本文主要以數值模擬的方式探討微管道中的電滲流場，所使用物理模式包括(i)描述電雙層分佈之Poisson-Boltzmann方程式(ii)描述外加電場電位勢分佈之Laplace方程式(iii)描述電滲流流場之包含電驅動力的Navier-Stokes方程式。而主要研究重點分為下列兩項：
一為針對電滲流流場中之壓力分佈問題進行探討，本文發現當電滲流達到完全發展流時其軸向(x方向)壓力梯度為零，而電雙層內仍存在一徑向(y方向)壓力梯度且不可忽略。
二為針對電滲流流場中之混合機制進行探討，電滲流在微流體晶片上侷限在低雷諾數下，慣性力極弱而無法達到紊流的狀態。如此一來，使得樣品的混合只能單靠本身的擴散作用，而必須有足夠長的混合管道及時間才能達到均勻的混合溶液。而最近的研究報告提出藉由對管道壁面的異質性處理，將使得流體在異質性壁面處產生迴流現象。本文藉由數值模擬的方式探討這些迴流區並應用其提升微管道中樣品之混合效果，而結果顯示表面異質性對混合效果提升許多。

This study is focused on the investigation of pressure distribution and mixing mechanism of electro-osmotic flows in microchannels using numerical simulation. The physical models are based on (i) the Poisson-Boltzmann equation for electrical double layer (EDL) potential, (ii) the Laplace equation for the externally applied electrostatic field, and (iii) the Navier-Stokes equations modified to account for the electro-kinetic body force. Our study consists of two main parts as expressed in the following:
First, we study the pressure distribution of electro-osmotic flows through microchannels. It is found that when the flow is fully developed, the pressure gradient along the x direction is zero. The pressure gradient in the y direction, however, is detected, and the gradient exists in the y direction through the electrical double layer.
Second, we study the mixing mechanism of the electro-osmotic flow. The electro-osmotic flow in microfluidic chips is limited to the low Reynolds number regime, thus the inertia forces are extremely weak and turbulence is unable to develop. Therefore, species mixing is strongly diffusion dominated, requiring both a lengthy channel and time to attain a homogeneous solution. Recent studies have shown that the introduction of oppositely charged surface heterogeneities to microchannel walls can result in regions of localized flow circulation within bulk flow. In this study, we investigate these circulation regions through numerical simulation, and then propose a method enhancing species mixing in microchannels.

[1] Manz, A., Graber, N. and Widmer, H. M., “ Miniaturized Total Chemical Analysis Systems: A Novel Concept for Chemical Sensing,” Sensors and Actuators,B1, 244-248,1990

[2] Tuckermann, D. B. and Pease, R. F. W., “ High-Performance Heat Sinks for VLSI,” IEEE Electron Device Lett.,2,126-129,1981

[3] Peng, X. F., Peterson, G. P. and Wang, B. X., “ Frictional Flow Characteristics of Water Flowing Through Rectangular Microchannel,” Exp. Heat Transfer, 7, 249-264,1994

[4] Mala, G. M. and Li, D., “ Flow Characteristics of Water in Microtubes,” Int. J. Heat Fluid Flow, 20,142-148,1999

[5] Qu, W., Mala, G. M. and Li, D., “ Pressure-Driven Water Flows in Trapezoidal Silicon Microchannels,” Int. J. Heat Mass Transfer, 43,353-364,2000

[6] Papautsky, I., Brazzle, J.,Ameel, T. A. and Frazier, A. B., “Laminar Fluid Behavior in Microchannels Using Micropolar Fluid Theory,” Sensors and Actuators A,73,101-108,1999

[7] Peng, X. F., Peterson, G. P. and Wang, B. X., “ Heat Transfer Characteristics of Water Flowing Through Microchannel,” Exp. Heat Transfer, 7, 265-283,1999

[8] Wang, B. X. and Peng, X. F., “ Experimental Investigation on Liquid Forced-Convection Heat Transfer Through Microchannels,” Int. J. Heat Mass Transfer, 37,73-82,1994

[9] Hunter, R. J., “ Zeta Potential in Colloid Science: Principles and Appliciations,” Academic Press, New York,1981

[10] Mala, G. M., Li, D., Werner, C., Jacobasch, H.-J. and Ning, Y. B., “ Flow Characteristics of Water Through a Microchannel between Two Parallel Plates with Electrokinetic Effects,” Int. J. Heat and Fluid Flow, 18,489-496,1997

[11] Yang, C. and Li, D., “ Electrokinetic Effects on Pressure-Driven Liquid Flows in Rectangular Microchannels,”, J. of Colloid and Interface Science, 194,95-107,1997

[12] Gravesen, P.,Branebjerg, J. and Jensen, O., “ Microfluidics-a review,” J. Micromech. Microeng.,3,168-182,1993

[13] Tiselius, A., “A New Apparatus for Electrophoretic Analysis of Colloidal Mixtures,” Trans. Faraday Soc.,33,524,1937

[14] Burgreen, D. and Nakache, F. R., “Electrokinetic Flow in Ultrafine Capillary Slits,” J. Phys. Chem., 68,1084-1091,1964

[15] Rice, C. L. and Whitehead, R., “ Electrokinetic Flow in a Narrow Cylindrical Capillary,” J. Phys. Chem., 69,4017-4024,1965

[16] Jorgenson, J. M. and Lukacs, K. D.,“ Zone Electrophoresis in Open-Tubular Glass Capillaries ,”Analytical Chemistry,53,1298-1302, 1981

[17] Andreev, V. P. and Lisin, E. E., “ On the Mathematical Model of Capillary Electrophoresis ,” Chromatographia,37,202-210,1993

[18] Andreev, V. P., Dubrovsky, S. G. and Stepanov, Y. V., “ Mathematical Modeling of Capillary Electrophoresis in Rectangular Channels,” J. Microcolumn Separations,9,443-450,1997

[19] Patankar, N. A. and Hu, H. H., “ Numerical Simulation of Electroosmotic Flow,” Analytical Chemistry, 70,1870-1881,1998

[20] Ermakov, S.V., Jacobson, S. C. and Ramsey, J. M., “ Computer Simulations of Electrokinetic Transport in Microfabricated Channel Structures,” Analytical Chemistry, 70,4494-4504,1998

[21] Ermakov, S.V., Jacobson, S. C. and Ramsey, J. M., “ Computer Simulations of Electrokinetic Injection Techniques in Microfluidic Devices ,” Analytical Chemistry,72,3512-3517,2000

[22] Hu, L., Harrison, J. D. and Masliyah, J. H., “ Numerical Model of Electrokinetic Flow for Capillary Electrophoresis,” J. Colloid and Interface Science, 215,300-312,1999

[23] Arulanandam, S. and Li, D., “ Liquid Transport in Rectangular Microchannels by Electroosmotic Pumping,” Colloids and Surfaces A: Physicochemical and Engineering Aspects, 161,89-102,2000

[24] Ren, L. and Li, D., “ Electroosmotic Flow in Heterogeneous Microchannels,” J. Colloid and Interface Science, 243,255-261,2001

[25] Yang, C., Li, D. and Masliyah, J. H., “ Modeling Forced Liquid Convection in Rectangular Microchannels with Electrokinetic Effects,” Int. J. Heat and Mass Transfer, 41,4229-4249,1998

[26] Hoffmann, K. A. and Chiang, S. T., “ Computational Fluid Dynamics for Engineers-Volume 1,” Wichita, Kansas,USA,1993

[27] Maynes, D. and Webb, B. W., “ Fully Developed Electro-Osmotic Heat Transfer in Microchannels,”Int. J. Heat and Mass Transfer, 46,1359-1369,2003

[28] Mitchell, M. J., Qiao, R. and Aluru, N. R., “ Meshless Analysis of Steady-State Electro-osmotic Transport,” J. MEMS,9,435-449,2000

[29] Yang, R. J., Fu, L. M. and Lin, Y. C., “ Electeoosmotic Flow in Microchannels,” J. Colloid and Interface Science,239,98-105,2001

[30] Alam, J. and Bowman, J. C., “ Energy-Conseving Simulation of Incompressible Electro-Osmotic and Pressure-Driven Flow,” Theoret. Comput. Fluid Dynamics,16,133-150,2002
[31] Sadri, R. M. and Floryan, J. M., “ Entry flow in a channel,” Computers & Fluids, 31,133-157,2002

[32] Knight, J., “ Microfluidics: Honey, I Shrunk the Lab,” Nature, 418,474-475,2002

[33] Liu, R. H., Stremler, M. A., Sharp, K. V., Olsen, M. G., Santiago, J. G., Adrian, R. J., Aref, H. and Beebe, D. J., “ Passive Mixing in a Three-Dimensional Serpentine Microchannel,” J. of MEMS, 9,190-197,2000

[34] Lee, Y. K., Deval, J., Tabeling, P. and Ho, C. M., “ Chaotic Mixing in Electrokinetically and Pressure Driven Micro Flows,” Proc. MEMS Conf. 2001,483-486,2001

[35] Oddy, M. H., Santiago, J. G. and Mikkelsen, J. C., “ Electrokinetic Instability Micromixing,” Analytical Chemistry, 73,5822-5832,2001

[36] Deval, J., Tabeling, P. and Ho, C. M., “ A Dielectrophoretic Chaotic Mixer,” Proc. MEMS Conf. 2002,36-39,2002

[37] Suzuki, H. and Ho, C. M., “ A Magnetic Force Driven Chaotic Micro-Mixer,” Proc. MEMS Conf. 2002,40-43,2002

[38] Qian, S. and Bau, H. H., “ A Chaotic Electroosmotic Stirrer,” Analytical Chemistry, 74,3616-3625,2002

[39] Erickson, D. and Li, D., “ Influence of Surface Heterogeneity on Electrokinetically Driven Microfluidic Mixing,” Langmuir,18,1883-1892
,2002

[40] Jeon, N. L., Dertinger, S. K. W., Chiu, D. T., Choi, I. S., Stroock, A. D. and Whitesides, G. M., “ Gerenation of Solution and Surface Gradients Using Microfluidic Systems,” Langmuir, 16,8311-8316,2000

[41] Ajdari, A., “ Electro-Osmosis on Inhomogeneously Charged Surfaced Surfaces,” Phys. Rev. Lett.,75,755-758,1995
[42] Ajdari, A., “ Generation of Transverse Fluid Currents and Forces by an Electric Field : Electro-Osmosis on Charge-Modulated and Undulate Surfaces,” Phys. Rev. E,53,4996-5005,1996

[43] Long, D. and Ajdari, A., “ Symmetry Properties of the Electrophoretic Motion of Pattern Colloidal particles,” Phys. Rev. Lett., 81,1529-1532,1998

[44] Stroock, A. D., Weck, M., Chiu, D. T., Huck, W. T. S., Kenis, P. J. A., Ismagilov, R. F. and Whitesides, G. M., “ Patterning Electro-osmotic Flow with Patterned Surface Charge,” Phys. Rev. Lett., 84,3314-3317,2000

[45] Xia, Y. and Whitesides, G. M., “ Soft Lithography,” Angew. Chem. Int. Ed.,37,550-575,1998

[46] Kenis, P. J. A., Ismagilov, R. F., and Whitesides, G. M., “ Microfabrication Inside Capillaries Using Multiphase Laminar Flow Patterning,” Science,285,83-85,1999

[47] Jeon, N. L., Choi, I. S., Xu, B. and Whitesides, G. M., “ Large-Area Patterning by Vacuum-Assisted Micromolding,” Advanced Matertrial,11, 946-950,1999

[48] Schasfoort, R. B. M., Schlautmann, S., Hendrikse, J. and Van den Berg, A., “ Field-Effect Flow Control for Microfabricated Fluidic Network,” Science,286,942-945,1999

[49] Moorthy, J., Khoury, C., Moore, J. S. and Beebe, D. J., “ Active Control of Electroosmotic Flow in Microchannels Using Light,” Sensors and Actuators B,75,223-229,2001

[50] Yang, R. J., Fu, L. M., and Hwang, C. C., “ Electroosmotic Entry Flow in a Microchannel,” J. Colloid and Interface Science,244,173-179,2001