Magnetohydrodynamic Electroosmotic Flow in Zeta Potential Patterned Micro-Parallel Channels
-
摘要: 研究了平行板微管道中二维磁流体(MHD)电渗流(EOF)在zeta电势调制下的流动.流体的流动是由两个外加水平电场和垂直磁场所产生的Lorentz力和电场力的组合驱动的.在滑移边界条件下,得到了流函数以及速度分布的解析解.详细讨论了速度随Hartmann数Ha、滑移长度B、电动宽度K等相关的无量纲参数量级变化的变化规律.结果表明,调制的壁面电势会产生一个垂直速度分量,从而导致涡旋的形成.此外,可以观察到,速度的大小随着滑移长度B和电动宽度K的增大而增大.值得注意的是,速度的大小随着Ha值的增大而减小,这与一维流动中Ha值存在临界值的情况不同.Abstract: Two-dimensional magnetohydrodynamic (MHD) electroosmotic flow (EOF) in zeta potential patterned micro-parallel channels was studied. The flow was driven by the combination of the Lorentz force and the electric field force produced due to an externally imposed vertical magnetic field and two horizontal electric fields. The analytical solutions of stream function and velocity distribution were obtained under the condition of hydrodynamic slippage. The variations of velocities with related non-dimensional parameters, such as Hartmann number Ha,slip length B and electrokinetic width K were addressed in detail. Results show that, the patterned charged surfaces induce a vertical velocity component leading to the formation of the vortexes. Also, the magnitudes of velocities increase with slip length B and electrokinetic width K.Moreover, it is interesting to note that the magnitudes of velocities become small with the increasing value of Ha, unlike the situation where there exists a critical value of Ha in one-dimensional flow. The present theoretical results can be utilized to design efficient microfluidic devices.
-
[1] GRAVESEN P, BRANEBJERG J, JENSEN O S. Microfluidics: a review[J]. Journal of Micromechanics and Microengineering,1993,3(4): 168. [2] BECKER H, GRTNER C. Polymer microfabrication methods for microfluidic analytical applications[J]. Electrophoresis,2000,21(1): 12-26. [3] ZIAIE B, BALDI A, LEI M, et al. Hard and soft micromachining for BioMEMS: review of techniques and examples of applications in microfluidics and drug delivery[J]. Advanced Drug Delivery Reviews,2004,56(2): 145-172. [4] NGUYEN N T, WU Z. Micromixers: a review[J]. Journal of Micromechanics and Microengineering,2005,15(2): R1-R16. [5] OHNO K, TACHIKAWA K, MANZ A. Microfluidics: applications for analytical purposes in chemistry and biochemistry[J]. Electrophoresis,2008,29(22): 4443-4453. [6] CULBERTSON C T, RAMSEY R S, RAMSEY J M. Electroosmotically induced hydraulic pumping on microchips: differential ion transport[J]. Analytical Chemistry,2000,72(10): 2285-2291. [7] DASGUPTA P K, LIU S. Electroosmosis: a reliable fluid propulsion system for flow injection analysis[J]. Analytical Chemistry,1994,66(11): 1792-1798. [8] BAU H H, ZHU J, QIAN S, et al. A magneto-hydrodynamically controlled fluidic network[J]. Sensors and Actuators B: Chemical,2003,88(2): 205-216. [9] QIAN S, BAU H H. Magneto-hydrodynamics based microfluidics[J]. Mechanics Research Communications,2009,36(1): 10-21. [10] JANG J, LEE S S. Theoretical and experimental study of MHD (magnetohydrodynamic) micropump[J]. Sensors and Actuators A: Physical,2000,80(1): 84-89. [11] NGUYEN N T. Micro-magnetofluidics: interactions between magnetism and fluid flow on the microscale[J]. Microfluid Nanofluid,2012,12: 1-16. [12] RIVERO M, CUEVAS S. Analysis of the slip condition in magnetohydrodynamic (MHD) micropumps[J]. Sensors and Actuators B: Chemical,2012,166: 884-892. [13] CHAKRABORTY S, PAUL D. Microchannel flow control through a combined electromagnetohydrodynamic transport[J]. Journal of Physics D: Applied Physics,2006,39(24): 5364-5371. [14] JIAN Y J, SI D Q, CHANG L, et al. Transient rotating electromagnetohydrodynamic micropumps between two infinite microparallel plates[J]. Chemical Engineering Science,2015,134: 12-22. [15] SI D Q, JIAN Y J. Electromagnetohydrodynamic (EMHD) micropump of Jeffrey fluids through two parallel microchannels with corrugated walls[J]. Journal of Physics D: Applied Physics,2015,48(8): 085501. [16] XIE Z Y, JIAN Y J. Entropy generation of two-layer magnetohydrodynamic electroosmotic flow through microparallel channels[J]. Energy,2017,139: 1080-1093. [17] STROOCK A D, WECK M, CHIU D T, et al. Patterning electro-osmotic flow with patterned surface charge[J]. Physical Review Letters,2000,84(15): 3314-3317. [18] BIDDISS E, ERICKSON D, LI D. Heterogeneous surface charge enhanced micromixing for electrokinetic flows[J]. Analytical Chemistry,2004,76(11): 3208-3213. [19] AJDARI A. Generation of transverse fluid currents and forces by an electric field: electro-osmosis on charge-modulated and undulated surfaces[J]. Physical Review E,1996,53(5): 4996-5005. [20] YARIV E. Electro-osmotic flow near a surface charge discontinuity[J]. Journal of Fluid Mechanics,2004,521: 181-189. [21] GHOSH U, CHAKRABORTY S. Electroosmosis of viscoelastic fluids over charge modulated surfaces in narrow confinements[J]. Physics of Fluids,2015,27(6): 062004. [22] GHOSH U, CHAKRABORTY S. Electrokinetics over charge-modulated surfaces in the presence of patterned wettability: role of the anisotropic streaming potential[J]. Physical Review E,2013,88(3): 033001. [23] MANDAL S, GHOSH U, BANDOPADHYAY A, et al. Electro-osmosis of superimposed fluids in the presence of modulated charged surfaces in narrow confinements[J]. Journal of Fluid Mechanics,2015,776: 390-429. [24] STONE H A, STROOCK A D, AJDARI A. Engineering flows in small devices: microfluidics toward a lab-on-a-chip[J]. Annual Review of Fluid Mechanics,2004,36: 381-411. [25] DATTA S, CHOUDHARY J N. Effect of hydrodynamic slippage on electro-osmotic flow in zeta potential patterned nanochannels[J]. Fluid Dynamics Research,2013,45(5): 055502. [26] AJDARI A.Electro-osmosis on inhomogeneously charged surfaces[J]. Physical Review Letters,1995,75(4): 755-758. [27] EIJKEL J C T. Liquid slip in micro- and nanofluidics: recent research and its possible implications[J]. Lab on a Chip,2007,7(3): 299-301. [28] JIAN Y J, CHANG L. Electromagnetohydrodynamic (EMHD) micropumps under a spatially non-uniform magnetic field[J]. AIP Advances,2015,5(5): 057121. [29] LIU Y P, JIAN Y J, LIU Q S, et al. Alternating current magnetohydrodynamic electroosmotic flow of Maxwell fluids between two micro-parallel plates[J]. Journal of Molecular Liquids,2015,211: 784-791. [30] 许丽娜, 菅永军. 柔性圆柱形微管道内的电动流动及传热研究[J]. 应用数学和力学, 2019,40(4): 408-418.(XU Lina, JIAN Yongjun. Electrokinetic flow and heat transfer in soft microtubes[J]. Applied Mathematics and Mechanics,2019,40(4): 408-418.(in Chinese)
点击查看大图
计量
- 文章访问数: 906
- HTML全文浏览量: 121
- PDF下载量: 231
- 被引次数: 0