本論文探討封閉半圓與正方形兩種不同的幾何微流道內懸浮粒子的控制與捕捉，提出利用電滲流的調整進行多粒子定點捕捉或指定軌跡追蹤的回饋控制策略。藉由改變埋設於液固界面下多個微電極片的電壓，可在管壁表面形成特定介達電位分布，以引起相鄰流體發生表面滑動，然後在微流道內產生相應之電滲流場。所提回饋控制策略根據粒子位置與指定軌跡的偏差來計算所需粒子速度，進而獲得最佳的電壓改變量。其目的為改善粒子操作的效率與精確性，並排除布朗運動所引起擾動的影響。文中亦討論表面停滯點的粒子捕捉問題，結合回饋控制策略及短距作用力場，前者可快速驅動收斂電滲流將粒子帶至停滯點附近，後者可確保該粒子被捕捉於停滯點，因此增強粒子捕捉效率並解決短距力場對遠距粒子失效的缺點。
在半圓形微流道的模擬研究中，採用文獻已有之電滲流解析解來計算流體速度。在正方形微流道的模擬研究中，先取得底部半圓弧之數值解，以此作為邊界值解出底部半圓解析解，然後利用該解析解來組合出所謂的正方形微流道半解析解，以加快流體速度的計算。

This thesis investigates the control and trapping of suspended particles in confined semicircular and square microchannels, and proposes a feedback control strategy to trap multiparticles at designated points or track their trajectories by adjusting the electroosmotic flow. Via modulating the voltages of the microelectrodes embedded beneath the liquid-solid interface, a specific zeta potential distribution on the channel’s surface can be induced to cause a surface slip of the adjacent liquid and create the corresponding electroosmotic flow field in the channel. The proposed feedback control strategy calculates the required particle’s velocity according to the deviation between each particle’s position and its designated trajectory, and hence acquires the optimal voltages. Its purpose is to improve the efficiency and accuracy of the particle manipulation and to eliminate the disturbance caused by the Brownian motion. This work also addresses the problem of trapping particles at the surface stagnation point. By combining the feedback control strategy with a short-range force field, the efficiency of particle trapping can be enhanced and the invalidity of the short-range force for particles at a distance can be overcome. The concept is that the former can drive the converging electroosmotic flow to bring the particles fast to the neighborhood of the stagnation point, whereas the latter can ensure the capture of the particles at that point.
In the simulation study on the semicircular microchannel, an analytical solution for the semicircular electroosmotic flow in the literature is adopted to calculate the fluid velocity. In the simulation study on the square microchannel, the numerical solution along the semicircular arc on the channel’s bottom is computed first, and the analytical solution of the bottom semicircle is then developed using the numerical solution as a boundary condition. This analytical solution is employed to yield the so-called semi-analytical solution for the square microchannel for rapid computation of the fluid velocity.

[1] A. Manz, N. Graber, and H. M. Widmer, "Miniaturized total chemical analysis systems: A novel concept for chemical sensing," Sensors and Actuators B: Chemical, vol. 1, pp. 244-248, 1990.

[2] Y. Ben and H. Chang, "Nonlinear smoluchowski slip velocity and micro-vortex generation," Journal of Fluid Mechanics, vol. 461, pp. 229-238, 2002.

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

[4] A. Ajdari, "Electro-osmosis on inhomogeneously charged surfaces," Physical Review Letters, vol. 75, pp. 755-758, 1995.

[5] H. Morgan and N. G. Green, AC Electrokinetics: Colloids and Nanoparticles. UK: Research Studies Press, 2003.

[6] H. A. Stone, A. D. Stroock, and A. Ajdari, "Engineering flows in small devices," Annual Review of Fluid Mechanics, vol. 36, pp. 381-411, 2004.

[7] T. M. Squires and S. R. Quake, "Microfluidics: Fluid physics at the nanoliter scale," Reviews of Modern Physics, vol. 77, pp. 977-1026, 2005.

[8] J. West, M. Becker, S. Tombrink, and A. Manz, "Micro total analysis systems: Latest achievements," Analytical Chemistry, vol. 80, pp. 4403-4419, 2008.

[9] R. J. Hunter, Zeta Potential in Colloid Science: Principles and Applications. New York: Academic Press, 1981.
 
[10] S. Ghosal, "Fluid mechanics of electroosmotic flow and its effect on band broadening in capillary electrophoresis," Electrophoresis, vol. 25, pp. 214-228, 2004.

[11] S. Qian and H. H. Bau, "A chaotic electroosmotic stirrer," Analytical Chemistry, vol. 74, pp. 3616-3625, 2002.

[12] E. Brunet and A. Ajdari, "Thin double layer approximation to describe streaming current fields in complex geometries: Analytical framework and applications to microfluidics," Physical Review E, vol. 73, p. 056306, 2006.

[13] S. Dukhin, R. Miller, and G. Kretzschmar, "On the theory of adsorption kinetics of ionic surfactants at fluid interfaces," Colloid & Polymer Science, vol. 261, pp. 335-339, 1983.

[14] D. Long, H. A. Stone, and A. Ajdari, "Electroosmotic flows created by surface defects in capillary electrophoresis," Journal of Colloid and Interface Science, vol. 212, pp. 338-349, 1999.

[15] A. D. Stroock, M. Weck, D. T. Chiu, W. T. S. Huck, P. J. A. Kenis, R. F. Ismagilov, and G. M. Whitesides, "Patterning electro-osmotic flow with patterned surface charge," Physical Review Letters, vol. 84, pp. 3314-3317, 2000.

[16] A. Ramos, H. Morgan, N. G. Green, and A. Castellanos, "AC electric-field-induced fluid flow in microelectrodes," Journal of Colloid and Interface Science, vol. 217, pp. 420-422, 1999.

[17] A. Ajdari, "Pumping liquids using asymmetric electrode arrays," Physical Review E, vol. 61, pp. 45-48, 2000.

[18] A. Gonzalez, A. Ramos, N. Green, A. Castellanos, and H. Morgan, "Fluid flow induced by nonuniform ac electric fields in electrolytes on microelectrodes. II. A linear double-layer analysis," Physical Review E, vol. 61, p. 4019, 2000.
 
[19] D. Holmes and H. Morgan, Particle Focusing and Separation Using Dielectrophoresis in a Microfluidic Device. Massachusetts: Kluwer Academic Publishers, 2001.

[20] J. Wu, Y. Ben, D. Battigelli, and H. C. Chang, "Long-range AC electroosmotic trapping and detection of bioparticles," Industrial & Engineering Chemistry Research, vol. 44, pp. 2815-2822, 2005.

[21] P. K. Wong, T. H. Wang, J. H. Deval, and C. M. Ho, "Electrokinetics in micro devices for biotechnology applications," IEEE/ASME Transactions on Mechatronics, vol. 9, pp. 366-376, 2004.

[22] J. Kreft, Y. L. Chen, and H. C. Chang, "Conformation and trapping rate of DNA at a convergent stagnation point," Physical Review E, vol. 77, p. 030801, 2008.

[23] 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, vol. 2, p. 044103, 2008.

[24] S. K. Thamida and H. C. Chang, "Nonlinear electrokinetic ejection and entrainment due to polarization at nearly insulated wedges," Physics of Fluids, vol. 14, p. 4315, 2002.

[25] D. Hou and H. C. Chang, "Electrokinetic particle aggregation patterns in microvortices due to particle-field interaction," Physics of Fluids, vol. 18, p. 071702, 2006.

[26] S. J. Liu, H. H. Wei, S. H. Hwang, and H. C. Chang, "Dynamic particle trapping, release, and sorting by microvortices on a substrate," Physical Review E, vol. 82, p. 026308, 2010.

[27] C. K. Sun, Y. C. Huang, P. C. Cheng, H. C. Liu, and B. L. Lin, "Cell manipulation by use of diamond microparticles as handles of optical tweezers," Journal of the Optical Society of America B, vol. 18, pp. 1483-1489, 2001.

[28] J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Optics Communications, vol. 207, pp. 169-175, 2002.

[29] M. Armani, S. Chaudhary, R. Probst, and B. Shapiro, "Using feedback control and microfluidics to steer individual particles," IEEE International Conference on Micro Electro Mechanical Systems, vol. 18, pp. 855-858, 2005.

[30] S. Chaudhary and B. Shapiro, "Arbitrary steering of multiple particles independently in an electro-osmotically driven microfluidic system," IEEE Transactions on Control Systems Technology, vol. 14, pp. 669-680, 2006.

[31] R. F. Probstein, Physicochemical Hydrodynamics, 2nd ed. New York: John Wiley and Sons, 1994.

[32] P. Attard, D. Antelmi, and I. Larson, "Comparison of the zeta potential with the diffuse layer potential from charge titration," Langmuir, vol. 16, pp. 1542-1552, 2000.

[33] A. Van Theemsche, J. Deconinck, B. Van den Bossche, and L. Bortels, "Numerical solution of a multi-ion one-potential model for electroosmotic flow in two-dimensional rectangular microchannels," Analytical Chemistry, vol. 74, pp. 4919-4926, 2002.

[34] L. Y. Yeo, H. C. Chang, P. P. Y. Chan, and J. R. Friend, "Microfluidic devices for bioapplications," Small, vol. 7, pp. 12-48, 2011.

[35] N. A. Patankar and H. H. Hu, "Numerical simulation of electroosmotic flow," Analytical Chemistry, vol. 70, pp. 1870-1881, 1998.