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Dynamics of a large population of red blood cells under shear flow

  • C. Minetti (a1), V. Audemar (a2), T. Podgorski (a2) and G. Coupier (a2)


An exhaustive description of the dynamics under shear flow of a large number of red blood cells in a dilute regime is proposed, which highlights and takes into account the dispersion in cell properties within a given blood sample. Physiological suspending fluid viscosity is considered, a configuration surprisingly seldom considered in experimental studies, as well as a more viscous fluid that is a reference in the literature. Stable and unstable flipping motions well described by Jeffery orbits or modified Jeffery orbits are identified, as well as transitions to and from tank-treading motion in the more viscous suspending fluid case. Hysteresis loops upon shear rate increase or decrease are highlighted for the transitions between unstable and stable orbits as well as for the transition between flipping and tank-treading. We identify which of the characteristic parameters of motion and of the transition thresholds depend on flow stress only or also on suspending fluid viscosity.


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Abkarian, M., Faivre, M. & Viallat, A. 2007 Swinging of red blood cells under shear flow. Phys. Rev. Lett. 98, 188302.
Abkarian, M. & Viallat, A. 2005 Dynamics of vesicles in a wall-bounded shear flow. Biophys. J. 89, 10551066.
Anczurowski, E. & Mason, S. G. 1967 The kinetics of flowing dispersions. III. Equilibrium orientations of rods and discs (experimental). J. Colloid Interface Sci. 23, 533546.
Bagchi, P. & Kalluri, R. M. 2009 Dynamics of nonspherical capsules in shear flow. Phys. Rev. E 80, 016307.
Barthès-Biesel, D. 2016 Motion and deformation of elastic capsules and vesicles in flow. Annu. Rev. Fluid Mech. 48 (1), 2552.
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.
Betz, T., Lenz, M., Joanny, J.-F. & Sykes, C. 2009 Atp-dependent mechanics of red blood cells. Proc. Natl Acad. Sci. USA 106, 1532115325.
Biben, T., Farutin, A. & Misbah, C. 2011 Three-dimensional vesicles under shear flow: numerical study of dynamics and phase diagram. Phys. Rev. E 83, 031921.
Bitbol, M. 1986 Red blood cell orientation in orbit c = 0. Biophys. J. 49, 10551068.
Brust, M., Schaefer, C., Doerr, R., Pan, L., Garcia, M., Arratia, P. E. & Wagner, C. 2013 Rheology of human blood plasma: viscoelastic versus newtonian behavior. Phys. Rev. Lett. 110, 078305.
Callens, N., Minetti, C., Coupier, G., Mader, M.-A., Dubois, F., Misbah, C. & Podgorski, T. 2008 Hydrodynamic lift of vesicles under shear flow in microgravity. Europhys. Lett. 83, 24002.
Canham, P. B. & Burton, A. C. 1968 Distribution of size and shape in populations of normal human red cells. Circ. Res. 22, 405422.
Chien, S. 1970 Shear dependence of effective cell volume as a determinant of blood viscosity. Science 168, 977979.
Chien, S. 1987 Red cell deformability and its relevance to blood flow. Annu. Rev. Phys. 49, 177192.
Cordasco, D. & Bagchi, P. 2013 Orbital drift of capsules and red blood cells in shear flow. Phys. Fluids 25, 091902.
Cordasco, D. & Bagchi, P. 2014 Intermittency and synchronized motion of red blood cell dynamics in shear flow. J. Fluid Mech. 759, 472488.
Cordasco, D., Yazdani, A. & Bagchi, P. 2014 Comparison of erythrocyte dynamics in shear flow under different stress-free configurations. Phys. Fluids 26, 041902.
Coupier, G., Kaoui, B., Podgorski, T. & Misbah, C. 2008 Noninertial lateral migration of vesicles in bounded Poiseuille flow. Phys. Fluids 20, 111702.
Danker, G., Biben, T., Podgorski, T., Verdier, C. & Misbah, C. 2007 Dynamics and rheology of a dilute suspension of vesicles: higher-order theory. Phys. Rev. E 76, 041905.
Deschamps, J., Kantsler, V. & Steinberg, V. 2009 Phase diagram of single vesicle dynamical states in shear flow. Phys. Rev. Lett. 102, 118105.
Dobbe, J. G. G., Hardeman, M. R., Streekstra, G. J., Strackee, J., Ince, C. & Grimbergen, C. A. 2002a Analyzing red blood cell-deformability distributions. Blood Cells 28, 373384.
Dobbe, J. G. G., Streekstra, G. J., Hardeman, M. R., Ince, C. & Grimbergen, C. A. 2002b Measurement of the distribution of red blood cell deformability using an automated rheoscope. Cytometry 50, 313325.
Dupire, J., Abkarian, M. & Viallat, A. 2015 A simple model to understand the effect of membrane shear elasticity and stress-free shape on the motion of red blood cells in shear flow. Soft Matt. 11, 83728382.
Dupire, J., Socol, M. & Viallat, A. 2012 Full dynamics of a red blood cell in shear flow. Proc. Natl Acad. Sci. USA 109, 2080820813.
Dupont, C., Delahaye, F., Barthès-Biesel, D. & Salsac, A.-V. 2016 Stable equilibrium configurations of an oblate capsule in shear flow. J. Fluid Mech. 791, 738757.
Dupont, C., Salsac, A.-V. & Barthès-Biesel, D. 2013 Off-plane motion of a prolate capsule in shear flow. J. Fluid Mech. 721, 180198.
Evans, J., Gratzer, W., Mohandas, N., Parker, K. & Sleep, J. 2008 Fluctuations of the red blood cell membrane: relation to mechanical properties and lack of atp dependence. Biophys. J. 94, 41344144.
Farutin, A., Aouane, O. & Misbah, C. 2012 Vesicle dynamics under weak flows: application to large excess area. Phys. Rev. E 85, 061922.
Farutin, A., Biben, T. & Misbah, C. 2010 Analytical progress in the theory of vesicles under linear flow. Phys. Rev. E 81, 061904.
Farutin, A. & Misbah, C. 2012 Squaring, parity breaking, and s tumbling of vesicles under shear flow. Phys. Rev. Lett. 109, 248106.
Fedosov, D. A., Pan, W., Caswell, B., Gompper, G. & Karniadakis, G. E. 2011 Predicting human blood viscosity in silico. Proc. Natl Acad. Sci. USA 108, 1177211777.
Fischer, T. M. & Korzeniewski, R. 2013 Threshold shear stress for the transition between tumbling and tank-treading of red blood cells in shear flow: dependence on the viscosity of the suspending medium. J. Fluid Mech. 736, 351365.
Fischer, T. M. 2007 Tank-tread frequency of the red cell membrane: dependence on the viscosity of the suspending medium. Biophys. J. 93, 25532561.
Fischer, T. M., Stöhr-Liesen, M. & Schmidt-Schönbein, H. 1978 The red cell as a fluid droplet: tank tread-like motion of the human erythrocyte membrane in shear flow. Science 202, 894896.
Fischer, T. M., Haest, C. W., Stöhr-Liesen, M., Schmid-Schönbein, H. & Skalak, R. 1981 The stress-free shape of the red blood cell membrane. Biophys. J. 34, 409422.
Foessel, E., Walter, J., Salsac, A.-V. & Barthès-Biesel, D. 2011 Influence of internal viscosity on the large deformation and buckling of a spherical capsule in a simple shear flow. J. Fluid Mech. 672, 477486.
Forsyth, A. M., Wan, J., Owrutsky, P. D., Abkarian, M. & Stone, H. A. 2011 Multiscale approach to link red blood cell dynamics, shear viscosity, and ATP release. Proc. Natl Acad. Sci. USA 108, 1098610991.
Fung, Y. C. 1993 Biomechanics: Mechanical Properties of Living Tissues. Springer.
Goldsmith, H. L. & Marlow, J. 1972 Flow behaviour of erythrocytes. I. rotation and deformation in dilute suspensions. Proc. R. Soc. Lond. B 182, 351384.
Grandchamp, X., Coupier, G., Srivastav, A., Minetti, C. & Podgorski, T. 2013 Lift and down-gradient shear-induced diffusion in red blood cell suspensions. Phys. Rev. Lett. 110, 108101.
Grau, M., Pauly, S., Ali, J., Walpurgis, K., Thevis, M., Bloch, W. & Suhr, F. 2013 RBC-NOS-dependent S-nitrosylation of cytoskeletal proteins improves RBC deformability. PLoS ONE 8, 110.
de Haas, K. H., Blom, C., van den Ende, D., Duits, M. H. G. & Mellema, J. 1997 Deformation of giant lipid bilayer vesicles in shear flow. Phys. Rev. E 56, 7132.
Hénon, S., Lenormand, G., Richert, A. & Gallet, F. 1999 A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers. Biophys. J. 76, 11451151.
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161179.
Kantsler, V., Segre, E. & Steinberg, V. 2008 Dynamics of interacting vesicles and rheology of vesicle suspension in shear flow. Europhys. Lett. 82, 58005.
Kantsler, V. & Steinberg, V. 2005 Orientation and dynamics of a vesicle in tank-treading motion in shear flow. Phys. Rev. Lett. 95, 258101.
Kantsler, V. & Steinberg, V. 2006 Transition to tumbling and two regimes of tumbling motion of a vesicle in shear flow. Phys. Rev. Lett. 96, 036001.
Keller, J. R. & Skalak, R. 1982 Motion of a tank-treading ellipsoidal particle in a shear flow. J. Fluid Mech. 120, 2747.
Kessler, S., Finken, R. & Seifert, U. 2009 Elastic capsules in shear flow: analytical solutions for constant and time-dependent shear rates. Eur. Phys. J. E 29, 399413.
Laadhari, A., Saramito, P. & Misbah, C. 2012 Vesicle tumbling inhibited by inertia. Phys. Fluids 24, 031901.
Lac, E. & Barthès-Biesel, D. 2005 Deformation of a capsule in simple shear flow: effect of membrane prestress. Phys. Fluids 17, 072105.
Lanotte, L., Mauer, J., Mendez, S., Fedosov, D. A., Fromental, J.-M., Claveria, V., Nicoud, F., Gompper, G. & Abkarian, M. 2016 Red cells dynamic morphologies govern blood shear thinning under microcirculatory flow conditions. Proc. Natl Acad. Sci. USA 113, 1328913294.
Lebedev, V. V., Turitsyn, K. S. & Vergeles, S. S. 2007 Dynamics of nearly spherical vesicles in an external flow. Phys. Rev. Lett. 99, 218101.
Levant, M. & Steinberg, V. 2016 Intermediate regime and a phase diagram of red blood cell dynamics in a linear flow. Phys. Rev. E 94, 062412.
Lim, H. W. G., Wortis, M. & Mukhopadhyay, R. 2002 Stomatocyte–discocyte–echinocyte sequence of the human red blood cell: evidence for the bilayer couple hypothesis from membrane mechanics. Proc. Natl Acad. Sci. USA 99, 1676616769.
Linderkamp, O. & Meiselman, H. J. 1982 Geometric, osmotic, and membrane mechanical properties of density-separated human red cells. Blood 59, 11211127.
Linderkamp, O., Wu, P. Y. K. & Meiselman, H. J. 1983 Geometry of neonatal and adult red blood cells. Ped. Res. 17, 250253.
Mader, M.-A., Ez-Zahraouy, H., Misbah, C. & Podgorski, T. 2007 On coupling between the orientation and shape of a vesicle under shear flow. Eur. Phys. J. E 22, 275.
Mader, M.-A., Vitkova, V., Abkarian, M., Viallat, A. & Podgorski, T. 2006 Dynamics of viscous vesicles in shear flow. Eur. Phys. J. E 19, 389.
Mauer, J., Mendez, S., Lanotte, L., Nicoud, F., Abkarian, M., Gompper, G. & Fedosov, D. A. 2018 Flow-induced transitions of red blood cell shapes under shear. Phys. Rev. Lett. 121, 118103.
Mendez, S. & Abkarian, M. 2018 In-plane elasticity controls the full dynamics of red blood cells in shear flow. Phys. Rev. Fluids 3, 101101.
Miccio, L., Memmolo, P., Merola, F., Netti, P. A. & Ferraro, P. 2015 Red blood cell as an adaptive optofluidic microlens. Nat. Comm. 6, 6502.
Mills, J. P., Qie, L., Dao, M., Lim, C. T. & Suresh, S. 2004 Nonlinear elastic and viscoelastic deformation of the human red blood cell with optical tweezers. Mol. Cell. Biomech. 1, 169180.
Minetti, C., Podgorski, T., Coupier, G. & Dubois, F. 2014 Fully automated digital holographic processing for monitoring the dynamics of a vesicle suspension under shear flow. Biomed. Opt. Expr. 5, 15541568.
Minetti, C., Vitkova, V., Dubois, F. & Bivas, I. 2016 Digital holographic microscopy as a tool to study the thermal shape fluctuations of lipid vesicles. Opt. Lett. 41, 18331836.
Misbah, C. 2006 Vacillating breathing and tumbling of vesicles under shear flow. Phys. Rev. Lett. 96, 028104.
Morris, D. R. & Williams, A. R. 1979 The effects of suspending medium viscosity on erythrocyte deformation and haemolysis in vitro. Biochim. Biophys. Acta 550, 288296.
Noguchi, H. & Gompper, G. 2005a Dynamics of fluid vesicles in shear flow: effect of membrane viscosity and thermal fluctuations. Phys. Rev. E 72, 011901.
Noguchi, H. & Gompper, G. 2005b Vesicle dynamics in shear and capillary flows. J. Phys. Cond. Matter 17, S3439.
Noguchi, H. & Gompper, G. 2007 Swinging and tumbling of fluid vesicles in shear flow. Phys. Rev. Lett. 98, 128103.
Olla, P. 1997 The lift on a tank-treading ellipsoidal cell in a shear flow. J. Phys. II France 7, 15331540.
Peng, Z., Mashayekh, A. & Zhu, Q. 2014 Erythrocyte responses in low-shear-rate flows: effects of non-biconcave stress-free state in the cytoskeleton. J. Fluid Mech. 742, 96118.
Pfafferott, C., Nash, G. & Meiselman, H. J. 1985 Red blood cell deformation in shear flow. Effects of internal and external phase viscosity and of in vivo aging. Biophys. J. 47, 695704.
Prado, G., Farutin, A., Misbah, C. & Bureau, L. 2015 Viscoelastic transient of confined red blood cells. Biophys. J. 108, 21262136.
Pries, A., Neuhaus, N. & Gaehtgens, P. 1992 Blood viscosity in tube flow: dependence on diameter and hematocrit. Am. J. Phys. 20, H1770H1778.
Ramanujan, S. & Pozrikidis, C. 1998 Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities. J. Fluid Mech. 361, 117143.
Rioual, F., Biben, T. & Misbah, C. 2004 Analytical analysis of a vesicle tumbling under a shear flow. Phys. Rev. E 69, 061914.
Rizzo, A., Corsetto, P. G., Montorfano, M. S., Zava, S., Tavella, S., Cancedda, R. & Berra, B. 2012 Effects of long-term space flight on erythrocytes and oxidative stress of rodents. PLoS ONE 7, e3261.
Rodak, B. F., Fritsma, G. A. & Doig, K. 2007 Hematology: Clinical Principles and Applications. Elsevier.
Roman, S., Lorthois, S., Duru, P. & Risso, F. 2012 Velocimetry of red blood cells in microvessels by the dual-slit method: effect of velocity gradients. Microvasc. Res. 84, 249261.
Roman, S., Merlo, A., Duru, P., Risso, F. & Lorthois, S. 2016 Going beyond 20 μm-sized channels for studying red blood cell phase separation in microfluidic bifurcations. Biomicrofluidics 10, 034103.
Ross, P. D. & Minton, A. P. 1977 Hard quasispherical model for the viscosity of hemoglobin solutions. Biochem. Biophys. Res. Commun. 76, 971976.
Shen, Z., Coupier, G., Kaoui, B., Polack, B., Harting, J., Misbah, C. & Podgorski, T. 2016 Inversion of hematocrit partition at microfluidic bifurcations. Microvasc. Res. 105, 4046.
Simmonds, M. J., Detterich, J. A. & Connes, P. 2014 Nitric oxide, vasodilation and the red blood cell. Biorheology 51, 121134.
Sinha, K. & Graham, M. D. 2015 Dynamics of a single red blood cell in simple shear flow. Phys. Rev. E 92, 042710.
Skotheim, J. M. & Secomb, T. W. 2007 Red blood cells and other nonspherical capsules in shear flow: oscillatory dynamics and the tank-treading-to-tumbling transition. Phys. Rev. Lett. 98, 078301.
Svelc, T. & Svetina, S. 2012 Stress-free state of the red blood cell membrane and the deformation of its skeleton. Cell. Mol. Biol. Lett. 17, 217227.
Vitkova, V., Coupier, G., Mader, M.-A., Kaoui, B., Misbah, C. & Podgorski, T. 2009 Tumbling of viscous vesicles in a linear shear field near a wall. J. Optoelectron. Adv. M. 11, 12181221.
Vitkova, V., Mader, M.-A., Polack, B., Misbah, C. & Podgorski, T. 2008 Micro-macro link in rheology of erythrocyte and vesicle suspensions. Biophys. J. 95, 3335.
Walter, J., Salsac, A.-V. & Barthès-Biesel, D. 2011 Ellipsoidal capsules in simple shear flow: prolate versus oblate initial shapes. J. Fluid Mech. 676, 318347.
Yazdani, A. Z. K. & Bagchi, P. 2011 Phase diagram and breathing dynamics of a single red blood cell and a biconcave capsule in dilute shear flow. Phys. Rev. E 84, 026314.
Zabusky, N. J., Segre, E., Deschamps, J., Kantsler, V. & Steinberg, V. 2011 Dynamics of vesicles in shear and rotational flows: modal dynamics and phase diagram. Phys. Fluids 23, 041905.
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Dynamics of a large population of red blood cells under shear flow

  • C. Minetti (a1), V. Audemar (a2), T. Podgorski (a2) and G. Coupier (a2)


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