STUDY OF AC ELECTROOSMOTIC FLOW DEVELOPED BY CO-PLANAR MICROELECTRODE ARRAY IN A SLIT MICROCHANNEL

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1 Proceedings of the International Conference on Mechanical Engineering 211 (ICME ecember 211, haka, Bangladesh ICME STUY O AC EECTROOSMOTIC OW EVEOPE BY CO-PANAR MICROEECTROE ARRAY IN A SIT MICROCHANNE Naheed erdos, Tariq Mahbb, and Noor Qdds* epartment of Mechanical Engineering, Bangladesh University of Engineering and Technology, haka-1, Bangladesh * nqdds@me.bet.ac.bd ABSTRACT Under the inflence of an AC electric field, electrolytes on a planar microelectrodes exhibit steady flid flow, termed as AC electro-osmosis. A nmerical model sing finite element scheme has been developed to solve the electrokinetic flow parameters of the AC electroosmosis in a slit microchannel. The soltion was obtained sing Poisson Navier Stokes Nernst Planck approach known as non eqilibrim model. A thin-layer, low-freqency, nonlinear analysis of the system is performed inclding aradaic crrents from electrochemical reactions at the electrodes. Net flow velocity is observed for different geometric parameters of electrodes. low and field characteristic are observed for the maximm velocity attained in the investigated range of freqency. The interesting conseqences of shape and field asymmetries, which generally lead to electro-osmotic pmping or electrophoretic motion in AC fields gives some basic isses for the microflidic devices.. Keywords: AC Electroosmosis, Microelectrode, Poisson-Nernst-Planck, aradaic crrent. 1. INTROUCTION Alternating electric fields can generate a net steady motion of aqeos saline soltions over microelectrode strctres. The term ac electro-osmosis (ACEO refers to the flid motion generated on top of electrodes by the interaction between an ac electric field and electrical charge that this field indces at the electrode/electrolyte interface i.e. charge indced in electrical doble layer. The mechanism of ac electro-osmotic driven flid flow has recently been shown to be capable of prodcing nidirectional pmping of liqid on a microscale, on asymmetric pairs of coplanar microelectrodes as demonstrated experimentally [1], theoretically [2], and nmerically [3]. Electrical forces are sed to transport, mix, separate, and maniplate varios moleclar or colloidal entities in microflidic chips [4-5]. Experimental reslts are compared with a simple model based on the interaction of the non-niform electric field [6-8]. At low potentials, the predicted velocities are in reasonable agreement with the experiments. Two different models for the simlation of the ac electroosmotic flow in a microchannel have been discssed where simplified model leads to a fast stationary soltion and the second model has analyzed all essential processes in the time domain [9]. However, aradaic crrents can occr in sch systems as a reslt of electrochemical reactions. A noneqilibrim 1 mathematical model of an ac electroosmotic system with electrochemical reactions is presented in [1]. inear and weakly nonlinear theoretical stdies were done for flid flow [11]. The effect of aradaic crrents on the electroosmotic slip velocity generated at the electrode/electrolyte interface is taken over the assmption of perfectly polarizable electrodes. Theoretical reslts are applied for analyzing the inflence of aradaic reactions on AC electroosmotic flows [12]. The combined action of two experimentally relevant effects, i.e aradaic crrents from electrochemical reactions at the electrodes and differences in ion mobilities of the electrolyte is taken into accont in the analyses of ac electro-osmosis [13]. Approximation made are negligible advective crrents, linearization of PNP eqations, thin layer approximation etc. Becase of these approximations, the reslts obtained are partial explanation of the mechanisms nderlying ac electro-osmosis with aradaic crrents. A complete analysis mst be flly nonlinear. Motivated by this, in order to extend previos theoretical analysis of aradaic crrents in ACEO by considering a symmetric electrolyte with ions of different mobilites, a low-freqency, complete nonlinear analysis of the system inclding aradaic crrents from electrochemical reactions at the electrodes is performed in the present stdy. ICME

2 2. ORMUATION O THE PROBEM 2.1 Geometry A coplanar arrangement of ac electroosmotic pmp as shown in ig 1 is considered. The stdied microflidic pmp can be represented by a single segment of a long microflidic channel. We assme that a microchannel consists of an infinitely large series of segments with periodic bondary conditions. The micro channel width is mch larger than the other characteristic dimensions of the segments, so the ac electroosmotic pmp can be described as a 2- object with length and height H. The electrodes have lengths E 1 and E 2, and they are separated by two gaps, namely, G 1 and G 2. A 1:1 aqeos soltion XY e.g., HCl placed on top of an array of electrodes sbjected to an ac signal. Above this plane, three distinct layers are distingished: compact, diffse, and diffsion. y ig 1: Schematic iagram of the Physical omain 2.2 Governing Eqation Two charged species are inclded in this model and the pair of ions are considered to be asymmetric in the sense that their mobilities are different. or simplicity, it is assmed that the cations react reversibly at the electrodes to prodce netral molecles according to a simple one-step one-electron redox process of the form X e X and that the electrodes are blocking for the anions. The electric potential obeys Poisson s eqation, The particle densities satisfy Nernst-Planck eqations, x G 2 /2 G 1 E 2 G 2 /2 =, = c ( c c φ (2 =, = c ( c c φ (3 =, = c c (4 The diffsion coefficients of, H, Cl - and water are m 2 s -1 9, = 2.32e m 2 s -1, 9 = 9.312e 9 = 2.2e E 1 2 ε φ = q, q = ( c c (1 m 2 s -1 respectively. To these eqations we mst add the Stokes eqation for the liqid motion, = (5 2 ρ( = η p q φ (6 H Table 1: Non dimensional parameter Symbol Parameter x = x imensionless x-coordinate y = y imensionless y-coordinate = imensionless delta operator = imensionless debye length h = H Height to length ratio r e = E1 E2 Electrode length ratio r g = G2 G1 Gap size ratio le = ( E1 E2 Eqivalent length t = t t t = imensionless time f = ft imensionless freqency c imensionless concentration of cation c imensionless concentration of anion c imensionless concentration of water φ φ =, φ = φ imensionless potential A = A φ imensionless amplitde,.75 = imensionless velocity p p = imensionless pressre 2c Ra ε η η Sc ρ ( ε / s = ( ε s / s 2 Rayleigh nmber (Ra=.372 Schmidt nmber (Sc=348 Compact layer relative thickness 2.3 Normalization A combination of eqations 7-12 and Table 1 gives the dimensionless form of the mathematical model. 2 1 φ = q,.5( 2 q = c c (7 ( c c c φ = (8 ( c c c φ = (9 ( c c = (1 ICME

3 1 Sc t = (11 2 Ra = ( p q φ ( Bondary Condition The bondary conditions at the OHP (y= for these fnctions are the continity of the displacement vector, assming a linear compact layer of width s and permittivity ε s ε s φ φs = ε (13 s where φs denotes the voltage drop across the compact layer φ s = V s ( x, t φ( y = (14 We assme that the electrodes are blocking to the anions, φ c = (15 whereas the flxes of positive and netral species are related throgh aradaic crrents, φ c = (16 e = (17 e To model this crrent we se the Btler-Volmer eqation β φs (1 β φs = K c exp K c exp (18 e with β as the transfer coefficient, where the reaction constants K = 1e -1 m 3 mol -1 s -1 (Reaction rate constant for water K = 1e -7 m 3 mol -1 s -1 (Reaction rate constant for H [13] Note that effects de to the adsorption of movable ions is not considered. 2.5 Comptational Procedre inite element method (EM is employed for solving the governing eqations. Poisson, Nernst Planck, Navier-Stokes and continity eqations are solved in a time dependent domain. In this analysis, the two dimensional problem geometries are discretized by trianglar mesh. Higher nmber of mesh elements is sed on the electrode srface. This facilitates captring the higher velocity gradient near the electrode srface arising from the no slip bondary condition. 3. RESUT AN ISCUSSION Vales of time averaged net velocity are calclated tilizing the developed non-eqilibrim model. These calclated vales are compared with the pblished nmerically compted reslts[6]. The percentage of error for the vale of calclated net velocity, when compared to the vales of [6] for dimensionless freqency, are within.949 %. Above the maximm error is 5.3%. So, vales of dimensionless freqency is taken in the range of.1 to 1 in the present stdy. Parametric dependencies compted by present model are plotted by empty markers. The Cervenka reslts are represented by filled markers in ig 2. ig 2: Comparison of present model and Cervenka model 3.1 Effect of aradaic Crrent The magnitde of time averaged net velocity is shown for asymmetric arrangements of electrodes taking aradaic crrents and no aradaic crrent in consideration. ig 3: Effect of aradaic crrent on net velocity ig 4: Net velocity withot aradaic crrent. No aradaic crrents means considering the electrodes as perfectly polarizable.aradaic crrents depolarize the electrode-electrolyte interface i.e charge leaks from the doble layer leading to lower electroosmotic ICME

4 velocity.this phenomenon is seen in ig 3. Net velocity decreases by an order becase of the effect of aradaic crrents. Net velocity (taken at logarithmic scale decreases by an order becase of the effect of aradaic crrents. ig 5: Net velocity with aradaic crrent velocities than asymmetric electrodes. or symmetric electrodes, flow reversal occrs at dimensionless freqency.6 and for asymmetric electrodes, it happens after the vale of dimensionless freqency.2 That means flow reversal occrs at a higher freqency when electrodes are symmetric. So, symmetric electrode arrangement is a better design considering flow reversal as for a certain range of freqency, desired net flow can be obtained. 3.3 Time Average Net Velocity ig 7 shows time averaged net velocity in the middle plane between two electrodes. Near the electrodes the velocity increases with the increasing distance from electrode, goes to a maximm at.25 µm above electrodes. The maximm velocity is.2 µm/s for the above case of dimensionless freqency.3. low reversal is after.149 µm above the electrode The velocity is parabolic in shape from the point.125 µm to the wall (.33 µm. No flow reversal is seen for this system when taking no aradaic crrents. Spatial direction x is taken positive from left to right side. Negative sign of velocity indicated the net flow is in the opposite direction of positive x. In the range of dimensionless freqency mentioned above in ig 4, velocities are negative. That means flid flows in the same direction for dimensionless freqency, ranging from.1 to 1while considering no aradaic crrent. low reversal occrs at dimensionless freqency,.5 in this system while taking aradaic crrent into consideration. lid velocity goes positive from negative direction as in ig 5. In both cases, the change in the magnitde of net velocity is low pto freqency.2. After this freqency, net velocity significantly increases. ig 7: Time averaged net velocity vector along a vertical line at the midpoint between the electrodes 3.4 ield Characteristics ig 8 shows the characteristics of velocity field (arrow plot, electric field (contor line and potential field (color. Electric field is very strong between two electrodes. The velocity is maximm at the edges of the electrodes. There is a strong vortex between electrodes. ig 6: Comparison of net velocity for asymmetric and symmetric electrode arrangement 3.2 Effect of Symmetry of Electrode ig 6 shows the comparison of net velocity for asymmetric and symmetric electrode arrangements. In comparison of magnitde, it is seen that for lower freqency symmetric electrode arrangement exerts lower net velocity than asymmetric arrangements. or higher velocities, symmetric electrodes exert higher net ig 6: Net velocity comparison for asymmetric and symmetric electrode arrangement 4. CONCUSION A flly nonlinear analysis is performed here to nderstand the mechanism of ac electroosmosis with aradaic crrents. Net velocity withot aradaic crrent srpasses net velocity with aradaic crrent and remains ICME

5 higher throghot the entire domain. Changes in velocity profile is sharper for aradaic crrent than no aradaic crrent. In the same region of freqency, flow reversal occrs while taking aradaic crrent into consideration where no flow reversal occrs withot aradaic crrent. Taking absolte vale of net velocity, symmetric electrode arrangement exerts lower net velocity than asymmetric arrangements at lower freqency. or higher velocities, symmetric electrodes exert higher net velocities than asymmetric electrodes. or symmetric electrodes, flow reversal occrs at dimensionless freqency =.6 and for asymmetric electrodes, it happens after the vale of dimensionless freqency = REERENCES 1. Green, N.G., Ramos, A., Morgan, H., and Castellanos A., 2, lid flow indced by microelectrodes. I. Experimental measrements, The American Physical Society, vol. 61, No Gonzalez, A., Ramos, A., Green, N. G., Castellanos, A. and Morgan, H., 2, lid flow indced by microelectrodes.ii. A linear doble-layer analysis, The American Physical Society, Vol. 61, No Green, N.G., Ramos, A., Gonzalez, A., Morgan, H. and Cstellanos, A., 22, lid flow indced by microelectrodes. I. Observations of streamlines and nmerical simlation, The American Physical Society, Physical Review E 66,2635, No Sqires, T. M. and Bazant, M. Z., 24, Indced charge electro-osmosis, ornal of lid Mechanics, Vol. 59, pp Hrdlicka,., Cervenka, P., Pribyl, M. and Snita,., 21, Mathematical modeling of AC electroosmosis in microflidic and nanoflidic chips sing eqilibrim and non-eqilibrim approaches, ornal of Appl Electrochem, Vol. 4, pp Hrdlicka,., Cervenka, P., Pribyl, M. and Snita,., 21, Toward high net velocities in AC electroosmosis micropmps based on asymmetric coplanar electroes, IEEE transactions on indstry applications, Vol. 46, No Gonzalez, A., Ramos, A., Sanchez, P. G. and Castellanos, A., 21 Effect of the combinded action of aradaic crrents and mobility differences in ac electroosmosis, The American Physical society, Physical Review E 81, Bazant, M. Z., Sqires, T. M., 24, Indced-Charge electrokinetic phenomena: theory and microflidin applications, The American Physical society, Vol. 92, No Pribyl, M. and Adamiak, K., 21, "Nmerical Models for AC Electroosmotic Micropmps," IEEE Transactions on Indstry Applications, Vol. 46, No Cervenka, P., Hrdlicka,., Pribyl, M. and Snita,., 21, "Stdy on aradaic and Colombic interactions at microelectrodes tilized in AC electroosmotic micropmps", Research work of Institte of Chemical Technology, Prage, epartment of Chemical Engineering, Technick a 5, Praha 6, Czech Repblic, MSMT no Ramos, A., González, A., García-Sánchez, P. and Castellanos, A., 27, "A linear analysis of the effect of aradaic crrents on traveling-wave electroosmosis", ornal of Colloid and Interface Science, Vol. 39, pp García-Sánchez, P., Ramos, A., González, A., 211, "Effects of aradaic crrents on AC electroosmotic flows with coplanar symmetric electrodes",colloids and Srfaces A:Physicochem. Eng. Aspects 376, pp González, A., Ramos, A., García-Sánchez, P. and 2 and Castellanos, A., 21," Effect of the combined action of aradaic crrents and mobility differences in ac electro-osmosis", Physical Review E 81, NOMENCATURE Symbol Meaning Unit A Amplitde (A c Concentration (mol m -3 f H G E n p R t T û x y ε φ η s q β iffsivity reqency The araday constant Micro channel height ength of periodic segment Gap size Electrode size Normal nit vector Pressre Molar gas constant Time Temperatre Net velocity Time averaged net velocity Spatial coordinate Spatial coordinate Electrolyte permittivity Electric potential ynamic viscosity The ebye length Compact layer width Space charge density Transfer coefficient lx (m 2 s -1 (s -1 (Cmol -1 Pa (K -1 mol -1 (s (K (ms -1 (ms -1 (m -1 (V (PaS Cm -3 Cm -2 ICME

arxiv:physics/ v2 [physics.flu-dyn] 8 Feb 2004

arxiv:physics/ v2 [physics.flu-dyn] 8 Feb 2004 Indced-charge lectrokinetic Phenomena: Theory and Microflidic Applications Martin Z. Bazant Department of Mathematics and Institte for Soldier Nanotechnologies Massachsetts Institte of Technology, Cambridge,