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Interplay of inertia and deformability on rheological properties of a suspension of capsules

  • Timm Krüger (a1) (a2), Badr Kaoui (a3) (a4) and Jens Harting (a4) (a5)
Abstract
Abstract

The interplay of inertia and deformability has a substantial impact on the transport of soft particles suspended in a fluid. However, to date a thorough understanding of these systems is still missing, and only a limited number of experimental and theoretical studies are available. We combine the finite-element, immersed-boundary and lattice-Boltzmann methods to simulate three-dimensional suspensions of soft particles subjected to planar Poiseuille flow at finite Reynolds numbers. Our findings confirm that the particle deformation and inclination increase when inertia is present. We observe that the Segré–Silberberg effect is suppressed with respect to the particle deformability. Depending on the deformability and strength of inertial effects, inward or outward lateral migration of the particles takes place. In particular, for increasing Reynolds numbers and strongly deformable particles, a hitherto unreported distinct flow focusing effect emerges, which is accompanied by a non-monotonic behaviour of the apparent suspension viscosity and thickness of the particle-free layer close to the channel walls. This effect can be explained by the behaviour of a single particle and the change of the particle collision mechanism when both deformability and inertia effects are relevant.

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Email address for correspondence: timm.krueger@ed.ac.uk
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C. K. Aidun  & J. R. Clausen 2010 Lattice-Boltzmann method for complex flows. Annu. Rev. Fluid Mech. 42, 439472.

P. Bagchi  & R. M. Kalluri 2010 Rheology of a dilute suspension of liquid-filled elastic capsules. Phys. Rev. E 81 (5), 056320.

J. M. Charrier , S. Shrivastava  & R. Wu 1989 Free and constrained inflation of elastic membranes in relation to thermoforming – non-axisymmetric problems. J. Strain Anal. Engng Design 24 (2), 5574.

Y.-L. Chen 2014 Inertia- and deformation-driven migration of a soft particle in confined shear and poiseuille flow. RSC Adv. 4 (34), 1790817916.

B. Chun  & A. J. C. Ladd 2006 Inertial migration of neutrally buoyant particles in a square duct: an investigation of multiple equilibrium positions. Phys. Fluids 18 (3), 031704.

G. Coupier , B. Kaoui , T. Podgorski  & C. Misbah 2008 Noninertial lateral migration of vesicles in bounded Poiseuille flow. Phys. Fluids 20 (11), 111702.

G. Danker , P. M. Vlahovska  & C. Misbah 2009 Vesicles in Poiseuille flow. Phys. Rev. Lett. 102 (14), 148102.

D. Di Carlo 2009 Inertial microfluidics. Lab on a Chip 9 (21), 30383046.

S. K. Doddi  & P. Bagchi 2008a Effect of inertia on the hydrodynamic interaction between two liquid capsules in simple shear flow. Intl J. Multiphase Flow 34 (4), 375392.

S. K. Doddi  & P. Bagchi 2008b Lateral migration of a capsule in a plane Poiseuille flow in a channel. Intl J. Multiphase Flow 34 (10), 966986.

A. Farutin  & C. Misbah 2013 Analytical and numerical study of three main migration laws for vesicles under flow. Phys. Rev. Lett. 110 (10), 108104.

T. M. Geislinger , B. Eggart , S. Braunmüller , L. Schmid  & T. Franke 2012 Separation of blood cells using hydrodynamic lift. Appl. Phys. Lett. 100 (18), 183701.

K. J. Humphry , P. M. Kulkarni , D. A. Weitz , J. F. Morris  & H. A. Stone 2010 Axial and lateral particle ordering in finite Reynolds number channel flows. Phys. Fluids 22 (8), 081703.

S. C. Hur , N. K. Henderson-MacLennan , E. R. B. McCabe  & D. Di Carlo 2011 Deformability-based cell classification and enrichment using inertial microfluidics. Lab on a Chip 11 (5), 912920.

S. C. Hur , H. T. K. Tse  & D. Di Carlo 2010 Sheathless inertial cell ordering for extreme throughput flow cytometry. Lab on a Chip 10 (3), 274280.

B. Kaoui , G. H. Ristow , I. Cantat , C. Misbah  & W. Zimmermann 2008 Lateral migration of a two-dimensional vesicle in unbounded Poiseuille flow. Phys. Rev. E 77 (2), 021903.

A. Kilimnik , W. Mao  & A. Alexeev 2011 Inertial migration of deformable capsules in channel flow. Phys. Fluids 23 (12), 123302.

Y. Kim  & M. C. Lai 2012 Numerical study of viscosity and inertial effects on tank-treading and tumbling motions of vesicles under shear flow. Phys. Rev. E 86 (6), 066321.

T. Krüger , S. Frijters , F. Günther , B. Kaoui  & J. Harting 2013 Numerical simulations of complex fluid–fluid interface dynamics. Eur. Phys. J., Spec. Top. 222 (1), 177198.

T. Krüger , F. Varnik  & D. Raabe 2011 Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method. Comput. Meth. Appl. 61 (12), 34853505.

A. Laadhari , P. Saramito  & C. Misbah 2012 Vesicle tumbling inhibited by inertia. Phys. Fluids 24 (3), 031901.

A. J. C. Ladd 1994 Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 285309.

L. G. Leal 1980 Particle motions in a viscous fluid. Annu. Rev. Fluid Mech. 12, 435476.

X. Li  & C. Pozrikidis 2000 Wall-bounded shear flow and channel flow of suspensions of liquid drops. Intl J. Multiphase Flow 26 (8), 12471279.

Z. Y. Luo , S. Q. Wang , L. He , F. Xu  & B. F. Bai 2013 Inertia-dependent dynamics of three-dimensional vesicles and red blood cells in shear flow. Soft Matt. 9 (40), 96519660.

J. M. Martel  & M. Toner 2012 Inertial focusing dynamics in spiral microchannels. Phys. Fluids 24 (3), 032001.

L. L. Munn  & M. M. Dupin 2008 Blood cell interactions and segregation in flow. Ann. Biomed. Engng 36 (4), 534544.

A. Nourbakhsh , S. Mortazavi  & Y. Afshar 2011 Three-dimensional numerical simulation of drops suspended in Poiseuille flow at non-zero Reynolds numbers. Phys. Fluids 23 (12), 123303.

P. Pranay , R. G. Henríquez-Rivera  & M. D. Graham 2012 Depletion layer formation in suspensions of elastic capsules in Newtonian and viscoelastic fluids. Phys. Fluids 24 (6), 061902.

X. Shan  & G. Doolen 1995 Multicomponent lattice-Boltzmann model with interparticle interaction. J. Stat. Phys. 81 (1), 379393.

L. Shi , T.-W. Pan  & R. Glowinski 2012 Lateral migration and equilibrium shape and position of a single red blood cell in bounded Poiseuille flows. Phys. Rev. E 86 (5), 056308.

S. J. Shin  & H. J. Sung 2011 Inertial migration of an elastic capsule in a Poiseuille flow. Phys. Rev. E 83 (4), 046321.

S. J. Shin  & H. J. Sung 2012 Dynamics of an elastic capsule in moderate Reynolds number Poiseuille flow. Intl J. Heat Fluid Flow 36, 167177.

R. Skalak , A. Tozeren , R. P. Zarda  & S. Chien 1973 Strain energy function of red blood cell membranes. Biophys. J. 13 (3), 245264.

T. Tanaka , T. Ishikawa , K. Numayama-Tsuruta , Y. Imai , H. Ueno , N. Matsuki  & T. Yamaguchi 2012 Separation of cancer cells from a red blood cell suspension using inertial force. Lab on a Chip 12 (21), 43364343.

A. Z. K. Yazdani , R. M. Kalluri  & P. Bagchi 2011 Tank-treading and tumbling frequencies of capsules and red blood cells. Phys. Rev. E 83 (4), 046305.

M. Zurita-Gotor , J. Bławzdziewicz  & E. Wajnryb 2012 Layering instability in a confined suspension flow. Phys. Rev. Lett. 108 (6), 068301.

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Journal of Fluid Mechanics
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