平行板微管道间Maxwell流体的高Zeta势周期电渗流动

长龙; 菅永军

doi:10.7498/aps.61.124702

摘要

本文研究了两平行板微管道中线性黏弹性流体的周期电渗流动, 其中线性黏弹性流体的本构关系是由广义Maxwell模型描述的. 将电渗力作为体力, 解析求解了非线性的Poisson-Boltzmann (P-B)方程, 柯西动量方程和广义Maxwell本构方程. 通过数值计算, 分析了无量纲壁面Zeta势0 、周期电渗流 (electroosmotic flow, EOF) 振荡雷诺数Re和无量纲弛豫时间 1 对速度剖面的影响. 结果表明: 对给定的电动宽度K(表示微管道的特征尺度与双电层厚度的比值)、弛豫时间 1 和振荡雷诺数Re, 高Zeta势0 产生较大的EOF速度振幅, 并且速度剖面的变化主要集中在双电层 (electric double-layer, EDL) 的狭窄的区域. 此外, 随着弛豫时间的增长流体的弹性显著增加, 速度的变化可以延伸到整个流动的区域中. 对给定的雷诺数Re, 较长的弛豫时间1 导致EOF速度剖面较快的变化, 且速度剖面的振幅逐渐增大.

关键词:

Abstract

In this study, semi-analytical solutions are presented for the time periodic (electroosmotic flow) of linear viscoelastic fluids between micro-parallel plates. The linear viscoelastic fluids used here are described by the general Maxwell model. The solution involves analytically solving the nonlinear Poisson-Boltzmann (P-B) equation, the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations, the influences of the dimensionless wall Zeta potential0, the periodic EOF electric oscillating Reynolds number Re, and normalized relaxation times 1 on velocity profiles are presented. Results show that for prescribed electrokinetic width K, relaxation time 1 and oscillating Reynolds number Re, higher Zeta potential 0 will lead to larger amplitude of EOF velocity, and the variation of velocity is restricted to a very narrow region close to the Electric double-layer. In addition, with the increase of relaxation time 1, the elasticity of the fluid becomes conspicuous and the velocity variations can be expanded to the whole flow field. For prescribed Re, longer relaxation time 1 will lead to quick change of the EOF velocity profile, and the amplitude becomes larger gradually.

Keywords:

作者及机构信息

长龙^1,2,
菅永军¹

1.
内蒙古大学数学科学学院, 呼和浩特 010021;

2.
内蒙古财经学院统计与数学学院, 呼和浩特 010051

基金项目: 国家自然科学基金(批准号: 11062005), 内蒙古自治区自然科学基金(批准号: 2010BS0107), 内蒙古大学学科带头人科研启动基金(批准号: Z20080211), 和内蒙古自治区自然科学基金重点项目(批准号: 2009ZD01)资助的课题

Authors and contacts

Chang Long^1,2,
Jian Yong-Jun¹

1.
School of Mechanical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021, China;

2.
School of Mathematics and Statistics, Inner Mongolia Finance and Economics College, Hohhot, Inner Mongolia 010051, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11062005), Ph. D. Programs Foundation of Ministry of Education of China (Grant No. 20111501120001), Opening Fund of State Key Laboratory of Nonlinear Mechanics, the Inner Mongolia Natural Science Foundation of China (Grant No. 2010BS0107), the research start up fund for excellent talents at Inner Mongolia University (Grant No. Z20080211), the support of Natural Science Key Fund of Inner Mongolia (Grant No: 2009ZD01), and the Key Programs of the Inner Mongolia Finances and Economic College.

参考文献

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[8]	Yang C, Li D, Masliyah J H 1998 Int. J. Heat Mass Transfer 41 4229
[9]	Arulanandam S, Li D 2000 Colloids Surf. A: Physicochem. Eng. Aspects 161 89
[10]	Bianchi F, Ferrigno R, Girault H H 2000 Anal. Chem. 72 1987
[11]	Wang C Y, Liu Y H, Chang C C 2008 Phys. Fluids 20 063105
[12]	Dutta P, Beskok A 2001 Anal. Chem. 73 5097
[13]	Keh H J, Tseng H C 2001 J. Colloid Interface Sci. 242 450
[14]	Kang Y J, Yang C, Huang X Y 2002 Int. J. Eng. Sci. 40 2203
[15]	Wang X M, Chen B, Wu J K 2007 Phys. Fluids 19 127101
[16]	Chakraborty S, Ray S 2008 Phys. Fluids 20 083602
[17]	Chakraborty S, Srivastava A K 2007 Langmuir 23 12421
[18]	Qu W L, Li D Q 2000 J. Colloid Interface Sci. 224 397
[19]	Jian Y J, Yang L G, Liu Q S 2010 Phys. Fluids 22 042001
[20]	Das S, Chakraborty S 2006 Anal. Chim. Acta 559 15
[21]	Chakraborty S 2007 Anal. Chim. Acta 605 175
[22]	Zhao C, Zholkovskij E, Masliyah J H, Yang C 2008 J. Colloid Interface Sci. 326 503
[23]	Vasu N, De S 2010 Colloids and Surfaces A: Physicochem. Eng. Aspects 368 44
[24]	Zhao C, Yang C 2010 Electrophoresis 31 973
[25]	Tang G H, Li X F, He Y L, Tao W Q 2009 J. Non-Newtonian fluid Mech. 157 133
[26]	Wang R J, Lin J Z, Li Z H 2005 Binmedical Microdevices 7 131
[27]	Zhang K, Lin J Z, Li Z H 2006 Appl. Math. Mech. ( English Edition) 27 575
[28]	Lin J Z, Zhang K, Li H J 2006 Chin. Phys. 15 2688
[29]	Liu Q S, Jian Y J, Yang L G 2011 J. Non-Newtonian fluid Mech. 166 478
[30]	Jian Y J, Liu Q S, Yang L G 2011 J. Non-Newtonian fluid Mech. 166 1304
[31]	Jian Y J, Liu Q S, Duan H Z, Chang L, Yang L G 2011 The Sixth International Conference on Fluid Mechanics (ICFM6), Guang Zhou, June 30-July 3, p616
[32]	Bird R B, Stewart W E, Lightfoot E N 2001 Transport phenomena, Second Edition (New York: Wiley-Interscience Publication) p242
[33]	Gong L, Wu J, Wang L, Cao K 2008 Phys. Fluids 20 063603
[34]	Goswami P, Chakraborty S 2009 Langmuir 26 581

施引文献

[1]	Stone H A, Stroock A D, Ajdari A 2004 Ann. Rev. Fluid Mech. 36 381
[2]	Bayraktar T, Pidugu S B 2006 Int. J. Heat Mass Transfer 49 815
[3]	Burgreen D, Nakache F R 1964 J. Phys. Chem. 68 1084
[4]	Levine S, Marriott J R, Neale G, Epstein N 1975 J. Colloid Interface Sci. 52 136
[5]	Tsao H K 2000 J. Colloid Interface Sci. 225 247
[6]	Kang Y J, Yang C, Huang X Y 2002 J. Colloid Interface Sci. 253 285
[7]	Hsu J P, Kao C Y, Tseng S J, Chen C J 2002 J. Colloid Interface Sci. 248 176
[8]	Yang C, Li D, Masliyah J H 1998 Int. J. Heat Mass Transfer 41 4229
[9]	Arulanandam S, Li D 2000 Colloids Surf. A: Physicochem. Eng. Aspects 161 89
[10]	Bianchi F, Ferrigno R, Girault H H 2000 Anal. Chem. 72 1987
[11]	Wang C Y, Liu Y H, Chang C C 2008 Phys. Fluids 20 063105
[12]	Dutta P, Beskok A 2001 Anal. Chem. 73 5097
[13]	Keh H J, Tseng H C 2001 J. Colloid Interface Sci. 242 450
[14]	Kang Y J, Yang C, Huang X Y 2002 Int. J. Eng. Sci. 40 2203
[15]	Wang X M, Chen B, Wu J K 2007 Phys. Fluids 19 127101
[16]	Chakraborty S, Ray S 2008 Phys. Fluids 20 083602
[17]	Chakraborty S, Srivastava A K 2007 Langmuir 23 12421
[18]	Qu W L, Li D Q 2000 J. Colloid Interface Sci. 224 397
[19]	Jian Y J, Yang L G, Liu Q S 2010 Phys. Fluids 22 042001
[20]	Das S, Chakraborty S 2006 Anal. Chim. Acta 559 15
[21]	Chakraborty S 2007 Anal. Chim. Acta 605 175
[22]	Zhao C, Zholkovskij E, Masliyah J H, Yang C 2008 J. Colloid Interface Sci. 326 503
[23]	Vasu N, De S 2010 Colloids and Surfaces A: Physicochem. Eng. Aspects 368 44
[24]	Zhao C, Yang C 2010 Electrophoresis 31 973
[25]	Tang G H, Li X F, He Y L, Tao W Q 2009 J. Non-Newtonian fluid Mech. 157 133
[26]	Wang R J, Lin J Z, Li Z H 2005 Binmedical Microdevices 7 131
[27]	Zhang K, Lin J Z, Li Z H 2006 Appl. Math. Mech. ( English Edition) 27 575
[28]	Lin J Z, Zhang K, Li H J 2006 Chin. Phys. 15 2688
[29]	Liu Q S, Jian Y J, Yang L G 2011 J. Non-Newtonian fluid Mech. 166 478
[30]	Jian Y J, Liu Q S, Yang L G 2011 J. Non-Newtonian fluid Mech. 166 1304
[31]	Jian Y J, Liu Q S, Duan H Z, Chang L, Yang L G 2011 The Sixth International Conference on Fluid Mechanics (ICFM6), Guang Zhou, June 30-July 3, p616
[32]	Bird R B, Stewart W E, Lightfoot E N 2001 Transport phenomena, Second Edition (New York: Wiley-Interscience Publication) p242
[33]	Gong L, Wu J, Wang L, Cao K 2008 Phys. Fluids 20 063603
[34]	Goswami P, Chakraborty S 2009 Langmuir 26 581

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