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Rotational electroosmotic slip flow of power-law fluid at high zeta potential in variable-section microchannel

Zhang Tian-Ge Ren Mei-Rong Cui Ji-Feng Chen Xiao-Gang Wang Yi-Dan

Rotational electroosmotic slip flow of power-law fluid at high zeta potential in variable-section microchannel

Zhang Tian-Ge, Ren Mei-Rong, Cui Ji-Feng, Chen Xiao-Gang, Wang Yi-Dan
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  • In this paper we study the rotating electroosmotic flow of a power-law fluid with Navier slip boundary conditions under high zeta potential subjected to the action of a vertical magnetic field in a variable cross-section microchannel. Without using the Debye–Hückel linear approximation, the finite difference method is used to numerically calculate the potential distribution and velocity distribution of the rotating electroosmotic flow subjected to an external magnetic field. When the behavior index n=1, the fluid obtained is a Newtonian fluid. The analysis results in this paper are compared with the analytical approximate solutions obtained in the Debye–Hückel linear approximation to prove the feasibility of the numerical method in this paper. In addition, the influence of behavior index n, Hartmann number Ha, rotation angular velocity Ω, electric width K and slip parameters β on the velocity distribution are discussed in detail. It is obtained that when the Hartmann number Ha > 1, the velocity decreases with the increase of the Hartmann number Ha; but when the Hartmann number Ha < 1, the magnitude of the x-direction velocity u increases with the augment of Ha.
      PACS:
      Corresponding author: Chen Xiao-Gang, xiaogang_chen@imut.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12062018, 12172333), the Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region, China (Grant No. NJYT22075), and the Natural Science Foundation of Inner Mongolia, China (Grant No. 2020MS01015).
    [1]

    Stone H A, Stroock A D, Ajdari A 2004 Annu. Rev. Fluid Mech. 36 381Google Scholar

    [2]

    Patel M, Kruthiventi S S H, Kaushik P 2020 Colloids Surf. B 193 111058Google Scholar

    [3]

    Srinivas, Bhadri 2016 Colloids Surf. A 492 144Google Scholar

    [4]

    Nekoubin N 2018 J. Non-Newtonian Fluid Mech. 260 54Google Scholar

    [5]

    Baños R D, Arcos J C, Bautista O, Méndez F, Merchán-Cruz E A 2021 J. Braz. Soc. Mech. Sci. 43 1Google Scholar

    [6]

    Baños R, Arcos J, Bautista O, Méndez F 2020 Defect Diffus. Forum 399 92Google Scholar

    [7]

    姜玉婷, 齐海涛 2015 64 174702Google Scholar

    Jiang Y T, Qi H T 2015 Acta Phys. Sin. 64 174702Google Scholar

    [8]

    Ajdari A 2002 Phys. Rev. E 65 16301Google Scholar

    [9]

    Chang C C, Wang C Y 2011 Phys. Rev. E 84 056320Google Scholar

    [10]

    Song J, Wang S W, Zhao M L, Li N 2020 Z. Naturforsch. A: Phys. Sci. 75 649Google Scholar

    [11]

    Shit G C, Mondal A, Sinha A, Kundu P K 2016 Colloids Surf. A 489 249Google Scholar

    [12]

    刘全生, 杨联贵, 苏洁 2013 62 144702Google Scholar

    Liu Q S, Yang L G, Su J 2013 Acta Phys. Sin. 62 144702Google Scholar

    [13]

    段娟, 陈耀钦, 朱庆勇 2016 65 034702Google Scholar

    Duan J, Chen Y Q, Zhu Q Y 2016 Acta Phys. Sin. 65 034702Google Scholar

    [14]

    Weston M C, Gerner M D, Fritsch I 2010 Anal. Chem. 82 3411Google Scholar

    [15]

    Jian Y J, Chang L 2015 AIP Adv. 5 057121Google Scholar

    [16]

    Xie Z Y, Jian Y J 2017 Colloids Surf. A 529 334Google Scholar

    [17]

    Habib U, Hayat T, Ahmad S, Alhodaly M S 2021 Int. Commun. Heat Mass Transfer 122 105111Google Scholar

    [18]

    Sarkar S, Ganguly S 2017 J. Non-Newtonian Fluid Mech. 250 18Google Scholar

    [19]

    Yang C H, Jian Y J, Xie Z Y, Li F Q 2020 Micromachines 11 418Google Scholar

    [20]

    Xie Z Y, Jian Y J 2017 Energy 139 1080Google Scholar

    [21]

    Wang S W, Li N, Zhao M L, Azese M N 2018 Z. Naturforsch. A: Phys. Sci. 73 825Google Scholar

    [22]

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

    [23]

    Bird R B, Armstrong R C, Hassager O, Curtiss C F, Middleman S 1978 Phys. Today 31 54Google Scholar

  • 图 1  变截面微通道中流体流动示意图

    Figure 1.  Schematic view of the flow in a variable cross-section microchannel.

    图 2  目前数值解与Chang和Wang[9]解析解的比较, 其中 β=0,K=30,Ω=100 rad/s, ˉψω=1 V, a=0, Ha=0, S=0

    Figure 2.  Comparison of the current numerical solution with the analytical solution of Chang and Wang [9], β=0,K=30,Ω=100 rad/s, ˉψω=1 V, a=0, Ha=0, S=0

    图 3  当无滑移边界条件时, 幂律流体行为指数n对外加磁场的旋转电渗流速度的影响, 其中β=0, K=10, Ω=100 rad/s,  ˉψω=5V, a=0.05, Ha=1, S=1

    Figure 3.  When there is a no-slip boundary condition, the influence of power-law fluid behavior index n on rotating electroosmotic flow velocity with the external magnetic field, β=0, K=10, Ω=100 rad/s, ˉψω=5V, a=0.05, Ha=1, S=1

    图 4  当存在滑移边界条件时, 幂律流体行为指数n对外加磁场的旋转电渗流速度的影响, 其中β=0.1, K=10, Ω=100 rad/s,  ˉψω=5 V, a=0.05, Ha=1, S=1

    Figure 4.  When there is a slip boundary condition, the influence of the power-law fluid behavior index n on the rotating electroosmotic flow velocity with an external magnetic field, β=0.1, K=10, Ω=100 rad/s, ˉψω=5 V, a=0.05, Ha=1, S=1

    图 5  哈特曼数Ha对外加磁场的旋转电渗流速度的影响, 其中n=0.8, K=10,  β=0.1, Ω=100 rad/s,  ˉψω=5 V, a=0.05, S=1

    Figure 5.  The influence of Hartmann number Ha on the velocity of rotating electroosmotic flow with external magnetic field, n=0.8, K=10, β=0.1, Ω=100 rad/s, ˉψω=5 V, a=0.05, S=1

    图 6  哈特曼数Ha对外加磁场的旋转电渗流速度的影响, 其中n=1.2, K=10,  β=0.1, Ω=100 rad/s, ˉψω=5 V, a=0.05, S=1

    Figure 6.  The influence of Hartmann number Ha on the velocity of rotating electroosmotic flow with external magnetic field, n=1.2, K=10, β=0.1, Ω=100 rad/s, ˉψω=5 V, a=0.05, S=1

    图 7  旋转角速度Ω对外加磁场的旋转电渗流速度的影响, 其中n=0.8,ˉψω=5V,a=0.05, Ha=1, S=1 (a)K=10, β=0.1; (b) K=10, β=0.1; (c) K=10, β=0; (d)K=20, β=0.1.

    Figure 7.  The influence of the rotational angular velocity Ω on the rotational electroosmotic flow velocity of the external magnetic field, n=0.8,ˉψω=V,a=0.05, Ha=1, S=1(a) K=10, β=0.1; (b) K=10, β=0.1; (c) K=10, β=0; (d)K=20, β=0.1

    图 8  旋转角速度Ω对外加磁场的旋转电渗流速度的影响, 其中n=1.2,ˉψω=5 V, a=0.05, Ha=1, S=1 (a) β=0.1, K=10. (b) β=0.1, K=10. (c) β=0, K=10. (d) β=0.1, K=30

    Figure 8.  The influence of the rotational angular velocity Ω on the rotational electroosmotic flow velocity of the external magnetic field, n=1.2,ˉψω=5 V, a=0.05, Ha=1, S=1 (a) β=0.1, K=10. (b) β=0.1, K=10. (c) β=0, K=10. (d) β=0.1, K=30

    图 9  电动宽度 K 对外加磁场的旋转电渗流速度分布的影响, 其中n=0.8, β = 0.1, Ω=100 rad/s, ˉψω=5 V,  a=0.05, Ha=1, S=1

    Figure 9.  The influence of the electric width K on the velocity distribution of rotating electroosmotic flow with external magnetic field, n=0.8, β = 0.1, Ω=100 rad/s, ˉψω=5 V, a=0.05, Ha=1, S=1

    图 10  电动宽度 K 对外加磁场的旋转电渗流速度分布的影响, 其中n=1.2,β = 0.1, Ω=100 rad/s, ˉψω=5 V, a=0.05, Ha=1, S=1

    Figure 10.  The influence of the electric width K on the velocity distribution of rotating electroosmotic flow with external magnetic field, n=1.2, β = 0.1, Ω=100 rad/s, ˉψω=5 V, a=0.05, Ha=1, S=1

    图 11  电动宽度 K 对外加磁场的旋转电渗流速度分布的影响, 其中n=1.2,β = 0, Ω=100 rad/s, ˉψω=5 V, a=0.05, Ha=1, S=1

    Figure 11.  The influence of the electric width K on the velocity distribution of rotating electroosmotic flow with external magnetic field, n=1.2, β = 0, Ω=100 rad/s, ˉψω=5 V, a=0.05, Ha=1, S=1

    图 12  滑移参数β对外加磁场的旋转电渗流速度的影响, 其中n=0.8,K=10,Ω=100 rad/s, ˉψω=5 V, a=0.05, Ha=1, S=1

    Figure 12.  The influence of the slip parameterβon the rotating electroosmotic flow velocity with an external magnetic field, n=0.8,K=10,Ω=100 rad/s, ˉψω=5 V, a=0.05, Ha=1, S=1

    图 13  滑移参数β对外加磁场的旋转电渗流速度的影响, 其中n=1.2,K=10,Ω=100 rad/s, ˉψω=5 V, a=0.05, Ha=1, S=1

    Figure 13.  The influence of the slip parameterβon the rotating electroosmotic flow velocity with an external magnetic field, n=1.2,K=10,Ω=100 rad/s, ˉψω=5 V, a=0.05, Ha=1, S=1

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  • [1]

    Stone H A, Stroock A D, Ajdari A 2004 Annu. Rev. Fluid Mech. 36 381Google Scholar

    [2]

    Patel M, Kruthiventi S S H, Kaushik P 2020 Colloids Surf. B 193 111058Google Scholar

    [3]

    Srinivas, Bhadri 2016 Colloids Surf. A 492 144Google Scholar

    [4]

    Nekoubin N 2018 J. Non-Newtonian Fluid Mech. 260 54Google Scholar

    [5]

    Baños R D, Arcos J C, Bautista O, Méndez F, Merchán-Cruz E A 2021 J. Braz. Soc. Mech. Sci. 43 1Google Scholar

    [6]

    Baños R, Arcos J, Bautista O, Méndez F 2020 Defect Diffus. Forum 399 92Google Scholar

    [7]

    姜玉婷, 齐海涛 2015 64 174702Google Scholar

    Jiang Y T, Qi H T 2015 Acta Phys. Sin. 64 174702Google Scholar

    [8]

    Ajdari A 2002 Phys. Rev. E 65 16301Google Scholar

    [9]

    Chang C C, Wang C Y 2011 Phys. Rev. E 84 056320Google Scholar

    [10]

    Song J, Wang S W, Zhao M L, Li N 2020 Z. Naturforsch. A: Phys. Sci. 75 649Google Scholar

    [11]

    Shit G C, Mondal A, Sinha A, Kundu P K 2016 Colloids Surf. A 489 249Google Scholar

    [12]

    刘全生, 杨联贵, 苏洁 2013 62 144702Google Scholar

    Liu Q S, Yang L G, Su J 2013 Acta Phys. Sin. 62 144702Google Scholar

    [13]

    段娟, 陈耀钦, 朱庆勇 2016 65 034702Google Scholar

    Duan J, Chen Y Q, Zhu Q Y 2016 Acta Phys. Sin. 65 034702Google Scholar

    [14]

    Weston M C, Gerner M D, Fritsch I 2010 Anal. Chem. 82 3411Google Scholar

    [15]

    Jian Y J, Chang L 2015 AIP Adv. 5 057121Google Scholar

    [16]

    Xie Z Y, Jian Y J 2017 Colloids Surf. A 529 334Google Scholar

    [17]

    Habib U, Hayat T, Ahmad S, Alhodaly M S 2021 Int. Commun. Heat Mass Transfer 122 105111Google Scholar

    [18]

    Sarkar S, Ganguly S 2017 J. Non-Newtonian Fluid Mech. 250 18Google Scholar

    [19]

    Yang C H, Jian Y J, Xie Z Y, Li F Q 2020 Micromachines 11 418Google Scholar

    [20]

    Xie Z Y, Jian Y J 2017 Energy 139 1080Google Scholar

    [21]

    Wang S W, Li N, Zhao M L, Azese M N 2018 Z. Naturforsch. A: Phys. Sci. 73 825Google Scholar

    [22]

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

    [23]

    Bird R B, Armstrong R C, Hassager O, Curtiss C F, Middleman S 1978 Phys. Today 31 54Google Scholar

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Publishing process
  • Received Date:  16 December 2021
  • Accepted Date:  03 March 2022
  • Available Online:  29 June 2022
  • Published Online:  05 July 2022

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