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Dynamics of particle migration in channel flow of viscoelastic fluids

Published online by Cambridge University Press:  23 November 2015

Gaojin Li ,
Gareth H. McKinley  and
Arezoo M. Ardekani
Gaojin Li
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
Gareth H. McKinley
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Arezoo M. Ardekani*
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
*
†Email address for correspondence: ardekani@purdue.edu
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Abstract

The migration of a sphere in the pressure-driven channel flow of a viscoelastic fluid is studied numerically. The effects of inertia, elasticity, shear-thinning viscosity, secondary flows and the blockage ratio are considered by conducting fully resolved direct numerical simulations over a wide range of parameters. In a Newtonian fluid in the presence of inertial effects, the particle moves away from the channel centreline. The elastic effects, however, drive the particle towards the channel centreline. The equilibrium position depends on the interplay between the elastic and inertial effects. Particle focusing at the centreline occurs in flows with strong elasticity and weak inertia. Both shear-thinning effects and secondary flows tend to move the particle away from the channel centreline. The effect is more pronounced as inertia and elasticity effects increase. A scaling analysis is used to explain these different effects. Besides the particle migration, particle-induced fluid transport and particle migration during flow start-up are also considered. Inertial effects, shear-thinning behaviour, and secondary flows are all found to enhance the effective fluid transport normal to the flow direction. Due to the oscillation in fluid velocity and strong normal stress differences that develop during flow start-up, the particle has a larger transient migration velocity, which may be potentially used to accelerate the particle focusing.

JFM classification

Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics Multiphase and Particle-laden Flows: Particle/fluid flow Non-Newtonian Flows: Viscoelasticity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 785 , 25 December 2015 , pp. 486 - 505
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Copyright
© 2015 Cambridge University Press 

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References

Abedijaberi, A. & Khomami, B. 2012 Sedimentation of a sphere in a viscoelastic fluid: a multiscale simulation approach. J. Fluid Mech. 694, 78–99.CrossRefGoogle Scholar
Amini, H., Sollier, E., Weaver, W. M. & Di Carlo, D. 2012 Intrinsic particle-induced lateral transport in microchannels. Proc. Natl Acad. Sci. USA 109, 11593–11598.CrossRefGoogle ScholarPubMed
Ardekani, A. A., Dabiri, S. & Rangel, R. H. 2008 Collision of multi-particle and general shape objects in a viscous fluid. J. Comput. Phys. 227, 10094–10107.CrossRefGoogle Scholar
Ardekani, A. M. & Rangel, R. H. 2008 Numerical investigation of particle–particle and particle-wall collisions in a viscous fluid. J. Fluid Mech. 596, 437–466.CrossRefGoogle Scholar
Arigo, M. T. & McKinley, G. H. 1997 The effects of viscoelasticity on the transient motion of a sphere in a shear-thinning fluid. J. Rheol. 41, 103–128.CrossRefGoogle Scholar
Arigo, M. T., Rajagopalan, D., Shapley, N. & McKinley, G. H. 1995 The sedimentation of a sphere through an elastic fluid. Part 1. Steady motion. J. Non-Newtonian Fluid Mech. 60, 225–257.CrossRefGoogle Scholar
Asmolov, E. S. 1999 The inertial lift on a spherical particle in a plane Poiseuille flow at large channel Reynolds number. J. Fluid Mech. 381, 63–87.CrossRefGoogle Scholar
Chhabra, R. P. 1993 Bubbles, Drops, and Particles in Non-Newtonian Fluids. CRC Press.Google 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, 460–465.CrossRefGoogle Scholar
Chun, B. & Ladd, A. J. C. 2006 Inertial migration of neutrally buoyant particles in a square duct: an investigation of multiple equilibrium positions. Phys. Fluids 18, 031704.CrossRefGoogle Scholar
D’Avino, G. & Maffettone, P. L. 2015 Particle dynamics in viscoelastic liquids. J. Non-Newtonian Fluid Mech. 215, 80–104.CrossRefGoogle Scholar
D’Avino, G., Maffettone, P. L., Greco, F. & Hulsen, M. A. 2010a Viscoelasticity-induced migration of a rigid sphere in confined shear flow. J. Non-Newtonian Fluid Mech. 165, 466–474.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, 1638–1645.CrossRefGoogle ScholarPubMed
D’Avino, G., Tuccillo, T., Maffettone, P. L., Greco, F. & Hulsen, M. A. 2010b Numerical simulations of particle migration in a viscoelastic fluid subjected to shear flow. Comput. Fluids 39, 709–721.CrossRefGoogle Scholar
Di Carlo, D. 2009 Inertial microfluidics. Lab on a Chip 9, 3038–3046.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, 094503.Google ScholarPubMed
Doostmohammadi, A. & Ardekani, A. M. 2013 Interaction between a pair of particles settling in a stratified fluid. Phys. Rev. E 88, 023029.CrossRefGoogle Scholar
Doostmohammadi, A., Dabiri, S. & Ardekani, A. M. 2014 A numerical study of the dynamics of a particle settling at moderate Reynolds numbers in a linearly stratified fluid. J. Fluid Mech. 750, 5–32.CrossRefGoogle Scholar
Duarte, A. S. R., Miranda, A. I. P. & Oliveira, P. J. 2008 Numerical and analytical modeling of unsteady viscoelastic flows: the start-up and pulsating test case problems. J. Non-Newtonian Fluid Mech. 154, 153–169.CrossRefGoogle Scholar
Fabris, D., Muller, S. J. & Liepmann, D. 1999 Wake measurements for flow around a sphere in a viscoelastic fluid. Phys. Fluids 11, 3599–3612.CrossRefGoogle Scholar
Feng, J., Hu, H. H. & Joseph, D. D. 1994 Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2. Couette and Poiseuille flows. J. Fluid Mech. 277, 271–301.CrossRefGoogle Scholar
Fetecau, C. & Fetecau, C. 2005 Unsteady flows of Oldroyd-B fluids in a channel of rectangular cross-section. Intl J. Non-Linear Mech. 40, 1214–1219.CrossRefGoogle Scholar
Gauthier, F., Goldsmith, H. L. & Mason, S. G. 1971 Particle motions in non-Newtonian media. II. Poiseuille Flow. Trans. Soc. Rheol. 15, 297–330.CrossRefGoogle Scholar
Giesekus, H. 1982 A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility. J. Non-Newtonian Fluid Mech. 11, 69–109.CrossRefGoogle Scholar
Gossett, D. R., Tse, H. T. K., Dudani, J. S., Goda, K., Woods, T. A., Graves, S. W. & Di Carlo, D. 2012 Inertial manipulation and transfer of microparticles across laminar fluid streams. Small 8, 2757–2764.CrossRefGoogle ScholarPubMed
Goyal, N. & Derksen, J. J. 2012 Direct simulations of spherical particles sedimenting in viscoelastic fluids. J. Non-Newtonian Fluid Mech. 183, 1–13.CrossRefGoogle Scholar
Guénette, R. & Fortin, M. 1995 A new mixed finite element method for computing viscoelastic flows. J. Non-Newtonian Fluid Mech. 60, 27–52.CrossRefGoogle Scholar
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media. Springer.CrossRefGoogle 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
Huang, P. Y., Feng, J., Hu, H. H. & Joseph, D. D. 1997 Direct simulation of the motion of solid particles in Couette and Poiseuille flows of viscoelastic fluids. J. Fluid Mech. 343, 73–94.CrossRefGoogle Scholar
Kang, K., Lee, S. S., Hyun, K., Lee, S. J. & Kim, J. M. 2014 DNA-based highly tunable particle focuser. Nat. Commun. 4, 1–7.Google Scholar
Karimi, A., Yazdi, S. & Ardekani, A. M. 2013 Hydrodynamic mechanisms of cell and particle trapping in microfluidics. Biomicrofluidics 7, 021501.CrossRefGoogle ScholarPubMed
Karnis, A., Goldsmith, H. L. & Mason, S. G. 1966 The flow of suspensions through tubes V. Inertial effects. Can. J. Chem. Engng 44, 181–193.CrossRefGoogle Scholar
Karnis, A. & Mason, S. G. 1966 Particle motions in sheared suspensions. XIX. Viscoelastic media. Can. J. Chem. Engng 10, 571–592.Google Scholar
Kim, Y. W. & Yoo, J. Y. 2008 The lateral migration of neutrally-buoyant spheres transported through square microchannels. J. Micromech. Microengng 18, 065015.CrossRefGoogle Scholar
Lee, W., Amini, H., Stone, H. A. & Di Carlo, D. 2010 Dynamic self-assembly and control of microfluidic particle crystals. Proc. Natl Acad. Sci. USA 107, 22413–22418.CrossRefGoogle ScholarPubMed
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. & Ardekani, A. M. 2014 Hydrodynamic interaction of microswimmers near a wall. Phys. Rev. E 90, 013010.CrossRefGoogle ScholarPubMed
Li, G., Karimi, A. & Ardekani, A. M. 2014 Effect of solid boundaries on swimming dynamics of microorganisms in a viscoelastic fluid. Rheol. Acta 53, 911–926.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. 2014a Inertio-elastic focusing of bioparticles in microchannels at high throughput. Nat. Commun. 5, 4120 1–9.CrossRefGoogle ScholarPubMed
Lim, H., Nam, J. & Shin, S. 2014b Lateral migration of particles suspended in viscoelastic fluids in a microchannel flow. Microfluid. Nanofluid. 17, 683–692.CrossRefGoogle Scholar
Lin, C. J., Peery, J. H. & Schowalter, W. R. 1970 Simple shear flow round a rigid sphere: inertial effects and suspension rheology. J. Fluid Mech. 44, 1–17.CrossRefGoogle Scholar
Matas, J. P., Morris, J. F. & Guazzelli, E. 2004 Inertial migration of rigid spherical particles in Poiseuille flow. J. Fluid Mech. 515, 171–195.CrossRefGoogle Scholar
Mikulencak, D. R. & Morris, J. F. 2004 Stationary shear flow around fixed and free bodies at finite Reynolds number. J. Fluid Mech. 520, 215–242.CrossRefGoogle Scholar
Nam, J., Lim, H., Kim, D., Jung, H. & Shin, S. 2012 Continuous separation of microparticles in a microfluidic channel via the elasto-inertial effect of non-Newtonian fluid. Lab on a Chip 12, 1347–1354.CrossRefGoogle Scholar
Pan, T. & Glowinski, R. 2005 Direct simulation of the motion of neutrally buoyant balls in a three-dimensional Poiseuille flow. C. R. Méc. 333, 884–895.CrossRefGoogle Scholar
Ramachandran, A. 2013 Secondary convection due to second normal stress differences: A new mechanism for the mass transport of solutes in pressure-driven flows of concentrated, non-colloidal suspensions. Soft Matt. 9, 6824–6840.CrossRefGoogle Scholar
Romeo, G., D’Avino, G., Greco, F., Netti, P. A. & Maffettone, P. L. 2013 Viscoelastic flow-focusing in microchannels: scaling properties of the particle radial distributions. Lab on a Chip 13, 2802–2807.CrossRefGoogle ScholarPubMed
Schleiniger, G. & Weinacht, R. J. 1991 A remark on the Giesekus viscoelastic fluid. J. Rheol. 35, 1157–1170.CrossRefGoogle Scholar
Schonberg, J. A. & Hinch, E. J. 1989 Inertial migration of a sphere in Poiseuille flow. J. Fluid Mech. 203, 517–524.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., Yu, Z. & Sun, B. 2008 Inertial migration of spherical particles in circular Poiseuille flow at moderately high Reynolds numbers. Phys. Fluids 20, 103307.CrossRefGoogle Scholar
Subramanian, G. & Koch, D. L. 2006 Inertial effects on the transfer of heat or mass from neutrally buoyant spheres in a steady linear velocity field. Phys. Fluids 18, 073302.CrossRefGoogle Scholar
Tehrani, M. A. 1996 An experimental study of particle migration in pipe flow of viscoelastic fluids. J. Rheol. 40, 1057–1077.CrossRefGoogle Scholar
Villone, M. M., D’Avino, G., Hulsen, M. A., Greco, F. & Maffettone, P. L. 2011 Simulations of viscoelasticity-induced focusing of particles in pressure-driven micro-slit flow. J. Non-Newtonian Fluid Mech. 166, 1396–1405.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 versus secondary flows. J. Non-Newtonian Fluid Mech. 195, 1–8.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, 266–273.CrossRefGoogle Scholar
Yang, B. H., Wang, J., Joseph, D. D., Hu, H. H., Pan, T. & Glowinski, R. 2005 Migration of a sphere in tube flow. J. Fluid Mech. 540, 109–131.CrossRefGoogle Scholar
Zeng, L., Balachandar, S. & Fischer, P. 2005 Wall-induced forces on a rigid sphere at finite Reynolds number. J. Fluid Mech. 536, 1–25.CrossRefGoogle Scholar
Zrehen, A. & Ramachandran, A. 2013 Demonstration of secondary currents in the pressure-driven flow of a concentrated suspension through a square conduit. Phys. Rev. Lett. 110, 018306.CrossRefGoogle ScholarPubMed
Zurita-Gotor, M., Blawzdziewicz, J. & Wajnryb, E. 2007 Swapping trajectories: A new wall-induced cross-streamline particle migration mechanism in a dilute suspension of spheres. J. Fluid Mech. 592, 447–469.CrossRefGoogle Scholar

Li et al. supplementary movie

The time history of the particle migration velocity during the flow start-up in a square channel filled with an Oldroyd-B fluid. The flow conditions are ReG=18.9, El=0.05 and =0. The contour plots represent the first normal stress difference.

Download Li et al. supplementary movie(Video)
Video 3.5 MB