本論文首先探討在半無窮平面區域，由帶電細長片上電動滑移速度所引起的微流體電滲流現象。文中推導出簡單多項式滑移速度生成之二維電滲流閉合解，然後利用多段三次樣條插值法和線性加成性來近似任意滑移速度分布，以獲得半無窮平面電滲流之通用解析解。另一方面，電動滑移速度在半圓區域會產生電滲微渦流，本文結合文獻之微渦流解析解和前述平面解，發展出一完整的半圓區域微渦流數學模型，具備符合真實操作情況和計算精確且收斂快速的優點。
　　本文接著討論在半圓區域，利用微渦流和底部短距吸引力來進行粒子定點捕捉的問題，目的為設計出最佳的微渦流結構和安排相應滑移速度。為此先在對稱微渦流結構內，根據粒子捕捉時間長短劃分出數個難易捕捉區域，然後針對不同粒子初始分布的捕捉需求，提出對應之滑移速度安排策略。粒子隨機分布的模擬研究證實，所提對應策略生成之微渦流結構能夠更有效地捕捉粒子於底部停滯點，相較於對稱微渦流結構，捕捉時間可減少百分之三十。

This thesis first investigates microfluidic electroosmotic flow set up by electrokinetic slip velocities over charged strips in a semi-infinite domain. A two-dimensional closed-form solution is derived for electroosmotic flow induced by a simple polynomial slip-velocity distribution over a surface. Using the cubic spline interpolation and superposition principle, an arbitrary slip-velocity distribution can be well approximated to provide a general analytical solution for electroosmotic flow in a semi-infinite plane. On the other hand, electrokinetic slip velocities would induce electroosmotic microvortices in a semicircular domain. The thesis combines an analytical solution for microvortices from the literature and the aforementioned planar solution to develop a complete mathematical model for microvortices in a semicircular area. This model not only satisfies practical operating conditions but also possesses accuracy and fast convergence in computation.
The thesis then addresses the problem of particle trapping at a specified point in a semicircular area using microvortices and short-range force from the bottom. The aim is to design the best microvortex structure and arrange the corresponding slip velocities. To this end, a symmetric microvortex structure is first analyzed to divide the semicircular area into several easy-to-trap and difficult-to-trap regions according to the duration of particle trapping time. Various arrangement strategies for slip velocities are then proposed to meet the requirements given by different initial distributions of particles. Simulation studies based on random particle distributions demonstrate that the microvortex structures caused by the proposed strategies can capture particles more efficiently at a stagnation point on the bottom. Compared to the symmetric microvortex structure, the trapping time can be reduced by 30%.

[1] Y. Ben and H. C. Chang, "Nonlinear Smoluchowski Slip Velocity and Micro-vortex Generation," J. Fluid Mech., 461, 229 (2002).

[2] Y. Ben, "Nonlinear Electrokinetic Phenomena in Microfluidic Devices," Ph.D. Dissertation, University of Notre Dame (2004).

[3] S. Dukhin and R. Miller, "On the Theory of Adsorption Kinetics of Ionic Surfactants at Fluid Interfaces 3. Generation of the Model,” Colloid Polym. Sci., 269, 923 (1991)

[4] A. González, A. Ramos, N. G. Green, A. Castellanos and H. Morgan, "Fluid Flow Induced by Nonuniform AC Electric Fields in Electrolytes on Microelectrodes. II. A Linear Double-layer Analysis," Phys. Rev. E, 61, 4019 (2000).

[5] T. M. Squires and M. Z. Bazant, "Induced-Charge Electro-osmosis," J. Fluid Mech., 509, 217 (2004).

[6] H. A. Stone, A. D. Stroock and A. Ajdari, "Engineering Flows in Small Devices," Annu. Rev. Fluid Mech., 36, 381 (2004).

[7] H. Morgan and N. G. Green, AC Electrokinetic: Colloids and Nanoparticles, Research Studies Press, Hertfordshire (2003).

[8] A. Manz, N Graber and H. M. Widmer, "Miniaturized Total Chemical Analysis Systems: A Novel Concept for Chemical Sensing," Sens. Actuator and B-Chem, 1, 244 (1990).

[9] D. J. Harrison and A. Van Den Berg, Micro Total Analysis Systems 98, Kluwer Academic Publishers, Netherlands (1998).

[10] S. Shoji, "Microfabrication Technologies and Micro-Flow Devices for Chemical and Bio-Chemical Micro Systems," Microprocesses Nanotechnol., 99, 72 (1999)

[11] P. Gravesen, J. Branebjerg and O. S. Jensen, "Microfluidics–A Review," J. Micromech. Microeng., 3, 168 (1993).

[12] S. Ghosal, "Fluid Mechanics of Electroosmotic Flow and Its Effect on Band Broadening in Capillary Electrophoresis," Electrophoresis, 25, 214 (2004).

[13] D. Hlushkou, D. Kandhai and U. Tallarek, "Coupled Lattice–Boltzmann and Finite‐Difference Simulation of Electroosmosis in Microfluidic Channels," Int. J. Numer. Meth. Fluids, 46, 507 (2004).

[14] L. Ren and D. Li, "Electroosmotic Flow in Heterogeneous Microchannels," J. Colloid Interface Sci., 243, 255 (2001).

[15] D. Erickson and D. Li, "Three-dimensional Structure of Electroosmotic Flow over Heterogeneous Surfaces," J. Phys. Chem. B, 107, 12212 (2003).

[16] S. Qian and H. H. Bau, "Theoretical Investigation of Electro-Osmotic Flows and Chaotic Stirring in Rectangular Cavities," Appl. Math. Model., 29, 726 (2005).

[17] D. Halpern and H. H. Wei, "Electroosmotic Flow in a Microcavity with Nonuniform Surface Charges," Langmuir, 23, 9505 (2007).
[18] E. Biddiss, D. Erickson and D. Li, "Heterogeneous Surface Charge Enhanced Micromixing for Electrokinetic Flows," Anal. Chem., 76, 3208 (2004).

[19] A. Ajdari, "Electro-Osmosis on Inhomogeneously Charged Surfaces," Phys. Rev. Lett., 75, 755 (1995).

[20] J. L. Anderson and W. Keith Idol, "Electroosmosis through Pores with Nonuniformly Charged Walls," Chem. Engng. Commun., 38, 93 (1985).

[21] D. Long, H. A. Stone and A. Ajdari, "Electroosmotic Flows Created by Surface Defects in Capillary Electrophoresis," J. Colloid Interface Sci., 212, 338 (1999).
[22] J. P. Gleeson, "Electroosmotic Flows with Random Zeta Potential," J. Colloid Interface Sci., 249, 217, (2002).

[23] S. Ghosal and Z. Lu, "Electroosmotic Flow and Zone Broadening in Microfluidic Channels of Variable Cross-Section and Wall Charge," Technical Proceedings of the 2002 International Conference on Simulation of Microsystems; Nano Science and Technology Insitute: San Juan (2002).

[24] N. G. Green, A. Ramos, A. González, H. Morgan and A. Castellanos, "Fluid Flow Induced by Nonuniform AC Electric Fields in Electrolytes on Microelectrodes. I. Experimental Measurements," Phys. Rev. E, 61, 4011 (2000).

[25] D. Holmes and H. Morgan, Particle Focusing and Separation Using Dielectrophoresis in a Microfluidic Device, Kluwer Academic Publishers, Massachusetts (2011).

[26] J. Wu, Y. Ben, D. Battigelli and H. C. Chang, "Long-Range AC Electroosmotic Trapping and Detection of Bioparticles," Ind. Eng. Chem. Res., 44, 2815 (2005).

[27] P. K. Wong, T. H. Wang, J. H. Deval and C. M. Ho, "Electrokinetics in Micro Devices for Biotechnology Applications," IEEE/ASME Trans. Mechatronics, 9, 366 (2004).

[28] J. Kreft, Y. L. Chen, and H. C. Chang, "Conformation and Trapping Rate of DNA at a Convergent Stagnation Point," Phys. Rev. E, 77, 030801(R) (2008).

[29] J. R. Du, Y. J. Juang, J. T. Wu and H. H. Wei, "Long-Range and Superfast Trapping of DNA Molecules in an AC Electrokinetic Funnel," Biomicrofluidics, 2, 44103 (2008).

[30] S. K. Thamida and H. C. Chang, "Nonlinear Electrokinetic Ejection and Entrainment Due to Polarization at Nearly Insulated Wedges," Phys. Fluids, 14, 4315 (2002).

[31] D. Hou and H. C. Chang, "Electrokinetic Particle Aggregation Patterns in Microvortices Due to Particle-field Interaction," Phys. Fluids, 18, 071702 (2006).

[32] Y. S. Yang, " Studies on Particles Assembly Using Micro-Vortices Driven by Electroosmosis on AC Electrodes," Master. Dissertation, National Cheng Kung University (2010).

[33] S. J. Liu, S. H. Hwang and H. H. Wei, "Nonuniform Electro-Osmotic Flow on Charged Strips and Its Use in Particle Trapping," Langmuir, 24, 13776 (2008).

[34] S. J. Liu, H. H. Wei, S. H. Hwang and H. C. Chang, "Dynamic Particle Trapping, Release, and Sorting by Microvortices on a Substrate," Phys. Rev. E, 82, 026308 (2010).

[35] H. C. Chang and G. Yossifon, "Understanding Electrokinetics at the Nanoscale: A Perspective," Biomicrofluidics, 3, 012001 (2009).

[36] L. Y. Yeo, D. Hou, S. Maheshswari and H. C. Chang, "Electrohydrodynamic Surface Microvortices for Mixing and Particle Trapping," Appl. Phys. Lett., 88, 233512 (2006).

[37] Y. W. Hsu, " Control and Trapping of Particles by Electroosmotic Flow in Semicircular and Square Microchannels," Master. Dissertation, National Cheng Kung University (2012).

[38] R. F. Probstein, Physicochemical Hydrodynamics: An Introduction, 2nd ed., John Wiley and Sons, New York (1994).

[39] L. Leal, Laminar Flow and Convective Transport Processes: Scaling Principles and Asymptotic Analysis, Butterworth-Heinemann College , Boston (1992).