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On the polydisperse particle migration and formation of chains in a square channel flow of non-Newtonian fluids

Published online by Cambridge University Press:  08 February 2022

Xiao Hu
Affiliation:
Key Laboratory of Fluid Transmission Technology of Zhejiang Province, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, PR China Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, Zhejiang 310027, PR China
Peifeng Lin
Affiliation:
Key Laboratory of Fluid Transmission Technology of Zhejiang Province, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, PR China
Jianzhong Lin*
Affiliation:
Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, Zhejiang 310027, PR China Faculty of Mechanical Engineering and & Mechanics, Ningbo University, Ningbo, Zhejiang 315201, PR China
Zuchao Zhu
Affiliation:
Key Laboratory of Fluid Transmission Technology of Zhejiang Province, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, PR China
Zhaosheng Yu
Affiliation:
Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, Zhejiang 310027, PR China
*
Email address for correspondence: mecjzlin@public.zju.edu.cn

Abstract

The migration of polydisperse particles and the formation of self-organized particle chains in a square channel flow of non-Newtonian fluids is studied. The effects of rheological behaviour of the fluid, solution concentration and flow rate are explored experimentally. The direct forcing/fictitious domain method is adopted to qualitatively verify the experiments and further analyse the mechanisms of particle migration and particle chain self-organization. The results show that only particles in viscoelastic fluids with negligible shear-thinning effect will remain at the channel centreline as the flow rate increases. The monodisperse particles reach the same velocity when migrating to the equilibrium position. However, in polydisperse suspensions, the smaller the particle diameter, the greater the velocity when the particle migrates to the equilibrium position. In a viscoelastic fluid, the polydisperse particles are more likely to self-organize into long particle chains along the channel centreline than the monodisperse particles, where the large and small particles are at the front and end of the chain. The dimensionless alignment factor (Af) is adopted to quantify the formation of particle chains, which is the largest in viscoelastic fluids and rapidly increases before decreasing to a stable value as the flow rate increases. For larger particle diameter ratios and stronger shear-thinning effect, the long particle chain self-organization is less obvious. The self-organizing particle chains at the channel centreline are strongly influenced by the fluid elastic properties and weakly by the inertial effect; however, the shear-thinning effect disperses the particles and prevents the formation of long straight particle chains.

Type
JFM Papers
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

Abbas, M., Magaud, P., Gao, Y. & Geoffroy, S. 2014 Migration of finite sized particles in a laminar square channel flow from low to high Reynolds numbers. Phys. Fluids 26 (12), 123301.CrossRefGoogle Scholar
Bird, R.B. & Carreau, J.P. 1968 A nonlinear viscoelastic model for polymer solutions and melts-I. Chem. Engng Sci. 23 (5), 427434.CrossRefGoogle Scholar
D'Avino, G., del Greco, F. & Maffettone, P.L. 2017 Particle migration due to viscoelasticity of the suspending liquid and its relevance in microfluidic devices. Annu. Rev. Fluid Mech. 49, 341360.CrossRefGoogle Scholar
D'Avino, G., Hulsen, M.A. & Maffettone, P.L. 2013 Dynamics of pairs and triplets of particles in a viscoelastic fluid flowing in a cylindrical channel. Comput. Fluids 86, 4555.CrossRefGoogle Scholar
D'Avino, G. & Maffettone, P.L. 2020 Numerical simulations on the dynamics of trains of particles in a viscoelastic fluid flowing in a microchannel. Meccanica 55, 317330.CrossRefGoogle Scholar
Del Giudice, F., D'Avino, G., Greco, F., Maffettone, P.L. & Shen, A.Q. 2018 Fluid viscoelasticity drives self-assembly of particle trains in a straight microfluidic channel. Phys. Rev. Appl. 10, 064058.CrossRefGoogle Scholar
Faxén, H. 1922 Der widerstand gegen die bewegung einer starren kugel in einer zähen flüssigkeit, die zwischen zwei parallelen ebenen wänden eingeschlossen ist. Ann. Phys. 373 (10), 89119.CrossRefGoogle Scholar
Feng, J., Huang, P.Y. & Joseph, D.D. 1996 Dynamic simulation of sedimentation of solid particles in an Oldroyd-B fluid. J. Non-Newtonian Fluid Mech. 63, 6388.CrossRefGoogle Scholar
Gao, Y.F., Magaud, P., Lafforgue, C., Colin, S. & Baldas, L. 2019 Inertial lateral migration and self-assembly of particles in bidisperse suspensions in microchannel flows. Microfluid Nanofluid 23, 93.CrossRefGoogle Scholar
Giesekus, H. 1978 Particle movement in flows of non-Newtonian fluids. Z. Angew. Math. Mech. 58, T26T37.Google Scholar
Gondret, P., Lance, M. & Petit, L. 2002 Bouncing motion of spherical particles in fluids. Phys. Fluids 14, 643652.CrossRefGoogle Scholar
Gupta, A., Magaud, P., Lafforgue, C. & Abbas, M. 2018 Conditional stability of particle alignment in finite-Reynolds-number channel flow. Phys. Rev. Fluids 3, 114302.CrossRefGoogle Scholar
Haddadi, H. & Di Carlo, D. 2017 Inertial flow of a dilute suspension over cavities in a microchannel. J. Fluid Mech. 811, 436467.CrossRefGoogle Scholar
Hood, K., Lee, S. & Roper, M. 2015 Inertial migration of a rigid sphere in three-dimensional Poiseuille flow. J. Fluid Mech. 765, 452479.CrossRefGoogle Scholar
Hu, X., Lin, J.Z., Chen, D.M. & Ku, X.K. 2020 Influence of non-Newtonian power law rheology on inertial migration of particles in channel flow. Biomicrofluidics 14, 014105.CrossRefGoogle ScholarPubMed
Hu, X., Lin, J.Z., Guo, Y. & Ku, X.K. 2021 Inertial focusing of elliptical particles and formation of self-organizing trains in a channel flow. Phys. Fluids 33, 013310.CrossRefGoogle Scholar
Hu, X., Lin, J.Z. & Ku, X.K. 2019 Inertial migration of circular particles in Poiseuille of power-law fluid. Phys. Fluids 31, 073306.Google Scholar
Hur, S.C., Tse, H.T. & Di Carlo, D. 2010 Sheathless inertial cell ordering for extreme throughput flow cytometry. Lab on a Chip 10, 274280.CrossRefGoogle ScholarPubMed
Hwang, W.R. & Hulsen, M.A. 2011 Structure formation of non-colloidal particles in viscoelastic fluids subjected to simple shear flow. Macromol. Mater. Engng 296, 321330.CrossRefGoogle Scholar
Jeffrey, D.J. 1982 Low-Reynolds-number flow between converging spheres. Mathematika 29 (1), 5866.CrossRefGoogle Scholar
Kahkeshani, S., Haddadi, H. & Di Carlo, D. 2016 Preferred interparticle spacings in trains of particles in inertial microchannel flows. J. Fluid Mech. 786, R3.CrossRefGoogle Scholar
Li, G.J., Mckinley, G.H. & Ardekani, A.M. 2015 Dynamics of particle migration in channel flow of viscoelastic fluids. J. Fluid Mech. 785, 486505.CrossRefGoogle Scholar
Li, Q., Abbas, M., Morris, J.F., Climent, E. & Magnaudet, J. 2020 Near-wall dynamics of a neutrally buoyant spherical particle in an axisymmetric stagnation point flow. J. Fluid Mech. 892, A32.CrossRefGoogle Scholar
Lim, E.J., Ober, T.J., Edd, J.F., Desai, S.P., Neal, D., Bong, K.W., Doyle, P.S., Mckinley, G.H. & Toner, M. 2014 Inertio-elastic focusing of bioparticles in microchannels at high throughput. Nat. Commun. 5, 4120.CrossRefGoogle ScholarPubMed
Lin, Z.W., Chen, S. & Gao, T. 2021 Q-tensor model for undulatory swimming in lyotropic liquid crystal polymers. J. Fluid Mech. 921, A25.CrossRefGoogle Scholar
Liu, B.R., Lin, J.Z., Ku, X.K. & Yu, Z.S. 2020 a Particle migration in bounded shear flow of Giesekus fluids. J. Nonnewton Fluid Mech. 276, 104233.CrossRefGoogle Scholar
Liu, C., Guo, J.Y., Tian, F., Yang, N., Yan, F.S., Ding, Y.P., Wei, J.Y., Hu, G.Q., Nie, G.J. & Sun, J.S. 2017 Field-free isolation of exosomes from extracellular vesicles by microfluidic viscoelastic flows. ACS Nano 11 (7), 69686976.CrossRefGoogle ScholarPubMed
Liu, C., Hu, G.Q., Jiang, X.Y. & Sun, J.S. 2015 Inertial focusing of spherical particles in rectangular microchannels over a wide range of Reynolds numbers. Lab on a Chip 15, 11681177.CrossRefGoogle Scholar
Liu, L.B., Xu, H., Xiu, H.B., Xiang, N. & Ni, Z.H. 2020 b Microfluidic on-demand engineering of longitudinal dynamic self-assembly of particles. Analyst 145, 51285133.CrossRefGoogle ScholarPubMed
Loon, S.V., Fransaer, J., Clasen, C. & Vermant, J. 2013 String formation in sheared suspensions in rheologically complex media: The essential role of shear thinning. J. Rheol. 58, 237254.CrossRefGoogle Scholar
Lyon, M.K., Mead, D.W., Elliott, R.E. & Leal, L.G. 2001 Structure formation in moderately concentrated viscoelastic suspensions in simple shear flow. J. Rheol. 45, 881890.CrossRefGoogle Scholar
Majji, M.V., Banerjee, S. & Morris, J.F. 2018 Inertial flow transitions of a suspension in Taylor–Couette geometry. J. Fluid Mech. 835, 936969.CrossRefGoogle Scholar
Majji, M.V. & Morris, J.F. 2018 Inertial migration of particles in Taylor–Couette flows. Phys. Fluids 30, 33303.CrossRefGoogle Scholar
Michele, J., Pätzold, R. & Donis, R. 1997 Alignment and aggregation effects in suspensions of spheres in non-Newtonian media. Rheol. Acta 16, 317321.CrossRefGoogle Scholar
Miura, K., Itano, T. & Sugihara-Seki, M. 2014 Inertial migration of neutrally buoyant spheres in a pressure-driven flow through square channels. J. Fluid Mech. 749, 320330.CrossRefGoogle Scholar
Morris, J.F. 2016 High-speed trains: In microchannels? J. Fluid Mech. 792, 14.CrossRefGoogle Scholar
Morris, J.F. 2020 Toward a fluid mechanics of suspensions. Phys. Rev. Fluids 5, 110519.CrossRefGoogle Scholar
Nakayama, S., Yamashita, H., Yabu, T., Itano, T. & Sugihara-Seki, M. 2019 Three regimes of inertial focusing for spherical particles suspended in circular tube flows. J. Fluid Mech. 871, 952969.CrossRefGoogle Scholar
Nie, D.M. & Lin, J.Z. 2020 Simulation of sedimentation of two spheres with different densities in a square tube. J. Fluid Mech. 896, A12.CrossRefGoogle Scholar
Oliveira, I.S.S.D., Otter, W.K.D. & Briels, W.J. 2013 Alignment and segregation of bidisperse colloids in a shear-thinning viscoelastic fluid under shear flow. Europhys. Lett. 101, 28002.CrossRefGoogle Scholar
Pasquino, R., D'Avino, G., Maffettone, P.L., Greco, F. & Grizzuti, N. 2014 Migration and chaining of noncolloidal spheres suspended in a sheared viscoelastic medium. Experiments and numerical simulations. J. Non-Newtonian Fluid Mech. 203, 18.CrossRefGoogle Scholar
Pednekar, S., Chun, J. & Morris, J.F. 2018 Bidisperse and polydisperse suspension rheology at large solid fraction. J. Rheol. 62 (2), 513526.CrossRefGoogle Scholar
Raihan, M.K., Li, D., Kummetz, A.J., Song, L., Yu, L.D. & Xuan, X.C. 2020 Vortex trapping and separation of particles in shear thinning fluids. Appl. Phys. Lett. 116, 183701.CrossRefGoogle Scholar
Scirocco, R., Jan, V. & Jan, M. 2004 Effect of the Viscoelasticity of the suspending fluid on structure formation in suspensions. J. Non-Newtonian Fluid Mech. 117, 183192.CrossRefGoogle Scholar
Seo, K.W., Kang, Y.J. & Lee, S.J. 2014 Lateral migration and focusing of microspheres in a microchannel flow of viscoelastic fluids. Phys. Fluids 26, 063301.CrossRefGoogle Scholar
Shao, X.M., Yu, Z.S. & Sun, B. 2008 Inertial migration of spherical particles in circular Poiseuille flow at moderately high Reynolds numbers. Phys. Fluids 20, 103307.CrossRefGoogle Scholar
Sojwal, M. & Morris, J.F. 2021 Particle motion in pressure-driven suspension flow through a symmetric T-channel. Intl J. Multiphase Flow 134, 103447.Google Scholar
Vigolo, D., Raadl, S. & Stone, H.A. 2014 Unexpected trapping of particles at a T junction. Proc. Natl Acad. Sci. 111 (13), 47704775.CrossRefGoogle ScholarPubMed
Wang, P., Yu, Z.S. & Lin, J.Z. 2018 Numerical simulations of particle migration in rectangular channel flow of Giesekus viscoelastic fluids. J. Non-Newtonian Fluid Mech. 262, 142148.CrossRefGoogle Scholar
Won, D. & Kim, C. 2004 Alignment and aggregation of spherical particles in viscoelastic fluid under shear flow. J. Non-Newtonian Fluid Mech. 117, 141146.CrossRefGoogle Scholar
Xia, Y., Xiong, H.B., Yu, Z.S. & Zhu, C.L. 2020 Effects of the collision model in interface-resolved simulations of particle-laden turbulent channel flows. Phys. Fluids 32, 103303.CrossRefGoogle Scholar
Yu, Z.S. & Shao, X.M. 2007 A direct-forcing fictitious domain method for particulate flows. J. Comput. Phys. 227, 292314.CrossRefGoogle Scholar
Yu, Z.S., Wang, P., Lin, J.Z. & Hu, H.H. 2019 Equilibrium positions of the elasto-inertial particle migration in rectangular channel flow of Oldroyd-B viscoelastic fluids. J. Fluid Mech. 868, 316340.CrossRefGoogle Scholar
Yu, Z.S., Xia, Y., Guo, Y. & Lin, J.Z. 2021 Modulation of turbulence intensity by heavy finite-size particles in upward channel flow. J. Fluid Mech. 913, A3.CrossRefGoogle Scholar
Supplementary material: File

Hu et al. supplementary movie 1

Numerical result of particle migration and chain self-organization.

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Supplementary material: File

Hu et al. supplementary movie 2

Particle migration and chain self-organization in PVP solution with Q=40μl/min.

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Supplementary material: File

Hu et al. supplementary movie 3

Particle migration and chain self-organization in PEO solution with Q=40μl/min.

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Supplementary material: File

Hu et al. supplementary movie 4

Particle migration and chain self-organization in HA solution with Q=40μl/min.

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Supplementary material: File

Hu et al. supplementary movie 5

Particle migration and chain self-organization in PVP solution with Q=300μl/min.

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File 3.9 MB
Supplementary material: File

Hu et al. supplementary movie 6

Particle migration and chain self-organization in PEO solution with Q=300μl/min.

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File 3.3 MB
Supplementary material: File

Hu et al. supplementary movie 7

Particle migration and chain self-organization in HA solution with Q=300μl/min.

Download Hu et al. supplementary movie 7(File)
File 4 MB