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Hydrodynamic pairing of soft particles in a confined flow

O. Aouane1,2,3,*, A. Farutin1,2, M. Thiébaud1,2, A. Benyoussef4, C. Wagner3, and C. Misbah1,2

  • 1Université Grenoble Alpes, LIPHY, F-38000, Grenoble, France
  • 2CNRS, LIPHY, F-38000, Grenoble, France
  • 3Experimental Physics, Saarland University, 66123 Saarbrücken, Germany
  • 4LMPHE, URAC 12, Faculté des Sciences, Université Mohammed V- Agdal, Rabat, Morocco

  • *Current address: Forschungszentrum Jülich GmbH, Helmholtz-Institute Erlangen-Nürnberg for Renewable Energy (IEK-11), Dynamics of Complex Fluids and Interfaces, Fürther Straße 248, 90429 Nürnberg, Germany.
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Phys. Rev. Fluids 2, 063102 – Published 30 June, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.063102

Abstract

The mechanism of hydrodynamics-induced pairing of soft particles, namely closed bilayer membranes (vesicles, a model system for red blood cells) and drops, is studied numerically with a special attention paid to the role of the confinement (the particles are within two rigid walls). This study unveils the complexity of the pairing mechanism due to hydrodynamic interactions. We find both for vesicles and for drops that two particles attract each other and form a stable pair at weak confinement if their initial separation is below a certain value. If the initial separation is beyond that distance, the particles repel each other and adopt a longer stable interdistance. This means that for the same confinement we have (at least) two stable branches. To which branch a pair of particles relaxes with time depends only on the initial configuration. An unstable branch is found between these two stable branches. At a critical confinement the stable branch corresponding to the shortest interdistance merges with the unstable branch in the form of a saddle-node bifurcation. At this critical confinement we have a finite jump from a solution corresponding to the continuation of the unbounded case to a solution which is induced by the presence of walls. The results are summarized in a phase diagram, which proves to be of a complex nature. The fact that both vesicles and drops have the same qualitative phase diagram points to the existence of a universal behavior, highlighting the fact that with regard to pairing the details of mechanical properties of the deformable particles are unimportant. This offers an interesting perspective for simple analytical modeling.

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References (51)

  1. R. Skalak and P. I. Branemark, Deformation of red blood cells in capillaries, Science 164, 717 (1969).
  2. P. Gaehtgens and H. Schmid-Schönbein, Mechanisms of dynamic flow adaptation of mammalian erythrocytes, Naturwissenschaften 69, 294 (1982).
  3. G. Tomaiuolo, L. Lanotte, G. Ghigliotti, C. Misbah, and S. Guido, Red blood cell clustering in poiseuille microcapillary flow, Phys. Fluids 24, 051903 (2012).
  4. M. Brust, O. Aouane, M. Thiébaud, D. Flormann, C. Verdier, L. Kaestner, M. W. Laschke, H. Selmi, A. Benyoussef, T. Podgorski, G. Coupier, C. Misbah, and C. Wagner, The plasma protein fibrinogen stabilizes clusters of red blood cells in microcapillary flows, Sci. Rep. 4, 4348 (2014).
  5. H. Wang and R. Skalak, Viscous flow in a cylindrical tube containing a line of spherical particles, J. Fluid Mech. 38, 75 (1969).
  6. S. Leichtberg, R. Pfeffer, and S. Weinbaum, Stokes flow past finite coaxial clusters of spheres in a circular cylinder, Int. J. Multiphase Flow 3, 147 (1976).
  7. B. Cui, H. Diamant, and B. Lin, Screened Hydrodynamic Interaction in a Narrow Channel, Phys. Rev. Lett. 89, 188302 (2002).
  8. B. Cui, H. Diamant, B. Lin, and S. A. Rice, Anomalous Hydrodynamic Interaction in a Quasi-Two-Dimensional Suspension, Phys. Rev. Lett. 92, 258301 (2004).
  9. H. Diamant, B. Cui, B. Lin, and S. A. Rice, Hydrodynamic interaction in quasi-two-dimensional suspensions, J. Phys.: Condens. Matter 17, S2787 (2005).
  10. T. Beatus, T. Tlusty, and R. Bar-Ziv, Phonons in a one-dimensional microfluidic crystal, Nat. Phys. 2, 743 (2006).
  11. T. Beatus, R. Bar-Ziv, and T. Tlusty, Anomalous Microfluidic Phonons Induced by the Interplay of Hydrodynamic Screening and Incompressibility, Phys. Rev. Lett. 99, 124502 (2007).
  12. I. Shani, T. Beatus, R. H. Bar-Ziv, and T. Tlusty, Long-range orientational order in two-dimensional microfluidic dipoles, Nat. Phys. 10, 140 (2014).
  13. P. J. A. Janssen, M. D. Baron, P. D. Anderson, J. Blawzdziewicz, M. Loewenberg, and E. Wajnryb, Collective dynamics of confined rigid spheres and deformable drops, Soft Matter 8, 7495 (2012).
  14. G. Breyiannis and C. Pozrikidis, Simple shear flow of suspensions of elastic capsules, Theor. Comput. Fluid Dyn. 13, 327 (2000).
  15. Y. Liu and W. K. Liu, Rheology of red blood cell aggregation by computer simulation, J. Comput. Phys. 220, 139 (2006).
  16. T. W. Secomb, B. Styp-Rekowska, and A. R. Pries, Two-dimensional simulation of red blood cell deformation and lateral migration in microvessels, Ann. Biomed. Eng. 35, 755 (2007).
  17. M. M. Dupin, I. Halliday, C. M. Care, L. Alboul, and L. L. Munn, Modeling the flow of dense suspensions of deformable particles in three dimensions, Phys. Rev. E 75, 066707 (2007).
  18. P. M. Vlahovska, T. Podgorski, and C. Misbah, Vesicles and red blood cells in flow: From individual dynamics to rheology, Comptes Rendus Phys. 10, 775 (2009).
  19. S. K. Doddi and P. Bagchi, Three-dimensional computational modeling of multiple deformable cells flowing in microvessels, Phys. Rev. E 79, 046318 (2009).
  20. J. L. McWhirter, H. Noguchi, and G. Gompper, Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries, Proc. Natl. Acad. Sci. USA 106, 6039 (2009).
  21. S. K. Veerapaneni, D. Gueyffier, D. Zorin, and G. Biros, A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D, J. Comput. Phys. 228, 2334 (2009).
  22. H. Zhao, A. H. G. Isfahani, L. N. Olson, and J. B. Freund, A spectral boundary integral method for flowing blood cells, J. Comput. Phys. 229, 3726 (2010).
  23. H. Zhao and E. S. G. Shaqfeh, Shear-induced platelet margination in a microchannel, Phys. Rev. E 83, 061924 (2011).
  24. J. L. McWhirter, H. Noguchi, and G. Gompper, Deformation and clustering of red blood cells in microcapillary flows, Soft Matter 7, 10967 (2011).
  25. J. B. Freund and M. M. Orescanin, Cellular flow in a small blood vessel, J. Fluid Mech. 671, 466 (2011).
  26. T. Krüger, F. Varnik, and D. Raabe, Particle stress in suspensions of soft objects, Phil. Trans. R. Soc. Lond. A 369, 2414 (2011).
  27. D. A. Fedosov, W. Pan, B. Caswell, G. Gompper, and G. E. Karniadakis, Predicting human blood viscosity in silico, Proc. Natl. Acad. Sci. USA 108, 11772 (2011).
  28. D. Alizadehrad, Y. Imai, K. Nakaaki, T. Ishikawa, and T. Yamaguchi, Quantification of red blood cell deformation at high-hematocrit blood flow in microvessels, J. Biomechanics 45, 2684 (2012).
  29. D. A. Reasor, J. R. Clausen, and C. K. Aidun, Coupling the lattice-Boltzmann and spectrin-link methods for the direct numerical simulation of cellular blood flow, Intl. J. Numer. Methods Fluids 68, 767 (2012).
  30. H. Zhao and E. S. G. Shaqfeh, The dynamics of a non-dilute vesicle suspension in a simple shear flow,J. Fluid Mech. 725, 709 (2013).
  31. M. Thiébaud and C. Misbah, Rheology of a vesicle suspension with finite concentration: A numerical study, Phys. Rev. E 88, 062707 (2013).
  32. J. B. Freund, Numerical simulation of flowing blood cells, Annu. Rev. Fluid Mech. 46, 67 (2014).
  33. D. Matsunaga, Y. Imai, T. Yamaguchi, and T. Ishikawa, Rheology of a dense suspension of spherical capsules under simple shear flow, J. Fluid Mech. 786, 110 (2015).
  34. S. H. Bryngelson and J. B. Freund, Capsule-train stability, Phys. Rev. Fluids 1, 033201 (2016).
  35. G. Ghigliotti, H. Selmi, L. E. Asmi, and C. Misbah, Why and how does collective red blood cells motion occur in the blood microcirculation? Phys. Fluids 24, 101901 (2012).
  36. C. Misbah, Vacillating Breathing and Tumbling of Vesicles Under Shear Flow, Phys. Rev. Lett. 96, 028104 (2006).
  37. H. Noguchi and G. Gompper, Swinging and Tumbling of Fluid Vesicles in Shear Flow, Phys. Rev. Lett. 98, 128103 (2007).
  38. A. Farutin, O. Aouane, and C. Misbah, Vesicle dynamics under weak flows: Application to large excess area, Phys. Rev. E 85, 061922 (2012).
  39. O. Aouane, M. Thiébaud, A. Benyoussef, C. Wagner, and C. Misbah, Vesicle dynamics in a confined poiseuille flow: From steady state to chaos, Phys. Rev. E 90, 033011 (2014).
  40. S. Ramanujan and C. Pozrikidis, Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: Large deformations and the effect of fluid viscosities, J. Fluid Mech. 361, 117 (1998).
  41. E. Lac and D. Barthès-Biesel, Deformation of a capsule in simple shear flow: Effect of membrane prestress, Phys. Fluids 17, 072105 (2005).
  42. S. Kessler, R. Finken, and U. Seifert, Swinging and tumbling of elastic capsules in shear flow, J. Fluid Mech. 605, 207 (2008).
  43. W. Helfrich, Elastic properties of lipid bilayers: Theory and possible experiments, Z. Naturforsch. C 28, 693 (1973).
  44. B. Kaoui, G. H. Ristow, I. Cantat, C. Misbah, and W. Zimmermann, Lateral migration of a two-dimensional vesicle in unbounded Poiseuille flow, Phys. Rev. E 77, 021903 (2008).
  45. P. B. Canham, The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell, J. Theor. Biol. 26, 61 (1970).
  46. C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow, Cambridge Texts in Applied Mathematics (Cambridge University Press, Cambridge, 1992).
  47. B. Kaoui, N. Tahiri, T. Biben, H. Ez-Zahraouy, A. Benyoussef, G. Biros, and C. Misbah, Complexity of vesicle microcirculation, Phys. Rev. E 84, 041906 (2011).
  48. R. M. Hochmuth, P. R. Worthy, and E. A. Evans, Red cell extensional recovery and the determination of membrane viscosity, Biophys. J. 26, 101 (1979).
  49. G. Tomaiuolo and S. Guido, Start-up shape dynamics of red blood cells in microcapillary flow, Microvasc. Res. 82, 35 (2011).
  50. G. Prado, A. Farutin, C. Misbah, and L. Bureau, Viscoelastic transient of confined red blood cells, Biophys. J. 108, 2126 (2015).
  51. G. Ghigliotti, T. Biben, and C. Misbah, Rheology of a dilute two-dimensional suspension of vesicles, J. Fluid Mech. 653, 489 (2010).

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Phys. Rev. Fluids 2, 063102– Published 30 June, 2017
  • Received 22 June 2016

©2017 American Physical Society

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