Skip to main content Accessibility help
×
Home
Hostname: page-component-56f9d74cfd-rpbls Total loading time: 0.344 Render date: 2022-06-27T10:52:42.426Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true }

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

Published online by Cambridge University Press:  27 June 2014

Timm Krüger*
Affiliation:
School of Engineering, University of Edinburgh, The King’s Buildings, Mayfield Road, Edinburgh EH9 3JL, UK Centre for Computational Science, University College London, 20 Gordon Street, London WC1H 0AJ, UK
Badr Kaoui
Affiliation:
Theoretische Physik I, Physikalisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
Jens Harting
Affiliation:
Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands Faculty of Science and Technology, Mesa+ Institute, University of Twente, 7500 AE Enschede, The Netherlands
*
Email address for correspondence: timm.krueger@ed.ac.uk

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.

Type
Papers
Copyright
© 2014 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

Aidun, C. K. & Clausen, J. R. 2010 Lattice-Boltzmann method for complex flows. Annu. Rev. Fluid Mech. 42, 439472.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, 6387.CrossRefGoogle Scholar
Bagchi, P. & Kalluri, R. M. 2010 Rheology of a dilute suspension of liquid-filled elastic capsules. Phys. Rev. E 81 (5), 056320.CrossRefGoogle ScholarPubMed
Barthès-Biesel, D. 1980 Motion of a spherical microcapsule freely suspended in a linear shear flow. J. Fluid Mech. 100 (4), 831853.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Chen, Y.-L. 2014 Inertia- and deformation-driven migration of a soft particle in confined shear and poiseuille flow. RSC Adv. 4 (34), 1790817916.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 (3), 031704.CrossRefGoogle Scholar
Coupier, G., Kaoui, B., Podgorski, T. & Misbah, C. 2008 Noninertial lateral migration of vesicles in bounded Poiseuille flow. Phys. Fluids 20 (11), 111702.CrossRefGoogle Scholar
Danker, G., Vlahovska, P. M. & Misbah, C. 2009 Vesicles in Poiseuille flow. Phys. Rev. Lett. 102 (14), 148102.CrossRefGoogle ScholarPubMed
Di Carlo, D. 2009 Inertial microfluidics. Lab on a Chip 9 (21), 30383046.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Fahraeus, R. & Lindqvist, T. 1931 The viscosity of blood in narrow capillary tubes. Am. J. Physiol. 96, 562568.Google Scholar
Farutin, A. & Misbah, C. 2013 Analytical and numerical study of three main migration laws for vesicles under flow. Phys. Rev. Lett. 110 (10), 108104.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Helfrich, W. 1973 Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. C 28 (11), 693703.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Kilimnik, A., Mao, W. & Alexeev, A. 2011 Inertial migration of deformable capsules in channel flow. Phys. Fluids 23 (12), 123302.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Laadhari, A., Saramito, P. & Misbah, C. 2012 Vesicle tumbling inhibited by inertia. Phys. Fluids 24 (3), 031901.CrossRefGoogle Scholar
Ladd, A. J. C. 1994 Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 285309.CrossRefGoogle Scholar
Leal, L. G. 1980 Particle motions in a viscous fluid. Annu. Rev. Fluid Mech. 12, 435476.CrossRefGoogle Scholar
Li, X. & Pozrikidis, C. 2000 Wall-bounded shear flow and channel flow of suspensions of liquid drops. Intl J. Multiphase Flow 26 (8), 12471279.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Martel, J. M. & Toner, M. 2012 Inertial focusing dynamics in spiral microchannels. Phys. Fluids 24 (3), 032001.CrossRefGoogle ScholarPubMed
Matas, J.-P., Morris, J. F. & Guazzelli, É. 2004 Inertial migration of rigid spherical particles in Poiseuille flow. J. Fluid Mech. 515, 171195.CrossRefGoogle Scholar
Munn, L. L. & Dupin, M. M. 2008 Blood cell interactions and segregation in flow. Ann. Biomed. Engng 36 (4), 534544.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Peskin, C. S. 2002 The immersed boundary method. Acta Numerica 11, 479517.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Salac, D. & Miksis, M. J. 2012 Reynolds number effects on lipid vesicles. J. Fluid Mech. 711, 122146.CrossRefGoogle Scholar
Schonberg, J. A. & Hinch, E. J. 1989 Inertial migration of a sphere in Poiseuille flow. J. Fluid Mech. 203, 517524.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Segré, G. & Silberberg, A. 1962b Behaviour of macroscopic rigid spheres in Poiseuille flow. Part 2. Experimental results and interpretation. J. Fluid Mech. 14, 136157.CrossRefGoogle Scholar
Shan, X. & Doolen, G. 1995 Multicomponent lattice-Boltzmann model with interparticle interaction. J. Stat. Phys. 81 (1), 379393.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Shin, S. J. & Sung, H. J. 2011 Inertial migration of an elastic capsule in a Poiseuille flow. Phys. Rev. E 83 (4), 046321.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Skalak, R., Tozeren, A., Zarda, R. P. & Chien, S. 1973 Strain energy function of red blood cell membranes. Biophys. J. 13 (3), 245264.CrossRefGoogle ScholarPubMed
Succi, S. 2001 The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press.Google Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Zurita-Gotor, M., Bławzdziewicz, J. & Wajnryb, E. 2012 Layering instability in a confined suspension flow. Phys. Rev. Lett. 108 (6), 068301.CrossRefGoogle Scholar

Krüger et al. supplementary movie

Visualisation of two exemplary simulations (Re = 50, Ca = 0.003 and Re = 333, Ca = 0.3) in quasi-steady state. The movie shows the 3D capsule configurations and a 2D slice of the lateral (in direction of the walls) velocity component in colour coding as function of time. The scaling of the velocity is identical for both simulations. In particular one can see that the lateral velocity activity for Re = 333 is much smaller than for Re = 50.

Download Krüger et al. supplementary movie(Video)
Video 9 MB
64
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Interplay of inertia and deformability on rheological properties of a suspension of capsules
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Interplay of inertia and deformability on rheological properties of a suspension of capsules
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Interplay of inertia and deformability on rheological properties of a suspension of capsules
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *