Finite element analysis of inertial migration of polymer vesicles in microtubule flow

Hao Peng; Zhang Li-Li; Ding Ming-Ming

doi:10.7498/aps.71.20220606

Abstract

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.

Keywords:

Authors and contacts

1.
Xinjiang Laboratory of Phase Transitions and Microstructures in Condensed Matter Physics, College of Physical Science and Technology, Yili Normal University, Yining 835000, China
2.
School of Chemical Engineering and Light Industry, Guangdong University of Technology, Guangzhou 510006, China

Corresponding author: Ding Ming-Ming, mmding@gdut.edu.cn

Funds: Project supported by the Xinjiang Uygur Autonomous Region key Laboratory Open Subject, China (Grant No. 2021D04015), the Xinjiang Uygur Autonomous Region University Science and Technology Plan Project, China (Grant No. XJEDU2021Y044), and the Doctoral Starting Fund of Yili Normal University, China (Grant No. 2021YSBS009).

[1]	Discher D E, Eisenberg A 2002 Science 297 967 Google Scholar
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[38]	Zhang R L, Han Y L, Zhang L L, Chen Q Y, Ding M M, Shi T F 2021 Colloids Surf. , A 609 125560 Google Scholar
[39]	Zhang Y L, Han Y L, Zhang L L, Chen Q Y, Ding M M, Shi T F 2020 Phys Fluids 32 103310 Google Scholar
[40]	Han Y L, Li R, Ding M M, Ye F, Shi T F 2021 Phys. Fluids 33 012010 Google Scholar
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Cited By

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)

Figure 1. Vesicle force analysis. (Shear gradient lift points to the channel wall, wall-induced lift points to the channel center).

DownLoad: Full-Size Img PowerPoint

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)

Figure 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).

DownLoad: Full-Size Img PowerPoint

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)

Figure 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)

DownLoad: Full-Size Img PowerPoint

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)

Figure 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).

DownLoad: Full-Size Img PowerPoint

图 5 囊泡初始位置对惯性迁移的影响

Figure 5. Effect of the initial vesicle position on the inertial migration.

DownLoad: Full-Size Img PowerPoint

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

Figure 6. Variations of vesicle lift with time at different initial positions: (a) Re = 50; (b) Re = 200.

DownLoad: Full-Size Img PowerPoint

图 7 囊泡膜模量对惯性迁移的影响

Figure 7. Effect of the modulus of vesicle membrane on the inertial migration.

DownLoad: Full-Size Img PowerPoint

图 8 不同膜黏度时囊泡的形变及其迁移位置轨迹图

Figure 8. Deformation of vesicles and their migration location trajectories at different membrane viscosities.

DownLoad: Full-Size Img PowerPoint

图 9 囊泡膜的黏度对惯性迁移的影响

Figure 9. Effect of vesicle membrane viscosity on the inertial migration.

DownLoad: Full-Size Img PowerPoint

图 10 囊泡膜厚对惯性迁移的影响

Figure 10. Effects of vesicle membrane thickness on inertial migration.

DownLoad: Full-Size Img PowerPoint

[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
[34]	Bah M G, Bilal H M, Wang J T 2020 Soft Matter 16 570 Google Scholar
[35]	Kim B, Chang C B, Park S G, Sunget H J 2015 Int. J. Heat Fluid Flow 54 87 Google Scholar
[36]	Han Y L, Lin H, Ding M M, Li R, Shi T F 2019 Soft Matter 15 3307 Google Scholar
[37]	Han Y L, Ding M M, Li R, Shi T F 2019 Chin. J. Polym. Sci. 38 776 Google Scholar
[38]	Zhang R L, Han Y L, Zhang L L, Chen Q Y, Ding M M, Shi T F 2021 Colloids Surf. , A 609 125560 Google Scholar
[39]	Zhang Y L, Han Y L, Zhang L L, Chen Q Y, Ding M M, Shi T F 2020 Phys Fluids 32 103310 Google Scholar
[40]	Han Y L, Li R, Ding M M, Ye F, Shi T F 2021 Phys. Fluids 33 012010 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
[48]	Kilimnik A, Mao W, Alexeev A 2011 Phys. Fluids 23 123302 Google Scholar

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