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Peristalsis is an important dynamic phenomenon in the field of biomedical research, and has great application prospects in microscale fluids. In recent years, this biomimetic (peristaltic) phenomenon has gained widespread attention due to its large-scale applications in various medical and industrial fields, such as radiation therapy, peristaltic blood pumps, and drug delivery systems. In this study, the electroosmotic flow and heat transfer characteristics are investigated under high wall Zeta potential and slip boundary conditions for a certain type of biological fluid that satisfies the Newtonian fluid model. Fluid flows under the joint action of external electric field, magnetic field, and Joule heating. Firstly, without using the Debye-Hückel linear approximation, the numerical solutions are given by using the Chebyshev spectral method for the nonlinear Poisson-Boltzmann equation, the fourth-order differential equation satisfied by the stream function, and the thermal energy equation. The results are compared with those obtained by using the Debye-Hückel linear approximation to demonstrate the effectiveness of the numerical method used in this study. Secondly, the effects of wall Zeta potential, Hartmann number
$H$ , electroosmotic parameter$m$ , slip parameter$\beta $ are discussed on the flow characteristics, peristaltic pumping, and trapping phenomena under electromagnetic environments, and the influence of Joule heating parameter$\gamma $ and Brinkman number$Br$ is explored on heat transfer characteristics. The results show that 1) wall Zeta potential plays an important role in controlling the velocity of fluid peristaltic flow; 2) the increase of electroosmotic parameter$m$ and slip parameter$\beta $ increases the flow velocity in the central region of the channel, while the increase of Hartmann number$H$ hinders the flow of fluid; 3) these flow behaviors exhibit opposite trends near the channel walls; 4) the number of streamlines captured by peristaltic transport decreases with Hartmann number$H$ and electroosmotic parameter$m$ increasing; 5) the increase of Joule heating parameter$\gamma $ and Brinkman number$Br$ leads temperature to rise.-
Keywords:
- electroosmotic flow /
- heat transfer characteristics /
- high Zeta potential /
- Chebyshev spectral methods
[1] Maiti S, Pandey S K, Misra J C 2022 J. Eng. Math. 135 8
Google Scholar
[2] Jaiswal S, Yadav P K 2022 Microfluid Nanofluid 26 100
Google Scholar
[3] Patel H R, Patel S D, Darji R 2022 Int. J. Thermofluids 16 100232
Google Scholar
[4] Sherief H H, Faltas M S, El-Sapa S 2019 Eur. J. Mech. B Fluids 77 211
Google Scholar
[5] Chandra S, Kumar Pandey S 2018 J. Phys. Conf. Ser. 1141 012092
Google Scholar
[6] Yasmin H, Nisar Z 2023 Mathematics 11 2673
Google Scholar
[7] Mishra N K, Sharma B K, Sharma P, Muhammad T, Pérez L M 2023 Sci. Rep. 13 14483
Google Scholar
[8] Guedri K, Lashin M M A, Abbasi A, Khan S U, Farooq W, Khan M I, Galal A M 2023 Chin. J. Phys. 83 650
Google Scholar
[9] Maraj E N, Akbar N S, Zehra I, Butt A W, Ahmed Alghamdi H 2023 J. Magn. Magn. Mater. 576 170774
Google Scholar
[10] Rafiq M, Shaheen S, Khan M I, Fadhl B M, Hassine S B H, ElDin S M 2023 Case Stud. Therm. Eng. 45 102990
Google Scholar
[11] Alfwzan W, Riaz A, Alammari M, Hejazi H, Tag El-Din E M 2023 Front. Phys. 11 1121849
Google Scholar
[12] Wang S, Li N, Zhao M, Azese M N 2018 Z. Naturforsch. A 73 825
Google Scholar
[13] Sheikholeslami M, Chamkha A J 2016 Numer. Heat Tr. A-Appl. 69 781
Google Scholar
[14] Tripathi D, Bhushan S, Bég O A 2016 Colloids Surf. A 506 32
Google Scholar
[15] Shapiro A H, Jaffrin M Y, Weinberg S L 1969 J. Fluid Mech. Dig. Arch. 37 799
Google Scholar
[16] Shit G C, Mondal A, Sinha A, Kundu P K 2016 Physica A 462 1040
Google Scholar
[17] Chakraborty S 2007 Anal. Chim. Acta 605 175
Google Scholar
[18] Bhardwaj A, Kumar A, Bhandari D S, Tripathi D 2024 Sensor. Actuat. A-Phys. 366 114956
[19] Verma L, Meher R 2023 Pramana 97 155
Google Scholar
[20] Chen L, Abbas M A, Khudair W S, Sun B 2022 Symmetry 14 953
Google Scholar
[21] Mahabub M, Ferdows M, Murtaza M G, Lorenzini G, Tzirtzilakis E E 2022 Mathem. Mod. Eng. Probl. 9 215
Google Scholar
[22] Madkhali H A 2023 Case Stud. Therm. Eng. 41 102655
Google Scholar
[23] Upreti H, Bartwal P, Pandey A K, Makinde O D 2023 Numer. Heat Transf. B: Fundam. 84 415
Google Scholar
[24] Yashkun U, Zaimi K, Sufahani S F, Eid M R, Ferdows M 2023 Appl. Math J. Chin. Univ. 38 373
Google Scholar
[25] Mishra N K, Sharma B K, Sharma P, Muhammad T, Pérez L M 2023 Sci. Rep. 13 1
Google Scholar
[26] Cordwell A, Chapple A A, Chung S, Wells F S, Willmott G R 2023 Soft Matter 19 4676
Google Scholar
[27] Ma N L, Sun Y, Jian Y 2023 Micromachines 14 1617
Google Scholar
[28] Sarkar S, Ganguly S 2017 J. Non-Newtonian Fluid 250 18
Google Scholar
[29] Kikuchi Y 1995 Microvasc. Res. 50 288
Google Scholar
[30] Ranjit N K, Shit G C, Tripathi D 2018 Microvasc. Res. 117 74
Google Scholar
[31] Sadeghi A, Kazemi Y, Saidi M H 2013 Nanosc. Microsc. Therm. 17 173
Google Scholar
[32] Tripathi D 2013 Math. Comput. Model 57 1270
Google Scholar
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图 1 流体流动示意图
Figure 1. Fluid flow diagram.
图 2 低Zeta势下P-B方程D-H近似解析解(蓝色)与切比雪夫谱方法(黄色)对比图, 其中$a = b = x = 0.5, \;\phi = $$ 0.05, \;d = 1.0, \;t = 0.0, \;F = 1.0$
Figure 2. Comparison between approximate analytical solution of D-H for P-B equation (blue) and Chebyshev spectrum method (yellow) at low Zeta potential, $a = b = x = $$ 0.5, \;\phi = 0.05, \;d = 1.0, \;t = 0.0, \;F = 1.0$.
图 3 低Zeta势下流动方程D-H线性近似结果(实线)与切比雪夫谱方法(圆点)对比图, 其中$a = b = x = 0.5,\; \phi = $$ 0.05, \;d = 1.0, \;t = 0.0, \;F = 1.0$
Figure 3. Comparison between the D-H approximate analytical solution (solid line) of nonlinear flow equation and Chebyshev-spectral method (dot) under the low Zeta potential, $a = b = x = 0.5, \, \;\phi = 0.05, \;d = 1.0, \;t = 0.0, \;F = 1.0$.
图 4 本文轴向速度分布与Tripathi[32]研究结果的比较, 其中${\zeta _1} \to 0, \;{\zeta _2} \to 0, \;H \to 0, \;{\beta _1} = {\beta _2} = \beta = 0$
Figure 4. Comparison between axial velocity distributions obtained by this study and Tripathi[32], where ${\zeta _1} \to 0,\; {\zeta _2} \to 0, $$ H \to 0,\; {\beta _1} = {\beta _2} = \beta = 0$.
图 5 不同参数值对轴向速度的影响($a = b = x = 0.5, \;\phi = 0.05, \; d = 1.0, \;F = 1.0 $) (a) H; (b) m; (c) ${\zeta _1}$; (d) ${\zeta _2}$; (e) ${\beta _1}$; (f) ${\beta _2}$
Figure 5. Effects of different parameter values on axial velocity: (a) H; (b) m; (c) ${\zeta _1}$; (d) ${\zeta _2}$; (e) ${\beta _1}$; (f) ${\beta _2}$. $a = b = x = 0.5, $$ \;\phi = 0.05, \;\; d = 1.0, \;F = 1.0$.
图 6 电渗参数$m$和Zeta电位对压力梯度的影响($ a = b = 0.5, {\text{ }}d = 1.0, {\text{ }}{\zeta _2} = - 1.5, {\text{ }}H = 2.0, \;{\beta _1} = 0.01, \;{\beta _2} = 0.005, {\text{ }}\phi {\text{ = 0}}{.05} $) (a) m; (b) ${\zeta _1}$
Figure 6. Effects of electroosmotic parameters $m$ and potential Zeta on pressure gradients: (a) m; (b) ${\zeta _1}$. $ a = b = 0.5, {\text{ }}d = 1.0, $$ {\text{ }}{\zeta _2} = - 1.5, {\text{ }}H = 2.0, \;{\beta _1} = 0.01, \;{\beta _2} = 0.005, {\text{ }}\phi {\text{ = 0}}{.05} $.
图 7 哈特曼数对流线分布$\psi $的影响($ \zeta_1 = - 1.5, ~\zeta_2 = -1, ~ m = 20, \beta_1 = 0.01, ~ \beta_2 = 0.005, ~\phi = 0.05 $) (a) $H \to 0\;$; (b) H = 2
Figure 7. Effect of Hammett number on streamline distribution $\psi $: (a) $H \to 0\;$; (b) H = 2. $ {\text{ }}{\zeta _1} = - 1.5{\text{ }}, \;{\zeta _2} = - 1{\text{ }}, {\text{ }}m = 20, {\beta _1} = $$ 0.01{\text{ }}, \;{\beta _2} = 0.005{\text{ }}, \;\phi = 0.05 $.
图 8 电渗参数对流线分布$\psi $的影响(${\zeta _1} = - 1.5, \;{\zeta _2} = $$ - 1, \; H = 2.0, \; {\beta _1} = 0.01, \;{\beta _2} = 0.005,\; \phi = 0.05$) (a) m = 5; (b) m = 20
Figure 8. Effects of electroosmotic parameters on the streamline distribution $\psi $: (a) m = 5; (b) m = 20.${\zeta _1} = - 1.5, \;{\zeta _2} = $$ - 1, \;H = 2.0, \;{\beta _1} = 0.01, \;{\beta _2} = 0.005, \;\phi = 0.05$
图 9 Zeta电位对流线分布$\psi $的影响($m = 20, \;H = 2.0, \; $$ {\beta _1} = 0.01, \;{\beta _2} = 0.005, \;\phi = 0.05$) (a) ${\zeta _1} = - 1$; (b) ${\zeta _1} = $$ - 1.5$; (c) ${\zeta _1} = - 2$
Figure 9. Effect of Zeta potential on streamline distribution $\psi $: (a) ${\zeta _1} = - 1$; (b) ${\zeta _1} = - 1.5$; (c) ${\zeta _1} = - 2$. $m = 20, \;H = $$ 2.0, \;{\beta _1} = 0.01, \;{\beta _2} = 0.005, \;\phi = 0.05$.
图 10 不同参数对温度分布$\theta $的影响($H = 2.0, \;{\beta _1} = 0.01, \;{\beta _2} = 0.005, \;\phi = s{t_2} = 0.05, \;{\zeta _1} = - 1.5, \;{\zeta _2} = - 1, x = 0.5, \;m = 20$) (a) m; (b) γ; (c) Br ; (d) st1
Figure 10. Influences of different parameters on temperature distribution $\theta $: (a) m; (b) γ; (c) Br ; (d) st1. $H = 2.0, \;{\beta _1} = 0.01, $$ \;{\beta _2} = 0.005, \;\phi = s{t_2} = 0.05, \;{\zeta _1} = - 1.5, \;{\zeta _2} = - 1, x = 0.5, \;m = 20$.
图 11 布林克曼数$Br$和速度滑移参数${\beta _1}$对努塞尔数$Nu$的影响($H = 2.0, \;{\beta _1} = 0.01, \;{\beta _2} = 0.005, \;\phi = s{t_2} = 0.05, \;{\zeta _1} = $$ - 1.5, \;{\zeta _2} = - 1, \;x = 0.5, \;m = 20$) (a) Br ; (b) β1
Figure 11. Influences of Brinkman number Br and slip parameter β1 on Nussle number: (a) Br ; (b) β1. $H = 2.0, \;{\beta _1} = 0.01, $$ \;{\beta _2} = 0.005, \;\phi = s{t_2} = 0.05, \;{\zeta _1} = - 1.5, \;{\zeta _2} = - 1, \;x = 0.5, \;m = 20$.
图 12 不同焦耳加热参数$\gamma $的等温图($H = 2.0, {\beta _1} = 0.01,$ ${\beta _2} = 0.005, $ $\phi = s{t_2} = 0.05, $ ${\zeta _1} = - 1.5, $ $ {\zeta _2} = - 1, $ $\;x = 0.5, $$ m = 20$) (a) $\gamma = - 2$; (b) $\gamma = 2$
Figure 12. Isothermal diagram of different joule heating parameters $\gamma $: (a) $\gamma = - 2$; (b) $\gamma = 2$. $H = 2.0, \;{\beta _1} = 0.01, $ $ {\beta _2} = 0.005,$ $ \phi = s{t_2} = 0.05, $ $ {\zeta _1} = - 1.5, $ ${\zeta _2} = - 1, $ $x = $$ 0.5, $ $ m = 20 $.
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[1] Maiti S, Pandey S K, Misra J C 2022 J. Eng. Math. 135 8
Google Scholar
[2] Jaiswal S, Yadav P K 2022 Microfluid Nanofluid 26 100
Google Scholar
[3] Patel H R, Patel S D, Darji R 2022 Int. J. Thermofluids 16 100232
Google Scholar
[4] Sherief H H, Faltas M S, El-Sapa S 2019 Eur. J. Mech. B Fluids 77 211
Google Scholar
[5] Chandra S, Kumar Pandey S 2018 J. Phys. Conf. Ser. 1141 012092
Google Scholar
[6] Yasmin H, Nisar Z 2023 Mathematics 11 2673
Google Scholar
[7] Mishra N K, Sharma B K, Sharma P, Muhammad T, Pérez L M 2023 Sci. Rep. 13 14483
Google Scholar
[8] Guedri K, Lashin M M A, Abbasi A, Khan S U, Farooq W, Khan M I, Galal A M 2023 Chin. J. Phys. 83 650
Google Scholar
[9] Maraj E N, Akbar N S, Zehra I, Butt A W, Ahmed Alghamdi H 2023 J. Magn. Magn. Mater. 576 170774
Google Scholar
[10] Rafiq M, Shaheen S, Khan M I, Fadhl B M, Hassine S B H, ElDin S M 2023 Case Stud. Therm. Eng. 45 102990
Google Scholar
[11] Alfwzan W, Riaz A, Alammari M, Hejazi H, Tag El-Din E M 2023 Front. Phys. 11 1121849
Google Scholar
[12] Wang S, Li N, Zhao M, Azese M N 2018 Z. Naturforsch. A 73 825
Google Scholar
[13] Sheikholeslami M, Chamkha A J 2016 Numer. Heat Tr. A-Appl. 69 781
Google Scholar
[14] Tripathi D, Bhushan S, Bég O A 2016 Colloids Surf. A 506 32
Google Scholar
[15] Shapiro A H, Jaffrin M Y, Weinberg S L 1969 J. Fluid Mech. Dig. Arch. 37 799
Google Scholar
[16] Shit G C, Mondal A, Sinha A, Kundu P K 2016 Physica A 462 1040
Google Scholar
[17] Chakraborty S 2007 Anal. Chim. Acta 605 175
Google Scholar
[18] Bhardwaj A, Kumar A, Bhandari D S, Tripathi D 2024 Sensor. Actuat. A-Phys. 366 114956
[19] Verma L, Meher R 2023 Pramana 97 155
Google Scholar
[20] Chen L, Abbas M A, Khudair W S, Sun B 2022 Symmetry 14 953
Google Scholar
[21] Mahabub M, Ferdows M, Murtaza M G, Lorenzini G, Tzirtzilakis E E 2022 Mathem. Mod. Eng. Probl. 9 215
Google Scholar
[22] Madkhali H A 2023 Case Stud. Therm. Eng. 41 102655
Google Scholar
[23] Upreti H, Bartwal P, Pandey A K, Makinde O D 2023 Numer. Heat Transf. B: Fundam. 84 415
Google Scholar
[24] Yashkun U, Zaimi K, Sufahani S F, Eid M R, Ferdows M 2023 Appl. Math J. Chin. Univ. 38 373
Google Scholar
[25] Mishra N K, Sharma B K, Sharma P, Muhammad T, Pérez L M 2023 Sci. Rep. 13 1
Google Scholar
[26] Cordwell A, Chapple A A, Chung S, Wells F S, Willmott G R 2023 Soft Matter 19 4676
Google Scholar
[27] Ma N L, Sun Y, Jian Y 2023 Micromachines 14 1617
Google Scholar
[28] Sarkar S, Ganguly S 2017 J. Non-Newtonian Fluid 250 18
Google Scholar
[29] Kikuchi Y 1995 Microvasc. Res. 50 288
Google Scholar
[30] Ranjit N K, Shit G C, Tripathi D 2018 Microvasc. Res. 117 74
Google Scholar
[31] Sadeghi A, Kazemi Y, Saidi M H 2013 Nanosc. Microsc. Therm. 17 173
Google Scholar
[32] Tripathi D 2013 Math. Comput. Model 57 1270
Google Scholar
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