缩放管中黏弹性流体电渗压力混合流模拟研究

杜昌隆; 夏威豪; 杨嘉杰; 李捷

doi:10.21656/1000-0887.430255

缩放管中黏弹性流体电渗压力混合流模拟研究

doi: 10.21656/1000-0887.430255

武汉理工大学船海与能源动力工程学院，武汉 430063

详细信息

作者简介:
杜昌隆(1996—)，男，硕士生(E-mail: ducl1025@qq.com)

通讯作者:
李捷(1982—)，男，副教授，博士生导师(通讯作者. E-mail: jieli@whut.edu.cn)

中图分类号: O357.3
计量
- 文章访问数: 320
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- PDF下载量: 34
- 被引次数: 0
出版历程
- 收稿日期: 2022-08-08
- 修回日期: 2023-02-15
- 刊出日期: 2023-06-01

Simulation of Electroosmotic and Pressure-Driven Mixed Flow of Viscoelastic Fluids in Converging-Diverging Tubes

School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, P.R.China

摘要

摘要: 电渗压力混合流已广泛应用于各种生化微流控领域中，其中黏弹性流体的弹性不稳定性不可忽视.采用黏弹性流体，对10∶1∶10的微通道缩放管中电渗压力混合驱动流动进行数值仿真.研究了不同压力和不同聚合物浓度对流体流动的影响，并分析了Newton流体与黏弹性流体在缩放管中速度分布的叠加原理.结果表明：反向压力使黏弹性流体展现出更大的不稳定性，使得入口涡流变大，压力每增大1 Pa涡流变大25 μm，而正向压力使涡流变小.较小反向压力时，入口涡流随着聚合物浓度的增大而增大，并逐渐趋于稳定.在较大反向压力下，涡流大小随着聚合物浓度的增大先升后降.
- 非Newton流体 /
- 微米通道 /
- 叠加原理 /
- 不稳定性 /
- 电渗流
Abstract: The electroosmotic and pressure-driven mixed flow was widely used in various biochemical microfluidic fields, where the elastic instability of the viscoelastic fluid cannot be ignored. A viscoelastic fluid was used to numerically simulate electroosmotic and pressure-driven mixed flow in a 10:1:10 microchannel converging-diverging tube. The effects of different pressures and different polymer concentrations on the fluid flow were studied, and the superposition principle for the velocity distributions of Newtonian fluids and viscoelastic fluids in converging-diverging tubes was analyzed. The results show that, the reverse pressure brings the viscoelastic fluid into higher instability, which makes the inlet vortex larger by 25 μm for every 1 Pa pressure increase. The positive pressure makes the eddy current smaller. For a relatively small reverse pressure, the inlet vortex increases with the polymer concentration and tends to be stable gradually. For a relatively large reverse pressure, the vortex size first increases and then decreases with the polymer concentration.
- non-Newtonian fluid /
- microfluidic channel /
- superposition principle /
- instability /
- electroosmotic flow

HTML全文

图 1 几何结构示意图

Figure 1. The structure diagram of the microchannel

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图 2 Γ=2速度分布验证

Figure 2. For Γ=2, the velocity distribution verification

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图 3 p=0 Pa, C_p=300 ppm, E=20 V，不同时刻的流线

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 3. For p=0 Pa, C_p=300 ppm, E=20 V, the streamlines at different moments

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图 4 p_out=3 Pa, C_p=300 ppm, E=20 V，不同时刻的流线

Figure 4. For p_out=3 Pa, C_p=300 ppm, E=20 V, the streamlines at different moments

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图 5 3个不同位置的速度随时间的变化

Figure 5. The change of the velocity with time at 3 different locations

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图 6 x=0，沿y轴的速度分布

Figure 6. The velocity distributions along the y axis

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图 7 C_p=300 ppm，入口处电势E=20 V，t=0.8 s时刻下的流线，p_out=0 Pa，采用不同的进口压力

Figure 7. For C_p=300 ppm, entrance potential E=20 V, the streamlines at t=0.8 s, p_out=0 Pa, with different inlet pressures

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图 8 涡流大小示意图

Figure 8. Schematic diagram of the vortex size

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图 9 E=20 V, C_p=300 ppm: 涡流大小随时间大小波动和不同出口压力下涡流的平均大小

Figure 9. For E=20 V, C_p=300 ppm: the vortex current size changing with time and the vortex current sizes under different outlet pressures

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图 10 E=20 V，涡流大小随聚合物浓度的变化

Figure 10. For E=20 V, the change of the vortex size with the polymer concentration

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图 11 通道中点速度的离散系数

Figure 11. The dispersion coefficient of the midpoint velocity of the channel

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图 12 p_out=5 Pa，沿y轴的速度分布

Figure 12. The velocity distributions along the y- axis, p_out=5 Pa

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表 1 模型部分参数

Table 1. Numerical simulation parameters

parameter name	value
ρ/(kg/m³)	1 000
η_s/(Pa·s)	0.001
E₀/(V/m)	20 000
ζ/mV	-110
C₀/(mol/m³)	0.01
T/K	300

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参考文献(22)

[1]	REUSS F F. Charge-induced flow[J]. Proceedings of the Imperial Society of Naturalists of Moscow, 1809, 3: 327-344.
[2]	RICE C L, WHITEHEAD R. Electrokinetic flow in a narrow cylindrical capillary[J]. Journal of Physical Chemistry, 1965, 69(11): 4017-4024. doi: 10.1021/j100895a062
[3]	刘浩, 娄钦, 黄一帆. T型微通道内液滴在幂律流体中运动机理的格子Boltzmann方法研究[J]. 应用数学和力学, 2022, 43(3): 255-271. doi: 10.21656/1000-0887.420182 LIU Hao, LOU Qin, HUANG Yifan. Study of movement mechanisms of droplets in power-law fluids in T-junction microchannels with the lattice Boltzmann method[J]. Applied Mathematics and Mechanics, 2022, 43(3): 255-271. (in Chinese) doi: 10.21656/1000-0887.420182
[4]	ZHAO C, ZHOLKOVSKIJ E, MASLIYAH J H, et al. Analysis of electroosmotic flow of power-law fluids in a slit microchannel[J]. Journal of Colloid & Interface Science, 2008, 326(2): 503-510.
[5]	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
[6]	AFONSO A M, ALVES M A, PINHO F T. Electro-osmotic flow of viscoelastic fluids in microchannels under asymmetric zeta potentials[J]. Journal of Engineering Mathematics, 2011, 71(1): 15-30. doi: 10.1007/s10665-010-9421-9
[7]	AFONSO A M, ALVES M A, PINHO F T. Analytical solution of mixed electro-osmotic/pressure driven flows of viscoelastic fluids in microchannels[J]. Journal of Non-Newtonian Fluid Mechanics, 2009, 159(1/3): 50-63.
[8]	SOUSA J J, AFONSO A M, PINHO F T, et al. Effect of the skimming layer on electro-osmotic-Poiseuille flows of viscoelastic fluids[J]. Microfluidics & Nanofluidics, 2011, 10(1): 107-122.
[9]	PARK H M, LEE W M. Effect of viscoelasticity on the flow pattern and the volumetric flow rate in electroosmotic flows through a microchannel[J]. Lab on a Chip, 2008, 8(7): 1163-1170. doi: 10.1039/b800185e
[10]	MONAZAMI R, MANZARI M T. Analysis of combined pressure-driven electroosmotic flow through square microchannels[J]. Microfluidics and Nanofluidics, 2007, 3(1): 123-126.
[11]	MONDAL M, MISRA R P, DE S. Combined electroosmotic and pressure driven flow in a microchannel at high zeta potential and overlapping electrical double layer[J]. International Journal of Thermal Sciences, 2014, 86(3): 48-59.
[12]	VAKILI M A, SADEGHI A, SAIDI M H, et al. Electrokinetically driven fluidic transport of power-law fluids in rectangular microchannels[J]. Colloids & Surfaces A: Physicochemical & Engineering Aspects, 2012, 414: 440-456.
[13]	HADIGOL M, NOSRATI R, RAISEE M. Numerical analysis of mixed electroosmotic/pressure driven flow of power-law fluids in microchannels and micropumps[J]. Colloids & Surfaces A: Physicochemical & Engineering Aspects, 2011, 374(1/3): 142-153.
[14]	DUTTA P, BESKOK A. Analytical solution of combined electroosmotic/pressure driven flows in two-dimensional straight channels: finite Debye layer effects[J]. Analytical Chemistry, 2001, 73(9): 1979-1986. doi: 10.1021/ac001182i
[15]	FERRÁS L, AFONSO A M, ALVES M A, et al. Electro-osmotic and pressure-driven flow of viscoelastic fluids in microchannels: analytical and semi-analytical solutions[J]. Physics of Fluids, 2016, 28(9): 093102. doi: 10.1063/1.4962357
[16]	高峰, 石则满, 冯鑫, 等. 微流控芯片中电渗流的数值模拟与仿真研究[J]. 传感器与微系统, 2017, 36(11): 53-55. https://www.cnki.com.cn/Article/CJFDTOTAL-CGQJ201711016.htm GAO Feng, SHI Zeman, FENG Xin, et al. Numerical simulation and simulation of electroosmosis in microfluidic chip[J]. Transducer and Microsystem Technologies, 2017, 36(11): 53-55. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-CGQJ201711016.htm
[17]	罗艳, 李鸣, 杨大勇. 微通道内电渗压力混合驱动幂律流体流动模拟[J]. 应用数学和力学, 2016, 37(4): 373-381. doi: 10.3879/j.issn.1000-0887.2016.04.005 LUO Yan, LI Ming, YANG Dayong. Simmulation of mixed electroosmotic and pressure-driven flows of power-law fluids in microchannels[J]. Applied Mathematics and Mechanics, 2016, 37(4): 373-381. (in Chinese) doi: 10.3879/j.issn.1000-0887.2016.04.005
[18]	BRYCE R M, FREEMAN M R. Extensional instability in electro-osmotic microflows of polymer solutions[J]. Physical Review E, 2010, 81(3): 36328. doi: 10.1103/PhysRevE.81.036328
[19]	SONG L, JAGDALE P, YU L D, et al. Electrokinetic instability in microchannel viscoelastic fluid flows with conductivity gradients[J]. Physics of Fluids, 2019, 31(8): 082001.
[20]	SOUSA P C, VEGA E J, SOUSA R G, et al. Measurement of relaxation times in extensional flow of weakly viscoelastic polymer solutions[J]. Rheologica Acta, 2017, 56(1): 11-20.
[21]	FERRÁS L, AFONSO A M, ALVES M A, et al. Newtonian and viscoelastic fluid flows through an abrupt 1∶4 expansion with slip boundary conditions[J]. Physics of Fluids, 2020, 32(4): 043103.
[22]	OISHI C M, WARTINS F, AFONSO A M, et al. A numerical study of the kernel-conformation transformation for transient viscoelastic fluid flows[J]. Journal of Computational Physics, 2015, 302: 653-673.