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微平行管道内Eyring流体的电渗滑移流动

姜玉婷 齐海涛

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微平行管道内Eyring流体的电渗滑移流动

姜玉婷, 齐海涛

Electro-osmotic slip flow of Eyring fluid in a slit microchannel

Jiang Yu-Ting, Qi Hai-Tao
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  • 研究了微平行管道内非牛顿流体––Eyring 流体在外加电场力和压力作用下的电渗流动. 在考虑微尺度效应, 电场作用, 非牛顿特性, 滑移边界等情况下, 建立Eyring流体在微平行管道内电渗流动的力学模型. 通过解线性Possion-Boltzmann方程和Cauchy动量方程, 给出Eyring 流体速度分布的精确解和近似解析解, 并探讨了上述因素对电渗流动的影响. 将电场力和压力对于Eyring流体电渗流动的速度分布的影响进行了比较分析, 得到有意义的结果.
    The electro-osmotic flow of a non-Newtonian fluid in a slit micro-channel under the Navier's slip boundary condition is investigated. The Eyring constitutive relationship model is adopted to describe the non-Newtonian characteristics of the flow driven by the applied electric field force and pressure. In consideration of the micro-scale effects, electric field, non-Newtonian behavior and slip boundary condition, a mechanical model is built and the effects of these factors on the flow are studied. Analytical expressions are derived for the electric potential and velocity profile by solving the linearized Poisson-Boltzmann equation and the modified Cauchy equation. Approximate expressions of the velocity distribution are also given and discussed. Furthermore, by comparing the effects of electric force with that of pressure on the velocity distribution, some meaningful conclusions are drawn from the obtained graphics.
      通信作者: 齐海涛, htqi@sdu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11102102, 11472161)、山东省自然科学基金(批准号:ZR2015AM011)和山东大学自主创新基金(批准号: 2013ZRYQ002)资助的课题.
      Corresponding author: Qi Hai-Tao, htqi@sdu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11102102, 11472161), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2015AM011), and the Independent Innovation Foundation of Shandong University, China (Grant No. 2013ZRYQ002).
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    Rice C L, Whitehead R 1965 J. Phys. Chem. 69 4017

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    Levine S, Marriott J R, Neale G, Epstein N 1975 J. Colloid Interface Sci. 52 136

    [5]

    Wang X M, Chen B, Wu J K 2007 Phys. Fluids 19 127101

    [6]

    Santiago J G 2001 Anal. Chem. 73 2353

    [7]

    Das S, Chakraborty S 2006 Anal. Chim. Acta 559 15

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    Chakraborty S 2007 Anal. Chim. Acta 605 175

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    Zhao C L, Zholkovskij E, Masliyah J H, Yang C 2008 J. Colloid Interface Sci. 326 503

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    Zhao C L, Yang C 2011 J. Non-Newtonian Fluid Mech. 166 1076

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    Berli C L A, Olivares M L 2008 J. Colloid Interface Sci. 320 582

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    Tang G H, Li X F, He Y L, Tao W Q 2009 J. Non-Newtonian Fluid Mech. 157 133

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    Hayat T, Afzal S, Hendi A 2011 App. Math. Mech. Engl. Ed. 32 1119

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    Chang L, Jian Y J 2012 Acta Phys. Sin. 61 124702 (in Chinese) [长龙, 菅永军 2012 物理学报 61 124702]

    [15]

    Liu Q S, Yang L G, Su J 2013 Acta Phys. Sin. 62 144702 (in Chinese) [刘全生, 杨连贵, 苏洁 2013 物理学报 62 144702]

    [16]

    Zheng L C, Zhang C L, Zhang X X, Zhang J H 2013 J. Franklin I. 350 990

    [17]

    Zhao M L, Wang S W, Wei S S 2013 J. Non-Newtonian Fluid Mech. 201 135

    [18]

    Xu S F, Wang J G 2013 Acta Phys. Sin. 62 124701 (in Chinese) [许少峰, 汪久根 2013 物理学报 62 124701]

    [19]

    Niu J, Fu C J, Tan W C 2012 PLoS ONE 7 e37274

    [20]

    Tan Z, Qi H T, Jiang X Y 2014 App. Math. Mech. Engl. Ed. 35 689

    [21]

    Kang J H, Zhou F B, Tan W C, Xia T Q 2014 J. Non-Newtonian Fluid Mech. 213 50

    [22]

    Ng C O, Qi C 2014 J. Non-Newtonian Fluid Mech. 208 118

    [23]

    Wang S W, Zhao M L, Li X C 2014 Cent. Eur. J. Phys. 12 445

    [24]

    Mondal M, Misra R P, De S 2014 Int. J. Therm Sci. 86 48

    [25]

    Xie Z Y, Jian Y J 2014 Colloids Surf. A 461 231

    [26]

    Yang F Q 2007 Appl. Phys. Lett. 90 133105

    [27]

    Eyring H 1936 J. Chem. Phys. 4 283

    [28]

    Bird R B, Armstrong R, Hassager O 1987 Dynamics of Polymeric Liquids (New York: John Wiley & Sons) pp169-253

    [29]

    Liu X L, Jiang M, Yang P R, Kaneta M 2005 ASME J. Tribology 127 70

    [30]

    Bosse M A, Araya H, Troncoso S A, Arce P E 2002 Electrophoresis 23 2149;

    [31]

    Afonso A M, Ferrás L L, Nóbrega J M, Alves M A, Pinho F T 2014 Microfluid. Nanofluid. 16 1131

  • [1]

    Hunter R J 1981 Zeta Potential in Colloid Science (New York: Academic Press) p15

    [2]

    Stone H A, Stroock A D, Ajdari A 2004 Ann. Rev. Fluid Mech. 36 381

    [3]

    Rice C L, Whitehead R 1965 J. Phys. Chem. 69 4017

    [4]

    Levine S, Marriott J R, Neale G, Epstein N 1975 J. Colloid Interface Sci. 52 136

    [5]

    Wang X M, Chen B, Wu J K 2007 Phys. Fluids 19 127101

    [6]

    Santiago J G 2001 Anal. Chem. 73 2353

    [7]

    Das S, Chakraborty S 2006 Anal. Chim. Acta 559 15

    [8]

    Chakraborty S 2007 Anal. Chim. Acta 605 175

    [9]

    Zhao C L, Zholkovskij E, Masliyah J H, Yang C 2008 J. Colloid Interface Sci. 326 503

    [10]

    Zhao C L, Yang C 2011 J. Non-Newtonian Fluid Mech. 166 1076

    [11]

    Berli C L A, Olivares M L 2008 J. Colloid Interface Sci. 320 582

    [12]

    Tang G H, Li X F, He Y L, Tao W Q 2009 J. Non-Newtonian Fluid Mech. 157 133

    [13]

    Hayat T, Afzal S, Hendi A 2011 App. Math. Mech. Engl. Ed. 32 1119

    [14]

    Chang L, Jian Y J 2012 Acta Phys. Sin. 61 124702 (in Chinese) [长龙, 菅永军 2012 物理学报 61 124702]

    [15]

    Liu Q S, Yang L G, Su J 2013 Acta Phys. Sin. 62 144702 (in Chinese) [刘全生, 杨连贵, 苏洁 2013 物理学报 62 144702]

    [16]

    Zheng L C, Zhang C L, Zhang X X, Zhang J H 2013 J. Franklin I. 350 990

    [17]

    Zhao M L, Wang S W, Wei S S 2013 J. Non-Newtonian Fluid Mech. 201 135

    [18]

    Xu S F, Wang J G 2013 Acta Phys. Sin. 62 124701 (in Chinese) [许少峰, 汪久根 2013 物理学报 62 124701]

    [19]

    Niu J, Fu C J, Tan W C 2012 PLoS ONE 7 e37274

    [20]

    Tan Z, Qi H T, Jiang X Y 2014 App. Math. Mech. Engl. Ed. 35 689

    [21]

    Kang J H, Zhou F B, Tan W C, Xia T Q 2014 J. Non-Newtonian Fluid Mech. 213 50

    [22]

    Ng C O, Qi C 2014 J. Non-Newtonian Fluid Mech. 208 118

    [23]

    Wang S W, Zhao M L, Li X C 2014 Cent. Eur. J. Phys. 12 445

    [24]

    Mondal M, Misra R P, De S 2014 Int. J. Therm Sci. 86 48

    [25]

    Xie Z Y, Jian Y J 2014 Colloids Surf. A 461 231

    [26]

    Yang F Q 2007 Appl. Phys. Lett. 90 133105

    [27]

    Eyring H 1936 J. Chem. Phys. 4 283

    [28]

    Bird R B, Armstrong R, Hassager O 1987 Dynamics of Polymeric Liquids (New York: John Wiley & Sons) pp169-253

    [29]

    Liu X L, Jiang M, Yang P R, Kaneta M 2005 ASME J. Tribology 127 70

    [30]

    Bosse M A, Araya H, Troncoso S A, Arce P E 2002 Electrophoresis 23 2149;

    [31]

    Afonso A M, Ferrás L L, Nóbrega J M, Alves M A, Pinho F T 2014 Microfluid. Nanofluid. 16 1131

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出版历程
  • 收稿日期:  2014-12-03
  • 修回日期:  2015-03-23
  • 刊出日期:  2015-09-05

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