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Elasto-inertial focusing and rotating characteristics of ellipsoidal particles in a square channel flow of Oldroyd-B viscoelastic fluids

Published online by Cambridge University Press:  14 October 2024

Xiao Hu Open the ORCID record for Xiao Hu [Opens in a new window] ,
Jianzhong Lin Open the ORCID record for Jianzhong Lin [Opens in a new window] ,
Zuchao Zhu ,
Zhaosheng Yu Open the ORCID record for Zhaosheng Yu [Opens in a new window] ,
Zhaowu Lin  and
Xiaojun Li
Xiao Hu
Affiliation:
Zhejiang Key Laboratory of Multiflow and Fluid Machinery, 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
Jianzhong Lin*
Affiliation:
Faculty of Mechanical Engineering and & Mechanics, Ningbo University, Ningbo, Zhejiang 315201, PR China Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, Zhejiang 310027, PR China
Zuchao Zhu
Affiliation:
Zhejiang Key Laboratory of Multiflow and Fluid Machinery, 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
Zhaowu Lin
Affiliation:
Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, Zhejiang 310027, PR China
Xiaojun Li
Affiliation:
Zhejiang Key Laboratory of Multiflow and Fluid Machinery, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, PR China
*
†Email address for correspondence: [email protected]
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Abstract

The elasto-inertial focusing and rotating characteristics of spheroids in a square channel flow of Oldroyd-B viscoelastic fluids are studied by the direct forcing/fictitious domain method. The rotational behaviours, changes in the equilibrium positions and travel distances are explored to analyse the mechanisms of spheroid migration in viscoelastic fluids. Within the present simulated parameters (1 ≤ Re ≤ 100, 0 ≤ Wi ≤ 2, 0.4 ≤ α ≤3), the results show that there are four kinds of equilibrium positions and six (five) kinds of rotational behaviours for the elasto-inertial migration of prolate (oblate) spheroids. We are the first to identify a new rotational mode for the migration of prolate spheroids. Only when the particles are initially located at a corner and wall bisector, some special initial orientations of the spheroids have an impact on the final equilibrium position and rotational mode. In other general initial positions, the initial orientation of the spheroid has a negligible effect. A higher Weissenberg number means the faster the particles migrate to the equilibrium position. The spheroid gradually changes from the corner (CO), channel centreline (CC), diagonal line (DL) and cross-section midline (CSM) equilibrium positions as the elastic number decreases, depending on the aspect ratio, initial orientation and rotational behaviour of the particles and the elastic number of the fluid. When the elastic number is less than the critical value, the types of rotational modes of the spheroids are reduced. By controlling the elastic number near the critical value, spheroids with different aspect ratios can be efficiently separated.

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics Multiphase and Particle-laden Flows: Multiphase flow Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 997 , 25 October 2024 , A32
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Copyright
© The Author(s), 2024. 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. 1976 Useful non-Newtonian models. Annu. Rev. Fluid Mech. 8 (1), 13–34.CrossRefGoogle Scholar
Choi, Y.S., Seo, K.W. & Lee, S.J. 2011 Lateral and cross-lateral focusing of spherical particles in a square microchannel. Lab on a Chip 11 (3), 460–465.CrossRefGoogle Scholar
Dabade, V., Marath, N.K. & Subramanian, G. 2015 Effects of inertia and viscoelasticity on sedimenting anisotropic particles. J. Fluid Mech. 778, 133–188.CrossRefGoogle Scholar
Daniel, C.P., Mehmet, T. & Patrick, S.D. 2007 Multifunctional encoded particles for high-throughput biomolecule analysis. Science 315, 1393–1396.Google 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, 341–360.CrossRefGoogle Scholar
D'Avino, G., Hulsen, M.A., Greco, F. & Mafettone, P.L. 2014 Bistability and metabistability scenario in the dynamics of an ellipsoidal particle in a sheared viscoelastic fluid. Phys. Rev. E 89, 043006.CrossRefGoogle Scholar
D'Avino, G., Hulsen, M.A., Greco, F. & Maffettone, P.L. 2019 Numerical simulations on the dynamics of a spheroid in a viscoelastic liquid in a wide-slit microchannel. J. Non-Newtonian Fluid Mech. 263, 33–41.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
Di Carlo, D., Edd, J.F., Humphry, K.J., Stone, H.A. & Toner, M. 2009 Particle segregation and dynamics in confined flows. Phys. Rev. Lett. 102 (9), 094503–094503.CrossRefGoogle ScholarPubMed
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), 89–119.CrossRefGoogle Scholar
Ferroudji, H., Rahman, M.A., Hadjadj, A., Ofei, T.N., Khaled, M.S., Rushd, S. & Gajbhiye, R.N. 2022 3D numerical and experimental modelling of multiphase flow through an annular geometry applied for cuttings transport. Intl J. Multiphase Flow 151, 104044.CrossRefGoogle Scholar
Haddadi, H. & Di Carlo, D. 2017 Inertial flow of a dilute suspension over cavities in a microchannel. J. Fluid Mech. 811, 436–467.CrossRefGoogle Scholar
Hamed, A., Lee, W. & Di Carlo, D. 2014 Inertial microfluidic physics. Lab on a Chip 14, 2739.Google Scholar
Ho, B.P. & Leal, L.G. 1974 Inertial migration of rigid spheres in two-dimensional unidirectional flows. J. Fluid Mech. 65, 365–400.CrossRefGoogle Scholar
Ho, B.P. & Leal, L.G. 1976 Migration of rigid spheres in a two-dimensional unidirectional shear flow of a second-order fluid. J. Fluid Mech. 76, 783–799.CrossRefGoogle Scholar
Hood, K., Lee, S. & Roper, M. 2015 Inertial migration of a rigid sphere in three-dimensional Poiseuille flow. J. Fluid Mech. 765, 452–479.CrossRefGoogle Scholar
Hu, X., Kang, X.F., Lin, J.Z., Lin, P.F., Bao, F.B. & Zhu, Z.C. 2023 a Comparison of ellipsoidal particle migration in square channel flow of power-law fluids with equivalent spheres. Intl J. Multiphase Flow 167, 104565.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 Scholar
Hu, X., Lin, J.Z., Lin, P.F. & Zhu, Z.C. 2023 b Rigid spheroid migration in square channel flow of power-law fluids. Intl J. Mech. Sci. 274, 108194.CrossRefGoogle Scholar
Hu, X., Lin, P.F., Lin, J.Z., Zhu, Z.C. & Yu, Z.S. 2022 On the polydisperse particle migration and formation of chains in a square channel flow of non-Newtonian fluids. J. Fluid Mech. 936, A5.CrossRefGoogle Scholar
Huang, H., Yang, X., Krafczyk, M. & Lu, X.Y. 2012 Rotation of spheroidal particles in Couette flows. J. Fluid Mech. 692, 369–394.CrossRefGoogle Scholar
Huang, H.B. & Lu, X.Y. 2017 An ellipsoidal particle in tube Poiseuille flow. J. Fluid Mech. 822, 664–688.CrossRefGoogle 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, 274–280.CrossRefGoogle ScholarPubMed
Iso, Y., Cohen, C. & Koch, D.L. 1996 a Orientation in simple shear flow of semi-dilute fiber suspensions 2. Highly elastic fluids. J. Non-Newtonian Fluid Mech. 62 (2–3), 135–153.CrossRefGoogle Scholar
Iso, Y., Koch, D.L. & Cohen, C. 1996 b Orientation in simple shear flow of semi-dilute fiber suspensions, 1. Weakly elastic fluids. J. Non-Newtonian Fluid Mech. 62 (2–3), 115–134.CrossRefGoogle Scholar
Jeffery, G.B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A Math. Phys. Engng Sci. 102, 161–179.Google Scholar
Kim, B. & Kim, J.M. 2016 Elasto-inertial particle focusing under the viscoelastic flow of DNA solution in a square channel. Biomicrofluidics 10 (2), 024111.CrossRefGoogle Scholar
Kroo, L.A., Jeremy, P.B., Noah, E., Manu, P. & Eric, S.G.S. 2022 A freely suspended robotic swimmer propelled by viscoelastic normal stresses. J. Fluid Mech. 944.CrossRefGoogle Scholar
Lashgari, I., Ardekani, M.N., Banerjee, I., Russom, A. & Brandt, L. 2017 Inertial migration of spherical and oblate particles in straight ducts. J. Fluid Mech. 819, 540–561.CrossRefGoogle Scholar
Leshansky, A.M., Bransky, A., Korin, N. & Dinnar, U. 2007 Tunable nonlinear viscoelastic “focusing” in a microfluidic device. Phys. Rev. Lett. 98, 234501.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, 486–505.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
Li, Y., Xia, Z.H. & Wang, L.P. 2022 Inertial migration of a neutrally buoyant oblate spheroid in three-dimensional square duct poiseuille flows. Intl J. Multiphase Flow 155, 104148.CrossRefGoogle Scholar
Li, Y.S., Xu, C.X. & Zhao, L.H. 2023 Rotational dynamics of a neutrally buoyant prolate spheroid in viscoelastic shear flows at finite Reynolds numbers. J. Fluid Mech. 958.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
Liu, B.R., Lin, J.Z., Ku, X.K. & Yu, Z.S. 2020 Particle migration in bounded shear flow of Giesekus fluids. J. Non-Newtonian Fluid Mech. 276, 104233.CrossRefGoogle Scholar
Liu, B.R., Lin, J.Z., Ku, X.K. & Yu, Z.S. 2021 Particle trajectory and orientation evolution of ellipsoidal particles in bounded shear flow of Giesekus fluids. Korea-Austral. Rheol. J. 33 (4), 343–355.CrossRefGoogle Scholar
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, 1168.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), 6968–6976.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, 881–890.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, 936–969.CrossRefGoogle Scholar
Manoorkar, S. & Morris, J.F. 2021 Particle motion in pressure-driven suspension flow through a symmetric T-channel. Intl J. Multiphase Flow 134, 103447.CrossRefGoogle Scholar
Masaeli, M., Sollier, E., Amini, H., Mao, W., Camacho, K., Doshi, N., Mitragotri, S., Alexeev, A. & Di Carlo, D. 2012 Continuous inertial focusing and separation of particles by shape. Phys. Rev. X 2, 031017.Google Scholar
Matas, J.P., Morris, J.F. & Élisabeth, G. 2009 Lateral force on a rigid sphere in large-inertia laminar pipe flow. J. Fluid Mech. 21, 59–67.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, 320–330.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, 952–969.CrossRefGoogle Scholar
Ouyang, Z.Y., Lin, Z.W., Lin, J.Z., Yu, Z.S. & Nhan, P.T. 2023 Cargo carrying with an inertial squirmer in a Newtonian fluid. J. Fluid Mech. 959.CrossRefGoogle Scholar
Park, W., Kwon, S., Chung, S.E., Lee, S.A. & Shin, S. 2008 Guided and fluidic self-assembly of microstructures using railed microfluidic channels. Nat. Mat. 7, 581–587.Google 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, 1–8.CrossRefGoogle Scholar
Qi, D. & Luo, L.S. 2003 Rotational and orientational behaviour of a three-dimensional spheroidal particles in Couette flows. J. Fluid Mech. 477, 201–213.CrossRefGoogle Scholar
Raoufi, M.A., Mashhadian, A., Niazmand, H., Asadnia, M., Razmjou, A. & Warkiani, M.E. 2019 Experimental and numerical study of elasto-inertial focusing in straight channels. Biomicrofluidics 13 (3), 034103.CrossRefGoogle Scholar
Reddy, M.M., Tiwari, P. & Singh, A. 2019 Effect of carrier fluid rheology on shear-induced particle migration in asymmetric T-shaped bifurcation channel. Intl J. Multiphase Flow 111, 272–284.CrossRefGoogle Scholar
Rosén, T., Lundell, F. & Aidun, C.K. 2014 Effect of fluid inertia on the dynamics and scaling of neutrally buoyant particles in shear flow. J. Fluid Mech. 738, 563–590.CrossRefGoogle Scholar
Saccone, D., Marchioli, C. & Marchis, M.D. 2022 Effect of roughness on elongated particles in turbulent channel flow. Intl J. Multiphase Flow 152, 104065.CrossRefGoogle Scholar
Segré, G. & Silberberg, A. 1961 Radial Poiseuille flow of suspensions. Nature 189, 209–210.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
Shichi, H., Yamashita, H., Seki, J., Itano, T. & Sugihara-Seki, M. 2017 Inertial migration regimes of spherical particles suspended in square tube flows. Phys. Rev. Fluids 2, 044201.CrossRefGoogle Scholar
Snijkers, F., D'Avino, G., Maffettone, P.L., Greco, F., Hulsen, M.A. & Vermant, J. 2011 Effect of viscoelasticity on the rotation of a sphere in shear-flow. J. Non-Newtonian Fluid Mech. 166 (7–8), 363–72.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
Villone, M.M., D'Avino, G., Hulsen, M.A., Greco, F. & Maffettone, P.L. 2013 Particle motion in square channel flow of a viscoelastic liquid: migration versus secondary flows. J. Non-Newtonian Fluid Mech. 195, 1–8.CrossRefGoogle Scholar
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, 142–148.CrossRefGoogle Scholar
Yang, X., Huang, H.B. & Lu, X.Y. 2017 The motion of a neutrally buoyant ellipsoid inside square tube flows. Adv. Appl. Math. Mech. 9 (2), 233–249.CrossRefGoogle Scholar
Yu, Z.S. & Shao, X.M. 2007 A direct-forcing fictitious domain method for particulate flows. J. Comput. Phys. 227, 292–314.CrossRefGoogle Scholar
Yu, Z.S. & Shao, X.M. 2010 Direct numerical simulation of particulate flows with a fictitious domain method. Intl J. Multiphase Flow 36, 127–134.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, 316–340.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