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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 velocityΩ , electric width K and slip parametersβ 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.[1] Stone H A, Stroock A D, Ajdari A 2004 Annu. Rev. Fluid Mech. 36 381
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[2] Patel M, Kruthiventi S S H, Kaushik P 2020 Colloids Surf. B 193 111058
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[3] Srinivas, Bhadri 2016 Colloids Surf. A 492 144
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[4] Nekoubin N 2018 J. Non-Newtonian Fluid Mech. 260 54
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[5] Baños R D, Arcos J C, Bautista O, Méndez F, Merchán-Cruz E A 2021 J. Braz. Soc. Mech. Sci. 43 1
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[6] Baños R, Arcos J, Bautista O, Méndez F 2020 Defect Diffus. Forum 399 92
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[7] 姜玉婷, 齐海涛 2015 64 174702
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Jiang Y T, Qi H T 2015 Acta Phys. Sin. 64 174702
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[8] Ajdari A 2002 Phys. Rev. E 65 16301
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[9] Chang C C, Wang C Y 2011 Phys. Rev. E 84 056320
Google Scholar
[10] Song J, Wang S W, Zhao M L, Li N 2020 Z. Naturforsch. A: Phys. Sci. 75 649
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[11] Shit G C, Mondal A, Sinha A, Kundu P K 2016 Colloids Surf. A 489 249
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[12] 刘全生, 杨联贵, 苏洁 2013 62 144702
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Liu Q S, Yang L G, Su J 2013 Acta Phys. Sin. 62 144702
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[13] 段娟, 陈耀钦, 朱庆勇 2016 65 034702
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Duan J, Chen Y Q, Zhu Q Y 2016 Acta Phys. Sin. 65 034702
Google Scholar
[14] Weston M C, Gerner M D, Fritsch I 2010 Anal. Chem. 82 3411
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[15] Jian Y J, Chang L 2015 AIP Adv. 5 057121
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[16] Xie Z Y, Jian Y J 2017 Colloids Surf. A 529 334
Google Scholar
[17] Habib U, Hayat T, Ahmad S, Alhodaly M S 2021 Int. Commun. Heat Mass Transfer 122 105111
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[18] Sarkar S, Ganguly S 2017 J. Non-Newtonian Fluid Mech. 250 18
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[19] Yang C H, Jian Y J, Xie Z Y, Li F Q 2020 Micromachines 11 418
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[20] Xie Z Y, Jian Y J 2017 Energy 139 1080
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[21] Wang S W, Li N, Zhao M L, Azese M N 2018 Z. Naturforsch. A: Phys. Sci. 73 825
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[22] Xie Z Y, Jian Y J 2014 Colloids Surf. A 461 231
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[23] Bird R B, Armstrong R C, Hassager O, Curtiss C F, Middleman S 1978 Phys. Today 31 54
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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= 1Figure 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= 1Figure 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 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=5 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 -
[1] Stone H A, Stroock A D, Ajdari A 2004 Annu. Rev. Fluid Mech. 36 381
Google Scholar
[2] Patel M, Kruthiventi S S H, Kaushik P 2020 Colloids Surf. B 193 111058
Google Scholar
[3] Srinivas, Bhadri 2016 Colloids Surf. A 492 144
Google Scholar
[4] Nekoubin N 2018 J. Non-Newtonian Fluid Mech. 260 54
Google Scholar
[5] Baños R D, Arcos J C, Bautista O, Méndez F, Merchán-Cruz E A 2021 J. Braz. Soc. Mech. Sci. 43 1
Google Scholar
[6] Baños R, Arcos J, Bautista O, Méndez F 2020 Defect Diffus. Forum 399 92
Google Scholar
[7] 姜玉婷, 齐海涛 2015 64 174702
Google Scholar
Jiang Y T, Qi H T 2015 Acta Phys. Sin. 64 174702
Google Scholar
[8] Ajdari A 2002 Phys. Rev. E 65 16301
Google Scholar
[9] Chang C C, Wang C Y 2011 Phys. Rev. E 84 056320
Google Scholar
[10] Song J, Wang S W, Zhao M L, Li N 2020 Z. Naturforsch. A: Phys. Sci. 75 649
Google Scholar
[11] Shit G C, Mondal A, Sinha A, Kundu P K 2016 Colloids Surf. A 489 249
Google Scholar
[12] 刘全生, 杨联贵, 苏洁 2013 62 144702
Google Scholar
Liu Q S, Yang L G, Su J 2013 Acta Phys. Sin. 62 144702
Google Scholar
[13] 段娟, 陈耀钦, 朱庆勇 2016 65 034702
Google Scholar
Duan J, Chen Y Q, Zhu Q Y 2016 Acta Phys. Sin. 65 034702
Google Scholar
[14] Weston M C, Gerner M D, Fritsch I 2010 Anal. Chem. 82 3411
Google Scholar
[15] Jian Y J, Chang L 2015 AIP Adv. 5 057121
Google Scholar
[16] Xie Z Y, Jian Y J 2017 Colloids Surf. A 529 334
Google Scholar
[17] Habib U, Hayat T, Ahmad S, Alhodaly M S 2021 Int. Commun. Heat Mass Transfer 122 105111
Google Scholar
[18] Sarkar S, Ganguly S 2017 J. Non-Newtonian Fluid Mech. 250 18
Google Scholar
[19] Yang C H, Jian Y J, Xie Z Y, Li F Q 2020 Micromachines 11 418
Google Scholar
[20] Xie Z Y, Jian Y J 2017 Energy 139 1080
Google Scholar
[21] Wang S W, Li N, Zhao M L, Azese M N 2018 Z. Naturforsch. A: Phys. Sci. 73 825
Google Scholar
[22] Xie Z Y, Jian Y J 2014 Colloids Surf. A 461 231
Google Scholar
[23] Bird R B, Armstrong R C, Hassager O, Curtiss C F, Middleman S 1978 Phys. Today 31 54
Google Scholar
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