pH调节的纳米平行通道中Powell-Eyring流体的电渗流动

长龙; 布仁满都拉; 娜仁; 孙艳军; 菅永军

doi:10.21656/1000-0887.450137

pH调节的纳米平行通道中Powell-Eyring流体的电渗流动

doi: 10.21656/1000-0887.450137

长龙^1,,
布仁满都拉²,
娜仁¹,
孙艳军¹,
菅永军^{3, 4, ,}

1.
内蒙古财经大学统计与数学学院，呼和浩特 010070
2.
内蒙古师范大学数学科学学院，呼和浩特 010022
3.
东华大学数学与统计学院, 上海 201620
4.
东华大学非线性科学研究所, 上海 201620

基金项目:

国家自然科学基金 12162003

国家自然科学基金 11862018

国家自然科学基金 12262026

内蒙古自治区自然科学基金 2024LHMS01010

内蒙古自治区自然科学基金 2024LHMS01008

内蒙古自治区高等学校创新团队发展计划 NMGIRT2323

自治区直属高校基本科研业务费 NCYWT23035

详细信息

作者简介:
长龙(1979—)，男，副教授，博士(E-mail: suolunga@163.com)

通讯作者:
菅永军(1974—)，男，教授，博士, 博士生导师(通讯作者. E-mail: jianyj@dhu.edu.cn)

中图分类号: O357.1
计量
- 文章访问数: 24
- HTML全文浏览量: 10
- PDF下载量: 5
- 被引次数: 0
出版历程
- 收稿日期: 2024-05-12
- 修回日期: 2024-06-07
- 刊出日期: 2025-01-01

Electroosmotic Flows of Powell-Eyring Fluids in pH-Regulated Parallel Plate Nanochannels

1.
School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, P.R.China
2.
College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, P.R.China
3.
School of Mathematics and Statistics, Donghua University, Shanghai 201620, P.R.China
4.
Institute of Nonlinear Sciences, Donghua University, Shanghai 201620, P.R.China

摘要

摘要: 在调节溶液pH值和盐浓度下, 利用同伦摄动法求解了纳米平行通道内Powell-Eyring流体的电渗流动(electroosmotic flow, EOF), 得到了近似解. 通过Chebyshev谱配置法验证了所得的近似解的准确性. 在此基础上, 研究了无量纲压力梯度G, 盐浓度M_KCI和pH值, Powell-Eyring流体和Newton流体的黏度之比γ对速度剖面u和体积流率(平均速度)Q的影响. 结果表明, 同伦摄动法的收敛速度较快, 仅需展开到一阶解就与数值解完全吻合; 同时, M_KCI, pH, γ和G对纳米通道中的电荷密度和Powell-Eyring流体电渗流速度具有显著影响.
- pH调节 /
- Powell-Eyring流体 /
- 电渗流动 /
- 官能团
Abstract: Under the adjustment of solution pH values and background salt concentrations, the electroosmotic flows of the Powell-Eyring fluids in parallel plate nanochannels were studied with the homotopic perturbation method, and approximate solutions were obtained. The accuracy of the obtained approximate solution was verified with the Chebyshev spectrum configuration method. On this basis, the effects of dimensionless pressure gradient G, background salt concentration M_KCI, the pH value, and the viscosity ratio γ of the Powell-Eyring fluid and the Newtonian fluid, on velocity profile u and volume flow rate (average velocity) Q, were studied. The results demonstrate that, the homotopy perturbation method converges rapidly, requiring only an expansion up to the 1st-order solution to perfectly match the numerical solution. Meanwhile, M_KCI, pH, γ and G have significant effects on the charge density and the electroosmotic flow velocity of the Powell-Eyring fluid in the nanochannel.
- pH-regulation /
- Powell-Eyring fluid /
- electroosmotic flow /
- functional group

HTML全文

图 1 物理模型示意图

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 1. Schematic diagram of the physical model

下载: 全尺寸图片幻灯片

图 2 不同pH对应的EOF速度分布

Figure 2. EOF velocity distributions for different pH values

下载: 全尺寸图片幻灯片

图 3 纯EOF速度分布

Figure 3. Pure EOF velocity distributions

下载: 全尺寸图片幻灯片

图 4 不同pH和θ对应的纯EOF速度分布(γ=0.3)

Figure 4. Pure EOF velocity distributions for different pH and θ values (γ=0.3)

下载: 全尺寸图片幻灯片

图 5 壁面剪切应力随pH的分布

Figure 5. Distribution of wall shear stress with pH

下载: 全尺寸图片幻灯片

图 6 体积流率分布

Figure 6. Volume flow rate distribution

下载: 全尺寸图片幻灯片

参考文献(37)

[1]	STONE H A, STROOCK A D, AJDARI A. Engineering flows in small devices: microfluidics toward a lab-on-a-chip[J]. Annual Review of Fluid Mechanics, 2004, 36 : 381-411. doi: 10.1146/annurev.fluid.36.050802.122124
[2]	BAYRAKTAR T, PIDUGU S B. Characterization of liquid flows inmicrofluidic systems[J]. International Journal of Heat and Mass Transfer, 2006, 49 (5/6): 815-824. http://www.researchgate.net/profile/Srikanth_Pidugu/publication/222039140_Characterization_of_liquid_flow_in_microfluidic_systems/links/00b7d5256133690ff4000000.pdf
[3]	LEVINE S, MARRIOTT J R, NEALE G, et al. Theory of electrokinetic flow in fine cylindrical capillaries at high zeta-potentials[J]. Journal of Colloid and Interface Science, 1975, 52 (1): 136-149. doi: 10.1016/0021-9797(75)90310-0
[4]	HSU J P, KAO C Y, TSENG S, et al. Electrokinetic flow through an elliptical microchannel: effects of aspect ratio and electrical boundary conditions[J]. Journal of Colloid and Interface Science, 2002, 248 (1): 176-184. doi: 10.1006/jcis.2001.8200
[5]	JIAN Y, YANG L, LIU Q. Time periodic electro-osmotic flow through amicroannulus[J]. Physics of Fluids, 2010, 22 (4): 042001. doi: 10.1063/1.3358473
[6]	LIN X H, ZHANG C B, GU J, et al. Poisson-Fokker-Planck model for biomolecules translocation through nanopore driven by electroosmotic flow[J]. Science China Physics, Mechanics & Astronomy, 2014, 57 (11): 2104-2113. http://www.onacademic.com/detail/journal_1000036502975210_5da5.html
[7]	李子瑞. 离子浓差极化效应及其在微纳流控分子富集系统中的应用进展[J]. 中国科学: 技术科学, 2018, 48 (11): 1151-1166. LI Zirui. Ion concentration polarization and its application in molecular preconcentration in micro-nanofluidic systems[J]. Scientia Sinica: Technologica, 2018, 48 (11): 1151-1166. (in Chinese)
[8]	邢靖楠, 菅永军. 矩形纳米管道中的电动能量转换效率[J]. 应用数学和力学, 2016, 37 (4): 363-372. doi: 10.3879/j.issn.1000-0887.2016.04.004 XING Jingnan, JIAN Yongjun. Electrokinetic energy conversion efficiency in rectangular nanochannels[J]. Applied Mathematics and Mechanics, 2016, 37 (4): 363-372. (in Chinese) doi: 10.3879/j.issn.1000-0887.2016.04.004
[9]	许丽娜, 菅永军. 柔性圆柱形微管道内的电动流动及传热研究[J]. 应用数学和力学, 2019, 40 (4): 408-418. doi: 10.21656/1000-0887.390155 XU Lina, JIAN Yongjun. Electrokinetic flow and heat transfer in soft microtubes[J]. Applied Mathematics and Mechanics, 2019, 40 (4): 408-418. (in Chinese) doi: 10.21656/1000-0887.390155
[10]	王爽, 菅永军. 周期壁面电势调制下平行板微管道中的电磁电渗流动[J]. 应用数学和力学, 2020, 41 (4): 396-405. doi: 10.21656/1000-0887.400151 WANG Shuang, JIAN Yongjun. Magnetohydrodynamic electroosmotic flow in zeta potential patterned micro-parallel channels[J]. Applied Mathematics and Mechanics, 2020, 41 (4): 396-405. (in Chinese) doi: 10.21656/1000-0887.400151
[11]	TANG G H, LI X F, HE Y L, et al. Electroosmotic flow of non-Newtonian fluid in microchannels[J]. Journal of Non-Newtonian Fluid Mechanics, 2009, 157 (1/2): 133-137. http://zhaojihong.gr.xjtu.edu.cn/c/document_library/get_file?folderId=1766831&name=DLFE-22707.pdf
[12]	LIU Q, JIAN Y, YANG L. Alternating current electroosmotic flow of the Jeffreys fluids through a slit microchannel[J]. Physics of Fluids, 2011, 23 (10): 102001. doi: 10.1063/1.3640082
[13]	TANG L, HAO Y, PENG L, et al. Ion current rectification properties of non-Newtonian fluids in conicalnanochannels[J]. Physical Chemistry Chemical Physics, 2024, 26 (4): 2895-2906. doi: 10.1039/D3CP05184F
[14]	姜玉婷, 齐海涛. 微平行管道内Eyring流体的电渗滑移流动[J]. 物理学报, 2015, 64 (17): 222-227. JIANG Yuting, QI Haitao. Electro-osmotic slip flow of Eyring fluid in a slit microchannel[J]. Acta Physica Sinica, 2015, 64 (17): 222-227. (in Chinese)
[15]	郑佳璇, 梁韵笛, 菅永军. 高zeta势下Phan-Thien-Tanner(PTT)流体的电渗微推进器[J]. 应用数学和力学, 2023, 44 (10): 1213-1225. ZHENG Jiaxuan, LIANG Yundi, JIAN Yongjun. Electroosmotic micro thrusters of Phan-Thien-Tanner (PTT) fluid at high zeta potential[J]. Applied Mathematics and Mechanics, 2023, 44 (10): 1213-1225. (in Chinese)
[16]	长龙, 布仁满都拉, 孙艳军, 等. 具有正弦波纹的平行板微通道中Jeffrey流体周期电渗流动[J]. 应用数学和力学, 2024, 45 (5): 622-636. CHANG Long, BUREN Mandula, SUN Yanjun, et al. Periodic electroosmotic flow of the Jeffrey fluid in microchannel between two sinusoidally wavy walls[J]. Applied Mathematics and Mechanics, 2024, 45 (5): 622-636. (in Chinese)
[17]	YANG J, CHEN Y, DU C, et al. Numerical simulation of electroosmotic mixing of non-Newtonian fluids in a micromixer with zeta potential heterogeneity[J]. Chemical Engineering and Processing: Process Intensification, 2023, 186 : 109339. doi: 10.1016/j.cep.2023.109339
[18]	YADAV P K, ROSHAN M. Mathematical modeling of blood flow in an annulus porous region between two coaxial deformable tubes: an advancement to peristaltic endoscope[J]. Chinese Journal of Physics, 2024, 88 : 89-109. doi: 10.1016/j.cjph.2024.01.017
[19]	POWELL R E, EYRING H. Mechanisms for the relaxation theory of viscosity[J]. Nature, 1944, 154 (3909): 427-428. doi: 10.1038/154427a0
[20]	ISLAM S, SHAH A, ZHOU C Y, et al. Homotopy perturbation analysis of slider bearing with Powell-Eyring fluid[J]. Zeitschrift Für Angewandte Mathematik und Physik, 2009, 60 (6): 1178-1193. doi: 10.1007/s00033-009-7034-9
[21]	HAYAT T, IQBAL Z, QASIM M, et al. Steady flow of an Eyring Powell fluid over a moving surface with convective boundary conditions[J]. International Journal of Heat and Mass Transfer, 2012, 55 (7/8): 1817-1822. http://www.xueshufan.com/publication/2078161903
[22]	PATIL P M, GOUDAR B. Impact of impulsive motion on the Eyring-Powell nanofluid flow across a rotating sphere in MHD convective regime: entropy analysis[J]. Journal of Magnetism and Magnetic Materials, 2023, 571 : 170590. doi: 10.1016/j.jmmm.2023.170590
[23]	AKBAR Y, HUANG S, ASHRAF M U, et al. Electrothermal analysis for reactive Powell Eyring nanofluid flow regulated by peristaltic pumping with mass transfer[J]. Case Studies in Thermal Engineering, 2023, 44 : 102828. doi: 10.1016/j.csite.2023.102828
[24]	GOSWAMI P, MONDAL P K, DUTTA S, et al. Electroosmosis of Powell-Eyring fluids under interfacial slip[J]. Electrophoresis, 2015, 36 (5): 703-711. doi: 10.1002/elps.201400473
[25]	LI F Q, JIAN Y J, XIE Z Y, et al. Electromagnetohydrodynamic flow of Powell-Eyring fluids in a narrow confinement[J]. Journal of Mechanics, 2017, 33 (2): 225-233. doi: 10.1017/jmech.2016.75
[26]	YEH L H, XUE S, JOO S W, et al. Field effect control of surface charge property and electroosmotic flow in nanofluidics[J]. The Journal of Physical Chemistry C, 2012, 116 (6): 4209-4216. doi: 10.1021/jp211496b
[27]	TSENG S, TAI Y H, HSU J P. Ionic current in a pH-regulated nanochannel filled with multiple ionic species[J]. Microfluidics and Nanofluidics, 2014, 17 (5): 933-941. doi: 10.1007/s10404-014-1384-0
[28]	MEI L, YEH L H, QIAN S. Buffer effect on the ionic conductance in a pH-regulated nanochannel[J]. Electrochemistry Communications, 2015, 51 : 129-132. doi: 10.1016/j.elecom.2014.12.020
[29]	SADEGHI M, SAIDI M H, SADEGHI A. Electroosmotic flow and ionic conductance in a pH-regulated rectangular nanochannel[J]. Physics of Fluids, 2017, 29 (6): 062002. doi: 10.1063/1.4986075
[30]	HSU J P, CHU Y Y, LIN C Y, et al. Ion transport in a pH-regulated conical nanopore filled with a power-law fluid[J]. Journal of Colloid and Interface Science, 2019, 537 : 358-365. doi: 10.1016/j.jcis.2018.11.020
[31]	BARMAN B, KUMAR D, GOPMANDAL P P, et al. Electrokinetic ion transport and fluid flow in a pH-regulated polymer-grafted nanochannel filled with power-law fluid[J]. Soft Matter, 2020, 16 (29): 6862-6874. doi: 10.1039/D0SM00709A
[32]	YANG M, BUREN M, CHANG L, et al. Time periodic electroosmotic flow in a pH-regulated parallel-plate nano- channel[J]. Physica Scripta, 2022, 97 (3): 030003. doi: 10.1088/1402-4896/ac52f9
[33]	BAG N. Impact of pH-regulated wall charge on the modulation of electroosmotic flow and transport of ionic species through slit nanochannels[J]. Colloid Journal, 2023, 85 (3): 315-325. doi: 10.1134/S1061933X23600033
[34]	CHUANG P Y, HSU J P. Electroosmotic flow, ionic current rectification, and selectivity of a conical nanopore modified with a pH-regulated polyelectrolyte layer: influence of functional groups profile[J]. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2023, 676 : 132240. doi: 10.1016/j.colsurfa.2023.132240
[35]	PENG L, ZHANG Z, TANG L, et al. Electrokinetic ion transport of viscoelastic fluids in a pH-regulated nanochannel[J]. Surfaces and Interfaces, 2024, 46 : 103957. doi: 10.1016/j.surfin.2024.103957
[36]	MEHTA S K, GHOSH A, MONDAL P K, et al. Electroosmosis of viscoelastic fluids in pH-sensitive hydrophobic microchannels: effect of surface charge-dependent slip length[J]. Physics of Fluids, 2024, 36 (2): 023101. doi: 10.1063/5.0181156
[37]	HE J H. Homotopy perturbation method: a new nonlinear analytical technique[J]. Applied Mathematics and Computation, 2003, 135 (1): 73-79. doi: 10.1016/S0096-3003(01)00312-5