Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-24T01:07:07.519Z Has data issue: false hasContentIssue false
  • English
  • Français

Equilibrium positions of the elasto-inertial particle migration in rectangular channel flow of Oldroyd-B viscoelastic fluids

Published online by Cambridge University Press:  11 April 2019

Zhaosheng Yu Open the ORCID record for Zhaosheng Yu [Opens in a new window] ,
Peng Wang ,
Jianzhong Lin  and
Howard H. Hu
Zhaosheng Yu*
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, PR China
Peng Wang
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, PR China
Jianzhong Lin*
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, PR China
Howard H. Hu
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315, USA
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, the lateral migration of a neutrally buoyant spherical particle in the pressure-driven rectangular channel flow of an Oldroyd-B fluid is numerically investigated with a fictitious domain method. The aspect ratio of the channel cross-section considered is 1 and 2, respectively. The particle lateral motion trajectories are shown for the bulk Reynolds number ranging from 1 to 100, the ratio of the solvent viscosity to the total viscosity being 0.5, and a Weissenberg number up to 1.5. Our results indicate that the lateral equilibrium positions located on the cross-section midline, diagonal line, corner and channel centreline occur successively as the fluid elasticity is increased, for particle migration in square channel flow with finite fluid inertia. The transition of the equilibrium position depends strongly on the elasticity number (the ratio of the Weissenberg number to the Reynolds number) and weakly on the Reynolds number. The diagonal-line equilibrium position occurs at an elasticity number ranging from roughly 0.001 to 0.02, and can coexist with the midline and corner equilibrium positions. When the fluid inertia is negligibly small, particles migrate towards the channel centreline, or the closest corner, depending on their initial positions and the Weissenberg number, and the corner attractive area first increases and then decreases as the Weissenberg number increases. For particle migration in a rectangular channel with an aspect ratio of 2, the transition of the equilibrium position from the midline, ‘diagonal line’ (the line where two lateral shear rates are equal to each other), off-centre long midline and channel centreline takes place as the Weissenberg number increases at moderate Reynolds numbers. An off-centre equilibrium position on the long midline is observed for a large blockage ratio of 0.3 (i.e. the ratio of the particle diameter to the channel height is 0.3) at a low Reynolds number. This off-centre migration is driven by shear forces, unlike the elasticity-induced rapid inward migration, which is driven by the normal force (pressure or first normal stress difference).

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics Multiphase and Particle-laden Flows: Particle/fluid flow Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 868 , 10 June 2019 , pp. 316 - 340
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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, 136–157.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.Google 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.Google 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, 341–360.Google Scholar
D’Avino, G. & Maffettone, P. L. 2015 Particle dynamics in viscoelastic liquids. J. Non-Newtonian Fluid Mech. 215, 80–104.Google 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.Google Scholar
Del Giudice, F., D’Avino, G., Greco, F., Netti, P. A. & Maffettone, P. 2015 Effect of fluid rheology on particle migration in a square-shaped microchannel. Microfluid. Nanofluid. 19 (1), 1–10.Google Scholar
Di, L., Lu, X. & Xuan, X. 2016 Viscoelastic separation of particles by size in straight rectangular microchannels: a parametric study for a refined understanding. Analyt. Chem. 88, 12303–12309.Google Scholar
Di Carlo, D., Irimia, D., Tompkins, R. G. & Toner, M. 2007 Continuous inertial focusing, ordering, and separation of particles in microchannels. Proc. Natl Acad. Sci. USA 104, 18892–18897.Google Scholar
Glowinski, R., Pan, T.-W., Hesla, T. I. & Joseph, D. D. 1999 A distributed Lagrange multiplier/fictitious domain method for particulate flows. Intl J. Multiphase Flow 25, 755–794.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.Google 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.Google Scholar
Hu, H. H., Patankar, N. A. & Zhu, M. Y. 2001 Direct numerical simulations of fluid–solid systems using the arbitrary Lagrangian–Eulerian technique. J. Comput. Phys. 169 (2), 427–462.Google 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.Google Scholar
Karnis, A. & Mason, S. G. 1966 Particle motions in sheared suspensions. XIX. Viscoelastic media. Trans. Soc. Rheol. 10, 571–592.Google Scholar
Kazuma, M., Tomoaki, I. & Masako, S. S. 2014 Inertial migration of neutrally buoyant spheres in a pressure-driven flow through square channels. J. Fluid Mech. 749, 320–330.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, 024111.Google Scholar
Kim, J. Y., Ahn, S. W., Lee, S. S. & Kim, J. M. 2012 Lateral migration and focusing of colloidal particles and DNA molecules under viscoelastic flow. Lab on a Chip 12, 2807–2814.Google Scholar
van Leer, B. 1979 Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J. Comput. Phys. 32, 101–136.Google Scholar
Leshansky, A. M., Bransky, A., Korin, N. & Dinnar, U. 2007 Tunable nonlinear viscoelastic focusing in a microfluidic device. Phys. Rev. Lett. 98, 234501.Google Scholar
Li, G., McKinley, G. H. & Ardekani, A. M. 2015 Dynamics of particle migration in channel flow of viscoelastic fluids. J. Fluid Mech. 785, 486–505.Google 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.Google Scholar
Liu, C., Hu, G., Jiang, X. & Sun, J. 2015a Inertial focusing of spherical particles in rectangular microchannels over a wide range of Reynolds numbers. Lab on a Chip 15, 1168–1177.Google Scholar
Liu, C., Xue, C., Chen, X., Shan, L., Tian, Y. & Hu, G. 2015b Size-based separation of particles and cells utilizing viscoelastic effects in straight microchannels. Analyt. Chem. 87, 6041–6048.Google Scholar
Lu, X., Liu, C., Hu, G. & Xuan, X. 2017 Particle manipulations in non-Newtonian microfluidics: a review. J. Colloid Interface Sci. 500, 182–201.Google 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.Google 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, 59–67.Google Scholar
Raffiee, A. H., Dabiri, S. & Ardekani, A. M. 2017 Elasto-inertial migration of deformable capsules in a microchannel. Biomicrofluidics 11 (6), 064113.Google Scholar
Segre, G. & Silberberg, A. 1961 Radial particle displacements in Poiseuille flow of suspensions. Nature 189, 209–210.Google 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.Google 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.Google Scholar
Trofa, M., Vocciante, M., D’Avino, G., Hulsen, M. A., Greco, F. & Maffettone, P. L. 2015 Numerical simulations of the competition between the effects of inertia and viscoelasticity on particle migration in Poiseuille flow. Comput. Fluids 107, 214–223.Google 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.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.Google Scholar
Wang, P., Yu, Z. & Lin, J. 2018 Numerical simulations of particle migration in rectangular channel flow of Giesekus viscoelastic fluids. J. Non-Newtonian Fluid Mech. 262, 142–148.Google Scholar
Xiang, N., Dai, Q. & Ni, Z. 2016 Multi-train elasto-inertial particle focusing in straight microfluidic channels. Appl. Phys. Lett. 109, 1–16.Google 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.Google Scholar
Yang, S., Lee, S. S., Ahn, S. W., Kang, K., Shim, W., Lee, G., Hyun, K. & Ju, M. K. 2012 Deformability-selective particle entrainment and separation in a rectangular microchannel using medium viscoelasticity. Soft Matt. 8, 5011–5019.Google Scholar
Yu, Z., Phan-Thien, N., Fan, Y. & Tanner, R. I. 2002 Viscoelastic mobility problem of a system of particles. J. Non-Newtonian Fluid Mech. 104, 87–124.Google Scholar
Yu, Z. & Shao, X. 2007 A direct-forcing fictitious domain method for particulate flows. J. Comput. Phys. 227, 292–314.Google Scholar
Yu, Z. & Wachs, A. 2007 A fictitious domain method for dynamic simulation of particle sedimentation in Bingham fluids. J. Non-Newtonian Fluid Mech. 145, 78–91.Google Scholar
Yu, Z., Wachs, A. & Peysson, Y. 2006 Numerical simulation of particle sedimentation in shear-thinning fluids with a fictitious domain method. J. Non-Newtonian Fluid Mech. 136, 126–139.Google Scholar
Yuan, D., Zhao, Q., Yan, S., Tang, S.-Y., Alici, G., Zhang, J. & Li, W. 2018 Recent progress of particle migration in viscoelastic fluids. Lab on a Chip 18 (4), 551–567.Google Scholar
Zhou, J. & Papautsky, I. 2013 Fundamentals of inertial focusing in microchannels. Lab on a Chip 13, 1121–1132.Google Scholar