颗粒在粘弹性流体中运动的若干问题研究

李振娜; 林建忠

doi:10.1007/s10409-022-09008-x

On the some issues of particle motion in the flow of viscoelastic fluids

doi: 10.1007/s10409-022-09008-x

Li Zhenna,
Lin Jianzhong^{*
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State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, China

Funds:

the National Natural Science Foundation of China Grant

More Information

Corresponding author: Lin Jianzhong, E-mail address: mecjzlin@public.zju.edu.cn (Jianzhong Lin)

摘要

摘要: 粘弹性流体约束剪切流中的颗粒运动在自然界中非常普遍且有着广泛的应用, 了解和掌握粘弹性流体中颗粒的运动特性具有重要的学术价值和实际意义. 本文首先介绍了相关的方程和特征参数, 然后着重讨论了以下几个问题: 颗粒的横向平衡位置, 多颗粒的相互作用和聚集, 多颗粒形成的链状结构以及非球形颗粒的运动. 最后强调了一些尚未解决的问题、挑战和未来的研究方向.
Abstract: Particle motion in confined shear flow of viscoelastic fluids is very common in nature and has a wide range of applications. Understanding and mastering the motion characteristics of particles in viscoelastic fluids has important academic value and practical significance. In this paper, we first introduce the related equations and characteristic parameter, and then emphasize the following issues: the lateral equilibrium position of particle; interaction and aggregation of multiple particles; the chain structure formed by multiple particles; and the motion of non-spherical particle. Finally, some unresolved issues, challenges, and future research directions are highlighted.
- Particle /
- Viscoelastic fluid /
- Shear flow

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1. Migration to a position between the center and the wall.

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2. The viscoelasticity-induced migration to the center.

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3. Particle trajectories in the channel cross-section.

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4. Lateral position of particle for different Wi.

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5. The pattern of particle migrations. a “Returning” pattern;b “Passing” pattern.

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6. Alignment of particle and distribution of extension force. a Wi = 0.5; b Wi = 1.5.

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7. Snapshots of the ellipsoids at different times.

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参考文献(76)

[1]	C. Xu, X. Yan, Y. Kang, L. You, Z. You, H. Zhang, and J. Zhang, Friction coefficient: A significant parameter for lost circulation control and material selection in naturally fractured reservoir, Energy 174, 1012 (2019).
[2]	X. Yan, Y. Kang, C. Xu, X. Shang, Z. You, and J. Zhang, Fracture plugging zone for lost circulation control in fractured reservoirs: Multiscale structure and structure characterization methods, Powder Tech. 370, 159 (2020).
[3]	G. D’Avino, P. L. Maffettone, F. Greco, and M. A. Hulsen, Viscoelasticity-induced migration of a rigid sphere in confined shear flow, J. Non-Newtonian Fluid Mech. 165, 466 (2010).
[4]	Z. Sheidaei, and P. Akbarzadeh, Analytical solution of the low Reynolds third-grade non-Newtonian fluids flow inside rough circular pipes, Acta Mech. Sin. 36, 1018 (2020).
[5]	T. Jiang, J. Ouyang, L. Zhang, and J. L. Ren, The SPH approach to the process of container filling based on non-linear constitutive models, Acta Mech. Sin. 28, 407 (2012).
[6]	R. P. Chhabra, Bubbles, Drops and Particles in Non-Newtonian Fluids (Taylor Francis Group, New York, 2007)
[7]	D. Di Carlo, D. Irimia, R. G. Tompkins, and M. Toner, Continuous inertial focusing, ordering, and separation of particles in microchannels, Proc. Natl. Acad. Sci. USA 104, 18892 18025477(2007).
[8]	A. M. Leshansky, A. Bransky, N. Korin, and U. Dinnar, Tunable nonlinear viscoelastic “focusing” in a microfluidic device, Phys. Rev. Lett. 98, 234501 17677908(2007).
[9]	S. Yang, J. Y. Kim, S. J. Lee, S. S. Lee, and J. M. Kim, Sheathless elasto-inertial particle focusing and continuous separation in a straight rectangular microchannel, Lab Chip 11, 266 20976348(2011).
[10]	A. Karimi, S. Yazdi, and A. M. Ardekani, Hydrodynamic mechanisms of cell and particle trapping in microfluidics, Biomicrofluidics 7, 021501 24404005(2013).
[11]	M. M. Villone, G. D’Avino, M. A. Hulsen, F. Greco, and P. L. Maffettone, Particle motion in square channel flow of a viscoelastic liquid: migration vs. secondary flows, J. Non-Newtonian Fluid Mech. 195, 1 (2013).
[12]	P. Wang, Z. Yu, and J. Lin, Numerical simulations of particle migration in rectangular channel flow of Giesekus viscoelastic fluids, J. Non-Newtonian Fluid Mech. 262, 142 (2018).
[13]	M. M. Villone, G. D’Avino, M. A. Hulsen, F. Greco, and P. L. Maffettone, Numerical simulations of particle migration in a viscoelastic fluid subjected to Poiseuille flow, Comput. Fluids 42, 82 (2011).
[14]	M. M. Villone, G. D’Avino, M. A. Hulsen, F. Greco, and P. L. Maffettone, Simulations of viscoelasticity-induced focusing of particles in pressure-driven micro-slit flow, J. Non-Newtonian Fluid Mech. 166, 1396 (2011).
[15]	E. J. Lim, T. J. Ober, J. F. Edd, S. P. Desai, D. Neal, K. W. Bong, P. S. Doyle, G. H. McKinley, and M. Toner, Inertio-elastic focusing of bioparticles in microchannels at high throughput, Nat. Commun. 5, 4120 24939508(2014).
[16]	G. Li, G. H. McKinley, and A. M. Ardekani, Dynamics of particle migration in channel flow of viscoelastic fluids, J. Fluid Mech. 785, 486 (2015).
[17]	B. Liu, J. Lin, X. Ku, and Z. Yu, Migration of spherical particles in a confined shear flow of Giesekus fluid, Rheol Acta 58, 639 (2019).
[18]	A. H. Raffiee, A. M. Ardekani, and S. Dabiri, Numerical investigation of elasto-inertial particle focusing patterns in viscoelastic microfluidic devices, J. Non-Newtonian Fluid Mech. 272, 104166 (2019).
[19]	K. W. Seo, Y. J. Kang, and S. J. Lee, Lateral migration and focusing of microspheres in a microchannel flow of viscoelastic fluids, Phys. Fluids 26, 063301 (2014).
[20]	K. W. Seo, H. J. Byeon, H. K. Huh, and S. J. Lee, Particle migration and single-line particle focusing in microscale pipe flow of viscoelastic fluids, RSC Adv. 4, 3512 (2014).
[21]	M. Trofa, M. Vocciante, G. D’Avino, M. A. Hulsen, F. Greco, and P. L. Maffettone, Numerical simulations of the competition between the effects of inertia and viscoelasticity on particle migration in Poiseuille flow, Comput. Fluids 107, 214 (2015).
[22]	Z. Yu, P. Wang, J. Lin, and H. H. Hu, Equilibrium positions of the elasto-inertial particle migration in rectangular channel flow of Oldroyd-B viscoelastic fluids, J. Fluid Mech. 868, 316 (2019).
[23]	C. Ni, and D. Jiang, Three-dimensional numerical simulation of particle focusing and separation in viscoelastic fluids, Micromachines 11, 908 33007973(2020).
[24]	S. Caserta, G. D’Avino, F. Greco, S. Guido, and P. L. Maffettone, Migration of a sphere in a viscoelastic fluid under planar shear flow: Experiments and numerical predictions, Soft Matter 7, 1100 (2011).
[25]	C. Liu, C. Xue, X. Chen, L. Shan, Y. Tian, and G. Hu, Size-based separation of particles and cells utilizing viscoelastic effects in straight microchannels, Anal. Chem. 87, 6041 25989347(2015).
[26]	S. Daugan, L. Talini, B. Herzhaft, and C. Allain, Aggregation of particles settling in shear-thinning fluids, Eur. Phys. J. E 7, 73 (2002).
[27]	D. D. Joseph, Y. J. Liu, M. Poletto, and J. Feng, Aggregation and dispersion of spheres falling in viscoelastic liquids, J. Non-Newtonian Fluid Mech. 54, 45 (1994).
[28]	G. Gheissary, and B. H. A. A. van den Brule, Unexpected phenomena observed in particle settling in non-Newtonian media, J. Non-Newtonian Fluid Mech. 67, 1 (1996).
[29]	D. Xie, G. G. Qiao, and D. E. Dunstan, Flow-induced aggregation of colloidal particles in viscoelastic fluids, Phys. Rev. E 94, 022610 27627363(2016).
[30]	W. R. Hwang, M. A. Hulsen, and H. E. H. Meijer, Direct simulations of particle suspensions in a viscoelastic fluid in sliding bi-periodic frames, J. Non-Newtonian Fluid Mech. 121, 15 (2004).
[31]	S. W. Ahn, S. S. Lee, S. J. Lee, and J. M. Kim, Microfluidic particle separator utilizing sheathless elasto-inertial focusing, Chem. Eng. Sci. 126, 237 (2015).
[32]	B. Liu, J. Lin, X. Ku, and Z. Yu, Particle migration in bounded shear flow of Giesekus fluids, J. Non-Newtonian Fluid Mech. 276, 104233 (2020).
[33]	B. Liu, J. Lin, X. Ku, and Z. Yu, Elasto-inertial particle migration in a confined simple shear-flow of Giesekus viscoelastic fluids, Particulate Sci. Tech. 39, 726 (2021).
[34]	S. H. Chiu, T. W. Pan, and R. Glowinski, A 3D DLM/FD method for simulating the motion of spheres in a bounded shear flow of Oldroyd-B fluids, Comput. Fluids 172, 661 (2018).
[35]	S. Yoon, M. A. Walkley, and O. G. Harlen, Two particle interactions in a confined viscoelastic fluid under shear, J. Non-Newtonian Fluid Mech. 185-186, 39 (2012).
[36]	Y. J. Choi, M. A. Hulsen, and H. E. H. Meijer, An extended finite element method for the simulation of particulate viscoelastic flows, J. Non-Newtonian Fluid Mech. 165, 607 (2010).
[37]	F. Snijkers, R. Pasquino, and J. Vermant, Hydrodynamic interactions between two equally sized spheres in viscoelastic fluids in shear flow, Langmuir 29, 5701 23600865(2013).
[38]	A. Vázquez-Quesada, and M. Ellero, SPH modeling and simulation of spherical particles interacting in a viscoelastic matrix, Phys. Fluids 29, 121609 (2017).
[39]	B. Liu, J. Lin, and X. Ku, Particle migration induced by hydrodynamic interparticle interaction in the Poiseuille flow of a Giesekus fluid, J Braz. Soc. Mech. Sci. Eng. 43, 106 (2021).
[40]	R. A. Vaia, and E. P. Giannelis, Polymer nanocomposites: status and opportunities, MRS Bull. 26, 394 (2001).
[41]	X. Sun, S. M. Tabakman, W. S. Seo, L. Zhang, G. Zhang, S. Sherlock, L. Bai, and H. Dai, Separation of nanoparticles in a density gradient: FeCo@C and gold nanocrystals, Angew. Chem. Int. Ed. 48, 939 19107884(2009).
[42]	J. Hao, T. W. Pan, R. Glowinski, and D. D. Joseph, A fictitious domain/distributed Lagrange multiplier method for the particulate flow of Oldroyd-B fluids: a positive definiteness preserving approach, J. Non-Newtonian Fluid Mech. 156, 95 (2009).
[43]	S. B. Devarakonda, J. Han, C. H. Ahn, and R. K. Banerjee, Bioparticle separation in non-Newtonian fluid using pulsed flow in micro-channels, Microfluid Nanofluid 3, 391 (2007).
[44]	J. Michele, R. Pätzold, and R. Donis, Alignment and aggregation effects in suspensions of spheres in non-Newtonian media, Rheol Acta 16, 317 (1977).
[45]	H. Giesekus, Particle movement in flows of non-Newtonian fluids, Z. Angew. Math. Mech. 58, T26 (1978)
[46]	D. Won, and C. Kim, Alignment and aggregation of spherical particles in viscoelastic fluid under shear flow, J. Non-Newtonian Fluid Mech. 117, 141 (2004).
[47]	R. Pasquino, G. D’Avino, P. L. Maffettone, F. Greco, and N. Grizzuti, Migration and chaining of noncolloidal spheres suspended in a sheared viscoelastic medium. Experiments and numerical simulations, J. Non-Newtonian Fluid Mech. 203, 1 (2014).
[48]	R. Pasquino, F. Snijkers, N. Grizzuti, and J. Vermant, Directed self-assembly of spheres into a two-dimensional colloidal crystal by viscoelastic stresses, Langmuir 26, 3016 20131839(2010).
[49]	R. Pasquino, F. Snijkers, N. Grizzuti, and J. Vermant, The effect of particle size and migration on the formation of flow-induced structures in viscoelastic suspensions, Rheol Acta 49, 993 (2010).
[50]	R. Pasquino, D. Panariello, and N. Grizzuti, Migration and alignment of spherical particles in sheared viscoelastic suspensions. A quantitative determination of the flow-induced self-assembly kinetics, J. Colloid Interface Sci. 394, 49 23266026(2013).
[51]	S. Van Loon, J. Fransaer, C. Clasen, and J. Vermant, String formation in sheared suspensions in rheologically complex media: The essential role of shear thinning, J. Rheology 58, 237 (2014).
[52]	W. R. Hwang, and M. A. Hulsen, Structure formation of non-colloidal particles in viscoelastic fluids subjected to simple shear flow, Macromol. Mater. Eng. 296, 321 (2011).
[53]	N. O. Jaensson, M. A. Hulsen, and P. D. Anderson, Simulations of the start-up of shear flow of 2D particle suspensions in viscoelastic fluids: Structure formation and rheology, J. Non-Newtonian Fluid Mech. 225, 70 (2015).
[54]	I. S. Santos de Oliveira, A. van den Noort, J. T. Padding, W. K. den Otter, and W. J. Briels, Alignment of particles in sheared viscoelastic fluids, J. Chem. Phys. 135, 104902 21932919(2011).
[55]	Y. J. Choi, and M. A. Hulsen, Alignment of particles in a confined shear flow of a viscoelastic fluid, J. Non-Newtonian Fluid Mech. 175-176, 89 (2012).
[56]	N. O. Jaensson, M. A. Hulsen, and P. D. Anderson, Direct numerical simulation of particle alignment in viscoelastic fluids, J. Non-Newtonian Fluid Mech. 235, 125 (2016).
[57]	B. R. Liu, J. Z. Lin, and X. K. Ku, Migration and alignment of three interacting particles in Poiseuille flow of Giesekus fluids, Fluids 6, 218 (2021).
[58]	J. Feng, P. Y. Huang, and D. D. Joseph, Dynamic simulation of sedimentation of solid particles in an Oldroyd-B fluid, J. Non-Newtonian Fluid Mech. 63, 63 (1996).
[59]	Y. Iso, D. L. Koch, and C. Cohen, Orientation in simple shear flow of semi-dilute fiber suspensions 1. Weakly elastic fluids, J. Non-Newtonian Fluid Mech. 62, 115 (1996).
[60]	Y. Iso, C. Cohen, and D. L. Koch, Orientation in simple shear flow of semi-dilute fiber suspensions 2. Highly elastic fluids, J. Non-Newtonian Fluid Mech. 62, 135 (1996).
[61]	L. G. Leal, The slow motion of slender rod-like particles in a second-order fluid, J. Fluid Mech. 69, 305 (1975).
[62]	O. G. Harlen, and D. L. Koch, Simple shear flow of a suspension of fibres in a dilute polymer solution at high Deborah number, J. Fluid Mech. 252, 187 (1993).
[63]	A. Kaur, A. Sobti, A. P. Toor, and R. K. Wanchoo, Motion of spheres and cylinders in viscoelastic fluids: Asymptotic behavior, Powder Tech. 345, 82 (2019).
[64]	J. Lin, Z. Ouyang, and X. Ku, Dynamics of cylindrical particles in the contraction flow of a second-order fluid, J. Non-Newtonian Fluid Mech. 257, 1 (2018).
[65]	D. Borzacchiello, E. Abisset-Chavanne, F. Chinesta, and R. Keunings, Orientation kinematics of short fibres in a second-order viscoelastic fluid, Rheol Acta 55, 397 (2016).
[66]	D. Z. Gunes, R. Scirocco, J. Mewis, and J. Vermant, Flow-induced orientation of non-spherical particles: Effect of aspect ratio and medium rheology, J. Non-Newtonian Fluid Mech. 155, 39 (2008).
[67]	E. Bartram, H. L. Goldsmith, and S. G. Mason, Particle motions in non-Newtonian media, Rheol Acta 14, 776 (1975).
[68]	S. J. Johnson, A. J. Salem, and G. G. Fuller, Dynamics of colloidal particles in sheared, non-Newtonian fluids, J. Non-Newtonian Fluid Mech. 34, 89 (1990).
[69]	G. D’Avino, M. A. Hulsen, F. Greco, and P. L. Maffettone, Bistability and metabistability scenario in the dynamics of an ellipsoidal particle in a sheared viscoelastic fluid, Phys. Rev. E 89, 043006 24827331(2014).
[70]	Y. Wang, Z. Yu, and J. Lin, Numerical simulations of the motion of ellipsoids in planar Couette flow of Giesekus viscoelastic fluids, Microfluid Nanofluid 23, 89 (2019).
[71]	G. D’Avino, M. A. Hulsen, F. Greco, and P. L. Maffettone, Numerical simulations on the dynamics of a spheroid in a viscoelastic liquid in a wide-slit microchannel, J. Non-Newtonian Fluid Mech. 263, 33 (2019).
[72]	N. Phan-Thien, and X. J. Fan, Viscoelastic mobility problem using a boundary element method, J. Non-Newtonian Fluid Mech. 105, 131 (2002).
[73]	H. Nguyen-Hoang, N. Phan-Thien, B. C. Khoo, X. J. Fan, and H. S. Dou, Completed double layer boundary element method for periodic fibre suspension in viscoelastic fluid, Chem. Eng. Sci. 63, 3898 (2008).
[74]	H. Lv, S. Tang, and W. Zhou, Direct numerical simulation of particle migration in a simple shear flow, Chin. Phys. Lett. 28, 84708 (2011)
[75]	C. W. Tai, S. Wang, and V. Narsimhan, Cross-stream migration of nonspherical particles in second-order fluid flows: Effect of flow profiles, AIChE J. 66, e1707 (2020).
[76]	C. W. Tai, S. Wang, and V. Narsimhan, Cross-stream migration of non-spherical particles in a second-order fluid—theories of particle dynamics in arbitrary quadratic flows, J. Fluid Mech. 895, A6 (2020).