双电层影响下的微通道分层流动及其稳定性研究
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摘要
微机电系统MEMS中的微流体系统在环境监测、化学分析、临床检测及微电子等领域有广泛应用。微流体力学研究特征尺度为微米的流体运动。与宏观系统不同,表面效应如双电层(Electrical Double Layer)成为微流动主要控制因素。本文以双电层效应为核心,首次建立了考虑双电层和壁面滑移联合影响下的单相流平均流场解析解和考虑双电层影响下的分层流平均流场解析解,重点研究了双电层影响下的单相流和分层微流动平均流与其稳定性,主要得到了以下结论:
(1)双电层使速度在壁面附近产生回流,通道越窄,则双电层效应越强,对流动的抑制作用也越强,回流越显著。将双电层与边界滑移的效应叠加,回流促使边界滑移速度指向流动相反方向,滑移加强了双电层对流动的抑制作用。将双电层、边界滑移和表观黏性修正三者叠加,滑移现象受双电层和表观黏性的耦合效应影响。若双电层效应强,滑移速度指向流动相反方向。若表观黏性效应强,则边界滑移被弱化,平均流有拐点出现。
(2)双电层的效应越强,则系统的临界雷诺数越小,临界波数越大,流动越易失稳。将双电层与边界滑移叠加,临界雷诺数比单独考虑双电层时小,边界滑移强化了双电层的作用。将表观黏性与边界滑移效应叠加,当表观黏性效应较强时,滑移对临界雷诺数的影响很小,不能增强系统的稳定性。将双电层、边界滑移和表观黏性修正三者叠加,双电层和表观黏性均能减小系统临界雷诺数。边界滑移受双电层和表观黏性的耦合影响较为复杂。若双电层效应强,则滑移速度指向流动相反方向,滑移协同双电层效应使流动稳定性减弱。若表观黏性效应强,则边界滑移的影响被弱化,表观黏性引起的平均流拐点,也将减小临界雷诺数。
(3)在去离子溶液和离子溶液构成的分层流系统中,离子溶液的双电层越强,则对流动的抑制作用越大,离子溶液一侧回流现象越显著。若两层液体均为离子溶液,则通道的两侧都形成双电层,共同对流动起抑制作用。双电层效应越强,则两侧回流越强,且黏性较小的一侧流体回流量大。两层流体的Zeta电势比值越大,上层流速受抑制的程度越高。
(4)对于去离子溶液和离子溶液构成的分层流系统,离子溶液的Zeta电势越大,流动越容易失稳。对于两层液体均为离子溶液的分层流,Zeta电势增大也使流动更易失稳。两者相比,均为离子溶液的分层流的稳定性差。通道越窄,则双电层效应强,分层流越易失稳。若黏性比大于1,相界面的位置越靠近上壁面,则系统越稳定,且黏性比越大,系统越不稳定。电导率对流动有稳定作用。
The microflow system of the MEMS technology is applied in fields of environmental monitoring, biochemical analysis, clinic testing and mivroelectronics etc. The flow system with the micron characteristic scale is called microflow. Comparing to the normal scale systems, the interface effects such as the Electrical Double Layer become a main factor to control the behavior of micro scale systems. In this paper, the analytical solution of single phase microflow under the combined effects of electrical double layer and boundary slip and the stratified microflow under the effect of the electrical double layer are established and solved for the first time. Furthermore, the stability of the above mean flows is studied. The main conclusions are as the following:
(i) A velocity backflow is raised in the near-wall-area. When the channel height is reduced and the Zeta potential is increased, the velocity is decreased and the backflow is strong. Combining the effects of electrical double layer and boundary slip, the backflow constrains the velocity to slide to the opposite direction and strengthen the restrain effect of electrical double layer so that the backflow is obvious. Combining the effects of electrical double layer, boundary slip and apparent viscosity, the slip velocity is controlled by the couple effects of the electrical double layer and apparent viscosity. The slip velocity is against the flow direction if the effect of electrical double layer is stronger than that of apparent viscosity. The slip velocity is small and an inflection point occurs when the effect of apparent viscosity is stronger than that of electrical double layer.
(ii) As the effect of the electrical double layer is becoming strong, the critical Reynolds number is reduced and the critical wave number is increased. The microflow is easily to lose stability. Combining the effects of electrical double layer and boundary slip, the critical Reynolds number is smaller than that of only electrical double layer is considered. The effect of boundary slip reinforces that of electrical double layer. Combining the effects of apparent viscosity and boundary slip, the critical Reynolds number hardly affects by boundary slip and The boundary slip cannot enhance the stability. Combining the effects of electrical double layer, boundary slip and apparent viscosity, the effects of electrical double layer and apparent viscosity decrease the critical Reynolds number corporately. When the effect of electrical double layer is strong, the effect of boundary slip can further weaken the stability of system. When the effect of apparent viscosity is strong, the effect of boundary slip is weakened and the inflection point decreases the critical Reynolds number.
(iii) With respect to the stratified flow consisting of deionized solution and ion solution, the stronger the electrical double layer effect is, the bigger the restrain force and the stronger the backflow on the side of the ion solution are. With respect to the stratified flow consisting of two different ion solutions, the backflow on both sides restrain the flow. The backflow on the side of flow with big viscosity effect is stronger than that with the small viscosity effect. The flow of upper layer is restrained more when the Zeta potential ratio is big.
(v) With respect to the stratified flow consisting of the deionized solution and ion solution, the critical Reynolds number is reduced when the Zeta potential of the ion solution increases. With respect to the stratified flow consisting of two different ion solutions, the Zeta potential also makes the stability of flow decreased. Comparing with the above two conditions, stratified ion solutions flow is more unstable. When the viscosity ratio is bigger than 1, the closer the interface to the upper wall, the more stable the flow is. The bigger the viscosity ratio is, the more unstable the flow is. The stability of flow is increased by the conductivity of solution.
(1)双电层使速度在壁面附近产生回流,通道越窄,则双电层效应越强,对流动的抑制作用也越强,回流越显著。将双电层与边界滑移的效应叠加,回流促使边界滑移速度指向流动相反方向,滑移加强了双电层对流动的抑制作用。将双电层、边界滑移和表观黏性修正三者叠加,滑移现象受双电层和表观黏性的耦合效应影响。若双电层效应强,滑移速度指向流动相反方向。若表观黏性效应强,则边界滑移被弱化,平均流有拐点出现。
(2)双电层的效应越强,则系统的临界雷诺数越小,临界波数越大,流动越易失稳。将双电层与边界滑移叠加,临界雷诺数比单独考虑双电层时小,边界滑移强化了双电层的作用。将表观黏性与边界滑移效应叠加,当表观黏性效应较强时,滑移对临界雷诺数的影响很小,不能增强系统的稳定性。将双电层、边界滑移和表观黏性修正三者叠加,双电层和表观黏性均能减小系统临界雷诺数。边界滑移受双电层和表观黏性的耦合影响较为复杂。若双电层效应强,则滑移速度指向流动相反方向,滑移协同双电层效应使流动稳定性减弱。若表观黏性效应强,则边界滑移的影响被弱化,表观黏性引起的平均流拐点,也将减小临界雷诺数。
(3)在去离子溶液和离子溶液构成的分层流系统中,离子溶液的双电层越强,则对流动的抑制作用越大,离子溶液一侧回流现象越显著。若两层液体均为离子溶液,则通道的两侧都形成双电层,共同对流动起抑制作用。双电层效应越强,则两侧回流越强,且黏性较小的一侧流体回流量大。两层流体的Zeta电势比值越大,上层流速受抑制的程度越高。
(4)对于去离子溶液和离子溶液构成的分层流系统,离子溶液的Zeta电势越大,流动越容易失稳。对于两层液体均为离子溶液的分层流,Zeta电势增大也使流动更易失稳。两者相比,均为离子溶液的分层流的稳定性差。通道越窄,则双电层效应强,分层流越易失稳。若黏性比大于1,相界面的位置越靠近上壁面,则系统越稳定,且黏性比越大,系统越不稳定。电导率对流动有稳定作用。
The microflow system of the MEMS technology is applied in fields of environmental monitoring, biochemical analysis, clinic testing and mivroelectronics etc. The flow system with the micron characteristic scale is called microflow. Comparing to the normal scale systems, the interface effects such as the Electrical Double Layer become a main factor to control the behavior of micro scale systems. In this paper, the analytical solution of single phase microflow under the combined effects of electrical double layer and boundary slip and the stratified microflow under the effect of the electrical double layer are established and solved for the first time. Furthermore, the stability of the above mean flows is studied. The main conclusions are as the following:
(i) A velocity backflow is raised in the near-wall-area. When the channel height is reduced and the Zeta potential is increased, the velocity is decreased and the backflow is strong. Combining the effects of electrical double layer and boundary slip, the backflow constrains the velocity to slide to the opposite direction and strengthen the restrain effect of electrical double layer so that the backflow is obvious. Combining the effects of electrical double layer, boundary slip and apparent viscosity, the slip velocity is controlled by the couple effects of the electrical double layer and apparent viscosity. The slip velocity is against the flow direction if the effect of electrical double layer is stronger than that of apparent viscosity. The slip velocity is small and an inflection point occurs when the effect of apparent viscosity is stronger than that of electrical double layer.
(ii) As the effect of the electrical double layer is becoming strong, the critical Reynolds number is reduced and the critical wave number is increased. The microflow is easily to lose stability. Combining the effects of electrical double layer and boundary slip, the critical Reynolds number is smaller than that of only electrical double layer is considered. The effect of boundary slip reinforces that of electrical double layer. Combining the effects of apparent viscosity and boundary slip, the critical Reynolds number hardly affects by boundary slip and The boundary slip cannot enhance the stability. Combining the effects of electrical double layer, boundary slip and apparent viscosity, the effects of electrical double layer and apparent viscosity decrease the critical Reynolds number corporately. When the effect of electrical double layer is strong, the effect of boundary slip can further weaken the stability of system. When the effect of apparent viscosity is strong, the effect of boundary slip is weakened and the inflection point decreases the critical Reynolds number.
(iii) With respect to the stratified flow consisting of deionized solution and ion solution, the stronger the electrical double layer effect is, the bigger the restrain force and the stronger the backflow on the side of the ion solution are. With respect to the stratified flow consisting of two different ion solutions, the backflow on both sides restrain the flow. The backflow on the side of flow with big viscosity effect is stronger than that with the small viscosity effect. The flow of upper layer is restrained more when the Zeta potential ratio is big.
(v) With respect to the stratified flow consisting of the deionized solution and ion solution, the critical Reynolds number is reduced when the Zeta potential of the ion solution increases. With respect to the stratified flow consisting of two different ion solutions, the Zeta potential also makes the stability of flow decreased. Comparing with the above two conditions, stratified ion solutions flow is more unstable. When the viscosity ratio is bigger than 1, the closer the interface to the upper wall, the more stable the flow is. The bigger the viscosity ratio is, the more unstable the flow is. The stability of flow is increased by the conductivity of solution.
引文
[1] Hetsroni G, Mosyak A, Pogrebnyak, E, et al. Fluid flow in micro-channels. 2005. 48(10): 1982-1998
[2] Chovan T, Guttman A. Microfabricated devices in biotechnology and biochemical processing. 2002. 20(3): 116-122
[3] Squires T M, Quake S R. Microfluidics: Fluid physics at the nanoliter scale. Reviews of Modern Physics, 2005. 77(3): 977-1026
[4] Karniadakis G E, Beskok A.微流动——基础与模拟.化学工业出版社:北京. 2002
[5] Ho C M, Tai Y C. Micro-Electro-Mechanical-Systems (MEMS) and Fluid Flows. Annual Reviews in Fluid Mechanics, 1998. 30(1): 579-612
[6] Zeng J, Korsmeyer T. Principles of droplet electrohydrodynamics for lab-on-a-chip. Royal Society of Chemistry, 2004. 4(4): 265-277
[7] Stone H A, Stroock A D, Ajdari A. Engineering flows in small devices: Microfluidics toward a lab-on-a-chip. Annual Review of Fluid Mechanics, 2004. 36(1): 381-411
[8] Erickson D. Towards numerical prototyping of labs-on-chip: modeling for integrated microfluidic devices. Microfluidics and Nanofluidics, 2005. 1(4): 301-318
[9]方肇伦.微流控分析芯片的制作及应用.化学工业出版社:北京. 2005
[10]林炳承,秦建华.微流控芯片实验室.科学出版社:北京. 2006
[11] Zheng B, Roach L S, Ismagilov R F. Screening of Protein Crystallization Conditions on a Microfluidic Chip Using Nanoliter-Size Droplets. Journal of the American Chemical Society, 2003. 125(37): 11170-11171
[12] Wang B X, Peng X F. Experimental investigation on liquid forced convection heat transfer through microchannels. International Journal of Heat and Mass Transfer, 1994. 37(Supplement 1): 73-82
[13] Song H, Tice J D, Ismagilov R F. A microfluidic system for controlling reaction networks in time. 2003. 42(7): 768-72
[14] Dittrich P S, Manz A. Lab-on-a-chip: microfluidics in drug discovery. Nature Reviews Drug Discovery 2006. 5(3): 210-218
[15] Hu X, Wang S, Juang Y J, et al. Five-cross microfluidic network design free of coupling between electrophoretic motion and electro-osmotic flow. Applied Physics Letters, 2006. 89: 084101
[16] Lee J S, Dylla-Spears R, Teclemariam N P, et al. Microfluidic four-roll mill for all flow types. Applied Physics Letters, 2007. 90(7): 074103
[17] Groisman A, Enzelberger M, Quake S R. Microfluidic memory and control devices. Science, 2003. 300(5621): 955
[18] Barker S L R, Ross D, Tarlov M J, et al. Control of flow direction in microfluidic devices with polyelectrolyte multilayers. Analytical Chemistry, 2000. 72(24): 5925-5929
[19] Thompson P A, Troian S M. A general boundary condition for liquid flow at solid surfaces. Nature, 1997. 389: 360-362
[20] Bayraktar T, Pidugu S B. Characterization of liquid flows in microfluidic systems. 2006. 49(5-6): 815-824
[21] Bhushan B. Introduction to Nanotechnology. Wiley: New York. 2003
[22] Rice C L, Whitehead R. Electrokinetic Flow in a Narrow Cylindrical Capillary. American Chemical Society, 1965. 69(11): 4017-4024
[23] Black W B, Graham M D. Slip, concentration fluctuations and flow instability in sheared polymer solutions. Macromolecules, 2001. 34(17): 5731–5733
[24] Koo J, Kleinstreuer C. Analysis of surface roughness effects on heat transfer in micro-conduits. International Journal of Heat and Mass Transfer, 2005. 48(13): 2625-2634
[25] Chan H B, Aksyuk V A, Kleiman R N, et al. Quantum mechanical actuation of microelectromechanical systems by the Casimir force. Science, 2001. 291(5510): 1941-1944
[26] Ngoma G D, Erchiqui F. Heat flux and slip effects on liquid flow in a microchannel. International Journal of Thermal Sciences, 2007. 46(11): 1076-1083
[27] Corbett J, McKeown P A, Peggs G N, et al. Nanotechnology: International Developments and Emerging Products. CIRP Annals-Manufacturing Technology, 2000. 49(2): 523-545
[28] Gad-el-Hak M. The fluid mechanics of microdevices-The Freeman Scholar Lecture. Journal of Fluids Engineering-Transactions of the Asme, 1999. 121(1): 5-33
[29]尤学一,郑敬茹.微间距平板Poiseuille流动的稳定性.纳米技术与精密工程,2007. 5(4): 319-322
[30]尤学一,郑湘君,郑敬茹.微尺度流道内液体表观黏性系数的分子理论.物理学报,2007. 56(004): 2323-2329
[31]尤学一,李胜华,肖厚蓬.微流道粗糙壁面对流动阻力和控制的影响.化学工程,2008. 36(008): 25-27
[32] Pfahler J, Harley J, Bau H, et al. Gas and liquid flow in small channels.American Society of Mechanical Engineers, 1991. 32: 49-60
[33] Harley J C, Bau H H, Zemel J N, et al. Gas flow in micro-channels. Journal of Fluid Mechanics, 1995. 284: 257-274
[34] Liu J Q, Tai Y C, Pong K C, et al., Micromachined channel/pressure sensor systems for micro flow studies. In The 7th International Conference Solid-State Sensors and Actuator, 1993. 995-998
[35] Breuer K S, Piekos E S, Gonzales D A. DSMC simulations of continuum flows. In AIAA Thermophysics Conference, San Diego. 1995. 19-22
[36] Gaitan M, Locascio L E. Embedded microheating elements in polymeric micro channels for temperature control and fluid flow sensing. 2004. 109(3): 335-344
[37] Hitt D L, McGarry M. Numerical simulations of laminar mixing surfaces in pulsatile microchannel flows. Mathematics and Computers in Simulation, 2004. 65(4-5): 399-416
[38] Santiago J G, Wereley S T, Meinhart C D, et al. A particle image velocimetry system for microfluidics. Experiments in Fluids 1998. 25(4): 316-319
[39] Meinhart C D, Wereley S T, Santiago, J G. PIV measurements of a microchannel flow. Experiments in Fluids 1999. 27(5): 414-419
[40] Evans J, Liepmann D, Pisano A P, Planar laminar mixer. In The 10th Annual International Workshop on MEMS, 1997. 26-30
[41] Schaaf S A, ChambréP L. Flow of rarefied gases. Princeton University Press: Princeton. 1961
[42] Derjaguin B V. Superdense water. Scientific American, 1970. 223(5): 52-71
[43] Derjaguin B V, Popovskij Y M, Altoiz B A. Liquid-crystalline state of the wall-adjacent layers of some polar liquids. Journal of Colloid and Interface Science, 1983. 96(2): 492-503
[44] Bau H H, Pfahler J N. Experimental Observations of Liquid Flow in Micro Conduits. In Proceedings of 39th AIAA Aerospace Sciences Meeting & Exhibit, Reno. NV. 2001. AIAA paper 2001-0722
[45] Yih C S. Stability of liquid flow down an inclined plane. Physics of Fluids, 1963. 6(3): 321-334
[46] Hickox C E. Instability due to viscosity and density stratification in axisymmetric pipe flow. Physics of Fluids, 1971. 14(2): 251
[47] Yiantsios S G, Higgins B G. Linear stability of plane Poiseuille flow of two superposed fluids. Physics of Fluids, 1988. 31(11): 3225
[48] Joseph D D, Renardy M, Saut J C. Hyperbolicity and change of type in the flow of viscoelastic fluids. Archive for Rational Mechanics and Analysis, 1985. 87(3): 213-251
[49] Renardy Y. Weakly nonlinear behavior of periodic disturbances in two-layer Couette-Poiseuille flow. Physics of Fluids, 1989. 1(10): 1666
[50] Coward A V, Renardy Y Y, Renardy M, et al. Temporal evolution of periodic disturbances in two-Layer couette Flow. Journal of Computational Physics, 1997. 132(2): 346-361
[51] Li J, Renardy Y Y, Renardy M. Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method. Physics of fluids, 2000. 12(2): 269
[52] Cao Q, Sarkar K, Prasad, A K. Direct numerical simulations of two-layer viscosity-stratified flow. International Journal of Multiphase Flow, 2004. 30(12): 1485-1508
[53] Khomami B, Su, K C. An experimental/theoretical investigation of interfacial instabilities in superposed pressure-driven channel flow of Newtonian and well characterized viscoelastic fluids: Part I: linear stability and encapsulation effects. Journal of Non-Newtonian Fluid Mechanics, 2000. 91(1): 59-84
[54] Sangalli M, Gallagher C T, Leighton D T, et al. Finite-amplitude waves at the interface between fluids with different viscosity: theory and experiments. Physical Review Letters, 1995. 75(1): 77-80
[55] Cao Q, Ventresca A L, Sreenivas K R, et al. Instability due to viscosity stratification downstream of a centerline injector. The Canadian Journal of Chemical Engineering, 2003. 81(5): 913-922
[56] Tanthapanichakoon W, Aoki N, Matsuyama K, et al. Design of mixing in microfluidic liquid slugs based on a new dimensionless number for precise reaction and mixing operations. Chemical Engineering Science, 2006. 61(13): 4220-4232
[57] Ho C M, Tai Y C. Micro-electro-mechanical systems and fluid flow. Annual review of fluid mechanics, 1998. 30: 579-612
[58] Zahn J D, Reddy V. Two phase micromixing and analysis using electrohydrodynamic instabilities. Microfluidics and Nanofluidics, 2006. 2(5): 399-415
[59] Jedlovszky P, Vinczeá, Horvai G. Properties of water/apolar interfaces as seen from Monte Carlo simulations. Journal of Molecular Liquids, 2004. 109(2): 99-108
[60] Robins I, Shaw J, Miller B, et al. Solute transfer by liquid/liquid exchange without mixing in micro-contactor devices. In 1st International Conference on Microreaction Technology, 1998. 35-46
[61] Burns J R, Ramshaw C. Development of a microreactor for chemical production. Chemical Engineering Research and Design, 1999. 77(3): 206-211
[62] TeGrotenhuis W E, Cameron R J, Butcher M G, et al. Microchannel devices for efficient contacting of liquids in solvent extraction. Separation Science and Technology, 1999. 34(6): 951-974
[63] TeGrotenhuis W E, Cameron R J, Viswanathan, V V, et al. Solvent extraction and gas absorption using microchannel contactors. In Proceedings of the 2nd international conference on microreaction technology, Ehrfeld W, Rinard I H, Wegeng R S, Eds. New Orleans. USA. 1998. 329
[64] Kamholz A E, Weigl B H, Finlayson, B A, et al. Quantitative analysis of molecular interaction in a microfluidic channel: the T-sensor. Analytical Chemistry, 1999. 71(23): 5340-5347
[65] Sato K, Hibara A, Tokeshi M, et al. Microchip-based chemical and biochemical analysis systems. Advanced Drug Delivery Reviews, 2003. 55(3): 379-391
[66] Tokeshi M, Minagawa T, Kitamori T. Integration of a microextraction system on a glass chip: ion-pair solvent extraction of Fe (II) with 4, 7-diphenyl-1, 10-phenanthrolinedisulfonic acid and tri-n-octylmethylammonium chloride. Analytical Chemistry, 2000. 72(7): 1711-1714
[67] Tokeshi M, Minagawa T, Kitamori T. Integration of a microextraction system: Solvent extraction of a Co-2-nitroso-5-dimethylaminophenol complex on a microchip. Journal of Chromatography A, 2000. 894(1-2): 19-23
[68] Sato K, Tokeshi M, Odake T, et al. Integration of an immunosorbent assay system: analysis of secretory human immunoglobulin A on polystyrene beads in a microchip. Analytical Chemistry, 2000. 72(6): 1144-1147
[69] Hisamoto H, Horiuchi T, Tokeshi M, et al. On-chip integration of neutral ionophore-based ion pair extraction reaction. Analytical Chemistry, 2001. 73(6): 1382-1386
[70] Kim H B, Ueno K, Chiba M, et al. Spatially-resolved fluorescence spectroscopic study on liquid/liquid extraction processes in polymer microchannels. Analytical Sciences, 2000. 16(8): 871-876
[71]方群,陈宏,蔡增轩.微流控芯片停流液-液萃取技术的研究.高等学校化学学报,2004. 25(6): 261-263
[72] Rayleigh L, On waves propagated along the plane surface of an elastic solid. In Proceedings of the London Mathematical Society, London, 1885.1: 4-11
[73] Zhou H, You X Y. Weakly Nonlinear Theory of Hydrodynamic Stability. Science in China (Series A), 1992. 35(12): 1486-1495
[74] Zhou H, You X Y. On Problems in the Weakly Nonlinear Theory of Hydrodynamic Stability and Its improvement. Acta Mechanica Sinica, 1993. 19(1): 1-12
[75] Squire H B, On the stability for three-dimensional disturbances of viscous fluid flow between parallel walls. In Proceedings of the Royal Society of London, 1933. 142: 621-628
[76] Schubauer G B, Skramstad H K. Fluid Dynamics-Laminar Boundary-Layer oscillations and stability of laminar flow. American Institute of Aeronautics and Astronautics, 2003. 41(7): 88-97
[77] Lin Z, Kerle T, Baker S M, et al. Electric field induced instabilities at liquid/liquid interfaces. 2001. 114: 2377
[78] Joo Cho K, Kim M U, Shin H D. Linear stability of two-dimensional steady flow in wavy-walled channels. Fluid Dynamics Research, 1998. 23(6): 349-370
[79] Min T, Kim J. Effects of hydrophobic surface on stability and transition. Physics of Fluids, 2005. 17: 108106
[80] You X Y, Zheng J R, Jing Q. Effects of boundary slip and apparent viscosity on the stability of microchannel flow. Forschung im Ingenieurwesen, 2007. 71(2): 99-106
[81] Schubauer G B, Klebaxoff P S. Contributions on the mechanics of boundary-layer transition. NACA TN 1955. 3489
[82] Klebanoff P S, Tidstrom K D, Sargent L M. The three-dimensional nature of boundary-layer instability. Journal of Fluid Mechanics, 1962. 12(1): 1-34
[83] Ross J A, Barnes F H, Burns J G, et al. The flat plate boundary layer. Part 3. Comparison of theory with experiment. Journal of Fluid Mechanics, 1970. 43: 819-832
[84] Gaster M. A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability. Journal of Fluid Mechanics, 1962. 14: 222-224
[85] Nayfeh A H. Stability of three-dimensional boundary layers. AIAA Journal, 1980. 18(4): 406–416
[86] Thomas L H. The stability of plane Poiseuille flow. Physical Review Letters, 1953. 91(4): 780-783
[87] Jordinson R. The flat plate boundary layer. Part 1. Numerical integration of the Orr-Sommerfeld equation. Journal of Fluid Mechanics, 1970. 43: 801-811
[88] Mercier B. An introduction to the numerical analysis of spectral methods. Lecture Notes in Physics, 1989. 318
[89] Zebib A. A Chebyshev method for the solution of boundary value problems. Journal of Computational Physics, 1984. 53(3): 443-455
[90] Boomkam P A M, Boersma B J, Miesen R H M. A chebyshev collocation method for solving two-phase flow stability problems. 1997. 132: 191-200
[91] Piessens R. Computing integral transforms and solving integral equations using Chebyshev polynomial approximations. Journal of Computational and Applied Mathematics, 2000. 121(1-2): 113-124
[92] Eyk N G, Poh S T. Parametric studies of microchannel conjugate liquid flows with Zeta potential effects. Journal of Electronics Manufacturing, 2000. 10(4): 237-252
[93] Yang C, Li D, Masliyah J H. Modeling forced liquid convection in rectangular microchannels with electrokinetic effects. International Journal of Heat and Mass Transfer, 1998. 41(24): 4229-4249
[94] Mohiuddin Mala G, Li D, Dale J D. Heat transfer and fluid flow in microchannels. International Journal of Heat and Mass Transfer, 1997. 40(13): 3079-3088
[95] Ermakov S V, Jacobson S C, Ramsey J M. Computer simulations of electrokinetic transport in microfabricated channel structures. Analytical Chemistry, 1998. 70(21): 4494-4504
[96] Bianchi F, Ferrigno R, Girault H H. Finite element simulation of an electroosmotic-driven flow division at a T-junction of microscale dimensions. Analytical Chemistry, 2000. 72(9): 1987-1993
[97] Probstein R F. Physicochemical hydrodynamics: an introduction. Wiley-Interscience: New York. 1994.
[98] Kirby B J, Hasselbrink Jr E F. Zeta potential of microfluidic substrates: 1. Theory, experimental techniques, and effects on separations. Journal of Chemical Physics, 2004. 25(2): 187-202
[99] Kirby B J, Hasselbrink Jr E F. Zeta potential of microfluidic substrates: 2. Data for polymers. Journal of Chemical Physics, 2004. 25(2): 203-213
[100] Mohiuddin Mala G, Yang C, Li D. Electrical double layer potential distribution in a rectangular microchannel. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 1998. 135(1-3): 109-116
[101] Shin S, Kang I, Cho Y K. A new method to measure zeta potentials of microfabricated channels by applying a time-periodic electric field in a T-channel. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2007. 294(1-3): 228-235
[102] Park H M, Hong S M. Estimation of the zeta potential and the dielectric constant using velocity measurements in the electroosmotic flows. Journal of Colloid and Interface Science, 2006. 304(2): 505-511
[103] Venditti R, Xuan X, Li D. Experimental characterization of the temperature dependence of zeta potential and its effect on electroosmotic flow velocity in microchannels. Microfluidics and Nanofluidics, 2006. 2(6): 493-499
[104] Arulanandam S, Li D. Determining Zeta Potential and Surface Conductance by Monitoring the Current in Electro-osmotic Flow. Journal of Colloid and Interface Science, 2000. 225(2): 421-428
[105] Ng E Y K, Poh S T. Parametric studies of microchannel conjugate liquid flows with zeta potential effects. Journal of Electronics Manufacturing, 2000. 10(4): 237-252
[106] Sze A, Erickson D, Ren L, et al. Zeta-potential measurement using the Smoluchowski equation and the slope of the current–time relationship in electroosmotic flow. Journal of Colloid And Interface Science, 2003. 261(2): 402-410
[107] Cohen H, Cooley J W. The numerical solution of the time-dependent Nernst-Planck equations. Biophysical Journal, 1965. 5(2): 145-162
[108] Ng E Y K, Tan, S T. Study of EDL effect on 3-D developing flow in microchannel with Poisson-Boltzmann and Nernst-Planck models. International journal for numerical methods in engineering, 2007. 71(7): 818-836
[109] Li D. Electrokinetics in microfluidics. Elsevier: Amsterdam. 2004
[110] Ren L, Li D. Improved understanding of the effect of electrical double layer on pressure-driven flow in microchannels. Analytica Chimica Acta, 2004. 531: 15-23
[111] Peng X F, Peterson G P, Wang B X. Frictional flow characteristics of water flowing through rectangular microchannels. Experimental Heat Transfer, 1994. 7(4): 249-264
[112] Ren L, Qu W, Li D. Interfacial electrokinetic effects on liquid flow in microchannels. International Journal of Heat and Mass Transfer, 2001. 44(16): 3125-3134
[113] Mohiuddin Mala G, Li D, Werner, C, et al. Flow characteristics of water through a microchannel between two parallel plates with electrokinetic effects. International Journal of Heat and Fluid Flow, 1997. 18(5): 489-496
[114] Ren L, Li D, Qu W. Electro-viscous effects on liquid flow in microchannels. Journal of colloid and interface science, 2001. 233(1): 12-22
[115] Kulinsky L, Wang Y, Ferrari M. Eletroviscous effects in microchannels. Proceedings of SPIE, 1999. 3606: 158-168
[116] Mohiuddin Mala G, Li D. Flow characteristics of water in microtubes. International Journal of Heat and Fluid Flow, 1999. 20(2): 142-148
[117] Levitt D G. Streaming potential: Continuum expression applicable to very small nonuniform ion channels. The Journal of Chemical Physics, 1990. 92(11): 6953-6957
[118] Farwig R. Stationary Solutions of Compressible Navier–Stokes Equations with Slip Boundary Conditions. Communications in Partial Differential Equations, 1989. 14(11): 1579-1606
[119] Kamholz A E. Proliferation of microfluidics in literature and intellectual property. Lab on a Chip, 2004. 4(2): 16N-20N
[120] Vinogradova O I. Slippage of water over hydrophobic surfaces. International Journal of Mineral Processing, 1999. 56(1-4): 31-60
[121] Granick S, Zhu Y, Lee H. Slippery questions about complex fluids flowing past solids. Nature Materials, 2003. 2(4): 221-227
[122] Bonaccurso E, Kappl M, Butt H J. Hydrodynamic force measurements: Boundary slip of water on hydrophilic surfaces and electrokinetic effects. Physics review letters, 2002. 88(7): 76103
[123]Ruckenstein E, Rajora P. On the no-slip boundary condition of hydrodynamics. Journal of Colloid and Interface Science, 1983. 96(2): 488-491
[124] Choi C H, Apparent slip flows in hydrophilic and hydrophobic microchannels. In 2003. 15: 2897.
[125] Lauga E, Cossu C. A note on the stability of slip channel flows. Physics of Fluids, 2005. 17(8): 088106
[126] Chu A K-H. Instability of Navier slip flow of liquids. 2004. 332(11): 895-900
[127] Watanabe K, Mizunuma H. Slip of Newtonian fluids at slid boundary. JSME international journal. Series B, fluids and thermal engineering, 1998. 41(3): 525-529
[128]Zhu Y, Granick S. Rate-dependent slip of Newtonian liquid at smooth surfaces. Physical Review Letters, 2001. 87(9): 96105
[129] Pfahler J, Harley J, Bau H, et al. Liquid transport in micron and submicron channels. Sensors and Actuators A: Physical, 1989. 22(1-3): 431-434
[130]文书明.微流边界层理论及其应用.冶金工业出版社:北京. 2002
[131] Gong L, Wu J-k. Resistance effect of electric double layer on liquid flow in microchannel. Applied Mathematics and Mechanics, 2006. 27(10): 1391-1398
[132] Gao Y, Wong T N, Yang C, et al. Transient two-liquid electroosmotic flow with electric charges at the interface. Colloids and Surfaces, 2005. 266(1-3): 117-128
[133] Gao Y, Wong T N, Chai J C, et al. Numerical simulation of two-fluid electroosmotic flow in microchannels. International Journal of Heat and Mass Transfer, 2005. 48(25-26): 5103-5111
[134] Gao Y, Wong T N, Yang C, et al. Two-fluid electroosmotic flow in microchannels. Journal of Colloid and Interface Science, 2005. 284(1): 306-314
[135] Lin Z, Kerle T, Baker S M, et al. Electric field induced instabilities at liquid/liquid interfaces. Journal of Chemical Physics 2001. 114(5): 2377
[136] Li Z X. Experimental study on flow characteristics of liquid in circular microtubes. Nanoscale and Microscale Thermophysical Engineering, 2003. 7(3): 253-265
[137] Xu B, Ooti K T, Wong N T, et al. Experimental investigation of flow friction for liquid flow in microchannels. International Communications in Heat and Mass Transfer, 2000. 27(8): 1165-1176
[138] Judy J, Maynes D, Webb B W. Characterization of frictional pressure drop for liquid flows through microchannels. International Journal of Heat and Mass Transfer, 2002. 45(17): 3477-3489
[139] Sharp K V, Adrian R J. Transition from laminar to turbulent flow in liquid filled microtubes. Experiments in Fluids, 2004. 36(5): 741-747
[140] Hao P F, He F, Zhu K Q. Flow characteristics in a trapezoidal silicon microchannel. Journal of Micromechanics and Microengineering, 2005. 15(6): 1362-1368
[141] Wang B X, Peng X F. Experimental investigation on liquid forced-convection heat transfer through microchannels. International Journal of Heat and Mass Transfer, 1994. 37(Supplement 1): 73-82
[142] Tretheway D C, Meinhart C D. Apparent fluid slip at hydrophobic microchannel walls. Physics of Fluids, 2002. 14(3): L9-L12
[143] Tardu S. Early transition in microchannels under EDL effect. Spie-Int Society Optical Engineering: Bellingham. 2004. 5345: 238
[144] Tardu S. The electric double layer effect on the microchannel flow stability and heat transfer. Superlattices and Microstructures, 2004. 35(3-6): 513-529
[145] Tardu S. Analysis of the electric double layer effect on microchannel flow stability. Microscale Thermophysical Engineering, 2004. 8(4): 383-401
[146] Tardu S. Interfacial electrokinetic effect on the microchannel flow linear stability. Journal of Fluids Engineering-Transactions of the Asme, 2004. 126(1): 10-13
[147] Orszag S A. Accurate solution of the Orr–Sommerfeld stability equation. Journal of Fluid Mechanics, 1971. 50(04): 689-703
[148] Orszag S A, Patera A T. Subcritical Transition to Turbulence in Plane Channel Flows. Physical Review Letters, 1980. 45(12): 989-993
[149] Thorpe S A. Experiments on the instability of stratified shear flows: miscible fluids. Cambridge Univ Press, 2006. 46(02): 299-319
[150] Peter J S. Linear stability theory and bypass transition in shear flows. Physics of Plasmas, 2000. 7(5): 1788-1794
[151] Yang J, Bhattacharyya A, Masliyah J H, et al. Oscillating laminar electrokinetic flow in infinitely extended rectangular microchannels. Journal of Colloid and Interface Science, 2003. 261(1): 21-31
[152] Hogberg M, Bewley T R, Henningson D S. Linear feedback control and estimation of transition in plane channel flow. Journal of Fluid Mechanics, 2003. 481: 149-175
[153] Sadr R, Yoda M, Gnanaprakasam P, et al. Velocity measurements inside the diffuse electric double layer in electro-osmotic flow. Applied Physics Letters, 2006. 89(4): 3
[154] Shi Y, Zhao T S, Guo Z. Simplified model and lattice Boltzmann algorithm for microscale electro-osmotic flows and heat transfer. International Journal of Heat and Mass Transfer, 2008. 51(3-4): 586-596
[155] Sia S K, Whitesides G M. Microfluidic devices fabricated in poly (dimethylsiloxane) for biological studies. Electrophoresis, 2003. 24(21): 3563-3576
[156] Marcos, Yang C, Wong T N, et al. Dynamic aspects of electroosmotic flow in rectangular microchannels. International Journal of Engineering Science, 2004. 42(13-14): 1459-1481
[157] Tang G Y, Yang C, Chai C J, et al. Modeling of Electroosmotic Flow and Capillary Electrophoresis with the Joule Heating Effect: The Nernst-Planck Equation versus the Boltzmann Distribution. Langmuir, 2003. 19(26): 10975-10984
[158] Ranganathan B T, Govindarajan R. Stabilization and destabilization of channel flow by location of viscosity-stratified fluid layer. Physics of Fluids, 2001. 13(1): 1-3
[159] Selvam B, Merk S, Govindarajan R, et al. Stability of miscible core-annular flows with viscosity stratification. Journal of Fluid Mechanics 2007. 592: 23-49
[2] Chovan T, Guttman A. Microfabricated devices in biotechnology and biochemical processing. 2002. 20(3): 116-122
[3] Squires T M, Quake S R. Microfluidics: Fluid physics at the nanoliter scale. Reviews of Modern Physics, 2005. 77(3): 977-1026
[4] Karniadakis G E, Beskok A.微流动——基础与模拟.化学工业出版社:北京. 2002
[5] Ho C M, Tai Y C. Micro-Electro-Mechanical-Systems (MEMS) and Fluid Flows. Annual Reviews in Fluid Mechanics, 1998. 30(1): 579-612
[6] Zeng J, Korsmeyer T. Principles of droplet electrohydrodynamics for lab-on-a-chip. Royal Society of Chemistry, 2004. 4(4): 265-277
[7] Stone H A, Stroock A D, Ajdari A. Engineering flows in small devices: Microfluidics toward a lab-on-a-chip. Annual Review of Fluid Mechanics, 2004. 36(1): 381-411
[8] Erickson D. Towards numerical prototyping of labs-on-chip: modeling for integrated microfluidic devices. Microfluidics and Nanofluidics, 2005. 1(4): 301-318
[9]方肇伦.微流控分析芯片的制作及应用.化学工业出版社:北京. 2005
[10]林炳承,秦建华.微流控芯片实验室.科学出版社:北京. 2006
[11] Zheng B, Roach L S, Ismagilov R F. Screening of Protein Crystallization Conditions on a Microfluidic Chip Using Nanoliter-Size Droplets. Journal of the American Chemical Society, 2003. 125(37): 11170-11171
[12] Wang B X, Peng X F. Experimental investigation on liquid forced convection heat transfer through microchannels. International Journal of Heat and Mass Transfer, 1994. 37(Supplement 1): 73-82
[13] Song H, Tice J D, Ismagilov R F. A microfluidic system for controlling reaction networks in time. 2003. 42(7): 768-72
[14] Dittrich P S, Manz A. Lab-on-a-chip: microfluidics in drug discovery. Nature Reviews Drug Discovery 2006. 5(3): 210-218
[15] Hu X, Wang S, Juang Y J, et al. Five-cross microfluidic network design free of coupling between electrophoretic motion and electro-osmotic flow. Applied Physics Letters, 2006. 89: 084101
[16] Lee J S, Dylla-Spears R, Teclemariam N P, et al. Microfluidic four-roll mill for all flow types. Applied Physics Letters, 2007. 90(7): 074103
[17] Groisman A, Enzelberger M, Quake S R. Microfluidic memory and control devices. Science, 2003. 300(5621): 955
[18] Barker S L R, Ross D, Tarlov M J, et al. Control of flow direction in microfluidic devices with polyelectrolyte multilayers. Analytical Chemistry, 2000. 72(24): 5925-5929
[19] Thompson P A, Troian S M. A general boundary condition for liquid flow at solid surfaces. Nature, 1997. 389: 360-362
[20] Bayraktar T, Pidugu S B. Characterization of liquid flows in microfluidic systems. 2006. 49(5-6): 815-824
[21] Bhushan B. Introduction to Nanotechnology. Wiley: New York. 2003
[22] Rice C L, Whitehead R. Electrokinetic Flow in a Narrow Cylindrical Capillary. American Chemical Society, 1965. 69(11): 4017-4024
[23] Black W B, Graham M D. Slip, concentration fluctuations and flow instability in sheared polymer solutions. Macromolecules, 2001. 34(17): 5731–5733
[24] Koo J, Kleinstreuer C. Analysis of surface roughness effects on heat transfer in micro-conduits. International Journal of Heat and Mass Transfer, 2005. 48(13): 2625-2634
[25] Chan H B, Aksyuk V A, Kleiman R N, et al. Quantum mechanical actuation of microelectromechanical systems by the Casimir force. Science, 2001. 291(5510): 1941-1944
[26] Ngoma G D, Erchiqui F. Heat flux and slip effects on liquid flow in a microchannel. International Journal of Thermal Sciences, 2007. 46(11): 1076-1083
[27] Corbett J, McKeown P A, Peggs G N, et al. Nanotechnology: International Developments and Emerging Products. CIRP Annals-Manufacturing Technology, 2000. 49(2): 523-545
[28] Gad-el-Hak M. The fluid mechanics of microdevices-The Freeman Scholar Lecture. Journal of Fluids Engineering-Transactions of the Asme, 1999. 121(1): 5-33
[29]尤学一,郑敬茹.微间距平板Poiseuille流动的稳定性.纳米技术与精密工程,2007. 5(4): 319-322
[30]尤学一,郑湘君,郑敬茹.微尺度流道内液体表观黏性系数的分子理论.物理学报,2007. 56(004): 2323-2329
[31]尤学一,李胜华,肖厚蓬.微流道粗糙壁面对流动阻力和控制的影响.化学工程,2008. 36(008): 25-27
[32] Pfahler J, Harley J, Bau H, et al. Gas and liquid flow in small channels.American Society of Mechanical Engineers, 1991. 32: 49-60
[33] Harley J C, Bau H H, Zemel J N, et al. Gas flow in micro-channels. Journal of Fluid Mechanics, 1995. 284: 257-274
[34] Liu J Q, Tai Y C, Pong K C, et al., Micromachined channel/pressure sensor systems for micro flow studies. In The 7th International Conference Solid-State Sensors and Actuator, 1993. 995-998
[35] Breuer K S, Piekos E S, Gonzales D A. DSMC simulations of continuum flows. In AIAA Thermophysics Conference, San Diego. 1995. 19-22
[36] Gaitan M, Locascio L E. Embedded microheating elements in polymeric micro channels for temperature control and fluid flow sensing. 2004. 109(3): 335-344
[37] Hitt D L, McGarry M. Numerical simulations of laminar mixing surfaces in pulsatile microchannel flows. Mathematics and Computers in Simulation, 2004. 65(4-5): 399-416
[38] Santiago J G, Wereley S T, Meinhart C D, et al. A particle image velocimetry system for microfluidics. Experiments in Fluids 1998. 25(4): 316-319
[39] Meinhart C D, Wereley S T, Santiago, J G. PIV measurements of a microchannel flow. Experiments in Fluids 1999. 27(5): 414-419
[40] Evans J, Liepmann D, Pisano A P, Planar laminar mixer. In The 10th Annual International Workshop on MEMS, 1997. 26-30
[41] Schaaf S A, ChambréP L. Flow of rarefied gases. Princeton University Press: Princeton. 1961
[42] Derjaguin B V. Superdense water. Scientific American, 1970. 223(5): 52-71
[43] Derjaguin B V, Popovskij Y M, Altoiz B A. Liquid-crystalline state of the wall-adjacent layers of some polar liquids. Journal of Colloid and Interface Science, 1983. 96(2): 492-503
[44] Bau H H, Pfahler J N. Experimental Observations of Liquid Flow in Micro Conduits. In Proceedings of 39th AIAA Aerospace Sciences Meeting & Exhibit, Reno. NV. 2001. AIAA paper 2001-0722
[45] Yih C S. Stability of liquid flow down an inclined plane. Physics of Fluids, 1963. 6(3): 321-334
[46] Hickox C E. Instability due to viscosity and density stratification in axisymmetric pipe flow. Physics of Fluids, 1971. 14(2): 251
[47] Yiantsios S G, Higgins B G. Linear stability of plane Poiseuille flow of two superposed fluids. Physics of Fluids, 1988. 31(11): 3225
[48] Joseph D D, Renardy M, Saut J C. Hyperbolicity and change of type in the flow of viscoelastic fluids. Archive for Rational Mechanics and Analysis, 1985. 87(3): 213-251
[49] Renardy Y. Weakly nonlinear behavior of periodic disturbances in two-layer Couette-Poiseuille flow. Physics of Fluids, 1989. 1(10): 1666
[50] Coward A V, Renardy Y Y, Renardy M, et al. Temporal evolution of periodic disturbances in two-Layer couette Flow. Journal of Computational Physics, 1997. 132(2): 346-361
[51] Li J, Renardy Y Y, Renardy M. Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method. Physics of fluids, 2000. 12(2): 269
[52] Cao Q, Sarkar K, Prasad, A K. Direct numerical simulations of two-layer viscosity-stratified flow. International Journal of Multiphase Flow, 2004. 30(12): 1485-1508
[53] Khomami B, Su, K C. An experimental/theoretical investigation of interfacial instabilities in superposed pressure-driven channel flow of Newtonian and well characterized viscoelastic fluids: Part I: linear stability and encapsulation effects. Journal of Non-Newtonian Fluid Mechanics, 2000. 91(1): 59-84
[54] Sangalli M, Gallagher C T, Leighton D T, et al. Finite-amplitude waves at the interface between fluids with different viscosity: theory and experiments. Physical Review Letters, 1995. 75(1): 77-80
[55] Cao Q, Ventresca A L, Sreenivas K R, et al. Instability due to viscosity stratification downstream of a centerline injector. The Canadian Journal of Chemical Engineering, 2003. 81(5): 913-922
[56] Tanthapanichakoon W, Aoki N, Matsuyama K, et al. Design of mixing in microfluidic liquid slugs based on a new dimensionless number for precise reaction and mixing operations. Chemical Engineering Science, 2006. 61(13): 4220-4232
[57] Ho C M, Tai Y C. Micro-electro-mechanical systems and fluid flow. Annual review of fluid mechanics, 1998. 30: 579-612
[58] Zahn J D, Reddy V. Two phase micromixing and analysis using electrohydrodynamic instabilities. Microfluidics and Nanofluidics, 2006. 2(5): 399-415
[59] Jedlovszky P, Vinczeá, Horvai G. Properties of water/apolar interfaces as seen from Monte Carlo simulations. Journal of Molecular Liquids, 2004. 109(2): 99-108
[60] Robins I, Shaw J, Miller B, et al. Solute transfer by liquid/liquid exchange without mixing in micro-contactor devices. In 1st International Conference on Microreaction Technology, 1998. 35-46
[61] Burns J R, Ramshaw C. Development of a microreactor for chemical production. Chemical Engineering Research and Design, 1999. 77(3): 206-211
[62] TeGrotenhuis W E, Cameron R J, Butcher M G, et al. Microchannel devices for efficient contacting of liquids in solvent extraction. Separation Science and Technology, 1999. 34(6): 951-974
[63] TeGrotenhuis W E, Cameron R J, Viswanathan, V V, et al. Solvent extraction and gas absorption using microchannel contactors. In Proceedings of the 2nd international conference on microreaction technology, Ehrfeld W, Rinard I H, Wegeng R S, Eds. New Orleans. USA. 1998. 329
[64] Kamholz A E, Weigl B H, Finlayson, B A, et al. Quantitative analysis of molecular interaction in a microfluidic channel: the T-sensor. Analytical Chemistry, 1999. 71(23): 5340-5347
[65] Sato K, Hibara A, Tokeshi M, et al. Microchip-based chemical and biochemical analysis systems. Advanced Drug Delivery Reviews, 2003. 55(3): 379-391
[66] Tokeshi M, Minagawa T, Kitamori T. Integration of a microextraction system on a glass chip: ion-pair solvent extraction of Fe (II) with 4, 7-diphenyl-1, 10-phenanthrolinedisulfonic acid and tri-n-octylmethylammonium chloride. Analytical Chemistry, 2000. 72(7): 1711-1714
[67] Tokeshi M, Minagawa T, Kitamori T. Integration of a microextraction system: Solvent extraction of a Co-2-nitroso-5-dimethylaminophenol complex on a microchip. Journal of Chromatography A, 2000. 894(1-2): 19-23
[68] Sato K, Tokeshi M, Odake T, et al. Integration of an immunosorbent assay system: analysis of secretory human immunoglobulin A on polystyrene beads in a microchip. Analytical Chemistry, 2000. 72(6): 1144-1147
[69] Hisamoto H, Horiuchi T, Tokeshi M, et al. On-chip integration of neutral ionophore-based ion pair extraction reaction. Analytical Chemistry, 2001. 73(6): 1382-1386
[70] Kim H B, Ueno K, Chiba M, et al. Spatially-resolved fluorescence spectroscopic study on liquid/liquid extraction processes in polymer microchannels. Analytical Sciences, 2000. 16(8): 871-876
[71]方群,陈宏,蔡增轩.微流控芯片停流液-液萃取技术的研究.高等学校化学学报,2004. 25(6): 261-263
[72] Rayleigh L, On waves propagated along the plane surface of an elastic solid. In Proceedings of the London Mathematical Society, London, 1885.1: 4-11
[73] Zhou H, You X Y. Weakly Nonlinear Theory of Hydrodynamic Stability. Science in China (Series A), 1992. 35(12): 1486-1495
[74] Zhou H, You X Y. On Problems in the Weakly Nonlinear Theory of Hydrodynamic Stability and Its improvement. Acta Mechanica Sinica, 1993. 19(1): 1-12
[75] Squire H B, On the stability for three-dimensional disturbances of viscous fluid flow between parallel walls. In Proceedings of the Royal Society of London, 1933. 142: 621-628
[76] Schubauer G B, Skramstad H K. Fluid Dynamics-Laminar Boundary-Layer oscillations and stability of laminar flow. American Institute of Aeronautics and Astronautics, 2003. 41(7): 88-97
[77] Lin Z, Kerle T, Baker S M, et al. Electric field induced instabilities at liquid/liquid interfaces. 2001. 114: 2377
[78] Joo Cho K, Kim M U, Shin H D. Linear stability of two-dimensional steady flow in wavy-walled channels. Fluid Dynamics Research, 1998. 23(6): 349-370
[79] Min T, Kim J. Effects of hydrophobic surface on stability and transition. Physics of Fluids, 2005. 17: 108106
[80] You X Y, Zheng J R, Jing Q. Effects of boundary slip and apparent viscosity on the stability of microchannel flow. Forschung im Ingenieurwesen, 2007. 71(2): 99-106
[81] Schubauer G B, Klebaxoff P S. Contributions on the mechanics of boundary-layer transition. NACA TN 1955. 3489
[82] Klebanoff P S, Tidstrom K D, Sargent L M. The three-dimensional nature of boundary-layer instability. Journal of Fluid Mechanics, 1962. 12(1): 1-34
[83] Ross J A, Barnes F H, Burns J G, et al. The flat plate boundary layer. Part 3. Comparison of theory with experiment. Journal of Fluid Mechanics, 1970. 43: 819-832
[84] Gaster M. A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability. Journal of Fluid Mechanics, 1962. 14: 222-224
[85] Nayfeh A H. Stability of three-dimensional boundary layers. AIAA Journal, 1980. 18(4): 406–416
[86] Thomas L H. The stability of plane Poiseuille flow. Physical Review Letters, 1953. 91(4): 780-783
[87] Jordinson R. The flat plate boundary layer. Part 1. Numerical integration of the Orr-Sommerfeld equation. Journal of Fluid Mechanics, 1970. 43: 801-811
[88] Mercier B. An introduction to the numerical analysis of spectral methods. Lecture Notes in Physics, 1989. 318
[89] Zebib A. A Chebyshev method for the solution of boundary value problems. Journal of Computational Physics, 1984. 53(3): 443-455
[90] Boomkam P A M, Boersma B J, Miesen R H M. A chebyshev collocation method for solving two-phase flow stability problems. 1997. 132: 191-200
[91] Piessens R. Computing integral transforms and solving integral equations using Chebyshev polynomial approximations. Journal of Computational and Applied Mathematics, 2000. 121(1-2): 113-124
[92] Eyk N G, Poh S T. Parametric studies of microchannel conjugate liquid flows with Zeta potential effects. Journal of Electronics Manufacturing, 2000. 10(4): 237-252
[93] Yang C, Li D, Masliyah J H. Modeling forced liquid convection in rectangular microchannels with electrokinetic effects. International Journal of Heat and Mass Transfer, 1998. 41(24): 4229-4249
[94] Mohiuddin Mala G, Li D, Dale J D. Heat transfer and fluid flow in microchannels. International Journal of Heat and Mass Transfer, 1997. 40(13): 3079-3088
[95] Ermakov S V, Jacobson S C, Ramsey J M. Computer simulations of electrokinetic transport in microfabricated channel structures. Analytical Chemistry, 1998. 70(21): 4494-4504
[96] Bianchi F, Ferrigno R, Girault H H. Finite element simulation of an electroosmotic-driven flow division at a T-junction of microscale dimensions. Analytical Chemistry, 2000. 72(9): 1987-1993
[97] Probstein R F. Physicochemical hydrodynamics: an introduction. Wiley-Interscience: New York. 1994.
[98] Kirby B J, Hasselbrink Jr E F. Zeta potential of microfluidic substrates: 1. Theory, experimental techniques, and effects on separations. Journal of Chemical Physics, 2004. 25(2): 187-202
[99] Kirby B J, Hasselbrink Jr E F. Zeta potential of microfluidic substrates: 2. Data for polymers. Journal of Chemical Physics, 2004. 25(2): 203-213
[100] Mohiuddin Mala G, Yang C, Li D. Electrical double layer potential distribution in a rectangular microchannel. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 1998. 135(1-3): 109-116
[101] Shin S, Kang I, Cho Y K. A new method to measure zeta potentials of microfabricated channels by applying a time-periodic electric field in a T-channel. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2007. 294(1-3): 228-235
[102] Park H M, Hong S M. Estimation of the zeta potential and the dielectric constant using velocity measurements in the electroosmotic flows. Journal of Colloid and Interface Science, 2006. 304(2): 505-511
[103] Venditti R, Xuan X, Li D. Experimental characterization of the temperature dependence of zeta potential and its effect on electroosmotic flow velocity in microchannels. Microfluidics and Nanofluidics, 2006. 2(6): 493-499
[104] Arulanandam S, Li D. Determining Zeta Potential and Surface Conductance by Monitoring the Current in Electro-osmotic Flow. Journal of Colloid and Interface Science, 2000. 225(2): 421-428
[105] Ng E Y K, Poh S T. Parametric studies of microchannel conjugate liquid flows with zeta potential effects. Journal of Electronics Manufacturing, 2000. 10(4): 237-252
[106] Sze A, Erickson D, Ren L, et al. Zeta-potential measurement using the Smoluchowski equation and the slope of the current–time relationship in electroosmotic flow. Journal of Colloid And Interface Science, 2003. 261(2): 402-410
[107] Cohen H, Cooley J W. The numerical solution of the time-dependent Nernst-Planck equations. Biophysical Journal, 1965. 5(2): 145-162
[108] Ng E Y K, Tan, S T. Study of EDL effect on 3-D developing flow in microchannel with Poisson-Boltzmann and Nernst-Planck models. International journal for numerical methods in engineering, 2007. 71(7): 818-836
[109] Li D. Electrokinetics in microfluidics. Elsevier: Amsterdam. 2004
[110] Ren L, Li D. Improved understanding of the effect of electrical double layer on pressure-driven flow in microchannels. Analytica Chimica Acta, 2004. 531: 15-23
[111] Peng X F, Peterson G P, Wang B X. Frictional flow characteristics of water flowing through rectangular microchannels. Experimental Heat Transfer, 1994. 7(4): 249-264
[112] Ren L, Qu W, Li D. Interfacial electrokinetic effects on liquid flow in microchannels. International Journal of Heat and Mass Transfer, 2001. 44(16): 3125-3134
[113] Mohiuddin Mala G, Li D, Werner, C, et al. Flow characteristics of water through a microchannel between two parallel plates with electrokinetic effects. International Journal of Heat and Fluid Flow, 1997. 18(5): 489-496
[114] Ren L, Li D, Qu W. Electro-viscous effects on liquid flow in microchannels. Journal of colloid and interface science, 2001. 233(1): 12-22
[115] Kulinsky L, Wang Y, Ferrari M. Eletroviscous effects in microchannels. Proceedings of SPIE, 1999. 3606: 158-168
[116] Mohiuddin Mala G, Li D. Flow characteristics of water in microtubes. International Journal of Heat and Fluid Flow, 1999. 20(2): 142-148
[117] Levitt D G. Streaming potential: Continuum expression applicable to very small nonuniform ion channels. The Journal of Chemical Physics, 1990. 92(11): 6953-6957
[118] Farwig R. Stationary Solutions of Compressible Navier–Stokes Equations with Slip Boundary Conditions. Communications in Partial Differential Equations, 1989. 14(11): 1579-1606
[119] Kamholz A E. Proliferation of microfluidics in literature and intellectual property. Lab on a Chip, 2004. 4(2): 16N-20N
[120] Vinogradova O I. Slippage of water over hydrophobic surfaces. International Journal of Mineral Processing, 1999. 56(1-4): 31-60
[121] Granick S, Zhu Y, Lee H. Slippery questions about complex fluids flowing past solids. Nature Materials, 2003. 2(4): 221-227
[122] Bonaccurso E, Kappl M, Butt H J. Hydrodynamic force measurements: Boundary slip of water on hydrophilic surfaces and electrokinetic effects. Physics review letters, 2002. 88(7): 76103
[123]Ruckenstein E, Rajora P. On the no-slip boundary condition of hydrodynamics. Journal of Colloid and Interface Science, 1983. 96(2): 488-491
[124] Choi C H, Apparent slip flows in hydrophilic and hydrophobic microchannels. In 2003. 15: 2897.
[125] Lauga E, Cossu C. A note on the stability of slip channel flows. Physics of Fluids, 2005. 17(8): 088106
[126] Chu A K-H. Instability of Navier slip flow of liquids. 2004. 332(11): 895-900
[127] Watanabe K, Mizunuma H. Slip of Newtonian fluids at slid boundary. JSME international journal. Series B, fluids and thermal engineering, 1998. 41(3): 525-529
[128]Zhu Y, Granick S. Rate-dependent slip of Newtonian liquid at smooth surfaces. Physical Review Letters, 2001. 87(9): 96105
[129] Pfahler J, Harley J, Bau H, et al. Liquid transport in micron and submicron channels. Sensors and Actuators A: Physical, 1989. 22(1-3): 431-434
[130]文书明.微流边界层理论及其应用.冶金工业出版社:北京. 2002
[131] Gong L, Wu J-k. Resistance effect of electric double layer on liquid flow in microchannel. Applied Mathematics and Mechanics, 2006. 27(10): 1391-1398
[132] Gao Y, Wong T N, Yang C, et al. Transient two-liquid electroosmotic flow with electric charges at the interface. Colloids and Surfaces, 2005. 266(1-3): 117-128
[133] Gao Y, Wong T N, Chai J C, et al. Numerical simulation of two-fluid electroosmotic flow in microchannels. International Journal of Heat and Mass Transfer, 2005. 48(25-26): 5103-5111
[134] Gao Y, Wong T N, Yang C, et al. Two-fluid electroosmotic flow in microchannels. Journal of Colloid and Interface Science, 2005. 284(1): 306-314
[135] Lin Z, Kerle T, Baker S M, et al. Electric field induced instabilities at liquid/liquid interfaces. Journal of Chemical Physics 2001. 114(5): 2377
[136] Li Z X. Experimental study on flow characteristics of liquid in circular microtubes. Nanoscale and Microscale Thermophysical Engineering, 2003. 7(3): 253-265
[137] Xu B, Ooti K T, Wong N T, et al. Experimental investigation of flow friction for liquid flow in microchannels. International Communications in Heat and Mass Transfer, 2000. 27(8): 1165-1176
[138] Judy J, Maynes D, Webb B W. Characterization of frictional pressure drop for liquid flows through microchannels. International Journal of Heat and Mass Transfer, 2002. 45(17): 3477-3489
[139] Sharp K V, Adrian R J. Transition from laminar to turbulent flow in liquid filled microtubes. Experiments in Fluids, 2004. 36(5): 741-747
[140] Hao P F, He F, Zhu K Q. Flow characteristics in a trapezoidal silicon microchannel. Journal of Micromechanics and Microengineering, 2005. 15(6): 1362-1368
[141] Wang B X, Peng X F. Experimental investigation on liquid forced-convection heat transfer through microchannels. International Journal of Heat and Mass Transfer, 1994. 37(Supplement 1): 73-82
[142] Tretheway D C, Meinhart C D. Apparent fluid slip at hydrophobic microchannel walls. Physics of Fluids, 2002. 14(3): L9-L12
[143] Tardu S. Early transition in microchannels under EDL effect. Spie-Int Society Optical Engineering: Bellingham. 2004. 5345: 238
[144] Tardu S. The electric double layer effect on the microchannel flow stability and heat transfer. Superlattices and Microstructures, 2004. 35(3-6): 513-529
[145] Tardu S. Analysis of the electric double layer effect on microchannel flow stability. Microscale Thermophysical Engineering, 2004. 8(4): 383-401
[146] Tardu S. Interfacial electrokinetic effect on the microchannel flow linear stability. Journal of Fluids Engineering-Transactions of the Asme, 2004. 126(1): 10-13
[147] Orszag S A. Accurate solution of the Orr–Sommerfeld stability equation. Journal of Fluid Mechanics, 1971. 50(04): 689-703
[148] Orszag S A, Patera A T. Subcritical Transition to Turbulence in Plane Channel Flows. Physical Review Letters, 1980. 45(12): 989-993
[149] Thorpe S A. Experiments on the instability of stratified shear flows: miscible fluids. Cambridge Univ Press, 2006. 46(02): 299-319
[150] Peter J S. Linear stability theory and bypass transition in shear flows. Physics of Plasmas, 2000. 7(5): 1788-1794
[151] Yang J, Bhattacharyya A, Masliyah J H, et al. Oscillating laminar electrokinetic flow in infinitely extended rectangular microchannels. Journal of Colloid and Interface Science, 2003. 261(1): 21-31
[152] Hogberg M, Bewley T R, Henningson D S. Linear feedback control and estimation of transition in plane channel flow. Journal of Fluid Mechanics, 2003. 481: 149-175
[153] Sadr R, Yoda M, Gnanaprakasam P, et al. Velocity measurements inside the diffuse electric double layer in electro-osmotic flow. Applied Physics Letters, 2006. 89(4): 3
[154] Shi Y, Zhao T S, Guo Z. Simplified model and lattice Boltzmann algorithm for microscale electro-osmotic flows and heat transfer. International Journal of Heat and Mass Transfer, 2008. 51(3-4): 586-596
[155] Sia S K, Whitesides G M. Microfluidic devices fabricated in poly (dimethylsiloxane) for biological studies. Electrophoresis, 2003. 24(21): 3563-3576
[156] Marcos, Yang C, Wong T N, et al. Dynamic aspects of electroosmotic flow in rectangular microchannels. International Journal of Engineering Science, 2004. 42(13-14): 1459-1481
[157] Tang G Y, Yang C, Chai C J, et al. Modeling of Electroosmotic Flow and Capillary Electrophoresis with the Joule Heating Effect: The Nernst-Planck Equation versus the Boltzmann Distribution. Langmuir, 2003. 19(26): 10975-10984
[158] Ranganathan B T, Govindarajan R. Stabilization and destabilization of channel flow by location of viscosity-stratified fluid layer. Physics of Fluids, 2001. 13(1): 1-3
[159] Selvam B, Merk S, Govindarajan R, et al. Stability of miscible core-annular flows with viscosity stratification. Journal of Fluid Mechanics 2007. 592: 23-49