Skip to main content
×
Home

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.

Copyright
Corresponding author
Email address for correspondence: timm.krueger@ed.ac.uk
References
Hide All
Aidun C. K. & Clausen J. R. 2010 Lattice-Boltzmann method for complex flows. Annu. Rev. Fluid Mech. 42, 439472.
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, 6387.
Bagchi P. & Kalluri R. M. 2010 Rheology of a dilute suspension of liquid-filled elastic capsules. Phys. Rev. E 81 (5), 056320.
Barthès-Biesel D. 1980 Motion of a spherical microcapsule freely suspended in a linear shear flow. J. Fluid Mech. 100 (4), 831853.
Barthès-Biesel D. & Rallison J. M. 1981 The time-dependent deformation of a capsule freely suspended in a linear shear flow. J. Fluid Mech. 113, 251267.
Charrier J. M., Shrivastava S. & Wu R. 1989 Free and constrained inflation of elastic membranes in relation to thermoforming – non-axisymmetric problems. J. Strain Anal. Engng Design 24 (2), 5574.
Chen Y.-L. 2014 Inertia- and deformation-driven migration of a soft particle in confined shear and poiseuille flow. RSC Adv. 4 (34), 1790817916.
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 (3), 031704.
Coupier G., Kaoui B., Podgorski T. & Misbah C. 2008 Noninertial lateral migration of vesicles in bounded Poiseuille flow. Phys. Fluids 20 (11), 111702.
Danker G., Vlahovska P. M. & Misbah C. 2009 Vesicles in Poiseuille flow. Phys. Rev. Lett. 102 (14), 148102.
Di Carlo D. 2009 Inertial microfluidics. Lab on a Chip 9 (21), 30383046.
Doddi S. K. & Bagchi P. 2008a Effect of inertia on the hydrodynamic interaction between two liquid capsules in simple shear flow. Intl J. Multiphase Flow 34 (4), 375392.
Doddi S. K. & Bagchi P. 2008b Lateral migration of a capsule in a plane Poiseuille flow in a channel. Intl J. Multiphase Flow 34 (10), 966986.
Eckstein E. C., Bailey D. G. & Shapiro A. H. 1977 Self-diffusion of particles in shear flow of a suspension. J. Fluid Mech. 79 (1), 191208.
Fahraeus R. & Lindqvist T. 1931 The viscosity of blood in narrow capillary tubes. Am. J. Physiol. 96, 562568.
Farutin A. & Misbah C. 2013 Analytical and numerical study of three main migration laws for vesicles under flow. Phys. Rev. Lett. 110 (10), 108104.
Geislinger T. M., Eggart B., Braunmüller S., Schmid L. & Franke T. 2012 Separation of blood cells using hydrodynamic lift. Appl. Phys. Lett. 100 (18), 183701.
Helfrich W. 1973 Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. C 28 (11), 693703.
Humphry K. J., Kulkarni P. M., Weitz D. A., Morris J. F. & Stone H. A. 2010 Axial and lateral particle ordering in finite Reynolds number channel flows. Phys. Fluids 22 (8), 081703.
Hur S. C., Henderson-MacLennan N. K., McCabe E. R. B. & Di Carlo D. 2011 Deformability-based cell classification and enrichment using inertial microfluidics. Lab on a Chip 11 (5), 912920.
Hur S. C., Tse H. T. K. & Di Carlo D. 2010 Sheathless inertial cell ordering for extreme throughput flow cytometry. Lab on a Chip 10 (3), 274280.
Kaoui B., Coupier G., Misbah C. & Podgorski T. 2009 Lateral migration of vesicles in microchannels: effects of walls and shear gradient. La Houille Blanche 2009 (5), 112119.
Kaoui B., Ristow G. H., Cantat I., Misbah C. & Zimmermann W. 2008 Lateral migration of a two-dimensional vesicle in unbounded Poiseuille flow. Phys. Rev. E 77 (2), 021903.
Kilimnik A., Mao W. & Alexeev A. 2011 Inertial migration of deformable capsules in channel flow. Phys. Fluids 23 (12), 123302.
Kim Y. & Lai M. C. 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.
Krüger T., Frijters S., Günther F., Kaoui B. & Harting J. 2013 Numerical simulations of complex fluid–fluid interface dynamics. Eur. Phys. J., Spec. Top. 222 (1), 177198.
Krüger T., Varnik F. & Raabe D. 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.
Laadhari A., Saramito P. & Misbah C. 2012 Vesicle tumbling inhibited by inertia. Phys. Fluids 24 (3), 031901.
Ladd A. J. C. 1994 Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 285309.
Leal L. G. 1980 Particle motions in a viscous fluid. Annu. Rev. Fluid Mech. 12, 435476.
Li X. & Pozrikidis C. 2000 Wall-bounded shear flow and channel flow of suspensions of liquid drops. Intl J. Multiphase Flow 26 (8), 12471279.
Luo Z. Y., Wang S. Q., He L., Xu F. & Bai B. F. 2013 Inertia-dependent dynamics of three-dimensional vesicles and red blood cells in shear flow. Soft Matt. 9 (40), 96519660.
Martel J. M. & Toner M. 2012 Inertial focusing dynamics in spiral microchannels. Phys. Fluids 24 (3), 032001.
Matas J.-P., Morris J. F. & Guazzelli É. 2004 Inertial migration of rigid spherical particles in Poiseuille flow. J. Fluid Mech. 515, 171195.
Munn L. L. & Dupin M. M. 2008 Blood cell interactions and segregation in flow. Ann. Biomed. Engng 36 (4), 534544.
Nourbakhsh A., Mortazavi S. & Afshar Y. 2011 Three-dimensional numerical simulation of drops suspended in Poiseuille flow at non-zero Reynolds numbers. Phys. Fluids 23 (12), 123303.
Peskin C. S. 2002 The immersed boundary method. Acta Numerica 11, 479517.
Pranay P., Henríquez-Rivera R. G. & Graham M. D. 2012 Depletion layer formation in suspensions of elastic capsules in Newtonian and viscoelastic fluids. Phys. Fluids 24 (6), 061902.
Salac D. & Miksis M. J. 2012 Reynolds number effects on lipid vesicles. J. Fluid Mech. 711, 122146.
Schonberg J. A. & Hinch E. J. 1989 Inertial migration of a sphere in Poiseuille flow. J. Fluid Mech. 203, 517524.
Segré G. & Silberberg A. 1962a Behaviour of macroscopic rigid spheres in Poiseuille flow. Part 1. Determination of local concentration by statistical analysis of particle passages through crossed light beams. J. Fluid Mech. 14 (1), 115135.
Segré G. & Silberberg A. 1962b Behaviour of macroscopic rigid spheres in Poiseuille flow. Part 2. Experimental results and interpretation. J. Fluid Mech. 14, 136157.
Shan X. & Doolen G. 1995 Multicomponent lattice-Boltzmann model with interparticle interaction. J. Stat. Phys. 81 (1), 379393.
Shi L., Pan T.-W. & Glowinski R. 2012 Lateral migration and equilibrium shape and position of a single red blood cell in bounded Poiseuille flows. Phys. Rev. E 86 (5), 056308.
Shin S. J. & Sung H. J. 2011 Inertial migration of an elastic capsule in a Poiseuille flow. Phys. Rev. E 83 (4), 046321.
Shin S. J. & Sung H. J. 2012 Dynamics of an elastic capsule in moderate Reynolds number Poiseuille flow. Intl J. Heat Fluid Flow 36, 167177.
Skalak R., Tozeren A., Zarda R. P. & Chien S. 1973 Strain energy function of red blood cell membranes. Biophys. J. 13 (3), 245264.
Succi S. 2001 The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press.
Tanaka T., Ishikawa T., Numayama-Tsuruta K., Imai Y., Ueno H., Matsuki N. & Yamaguchi T. 2012 Separation of cancer cells from a red blood cell suspension using inertial force. Lab on a Chip 12 (21), 43364343.
Yazdani A. Z. K., Kalluri R. M. & Bagchi P. 2011 Tank-treading and tumbling frequencies of capsules and red blood cells. Phys. Rev. E 83 (4), 046305.
Zurita-Gotor M., Bławzdziewicz J. & Wajnryb E. 2012 Layering instability in a confined suspension flow. Phys. Rev. Lett. 108 (6), 068301.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 1
Total number of PDF views: 116 *
Loading metrics...

Abstract views

Total abstract views: 419 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 24th November 2017. This data will be updated every 24 hours.