本文主要以數值模擬方式探討微流體在電滲效應下之流體行為，並細部探討溶液內之離子分佈，所使用的物理模式包括(1)描述離子濃度分佈之Nernst-Planck方程式、(2)描述壁面電雙層之Poisson方程式、(3)描述外加電場分佈之Laplace方程式、及(4)描述電滲流流場之Narvier-Stokes方程式，並在物體力部分加入電驅動力之修正。
在電滲效應內，主要是來自淨電荷密度所反應的壁面電位勢，以及外加電壓之電場電位勢的交互作用，本文將針對這兩種電位勢強度作一關聯性的比較，以分析離子分佈受流場與電場所影響之範圍，並以直角彎管幾何模型進行模擬，發現在一般的電場強度下緩衝液濃度為 時，壁面電位勢效應會小於外加電場效應的狀況，特別在管道彎曲的區域內，離子分佈就不再單純呈現Boltzmann分佈，這會影響速度上的變化，在直角彎管部分，內側流速會有減緩的現象；另外，在本文後段探討封閉管道之電滲流流場，由於受到封閉端的影響而產生壓力上的變化，會在內部產生兩個上下對稱的渦漩現象，對此一流場結構，我們考慮電雙層厚度對速度分佈影響之效應，並詳細地分析封閉管道流場機制。

This study focuses on the investigation of the electroosmotic fluidic behavior and discusses its ionic distribution of bulk solution in details. The physical models are based on (1) the Nernst-Planck equations for the ionic concentration distribution, (2) the Poisson equation for electrical double layer (EDL) potential, (3) the Laplace equation for the externally applied electrostatic field, and (4) the Nariver-Stokes equations modified for the electroosmotic flow to include the body force effect induced by the electro-kinetic force.
The major force driven of the electroosmotic flow (EOF) is due to the interaction between the zeta potential that is due to the net charge density and the external electrical potential. In this study, we make a comparison between the two different potential effects and try to find a range of the variation of ionic concentration distribution induced by the flow and electrical field. In numerical process, we compute ionic variation by modeling the flow over a right-angled elbow. For a bulk concentration, the zeta potential effect near the wall is less than the external electrical potential effect. The ions in diffuse layer are no longer presented by the Boltzmann distribution in this condition, particularly near the right-angled region. The inner side velocity is retarded by the variation of the ionic distribution in the region. In addition, the EOF flow field in a closed cavity is also studied in the last chapter. The pressure rise induced by the closed ends forms the flow field to be a parabolic velocity profile. It creates two symmetric vortices at top and bottom in the cavity. We further study how the EDL thickness affects the velocity profile and analyze its mechanism in details.

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

[2] W. B. Russel, D.A. Saville, and W.R. Schowalter, “Colloidal Dispersions,
Cambridge Monographs on Mechanics and Applied Mathematics,“
Cambridge University Press, Cambridge, 1989.

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

[4] R. F. Probstein, “Physicochemical Hydrodynamics: An Introduction,” 2nd
ed., John Wiley and Sons, New York, 1994.

[5] S. Hjerten, “Free Zone Electrophoresis,” Chromatorgr. Rev., 9, 122-219,
1967.

[6] J. W. Jorgenson, and K. D. Lukacs, “Zone Electrophoresis in Open-Tubular
Glass Capillaries,” Anal. Chem., 53, 1298-1302, 1981.

[7] S. Terabe. K. Otsuka, A. Tsuchiya, and T. Ando, “Electrokinetic
Separation with Micellar Soulution and Open-Tubular Capillaries,” Anal.
Chem., 567, 111-113, 1984.

[8] S. Hjerten, J. L. Liao, K. J. Yao, “Theoretical and Experimental Study of
High Performance Electrophoretic Mobilization of Isoelectric Focused
Protein Zones,” J. Chromatogr., 387, 127-138, 1987.

[9] A. S. Cohen, B. L. Karger, "High-Performance Sodium Dodecyl Sulfate
Polyacrylamide Gel Capillary Electrophoresis of Peptides and Proteins," J.
Chromatogr., 397, 409-417, 1987.

[10] C. Yang, and D. Li, “Analysis of Electrokinetic Effects on the Liquid
Flow in the Rectangular Microchennels,“ J.Colloid Interface Sci, 248,
524-527, 2002.

[11] H. J. Keh, and H.C. Tseng, “Transient Electrokinetic Flow in Fine
Capillaries,” J.Colloid Interface Sci., 242, 450-459, 2001.

[12] J. P. Hsu, C. Y. Kao, S. Tseng, and C. J. Chen, “Electrokinetic Flow
through an Elliptical Microchannel: Effects of Aspect Ratio and Electrical
Boundary Conditions,” J.Colloid Interface Sci., 248, 176-184, 2002.

[13] Y. J. Kang, C. Yang, and X. Y. Huang, ”Electroosmotic Flow in a
Capillary Annulus with High Zeta Potentials,” J.Colloid Interface Sci., 253,
285-294, 2002.

[14] J. Yang, and D. Y. Kwok, “Effect of Liquid Slip in Electrokinetic
Parallel-Plate Microchannel Flow,” J.Colloid Interface Sci., 260, 225-233,
2003.

[15] T. Osuga, “Comparison of Growth of Laminar Flows in
Capillary-Poiseuille, Electroosmotic Flow and Electroosmotic Circulation,”
Jpn. J. App. Phy., 38, 6564-6567, 1999.

[16] N. A. Patankar, and H.H. Hu, “Numerical Simulation of Electroosmotic
Flow,” Anal. Chem, 70, 1870-1881, 1998.

[17] S. C. Ermakov, S. C. Jacoson, and J.M. Ramsey, “Coumpter Simulations
of Electrokinetic Transport in Microfabricated Channel Structures,”
Anal.Chem.,70, 4494-4504, 1998.

[18] J.Y. Lin, L. M. Fu, and R.J. Yang, “Numerical Simulation of
Electrokinetic Focusing in Microfluidic Chips,” J. Micromech. Microeng., 12,
1-7, 2002.

[19] L.M. Fu, R.J. Yang, G.B. Lee, and Y.J. Pan, “Multiple Injection
Techniques for Microfluidic Sample Handling,” Electrophoresis, 17,
3026-3032, 2003.

[20] D. Sinton, L. Ren, and D. Li, “A Dynamic Loading Method for
Controlling On-Chip Microfluidic Sample Injection,” J.Colloid Interface Sci.,
266, 448-456,2003.

[21] A. E. Kamholz, B. H. Weigl, B. A. Finlayson, and P. Yager, “Quantitative
Analysis of Molecular Interaction in a Microfluidic Channel : The T-Sensor,”
Anal. Chem., 71, 5340-5347, 1999.

[22] M. H. Oddy, J. G. Santiago, and J. C. Mikkelsen, “Electrokinetic
Instability Micromixing,” Anal. Chem., 73, 5822-5832, 2001.

[23] A. Ajdara, “Electro-Osmosis on Inhomogenously Charged Surfaces,”
Phy. Rev. Lett., 75, 755-758, 1995.

[24] A. Ajdara, “Generation of Transverse Fluid Currents and Forces by an
Eelectric Field: Electro-Osmosis on Charge-Modulated and Undulated
Surfaces,” Phy.Rev. E, 53, 4996-5005, 1996.

[25] A. E. Herr, J.I. Molho, J.G. Santiago, M.G. Mungal, and T.W. Kenny,
“Electroosmotic Capillary Flow with Nonuniform Zeta Potential,” Anal.
Chem., 72, 1053-1057, 2000.

[26] D. Erickson, and D. Li, “Microchannel Flow with Patchwise and
Periodic Surface Heterogeneity,” Langmuir, 18, 8949-8959, 2002.

[27] C.C. Chang, and R.J. Yang, “Computational Analysis of
Electrokinetically Driven Flow Mixing in Microchannels with Patterned
Blocks,” J. Micromech. Microeng., 14, 550-558, 2004.

[28] T. B. Jones, J. D. Fowler, Y. S. Chang, C. J. Kim, “Frequencybased
Relationship of Electrowetting and Dielectrophoretic Liquid Microactuation,”
Langmuir, 19, 7646-7651, 2003.

[29] T. B. Jones, K. L. Wang, and D. J. Yao, “Frequency-Dependent
Electromechanics of Aqueous Liquids: Electrowetting and
Dielectrophoresis,” Langmuir, 20, 2813-2818, 2004.

[30] P. Attard, D. Antelmi, and I. Larson, “Comparsion of the Zeta Potential
with the Diffuse Layer Potential from Charge Titration,” Langmuir, 16,
1542-1552, 2000.

[31] A.V. Theemsche, J. Deconinck, B. V. Bossche, and L. Bortels,
“Numerical Solution of a Multi-Ion One-Potential Model for Electroosmotic
Flow in Two-Dimensional Rectangular Microchannels,” Anal. Chem., 74,
4919-4926, 2002.

[32] G. Gouy, “Constitution of the Electric Charge at the Surface of an
Electrolyte,” J. Phys. Chem., 9, 457-468, 1910.

[33] D.L. Chapman, “A Contribution to the Theory of Electrocapillarity,”
Philos. Mag., 6, 475-481, 1913.

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

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

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

[37] X Y. Chen, K.C. Toh, J.C. Chai, and C. Yang, “Developing
Pressure-Driven Liquid Flow in Microchannels under the Electrokinetic
Effect,” Int. J. Eng. Sci, 42, 609-622, 2004.

[38] R. M. Sadri, and J. M. Floryan, “Entry Flow in a Channel,” Computers
＆ Fluids, 31, 133-157, 2002.

[39] H. Kinoshita, M. Oshima, J-W. Hong, T. Fujii, T. Saga, and
T. Kobayashi, "Micro PIV Measurement of Electroosmotic Flow",
Proceedings of the MicroTAS2002 Symposium , 1, 374-376, 2002.
(Nov. 3-7, Nara, Japan, 2002)

[40] D. Sinton, and D. Li, “Electroosmotic Velocity Profiles in
Microchannels,” Colloids and Surface A : Physicochem. Eng., 222, 273-283,
2003.

[41] L. M. Fu, R. J. Yang, and G. B. Lee, “Analysis of Geometry Effects on
Band Spreading of Microchip Electrophoresis,” 23, 602-612, 2003.

[42] S. C. Jacobson, and R. Hergenröden, L. B. Koutny, R. J. Warmack, and
J. Mlchael Ramsey, “Effects of Injection Schemes and Column Geometry on
the Performance of Microchip Electrophoresis Devices,” Anal. Chem., 66,
1107-1118, 1994.

[43] D. Nicolae, P. L. Paul, E. Miko, “Heat Transfer in a MEMs for
Microfluidics,” Sensors and Actuators, A 105, 137-149, 2003.

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

[45] D. Erickson, D. Sinton, and D. Li, “Joule Heating and Heat Transfer
in Poly (dimethylisiloxane) Microfliudic Systems,” Lab Chip, 3, 141-149,
2003.

[46] G. Y. Tang, C. Yang, J. C. Chai, and H.Q. Gong, “Joule Heating Effect on
Electroosmotic Flow and Mass Species Transport in a Microcapillary,” Int. J.
Heat Mass Transfer, 47, 215-227, 2004.