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Suppression of the Segré–Silberberg effect by polymer additives

Published online by Cambridge University Press:  28 January 2025

Daekwon Jin
Affiliation:
Department of Energy Systems Research, Ajou University, Suwon 16499, Republic of Korea
Jee In Park
Affiliation:
Department of Energy Systems Research, Ajou University, Suwon 16499, Republic of Korea
Jae Bem You
Affiliation:
Department of Chemical Engineering, Kyungpook National University, Daegu 41566, Republic of Korea Department of Chemical Engineering and Applied Chemistry, Chungnam National University, Daejeon 34134, Republic of Korea
Younghun Kim
Affiliation:
Department of Chemical Engineering, Kwangwoon University, Seoul 01897, Republic of Korea
Hyomin Lee
Affiliation:
Department of Chemical & Biological Engineering, Jeju National University, Jeju 63243, Republic of Korea
Ju Min Kim*
Affiliation:
Department of Energy Systems Research, Ajou University, Suwon 16499, Republic of Korea Department of Chemical Engineering, Ajou University, Suwon 16499, Republic of Korea
*
Email address for correspondence: jumin@ajou.ac.kr

Abstract

Particle-laden flow through conduits is ubiquitous in both natural and industrial systems. In such flows, particles often migrate across the main fluid stream, resulting in non-uniform spatial distribution owing to particle–fluid and particle–particle interactions. The most relevant lateral particle migration mechanism by particle–fluid interaction is the Segré–Silberberg effect, which is induced by the inertial forces exerted on a particle, as the flow rate increases. However, methods to suppress it have not been suggested yet. Here, we demonstrate that adding a small amount of polymer to the particle-suspending solvent effectively suppresses the Segré–Silberberg effect in a square channel. To accurately determine the position of the particles within the channel cross-sections, we devised a dual-view imaging system applicable to microfluidic systems. Our analyses show that the Segré–Silberberg effect is effectively suppressed in a square microchannel due to the balance between the inertial and elastic forces at an optimal polymer concentration while maintaining nearly constant shear viscosity.

Type
JFM Papers
Copyright
© The Author(s), 2025. Published by Cambridge University Press

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References

Amini, H., Lee, W. & Di Carlo, D. 2014 Inertial microfluidic physics. Lab on a Chip 14 (15), 27392761.CrossRefGoogle ScholarPubMed
Bird, R.B., Armstrong, R.C. & Hassager, O. 1987 Dynamics of Polymeric Liquids. Vol. 1: Fluid Mechanics. John Wiley and Sons.Google Scholar
Boffi, D., Brezzi, F. & Fortin, M. 2013 Mixed Finite Element Methods and Applications. Springer.CrossRefGoogle Scholar
Brust, M., Schaefer, C., Doerr, R., Pan, L., Garcia, M., Arratia, P.E. & Wagner, C. 2013 Rheology of human blood plasma: viscoelastic versus Newtonian behavior. Phys. Rev. Lett. 110 (7), 78305.CrossRefGoogle ScholarPubMed
Camesasca, M., Kaufman, M. & Manas-Zloczower, I. 2006 Quantifying fluid mixing with the Shannon entropy. Macromol. Theory Simul. 15 (8), 595607.CrossRefGoogle Scholar
Chilcott, M.D. & Rallison, J.M. 1988 Creeping flow of dilute polymer solutions past cylinders and spheres. J. Non-Newtonian Fluid Mech. 29, 381432.CrossRefGoogle Scholar
Coates, P.J., Armstrong, R.C. & Brown, R.A. 1992 Calculation of steady-state viscoelastic flow through axisymmetric contractions with the EEME formulation. J. Non-Newtonian Fluid Mech. 42 (1–2), 141188.CrossRefGoogle Scholar
D'Avino, G., 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., Romeo, G., Villone, M.M., Greco, F., Netti, P.A. & Maffettone, P.L. 2012 Single line particle focusing induced by viscoelasticity of the suspending liquid: theory, experiments and simulations to design a micropipe flow-focuser. Lab on a Chip 12 (9), 16381645.CrossRefGoogle ScholarPubMed
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), 94503.CrossRefGoogle ScholarPubMed
Di Carlo, D., Irimia, D., Tompkins, R.G. & Toner, M. 2007 Continuous inertial focusing, ordering, and separation of particles in microchannels. PNAS 104 (48), 1889218897.CrossRefGoogle ScholarPubMed
Dinic, J. & Sharma, V. 2020 Flexibility, extensibility, and ratio of Kuhn length to packing length govern the pinching dynamics, coil-stretch transition, and rheology of polymer solutions. Macromolecules 53 (12), 48214835.CrossRefGoogle Scholar
Dinic, J., Zhang, Y., Jimenez, L.N. & Sharma, V. 2015 Extensional relaxation times of dilute, aqueous polymer solutions. ACS Macro Lett. 4 (7), 804808.CrossRefGoogle ScholarPubMed
Douglas-Hamilton, D.H., Smith, N.G., Kuster, C.E., Vermeiden, J.P.W. & Althouse, G.C. 2005 Capillary-loaded particle fluid dynamics: effect on estimation of sperm concentration. J. Androl. 26 (1), 115122.CrossRefGoogle ScholarPubMed
Entov, V.M. & Hinch, E.J. 1997 Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid. J. Non-Newtonian Fluid Mech. 72 (1), 3153.CrossRefGoogle Scholar
Fattal, R. & Kupferman, R. 2005 Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation. J. Non-Newtonian Fluid Mech. 126 (1), 2337.CrossRefGoogle Scholar
Glowinski, R., Hu, H.H., Joseph, D.D., Pan, T.W., Wang, J. & Yang, B.H. 2005 Migration of a sphere in tube flow. J. Fluid Mech. 540, 109131.Google Scholar
Guazzelli, E. & Morris, J.F. 2011 A Physical Introduction to Suspension Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Han, M., Kim, C., Kim, M. & Lee, S. 1999 Particle migration in tube flow of suspensions. J. Rheol. 43 (5), 11571174.CrossRefGoogle Scholar
Ho, B.P. & Leal, L.G. 1974 Inertial migration of rigid spheres in two-dimensional unidirectional flows. J. Fluid Mech. 65 (2), 365400.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 (4), 783799.CrossRefGoogle Scholar
James, D.F. 2009 Boger fluids. Annu. Rev. Fluid Mech. 41, 129142.CrossRefGoogle Scholar
Jang, I., Lee, W.J., Jin, D. & Kim, J.M. 2022 Effects of flow history on extensional rheological properties of wormlike micelle solution. RSC Adv. 12 (51), 3290332911.CrossRefGoogle ScholarPubMed
Jung, Y., Shim, T.S. & Kim, J.M. 2022 Facile microfluidic method for measuring the relaxation time of dilute polymer solution based on viscoelastic particle focusing. Korean J. Chem. Engng 39 (9), 23182323.CrossRefGoogle Scholar
Kang, K., Lee, S.S., Hyun, K., Lee, S.J. & Kim, J.M. 2013 DNA-based highly tunable particle focuser. Nat. Commun. 4 (1), 2567.CrossRefGoogle ScholarPubMed
Keunings, R. 1986 On the high Weissenberg number problem. J. Non-Newtonian Fluid Mech. 20, 209226.CrossRefGoogle Scholar
Kim, B., Lee, S.S., Yoo, T.H., Kim, S., Kim, S.Y., Choi, S. & Kim, J.M. 2019 Normal stress difference–driven particle focusing in nanoparticle colloidal dispersion. Sci. Adv. 5 (6), eaav4819.CrossRefGoogle ScholarPubMed
Koh, J., Kim, J., Shin, J.H. & Lee, W. 2014 Fabrication and integration of microprism mirrors for high-speed three-dimensional measurement in inertial microfluidic system. Appl. Phys. Lett. 105 (11), 114103.CrossRefGoogle Scholar
Larson, R.G. 2013 Constitutive Equations for Polymer Melts and Solutions: Butterworths Series in Chemical Engineering. Butterworth-Heinemann.Google Scholar
Leshansky, A.M., Bransky, A., Korin, N. & Dinnar, U. 2007 Tunable nonlinear viscoelastic ‘focusing’ in a microfluidic device. Phys. Rev. Lett. 98 (23), 234501.CrossRefGoogle Scholar
Li, G., McKinley, G.H. & Ardekani, A.M. 2015 Dynamics of particle migration in channel flow of viscoelastic fluids. J. Fluid Mech. 785, 486505.CrossRefGoogle Scholar
Lunsmann, W.J., Genieser, L., Armstrong, R.C. & Brown, R.A. 1993 Finite element analysis of steady viscoelastic flow around a sphere in a tube: calculations with constant viscosity models. J. Non-Newtonian Fluid Mech. 48 (1–2), 6399.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
Marnot, A., Dobbs, A. & Brettmann, B. 2022 Material extrusion additive manufacturing of dense pastes consisting of macroscopic particles. MRS Commun. 12 (5), 483494.CrossRefGoogle ScholarPubMed
Martel, J.M. & Toner, M. 2014 Inertial focusing in microfluidics. Annu. Rev. Biomed. Engng 16 (1), 371396.CrossRefGoogle ScholarPubMed
Matas, J.P., Morris, J.F. & Guazzelli, E. 2004 Lateral forces on a sphere. Oil Gas Sci. Technol. 59 (1), 5970.CrossRefGoogle Scholar
Matas, J.P., Morris, J.F. & Guazzelli, E. 2009 Lateral force on a rigid sphere in large-inertia laminar pipe flow. J. Fluid Mech. 621, 5967.CrossRefGoogle Scholar
McKinley, G.H., Armstrong, R.C. & Brown, R. 1993 The wake instability in viscoelastic flow past confined circular cylinders. Phil. Trans. R. Soc. Lond. A Phys. Engng Sci. 344 (1671), 265304.Google Scholar
Mewis, J. & Wagner, N.J. 2012 Colloidal Suspension Rheology. Cambridge University Press.Google Scholar
Oliveira, P.J. 2003 Asymmetric flows of viscoelastic fluids in symmetric planar expansion geometries. J. Non-Newtonian Fluid Mech. 114 (1), 3363.CrossRefGoogle Scholar
Peterlin, A. 1966 Hydrodynamics of macromolecules in a velocity field with longitudinal gradient. J. Polym. Sci. B Polym. Lett. 4 (4), 287291.CrossRefGoogle Scholar
Remmelgas, J. & Leal, L.G. 2000 Computational studies of the FENE-CR model in a two-roll mill. J. Non-Newtonian Fluid Mech. 89 (3), 231249.CrossRefGoogle Scholar
Rodd, L.E., Cooper-White, J.J., Boger, D.V. & McKinley, G.H. 2007 Role of the elasticity number in the entry flow of dilute polymer solutions in micro-fabricated contraction geometries. J. Non-Newtonian Fluid Mech. 143 (2–3), 170191.CrossRefGoogle Scholar
Satrape, J.V. & Crochet, M.J. 1994 Numerical simulation of the motion of a sphere in a Boger fluid. J. Non-Newtonian Fluid Mech. 55 (1), 91111.CrossRefGoogle Scholar
Segre, G. & Silberberg, A. 1961 Radial particle displacements in Poiseuille flow of suspensions. Nature 189, 209210.CrossRefGoogle Scholar
Seo, K.W., Byeon, H.J., Huh, H.K. & Lee, S.J. 2014 b Particle migration and single-line particle focusing in microscale pipe flow of viscoelastic fluids. RSC Adv. 4 (7), 35123520.CrossRefGoogle Scholar
Seo, K.W., Kang, Y.J. & Lee, S.J. 2014 a Lateral migration and focusing of microspheres in a microchannel flow of viscoelastic fluids. Phys. Fluids 26 (6), 63301.CrossRefGoogle Scholar
Tabeling, P. 2023 Introduction to Microfluidics. Oxford University Press.CrossRefGoogle Scholar
Tehrani, M.A. 1996 An experimental study of particle migration in pipe flow of viscoelastic fluids. J. Rheol. 40 (6), 10571077.CrossRefGoogle Scholar
Tirtaatmadja, V., McKinley, G.H. & Cooper-White, J.J. 2006 Drop formation and breakup of low viscosity elastic fluids: effects of molecular weight and concentration. Phys. Fluids 18, 4.CrossRefGoogle 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 vs secondary flows. J. Non-Newtonian Fluid Mech. 195, 18.CrossRefGoogle Scholar
Wang, Q., Yuan, D. & Li, W. 2017 Analysis of hydrodynamic mechanism on particles focusing in micro-channel flows. Micromachines 8 (7), 197.CrossRefGoogle ScholarPubMed
Xie, X., Zhang, L., Shi, C. & Liu, X. 2022 Prediction of lubrication layer properties of pumped concrete based on flow induced particle migration. Constr. Build. Mater. 322, 126115.CrossRefGoogle Scholar
Xue, S.-C., Phan-Thien, N. & Tanner, R.I. 1998 Three dimensional numerical simulations of viscoelastic flows through planar contractions. J. Non-Newtonian Fluid Mech. 74 (1), 195245.CrossRefGoogle Scholar
Yang, S., Kim, J.Y., Lee, S.J., Lee, S.S. & Kim, J.M. 2011 Sheathless elasto-inertial particle focusing and continuous separation in a straight rectangular microchannel. Lab on a Chip 11 (2), 266273.CrossRefGoogle Scholar
Yang, S., Lee, S.S., Ahn, S.W., Kang, K., Shim, W., Lee, G., Hyun, K. & Kim, J.M. 2012 Deformability-selective particle entrainment and separation in a rectangular microchannel using medium viscoelasticity. Soft Matt. 8 (18), 50115019.CrossRefGoogle Scholar
Zhang, J., Yan, S., Yuan, D., Alici, G., Nguyen, N., Ebrahimi Warkiani, M. & Li, W. 2016 Fundamentals and applications of inertial microfluidics: a review. Lab on a Chip 16 (1), 1034.CrossRefGoogle Scholar
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