本論文所呈現的內容為電滲流(Electroosmotic flow，EOF)相關之應用，而目的是表現簡易製作流程與高效率操作的實驗室晶片(Lab-on-chip，LOC)。本論文主要包含下列幾個部份：直流電滲流(DC EOF)在微彎管道中的應用、直流電滲流於Z字型管道之應用、直流電滲流於微管道中尖型阻塊處非線性流場之研究與交流電滲流(AC EOF)於微管道中的流場探討。
第一章介紹電動現象，針對電滲流的形成與理論進行描述。第二章為實驗方法與儀器架設，介紹電滲流實驗中所需之實驗架設。第三章利用數值方法針對具有曲率之微彎管道，通以直流與交流電場進行流場討論。在直流電場條件下，針對不同曲率的微彎管進行速度與二次流的流場分佈的研究討論。透過丁恩數(Dean number，Dn)我們可以描述曲率效應對於直流電滲流場的影響，研究結果指出在C/A (C：微彎管之曲率半徑，A：1/2的矩型彎管道高)值減小時，曲率效應與二次流的強度增強。針對交流電場在頻率範圍為2 kHz ~ 11 kHz，同樣進行速度與二次流流場分佈研究。數值研究結果顯示在高頻交流電場的條件下，管道中心速度與二次流強度隨著電場頻率增加而減弱。當頻率達到3 kHz時，二次流強度已減弱至無法對於管道軸心方向的流場有任何的影響，所以在這條件下，也沒能觀察到渦漩產生。
第四章主要利用數值與實驗方法驗證，證明在兩種轉角設計(尖銳型與平型)在Z字型管道中利用直流電滲流進行混合的效率。在尖銳型轉角設計中，由於轉角內側電場強度高於外側，進而流體速度在內側高於管壁外側，這樣的速度梯度分佈下產生所謂的賽道效應，經由此現象增強流體間的擴散效應進而達到提高混合效率，由模擬結果顯示其混合效率達到88.83％。然而尖銳型轉角設計在晶片清洗過程中易於轉角處殘留液體或氣泡。為排除此不便處著手設計平型轉角，平型轉角設計有如一漸縮漸擴管，不但可以增強混合效率更可以避免清洗過程中所殘留的液體或氣泡。由尺度分析顯示平型轉角設計可有效率增進混合距離，實驗結果也證實其混合效率高達94.30％，因此研究結果證明平型轉角設計的混合效率高於尖銳型轉角設計，最後針對平型轉角設計，利用田口分析結果得到影響效率的參數為轉角數與平型轉角設計的高度，其分析與實驗結果相同。
第五章主要研究在直流電場下，發生於管道中楔型塊尖端處的渦漩，此渦漩強度與電解液濃度與電場強度有關，透過在管道中佈滿粒子可觀測此渦漩結構，此渦漩主要成因為電解液於楔型塊尖端處發生濃度耗散，進而影響表面電荷與電位分佈所致。進一步利用此現象於微流體混合機制，根據實驗結果顯示，在進入混合區前端時，混合效率約為3％，經過混合區後，混合效率提升至78％。
第六章主要經由實驗研究三種不同形式的交流電滲流機制對於微混合效率之影響，三種不同形式的機制分別為：電容充電(Capacitive charging，CC)、法拉第充電(Faradaic charging，FC)與非對稱極化(Asymmetric polarization，AP)。研究結果顯示經由法拉第充電機制所產生的渦漩，強度大於電容充電機制而且可增進混合效應。然而在法拉第充電機制中，交流電場頻率必須小心控制避免法拉第反應發生導致電極損害。經由實驗證實，非對稱極化機制誘發的渦漩強度大於電容或是法拉第充電機制所產生的渦漩並且產生更好的混合效率。兩種非對稱極化之晶片設計成對稱型與非對稱型電極配置，兩種設計的混合效率在啟動電場後60秒量測結果分別為56.49％與71.77％。實驗結果顯示，在非對稱極化機制下非對稱電極配置比起其餘兩種機制更適合於微流體之混合應用。
第七章總結前述各章之重點，並提供未來研究方向與應用之可能性。

This thesis presents the applications of electroosmotic flow (EOF) toward achieving easy fabrication and high performance operation of lab-on-chip (LOC). The primary parts of the thesis concern the DC EOF in a curved microchannel, in a zigzag microchannel, and with a sharp corner in a microchannel, as well as the AC EOF in a microchannel.
Classic electrokinetic phenomena are discussed in Chapter 1, and the experiments are introduced in Chapter 2. The numerical investigation of electroosmotic flows driven by externally applied DC and AC electric fields in curved microchannels are given in Chapter 3. For the DC electric driving field, the velocity distribution and secondary flow patterns are investigated in microchannels with various curvature ratios. We use the Dean number to describe the curvature effect of the flow field in the DC electric field. The results show that the effect of the curvatures and the strengths of the secondary flows become stronger when the curvature ratio of C/A is smaller (where C is the radius of curvature of the microchannel and A is the half-height of the rectangular curved tube). For the AC electric field, the velocity distribution and secondary flow patterns are investigated for driving frequencies in the range of 2.0 kHz (Wo = 0.71) to 11 kHz (Wo = 1.66). The numerical results reveal that the velocity at the center of the microchannel becomes lower at higher AC electric field frequencies and that the strength of the secondary flow decreases. When the applied frequency exceeds 3.0 kHz (Wo = 0.87), vortices are no longer observed at the corners of the microchannel. Therefore, it can be concluded that the secondary flow induced at higher AC electric field frequencies has virtually no effect on the axial flow field in the microchannel.
Chapter 4 presents numerical and experimental investigations concerning the mixing of electroosmotic flows in zigzag microchannels with two different corner geometries, namely, sharp corners and flat corners. In the zigzag microchannel with sharp corners, the flow travels more rapidly near the inner wall of the corner than near the outer wall as a result of the higher electric potential drop. The resulting velocity gradient induces a racetrack effect, which enhances diffusion within the fluid and hence, improves the mixing performance. The simulated results reveal that the mixing index is approximately 88.83%. However, the sharp-corner geometry causes residual liquid or bubbles to become trapped in the channel at the point where the flow is almost stationary when the channel is in the cleaning process. Accordingly, a zigzag microchannel with a flat-corner geometry is developed. The flat-corner geometry forms a convergent-divergent type nozzle, which not only enhances the mixing performance in the channel, but also prevents the accumulation of residual liquid or bubbles. A scaling analysis shows that this corner geometry leads to an effective increase in the mixing length and the experimental results also show that the mixing index is increased to 94.30% in the flat-corner zigzag channel. Hence, the results demonstrate that the mixing index of the flat-corner zigzag channel is superior to that of the conventional sharp-corner microchannel. Finally, the results of the Taguchi analysis indicate that the attainable mixing index is determined primarily by the number of corners in the microchannel and by the flow passing height at each corner.
The aim of chapter 5 is the study of vortices occurred when sharp wedges are set in a micochannel where electroosmotic flow occurred: vortices are induced near the wedges when a DC electric field is imposed. The strength of the induced vortices depends on the concentration of electrolytes and the intensity of the electric field. Latex particles are used to aid the flow visualization. The formation of vortices is due to the concentration depletion in the microchannel, and they can be used as a micromixer. The experimental results show that the vortex structures created within the mixing section increase the mixing index from a value of 3 % in the upstream region of the microchannel to 78% at the outlet of the mixing section.
The purpose of chapter 6 is to perform an experimental investigation into the micro-mixing capabilities of three different types of AC electroosmotic flow (ac EOF), namely capacitive charging (CC), Faradaic charging (FC), and asymmetric polarization (AP). The results show that vortex structures generated by the FC phenomenon are stronger than those induced by the CC mechanism and, therefore, provide an improved mixing effect. However, in the FC system, the frequency of the external AC voltage must be carefully controlled to avoid electrode damage as a result of Faradaic reactions. The experimental results indicate that the AP polarization effect induces more powerful vortex structures than either the CC method or the FC method, and therefore yields a better mixing efficiency. Two AP-based micromixers were fabricated with symmetric and asymmetric electrode configurations, respectively. The mixing indices achieved by the two devices after an elapsed time of 60 seconds are found to be 56.49 % and 71.77 %, respectively. Thus, the results show that the device with an asymmetric electrode configuration represents a more suitable solution for micro-mixing applications in microfluidic devices.

Ajdari A (2000) Pumping liquids using asymmetric electrode arrays. Phys Rev E 61: R45-R48
Alarie JP, Jacobson SC, Culbertson CT, Ramsey JM (2000) Effects of the electric field distribution on microchip valving performance. Electrophoresis 21: 100-106
Alarie JP, Jacobson SC, Ramsey JM (2001) Electrophoretic injection bias in a microchip valving scheme. Electrophoresis 22: 312-317
Bazant MZ, Squires TM (2004) Induced-charge electrokinetic phenomena: Theory and microfluidic applications. Phys Rev Lett 92: 066101
Bazant MZ, Thornton K, Ajdari A (2004) Diffuse-charge dynamics in electrochemical systems. Phys Rev E 70: 021506
Bazant MZ, Urbanski JP, Levitan JA, Subramanian K, Kilic MS, Jones A, Thorsen T (2007) Electrolyte dependence of AC electro-osmosis. Proceedings of 11th International Conference on Miniaturized Systems for Chemistry and Life Sciences (MicroTAS) 2875-2878.
Brown ABD, Smith CG, Rennie AR (2001) Pumping of water with ac electric fields applied to asymmetric pairs of microelectrodes. Phys Rev E 63: 016305 Part 2
Chang CC, Yang RJ (2007) Electrokinetic mixing in microfluidic systems. Microfluid Nanofluid 3: 501-525
Chen JK, Yang RJ (2007) Electroosmotic flow mixing in zigzag microchannels. Electrophoresis 28: 975-983
Chu KT, Bazant MZ (2006) Nonlinear electrochemical relaxation around conductors. Phys Rev E 74: 011501
Cui L, Morgan H (2000) Design and fabrication of travelling wave dielectrophoresis structures. J Micromech Microeng 10: 72-79
Cummings EB, Griffiths SK, Nilson RH, Paul PH (2000) Conditions for similitude between the fluid velocity and electric field in electroosmotic flow. Anal Chem 72: 2526-2532
Dertinger SKW, Chiu DT, Jeon NL, Whitesides G.M (2001) Generation of gradients having complex shapes using microfluidic networks. Anal Chem 73: 1240-1246
Drese KS (2004) Optimization of interdigital micromixers via analytical modeling - exemplified with the SuperFocus mixer. Chem Eng J 101: 403-407
Duffy DC, McDonald JC, Schueller OJA, Whitesides G.M (1998) Rapid prototyping of microfluidic systems in poly(dimethylsiloxane). Anal Chem 70: 4974-4984
Duffy DC, Schueller OJA, Brittain ST, Whitesides G.M (1999) Rapid prototyping of microfluidic switches in poly(dimethyl siloxane) and their actuation by electro-osmotic flow. J Micromech Microeng 9: 211-217
Fan LS, Tai YC, Muller RS (1988) Integrated Movable Micromechanical Structures for Sensors and Actuators. IEEE T Electron Dev 35: 724-730
Fan LS, Tai YC, Muller RS (1989) IC-Processed Electrostatic Micromotors. Sensor Actuat 20: 41-47
Fung, Y. C. 1990 Biomechamics, Motion, Flow, Stress, and Growth, Springer-Verlag, New York
Gangwal S, Cayre OJ, Bazant MZ, Velev OD (2008) Induced-charge electrophoresis of metallodielectric particles. Phys Rev Lett 100: 058302
Glasgow I, Batton J, Aubry N (2004) Electroosmotic mixing in microchannels. Lab Chip 4: 558-562
Gonzalez A, Ramos A, Green NG, Castellanos A, Morgan H (2000) Fluid flow induced by nonuniform ac electric fields in electrolytes on microelectrodes. II. A linear double-layer analysis. Phys Rev E 61: 4019-4028
Green NG, Ramos A, Gonzalez A, Morgan H, Castellanos A (2000) Fluid flow induced by nonuniform ac electric fields in electrolytes on microelectrodes. I. Experimental measurements. Phys Rev E 61: 4011-4018
Green NG, Ramos A, Gonzalez A, Morgan H, Castellanos A (2002) Fluid flow induced by nonuniform ac electric fields in electrolytes on microelectrodes. III. Observation of streamlines and numerical simulation. Phys Rev E 66: 026305 Part 2
Hardt S, Drese KS, Hessel V, Schonfeld F (2005) Passive micromixers for applications in the microreactor and μTAS fields. Microfluid Nanofluid 1: 108-118
Hardt S, Schönfeld F. (2003) Laminar mixing in different interdigital micromixers: II. Numerical simulations. AIChE J 49: 578-584
Hessel V, Hardt S, Löwe H, Schönfeld F (2003) Laminar mixing in different interdigital micromixers: I. Experimental characterization. AIChE J 49: 566-577
Howell PB, Mott DR, Golden JP, Ligler FS (2004) Design and evaluation of a Dean vortex-based micromixer. Lab Chip 4: 663-669
Hu GQ, Gao YL, Sherman PM, Li DQ (2005) A microfluidic chip for heterogeneous immunoassay using electrokinetical control. Microfluid Nanofluid 1: 346-355
Hu YD, Lee JSH, Werner C, Li DQ (2006) Electrokinetically controlled concentration gradients in micro-chambers in microfluidic systems. Microfluid Nanofluid, 2: 141-153
Hunter RJ (1986) Zeta Potential in Colloid Science Principles and Applications, Academic Press, London
Jiang F, Drese KS, Hardt S, Kupper M, Schönfeld F (2004) Helical flows and chaotic mixing in curved micro channels. AIChE J 50: 2297-2305
Johnson TJ, Locascio LE (2002) Characterization and optimization of slanted well designs for microfluidic mixing under electroosmotic flow. Lab Chip 2: 135-140
Kamholz AE, Weigl BH, Finlayson BA, Yager P (1999) Quantitative analysis of molecular interaction in a microfluidic channel: The T-sensor. Anal Chem 71: 5340-5347
Knight JB, Vishwanath A, Brody JP, Austin RH (1998) Hydrodynamic focusing on a silicon chip: Mixing nanoliters in microseconds. Phys Rev Lett 80: 3863-3866
Lastochkin D, Zhou RH, Wang P, Ben YX, Chang HC (2004) Electrokinetic micropump and micromixer design based on ac faradaic polarization. J Appl Phys 96: 1730-1733
Lazar IM, Karger BL (2002) Multiple open-channel electroosmotic pumping system for microfluidic sample handling. Anal Chem 74: 6259-6268
Levitan JA, Devasenathipathy S, Studer V, Ben YX, Thorsen T, Squires TM, Bazant MZ (2005) Experimental observation of induced-charge electro-osmosis around a metal wire in a microchannel. Colloid Surface A 267: 122-132
Lin CH, Fu LM, Chien YS (2004) Microfluidic T-form mixer utilizing switching electroosmotic flow. Anal Chem 76: 5265-5272
Lin CH, Tsai CH, Fu LM (2005) A rapid three-dimensional vortex micromixer utilizing self-rotation effects under low Reynolds number conditions. J Micromech Microeng 15: 935-943
Löb P, Drese KS, Hessel V, Hardt S, Hofmann C, Löwe H, Schenk R, Schönfeld F, Werner B (2004) Steering of liquid mixing speed in interdigital micro mixers - from very fast to deliberately slow mixing. Chem Eng Technol 27: 340-345
Luo WJ (2004) Transient electroosmotic flow induced by DC or AC electric fields in a curved microtube. J Colloid Interf Sci 278: 497-507
Luo WJ, Pan YJ, Yang RJ (2005) Transient analysis of electro-osmotic secondary flow induced by dc or ac electric field in a curved rectangular microchannel. J Micromech Microeng 15: 463-473
McDonald JC, Duffy DC, Anderson JR, Chiu DT, Wu HK, Schueller OJA, Whitesides G.M (2000) Fabrication of microfluidic systems in poly(dimethylsiloxane). Electrophoresis 21: 27-40
McDonald JC, Whitesides GM (2002) Poly(dimethylsiloxane) as a material for fabricating microfluidic devices. Accounts Chem Res 35: 491-499
Mengeaud V, Josserand J, Girault HH (2002) Mixing processes in a zigzag microchannel: Finite element simulations and optical study. Anal Chem 74: 4279-4286
Minerick AR, Ostafin AE, Chang HC (2002) Electrokinetic transport of red blood cells in microcapillaries. Electrophoresis 23: 2165-2173
Morgan H, Green NG, Hughes MP, Monaghan W, Tan TC (1997) Large-area travelling-wave dielectrophoresis particle separator. J Micromech Microeng 7: 65-70
Nishimura T, Kojima N (1995) Mass-transfer enhancement in a symmetrical sinusoidal wavy-walled channel for pulsatile flow. Int J Heat Mass Transf 38: 1719-1731
Olesen LH, Bruus H, Ajdari A (2006) ac electrokinetic micropumps: The effect of geometrical confinement, Faradaic current injection, and nonlinear surface capacitance. Phys Rev E 73: 056313
Ookawara S, Higashi R, Street D, Ogawa K (2004) Feasibility study on concentration of slurry and classification of contained particles by microchannel. Chem Eng J 101: 171-178
Ramos A, Morgan H, Green NG, Castellanos A (1998) Ac electrokinetics: a review of forces in microelectrode structures. J Phys D: Appl Phys 31: 2338-2353
Ramos A, Morgan H, Green NG, Gonzalez A, Castellanos A (2005) Pumping of liquids with traveling-wave electroosmosis. J Appl Phys 97: 084906
Růžička J, Hansen EH (1988) Flow Injection Analysis: 2nd , John Wiley & Sons, New York
Park SY, Russo CJ, Branton D, Stone HA (2006) Eddies in a bottleneck: An arbitrary Debye length theory for capillary electroosmosis. J Colloid Interf Sci 297: 832-839
Probstein RF (1994) Physicochemical Hydrodynamics. Wiley–Interscience, New York.
Santiago, J. G. 2001 Electroosmotic flows in microchannels with finite inertial and pressure forces Anal. Chem. 73, 2353-2365
Schönfeld F, Hardt S (2004) Simulation of helical flows in microchannels. AIChE J 50: 771-778
Squires TM, Bazant MZ (2004) Induced-charge electro-osmosis. J Fluid Mech 509: 217-252
Studer V, Pepin A, Chen Y, Ajdari A (2004) An integrated AC electrokinetic pump in a microfluidic loop for fast and tunable flow control. Analyst 129: 944-949
Taguchi G., Yokoyama T, Wu Y (1993) Quality Engineering Series, Vol. 4, Taguchi Methods: Design of Experiments, AS
Takhistov P, Duginova K, Chang HC (2003) Electrokinetic mixing vortices due to electrolyte depletion at microchannel junctions. J Colloid Interf Sci 263: 133-143
Thamida SK, Chang HC (2002) Nonlinear electrokinetic ejection and entrainment due to polarization at nearly insulated wedges. Phys Fluids 14: 4315-4328
Trau M, Saville DA, Aksay IA (1997) Assembly of colloidal crystals at electrode interfaces. Langmuir 13: 6375-6381
Ueda M, Hayama T, Takamura Y, Horiike Y, Dotera T, Baba Y (2004) Curvature entropy trapping of long DNA under hydrodynamic flows in microfluidic devices. Jpn J Appl Phys 43: 1649-1650
Urbanski JP, Thorsen T, Levitan JA, Bazant MZ (2006) Fast AC electro-osmotic micropumps with nonplanar electrodes. Appl Phys Lett 89: 143598
Vanka SP, Luo G., Winkler CM (2004) Numerical study of scalar mixing in curved channels at low Reynolds numbers. AIChE J 50, 2359-2368
White FM (1991) Viscous Fluid Flow, McGRAW-HILL, New York
Winters KH (1987) A bifurcation study of laminar-flow in a curved tube of rectangular cross-section. J Fluid Mech 180: 343-369
Wu CH, Chen JK, Yang RJ (2007) Electrokinetically driven flow control using bare electrodes. Microfluid Nanofluid 3: 485-494
Wu J, Ben YX, Chang HC (2005) Particle detection by electrical impedance spectroscopy with asymmetric-polarization AC electroosmotic trapping. Microfluid Nanofluid 1: 161-167
Yamaguchi Y, Takagi F, Watari T, Yamashita K, Nakamura H, Shimizu H, Maeda H (2004a) Interface configuration of the two layered laminar flow in a curved microchannel. Chem Eng J 101: 367-372
Yamaguchi Y, Takagi F, Yamashita K, Nakamura H, Maeda H, Sotowa K, Kusakabe K, Yamasaki Y, Morooka S (2004b) 3-D simulation and visualization of laminar flow in a microchannel with hair-pin curves. AIChE J 50: 1530-1535
Yang RJ, Fu LM, Hwang CC (2001) Electroosmotic entry flow in a microchannel. J Colloid Interface Sci 244: 173-179
Yang RJ, Luo WJ (2002) Flow bifurcations in a thin gap between two rotating spheres. Theor Comp Fluid Dyn 16: 115-131
Yeh SR, Seul M, Shraiman BI (1997) Assembly of ordered colloidal aggregates by electric-field-induced fluid flow. Nature 386: 57-59
Yossifon G, Frankel I, Miloh T (2006) On electro-osmotic flows through microchannel junctions. Phys Fluids 18: 117108
Zeng SL, Chen CH, Mikkelsen JC, Santiago JG (2001) Fabrication and characterization of electroosmotic micropumps. Sensor Actuat B-Chem 79: 107-114