CA, in 1995 and 2000,respectively.

In 1999–2000, he was a Senior Electrical Engi-neer with Halo Data Devices, Inc., San Jose, CA,

where he focused on the development of microdrives for portable informationstorage applications. While at Stanford, he worked with Dr. Kenny in theStanford Microstructures and Sensors Laboratory and focused his Ph.D. workon high-performance tunneling MEMS sensors. He currently oversees graduatestudents in the Micro-Systems and Control Laboratory, research activities ofwhich cover a variety of areas such as biomimetic array chips for bio-objectmanipulation targeting for tissue engineering/drug screening applications, BioLab on a chip, biomedical instruments, microphotonics, and advanced tunableMEMS gratings for optical communication applications, and microsystem ro-bust/optimal control. Since Autumn 2000, he has been with National Tsing-HuaUniversity, as an Assistant Professor in the Power Mechanical EngineeringDepartment and a joint faculty member in the Institute of Nano Engineeringand Micro Systems. Currently, he is an Associate Professor with NationalTsing Hua University.

Documents

A Bubble-Free AC Electrokinetic Micropump Using the Asymmetric Capacitance-Modulated Microelectrode Array for Microfluidic Flow Control