本文在探討微渠道內邊界滑動效應對電滲流動（electroosmotic flow，EOF）之影響。描述電滲流動的統御方程式包含：（1）Poisson-Boltzmann方程式，用以描述微渠道內電雙層（electric double layer，EDL）電位勢（electric potential）分佈；（2）Laplace方程式，用以描述外加電場電位勢分佈；（3）具電驅動物體力（electrokinetic body force）之Navier-Stokes方程式，用以描述微渠道內速度場分佈。使用的無因次化參數有滑動係數（slip coefficient）α、雷諾數（Reynolds number）Re及電雙層厚度參數（EDL thickness parameter）κ，其中Re數可表示成zeta電位勢與外加電場的強度。藉由數值模擬的方式，我們求解如下應用於微流體晶片的流場型態：
一、平板微渠道（parallel-plate microchannels）
二、T型及十字型微渠道（T-shape and cross-section microchannels）
這裡我們使用Navier滑動邊界修正流體於壁面上的速度，模擬出壁面滑動現象，探討邊界滑動之影響。此外，我們亦探討Re數、κ值對速度、流率及電雙層電勢能之影響。結果顯示，在流場內邊界滑動、zeta電位勢、外加電場及電雙層厚度對電滲流場影響甚大。

The effect of liquid slip on electroosmotic flow（EOF）in microchannels is studied in this paper. The governing equations used to describe electroosmotic flow include:（1）Poisson-Boltzmann equation for the electric field of electric double layer（EDL）,（2）Laplace equation for the applied electric field, and（3）Navier-Stokes equations with electrokinetic body force for the velocity field. By using numerical simulation, the influence of the various parameters such as the , the slip coefficient, Re, the Reynolds number characterizing the zeta potential and the applied electrical field, and κ, double-layer thickness parameter, on the flow distribution is investigated. Two researchable subjects which have practical applications in microfluidic chip can be considered as follows：
The first is the electroosmotic flow through microchannels between two parallel plates with boundary slip.
The second is the effect of liquid slip on electroosmotic flow in T-shape and cross-section microchannels.
Here we use Navier slip boundary condition to correct the fluid velocity at fluid-wall interface for the simulation of liquid slip. In addition, the variation of the velocity profile, flow rate, stream contours, and EDL potential with Re and κ are discussed in detail. Results show that liquid slip, zeta potential, applied electrical field, and double-layer thickness have significant influence.

[1]Manz, A., Graber, N. and Widmer, H. M., “Miniaturized total chemical analysis system: a novel concept for chemical sensing,” Sensors and Actuators B1,224-248（1990）

[2]Tuckermann, D. B., and Pease, R. F. W., “High-performance heat sinks for VLSI,” IEEE Electron Decice Lett.,2,126-129（1981）

[3]Tuckermann, D. B., and Pease, R. F. W., “Optimized convective cooling using micromachined structrues,” J. Electrochem. Soc., 129, c98（1982）

[4]Mala, G. M. and Li, D., “Flow characteristics of water in microtubes,” Int. J. Heat Fluid Flow,20,142-148（1999）

[5]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）

[6]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）

[7]Wang, B. X. and Peng, X. F., “Experimental investigation on liquid forced-convection heat transfer through microchannels,” Int. J. Heat Mass Transferm,37,73-81（1994）

[8]Hunter, Robert J., “Zeta potential in colloid science: principles and applications,” Academic Press, New York（1981）

[9]George Em Karniadakis, Ali Beskok ,”Micro flows: fundamentals and simulation,” Academic Press, New York（2002）

[10]Probstein, Ronald F.,“Physicochemical hydrodynamics an introduction,”Academic Press, New York（1994）

[11]Burgeen, D. and Nakache, F., ”Electrokinetic flow in ultrafine capillary slits,”J. Phys. Chem.,68,1084-1091（1964）

[12]Rice, C. L., Whitehead, R., “Electrokinetic flow in a narrow cylindrical capillary,” J. Phys. Chem.,69,4017-4023（1965）

[13]Levine, S., Marriott, J. R., Neale, G. and Epstein, N., “Theory of electrokinetic flow in fine cylindrical capillaries at high zeta potential,” Journal of Colloid Science,52,136-149（1975）

[14]Yang, C., Li, D., Masliyah, Jacob H., “Modeling forced liquid convection in rectangular microchannels with electrokinetic effects ,” Int. J. Heat Mass Transfer, 41,4229-4249（1998）

[15]Yang, C., Li D., “Analysis of electrokinetic effects on the liquid flow in rectangular microchannels,” Colloids Surf. A, 143, 339-353（1998）

[16]Mala, G. M.,Li, D., Dale, J. D., “Heat transfer and fluid flow in microchannels,”Int. J. Heat Mass Transfer,40,3079-3088（1997）

[17]Bowen, W. Richard, Jenner, F., “Electroviscous effects in charged capillaries,” J. Colloid Interface Sci.,173,388-395（1998）

[18]Patankar, N. A.,and Hu, H. H., “Numerical simulation of electroosmotic flow,” Anal. Chem.,70,1870-1881（1998）

[19]Yang, R. J.,Fu, L. M., and Hwang ,C. C., “Electroosmotic entry flow in a microchannel,” J. Colloid Interface Sci., 224,173-179（2001）

[20]Yang, R. J.,Fu, L. M., and Hwang, C. C., “Electroosmotic flow in microchannel,” J. Colloid Interface Sci.,239,98-105（2001）

[21]Yanuar, K. W.,Udagawa, H.,” Drag reduction of Newtonian fluid in a circular pipe with a highly water-repellent wall,” J. Fluid Mech., 381,225-238（1999）

[22]Tretheway , D. C., Meinhart, C. D., ” Apparent fluid slip at hydrophobic microchannel walls,” Physics of Fluids,14,L9-L12（2002）

[23]Zhu, Y.,Granick, S., ”Rate-dependent slip of Newtonian liquid at smooth surfaces,”Phys. Rev. Lett., 87，096105（2001）

[24]Schweiss, R., Welzel, P. B.,Werner , C., Knoll, W.,”Interfacial charge of organic thin films characterized by streaming potential and streaming current measurements,” Colloids Surf. A, 195,97-102（2001）

[25]Craig ,V. S. J., Neto, C.,and Williams ,D. R. M., “Shear-dependent boundary slip in an aqueous Newtonian liquid,” Phys. Rev. Lett., 87,054504（2001）

[26]Thompson, P. A.,Troian,S. M. ”A general boundary condition for liquid flow at solid surfaces,”Nature,389, 360-362（1997）

[27]Yang, J.,Kwok, D. Y.,“Analytical treatment of electrokinetic microfluidics in hydrophobic microchannels,” Analytica Chemica Acta,507,39-53（2004）

[28]Yang , J., and , Kwok, D. Y., “Effect of liquid slip in electrokinetic parallel-plate microchannel flow,” J. Colloid Interface Sci., 260, 225-233（2003）

[29]Yang , J., and , Kwok, D. Y., “Time-dependent laminar electrokinetic slip flow in infinitely extended rectangular microchannels, ” J. chem. Phys.,118,354-363（2003）

[30]Yang , J., and , Kwok, D. Y., “A new method to determine zeta potential and slip coefficient simultaneously,” J. Phys. Chem. B , 106, 12851-12855（2002）

[31]Yang , J.,and , Kwok, D. Y., “Microfluid flow in circular microchannel with electrokinetic effect and navier slip condition,” Langmuir, 19, 1047-1053（2003）

[32]Grimes, B. A., and Liapis ,A. I., “Expressions for evaluating the possibility of slip at the liquid-solid interface in open tube capillary electrochromatography,” J. Colloid Interface Sci.,263, 113-118（2003）

[33]Lianguang Hu, Jed D. Harrison, and Jacob H. Masliyah,” Numerical model of electrokinetic flow for capillary electrophoresis,” J. Colloid Interface Sci.,215,300-312（1999）

[34]傅龍明,”微晶片電滲流場之分析與應用,”成功大學博士論文,2001年

[35]張志彰,”微管道電滲流流場之壓力分佈與混合機制分析,”成功大學碩士論文,2003年

[36]Tannehill, J. C.,Anderson, D. A.,Pletcher, R. H.,”Computational fluid mechanics and heat transfer,”Academic Press, New York（1997）

[37]Patankar, S. V. and Spalding, D. B.”A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows,” Int. J. Heat Mass Transfer,15,1787-1806（1972）

[38]Patankar, S. V.,” Numerical heat transfer and fluid flow,” Academic Press, Washington, D. C.（1980）

[39]Erickson, D., Li, D.,” Influence of surface heterogeneity on electro- kinetically driven microfluidic mixing,” Langmuir,18,1883-1892（2002）

[40]Herr, A. E., Molho, J. I., Santiago, J. G., Mungal, G. M., Kenny, T. W.,”Electroosmotic capillary flow with nonuniform zeta potential,” Anal. Chem.,72,1053-1057（2000）

[41]Fu, L. M., Lin, J. Y.,and Yang, R. J., “Analysis of electroosmotic flow with step change in zeta potential,”J. Colloid Interface Sci., 258, 266-275（2003）

[42]Harrison, D., Manz, A., Fan, Z., Ludi, H., and Widmer, H.,“Capillary electrophoresis and sample injection systems integrated on a planar glass chip,” Anal. Chem.,64,1926-1932（1992）

[43]Seiler, K., Harrison, D., Manz, A.,” Planar glass chips for capillary electrophoresis: repetitive sample injection, quantitation, and separation efficiency,”Anal. Chem.,65, 1491-1488（1993）

[44]Effenhauser, C. S. and Manz, A.,“Glass chip for high-speed capillary electrophoresis separations with submicrometer plate heights,”Anal. Chem.,65,2637-2642（1993）

[45]Lee, G. B., Hwei, B. H., Huang, G. R.,”Micromachined pre-focused m×n flow switches for continuous multi-sample injection,” Journal of Micromechanics and Microengineering,11,1-8（2001）

[46]Culbertson, C. T., Ramsey, S. R., Ramsey, J. M.,”Electroosmotically induced hydraulic pumping on microchips: differential ion transport,” Anal. Chem.,72,2285-2291（2000）

[47]Ermakov, S. V., Jacobson, S. C., Ramsey, J. M.,“Computer simulation of electrokinetic transport in micro fabricated channel structures,” Anal. Chem.,70,4494-4504（1998）

[48]Bianchi, F., Ferrigno, R., Girault, H. H., “Finite element simulation of an electroosmotic-driven flow division at a T-junction of microscale dimension,” Anal. Chem.,72,1987- 1993（2000）

[49]Maynes, D., Webb, B. W., “The effect of viscous dissipation in thermally fully-developed electro-osmotic heat transfer in microchannels,” Int. J. Heat Mass Transfer,47,987-999（2004）

[50]Qu, W., Li, D.,”A model for overlapped EDL field,”Journal of Colloid and Interface Science,224,397-407（2000）

[51]McNamara, G.,Zanetti, G.,”Use of the Boltzmann equation to simulate lattice-gas automata,”Phys. Rev. Lett., 61, 2332-2335（1988）

[52]Shaw, Duncan J., ”Introduction to colloid and surface chemistry,” Academic Press, Oxford（1992）

[53]Tiselius, A., “A new apparatus for electrophoretic analysis of colloidal mixtures,” Trans. Faraday Soc.,33, 524（1937）