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采用基于流固耦合的有限元方法, 对二维模型中高分子囊泡在微管流中惯性迁移现象进行了系统研究, 分析了囊泡因受到流体作用力而形变并发生惯性迁移现象的机理. 研究表明: 随着雷诺数的增大, 囊泡惯性迁移的平衡位置离其初始位置越来越远; 随着阻塞比的增加, 囊泡惯性迁移后的平衡位置越来越接近壁面. 对于囊泡膜的模量和黏度以及膜厚, 结果表明模量和黏度决定了囊泡的变形程度, 模量对囊泡平衡位置影响较小, 但增大黏度和膜厚会促进囊泡的平衡位置偏向管道中心. 本研究有助于进一步明晰囊泡在惯性迁移过程中的形变和平衡位置, 为囊泡在药物输运、化学反应和生理过程的应用提供可靠的计算依据.The finite element method based on fluid-structure interaction is used to systematically study the inertial migration of polymer vesicles in microtubule flow with a two-dimensional model, and the mechanism of the vesicles deformed by the fluid and the inertial migration phenomena are analyzed. The studies show that with the increase Reynolds number, the equilibrium position of vesicle inertial migration is farther and farther from its initial position; with the increase of blocking ratio, the equilibrium position of vesicle inertial migration is closer to the wall surface. For the modulus and viscosity of the vesicle membrane and for the membrane thickness, the results show that the modulus and viscosity determine the degree of deformation of the vesicle, and the modulus has little effect on the equilibrium position of the vesicle, but increases the viscosity, and the membrane thickness will promote the equilibrium position of the vesicle to be biased toward the center of the tube. This study helps to further clarify the deformation and equilibrium position of vesicles during inertial migration, and provides a reliable computational basis for the application of vesicles in drug transport, chemical reactions and physiological processes.
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Keywords:
- inertial migration /
- polymer vesicle /
- finite element /
- Reynolds number
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图 1 囊泡受力分析图(剪切梯度升力指向通道壁面, 壁面诱导升力指向通道中心)
Fig. 1. Vesicle force analysis. (Shear gradient lift points to the channel wall, wall-induced lift points to the channel center).
图 2 (a) 囊泡惯性迁移示意图; (b)—(d) 不同时刻囊泡周围流速图 (管道宽为H = 150 μm、长为D = 1300 μm, 囊泡半径为a = 20 μm, 囊泡膜厚1 μm, 囊泡内外均为水. 膜的杨氏模量为5000 Pa. 管道入口速度为V, 囊泡表面到管道壁面的距离为L)
Fig. 2. (a) Schematic representation of the vesicle inertial migration; (b)–(d) flow velocity around vesicles at different times (The channel width is H = 150 μm and length is D = 1300 μm. The vesicle radius is a = 20 μm and the vesicle membrane is 1 μm thick. Water is both inside and outside the vesicles. The Young’s modulus of the membrane is 5000 Pa. The inlet speed is V, L is distance from the vesicle surface to the channel wall).
图 3 不同阻塞比下, 雷诺数对惯性迁移平衡位置的影响 (r代表囊泡达到平衡位置后质心的纵坐标. 黑色虚线代表Matas等[8]的实验报道结果, 其颗粒直径为190 μm—1 mm, 管道宽度为8 mm, 即颗粒的阻塞比范围为0.0238—0.125)
Fig. 3. Effect of Reynold numbers on the equilibrium position of inertial migration with different blocking ratios (r represents the ordinate of the centroid of the vesicle after reaching the equilibrium position. The black dashed line represents the experimentally reported results of Matas et al.[8] with particle diameters of 190 μm–1 mm and pipe widths of 8 mm, i.e. the particle blocking ratios ranged from 0.0238 to 0.125)
图 4 不同雷诺数和阻塞比下囊泡升力随时间的变化图 (a) Re = 100, κ = 0.1, 0.3, 0.5; (b) Re = 50, 100, 250, κ = 0.3 (F为升力, 即是壁面诱导升力与剪切梯度升力的总和, 方向为管道径向)
Fig. 4. Plot of vesicle lift over time under different Reynolds numbers and blocking ratios: (a) Re = 100, κ = 0.1, 0.3, 0.5; (b) Re = 50, 100, 250, κ = 0.3 (Lift is the sum of wall-induced lift and shear gradient lift, in the tube radial).
图 5 囊泡初始位置对惯性迁移的影响
Fig. 5. Effect of the initial vesicle position on the inertial migration.
图 6 不同初始位置时囊泡升力随时间的变化 (a) Re = 50; (b) Re = 200
Fig. 6. Variations of vesicle lift with time at different initial positions: (a) Re = 50; (b) Re = 200.
图 7 囊泡膜模量对惯性迁移的影响
Fig. 7. Effect of the modulus of vesicle membrane on the inertial migration.
图 8 不同膜黏度时囊泡的形变及其迁移位置轨迹图
Fig. 8. Deformation of vesicles and their migration location trajectories at different membrane viscosities.
图 9 囊泡膜的黏度对惯性迁移的影响
Fig. 9. Effect of vesicle membrane viscosity on the inertial migration.
图 10 囊泡膜厚对惯性迁移的影响
Fig. 10. Effects of vesicle membrane thickness on inertial migration.
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[1] Discher D E, Eisenberg A 2002 Science 297 967
Google Scholar
[2] Thery C, Ostrowski M, Segura E 2009 Nat. Rev. Immunol. 9 581
Google Scholar
[3] Yingchoncharoen P, Kalinowski D S, Richardson D R 2016 Pharmacol. Rev. 68 701
Google Scholar
[4] Finean J B 1983 Trends Biochem. Sci. 8 225
Google Scholar
[5] Rubinow S I, Keller J B 1961 J. Fluid Mech. 11 447
Google Scholar
[6] Saffman P G 2006 J. Fluid Mech. 22 385
Google Scholar
[7] Asmolov E S 1999 J. Fluid Mech. 381 63
Google Scholar
[8] Matas J P, Morris J F, Guazzelli É 2004 J. Fluid Mech. 515 171
Google Scholar
[9] Matas J P, Glezer V, Guazzelli E 2004 Phys. Fluids 16 4192
Google Scholar
[10] Coupier G, Kaoui B, Podgorski T 2008 Phys. Fluids 20 111702
Google Scholar
[11] Risso F, Colle-Paillot F, Zagzoule M 2006 J. Fluid Mech. 547 149
Google Scholar
[12] Bagchi P 2007 Biophys. J. 92 1858
Google Scholar
[13] Lázaro G R, Hernández-Machado A, Pagonabarraga I 2014 Soft Matter 10 7207
Google Scholar
[14] Bächer C, Schrack L, Gekle S 2017 Phys. Rev. Fluids 2 013102
Google Scholar
[15] Abay A, Recktenwald S M, John T 2020 Soft Matter 16 534
Google Scholar
[16] Segr G, Silberberg A 1961 Nature 189 209
Google Scholar
[17] Carlo D D 2009 Lab Chip 9 3038
Google Scholar
[18] Carlo D D, Edd J F, Humphry K J 2009 Phys. Rev. Lett. 102 094503
Google Scholar
[19] Feng J, Hu H H, Joseph D D 1994 J. Fluid Mech. 277 271
Google Scholar
[20] Brenner H 1961 Chem. Eng. Sci. 16 242
Google Scholar
[21] Carlo D D, Irimia D, Tompkins R G 2007 P Natl. Acad. Sci. U. S. A. 104 18892
Google Scholar
[22] Morita Y, Itano T, Sugihara-Seki M 2017 J. Fluid Mech. 813 750
Google Scholar
[23] Yao T L, Yu Z S, Shao X M 2014 J. Mech. Electr. Eng. 31 301
Google Scholar
[24] Nakayama S, Yamashita H, Yabu T 2019 J. Fluid Mech. 871 952
Google Scholar
[25] Salac D, Miksis M J 2012 J. Fluid Mech. 711 122
Google Scholar
[26] Mach A J, Carlo D D 2010 Biotechnol. Bioeng. 107 302
Google Scholar
[27] Doddi S K, Bagchi P 2008 Int. J. Multiphase Flow 34 966
Google Scholar
[28] Sun D K, Bo Z 2015 Int. J. Heat Mass Transfer 80 139
Google Scholar
[29] Shin S J, Sung H J 2011 Phys. Rev. E:Stat. Nonlinear Soft Matter Phys. 83 046321
Google Scholar
[30] Alghalibi D, Rosti M E, Brandt L 2019 Phys. Rev. Fluids 4 104201
Google Scholar
[31] Krüger T, Kaoui B, Harting J 2013 J. Fluid Mech. 751 725
Google Scholar
[32] Hur S C, Henderson-Maclennan N K, Mccabe E R B, Carlo D D 2011 Lab Chip 11 912
Google Scholar
[33] Hotz J, Meier W 1998 Langmuir 14 1031
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[41] Li Y X, Xing B H, Ding M M, Shi T F, Sun Z Y 2021 Soft Matter 17 9154
Google Scholar
[42] Zhang R L, Ding M M, Duan X Z, Shi T F 2021 Phys. Fluids 33 121901
Google Scholar
[43] Zeng L, Najjar F, Balachandar S, Fischer P 2009 Phys. Fluids 21 1
Google Scholar
[44] Esfahani S A, Hassani K, Espino D M 2019 Comput. Meth. Biomech. Biomed. Eng. 22 288
Google Scholar
[45] Espino D M, Shepherd D, Hukins D 2015 Eur. J. Mech. B. Fluids 51 54
Google Scholar
[46] Lac E, BarthèS B D 2005 Phys. Fluids 17 072105
Google Scholar
[47] Shin S J, Sung H 2012 Int. J. Heat Fluid Flow. 36 167
Google Scholar
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Google Scholar
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