Skip to main content Accessibility help

Reorientation of a single red blood cell during sedimentation

  • D. Matsunaga (a1), Y. Imai (a2), C. Wagner (a3) and T. Ishikawa (a1) (a4)


The reorientation phenomenon of a single red blood cell during sedimentation is simulated using the boundary element method. The cell settles downwards due to a density difference between the internal and external fluids, and it changes orientation toward a vertical orientation regardless of Bond number or viscosity ratio. The reorientation phenomenon is explained by a shape asymmetry caused by the gravitational driving force, and the shape asymmetry increases almost linearly with the Bond number. When velocities are normalised by the driving force, settling/drifting velocities are weak functions of the Bond number and the viscosity ratio, while the angular velocity of the reorientation drastically changes with these parameters: the angular velocity is smaller for lower Bond number or higher viscosity ratio. As a consequence, trajectories of the sedimentation are also affected by the angular velocity, and blood cells with slower reorientation travel longer distances in the drifting direction. We also explain the mechanism of the reorientation using an asymmetric dumbbell. From the analysis, we show that the magnitude of the angular velocity is explained by two main factors: the shape asymmetry and the instantaneous orientation angle.


Corresponding author

Email address for correspondence:


Hide All
Baskurt, O., Neu, B. & Meiselman, J. H. 2012 Red Blood Cell Aggregation. CRC Press.
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.
Blake, J. R. 1971 A note on the image system for a stokeslet in a no-slip boundary. Math. Proc. Camb. 70, 303310.
Boedec, G., Jaeger, M. & Leonetti, M. 2012 Settling of a vesicle in the limit of quasispherical shapes. J. Fluid Mech. 690, 227261.
Boedec, G., Jaeger, M. & Leonetti, M. 2013 Sedimentation-induced tether on a settling vesicle. Phys. Rev. E 88, 010702.
Boedec, G., Leonetti, M. & Jaeger, M. 2011 3d vesicle dynamics simulations with a linearly triangulated surface. J. Comput. Phys. 230 (4), 10201034.
Boltz, H.-H. & Kierfeld, J. 2015 Shapes of sedimenting soft elastic capsules in a viscous fluid. Phys. Rev. E 92, 033003.
Brochard, F. & Lennon, J. F. 1975 Frequency spectrum of the flicker phenomenon in erythroctes. J. Phys. (Paris) 36 (11), 10351047.
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.
Canham, P. B., Jay, A. W. L. & Tilsworth, E. 1971 The rate of sedimentation of individual human red blood cells. J. Cell. Physiol. 78 (3), 319331.
Dimitrakopoulos, P. 2012 Analysis of the variation in the determination of the shear modulus of the erythrocyte membrane: effects of the constitutive law and membrane modeling. Phys. Rev. E 85, 041917.
Dupire, J., Socol, M. & Viallat, A. 2012 Full dynamics of a red blood cell in shear flow. Proc. Natl Acad. Sci. USA 109 (51), 2080820813.
Evans, E. & Fung, Y. C. 1972 Improved measurements of the erythrocyte geometry. Microvasc. Res. 4 (4), 335347.
Foessel, É., Walter, J., Salsac, A.-V. & Barthès-Biesel, 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.
Freund, J. B. 2007 Leukocyte margination in a model microvessel. Phys. Fluids 19 (2), 023301.
Gov, N. & Safran, S. A. 2005 Red blood cell shape and fluctuations: cytoskeleton confinement and atp activity. J. Biol. Phys. 31 (3–4), 453464.
Groom, A. C. & Anderson, J. C. 1972 Measurement of the size distribution of human erythrocytes by a sedimentation method. J. Cell. Physiol. 79 (1), 127137.
Guazzelli, E. & Hinch, J. 2011 Fluctuations and instability in sedimentation. Annu. Rev. Fluid Mech. 43 (1), 97116.
Happel, J. & Brenner, H. 1963 Low Reynolds number hydrodynamics with special applications to particulate media. Martinus Nijhoff.
Helfrich, W. 1973 Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. C 28, 693703.
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 (2), 11451151.
Hoffman, J. F. & Inoué, S. 2006 Directly observed reversible shape changes and hemoglobin stratification during centrifugation of human and amphiuma red blood cells. Proc. Natl Acad. Sci. USA 103 (8), 29712976.
Huang, Z. H., Abkarian, M. & Viallat, A. 2011 Sedimentation of vesicles: from pear-like shapes to microtether extrusion. New J. Phys. 13 (3), 035026.
Hwang, W. C. & Waugh, R. E. 1997 Energy of dissociation of lipid bilayer from the membrane skeleton of red blood cells. Biophys. J. 72 (6), 26692678.
Jay, A. W. L. & Canham, P. B. 1972 Sedimentation of single human red blood cells. Differences between normal and glutaraldehyde fixed cells. J. Cell. Physiol. 80 (3), 367372.
Kim, S. & Karrila, J. S. 1991 Microhydrodynamics – Principles and Selected Applications. Dover.
Koh, C. J. & Leal, L. G. 1989 The stability of drop shapes for translation at zero reynolds number through a quiescent fluid. Phys. Fluids A 1 (8), 13091313.
Li, L., Manikantan, H., Saintillan, D. & Spagnolie, S. 2013 The sedimentation of flexible filaments. J. Fluid Mech. 735, 705736.
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 (26), 1676616769.
Matsunaga, D., Imai, Y., Omori, T., Ishikawa, T. & Yamaguchi, T. 2014 A full GPU implementation of a numerical method for simulating capsule suspensions. J. Biomech. Sci. Engng 14, 00039.
Matsunaga, D., Imai, Y., Yamaguchi, T. & Ishikawa, T. 2015 Deformation of a spherical capsule under oscillating shear flow. J. Fluid Mech. 762, 288301.
Matsunaga, D., Imai, Y., Yamaguchi, T. & Ishikawa, T. 2016 Rheology of a dense suspension of spherical capsules under simple shear flow. J. Fluid Mech. 786, 110127.
Meyer, M., Desbrun, M., Schröder, P. & Barr, A. 2003 Discrete differential-geometry operators for triangulated 2-manifolds. In Mathematics and Visualization (ed. Hege, H.-C. & Polthier, K.), pp. 3557. Springer.
Mogami, Y., Ishii, J. & Baba, A. S. 2001 Theoretical and experimental dissection of gravity-dependent mechanical orientation in gravitactic microorganisms. Biol. Bull. 201, 2633.
Nix, S., Imai, Y., Matsunaga, D., Yamaguchi, T. & Ishikawa, T. 2014 Lateral migration of a spherical capsule near a plane wall in stokes flow. Phys. Rev. E 90, 043009.
Omori, T., Ishikawa, T., Imai, Y. & Yamaguchi, T. 2013 Shear-induced diffusion of red blood cells in a semi-dilute suspension. J. Fluid Mech. 724, 154174.
Ou-Yang, Z. & Helfrich, W. 1989 Bending energy of vesicle membranes: general expressions for the first, second, and third variation of the shape energy and applications to spheres and cylinders. Phys. Rev. A 39, 52805288.
Peltomaki, M. & Gompper, G. 2013 Sedimentation of single red blood cells. Soft Matt. 9, 83468358.
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.
Pozrikidis, C. 1990 The instability of a moving viscous drop. J. Fluid Mech. 210, 121.
Pozrikidis, C. 1992a Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.
Pozrikidis, C. 1992b The buoyancy-driven motion of a train of viscous drops within a cylindrical tube. J. Fluid Mech. 237, 627648.
Pozrikidis, C. 1995 Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow. J. Fluid Mech. 297, 123152.
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.
Saintillan, D., Shaqfeh, E. S. G. & Darve, E. 2006 The growth of concentration fluctuations in dilute dispersions of orientable and deformable particles under sedimentation. J. Fluid Mech. 553, 347388.
Sinha, K. & Graham, M. D. 2015 Dynamics of a single red blood cell in simple shear flow. Phys. Rev. E 92, 042710.
Skalak, R., Tozeren, A., Zarda, R. P. & Chien, S. 1973 Strain energy function of red blood cell membranes. Biophys. J. 13 (3), 245264.
Suárez, I. R., Leidy, C., Téllez, G., Gay, G. & Gonzalez-Mancera, A. 2013 Slow sedimentation and deformability of charged lipid vesicles. PLoS ONE 8 (7), e68309.
Sui, Y., Chew, Y. T., Roy, P. & Low, H. T. 2008 A hybrid method to study flow-induced deformation of three-dimensional capsules. J. Comput. Phys. 227 (12), 63516371.
The Japanese Society for Laboratory Hematology 2003 Blood Test Standard, 2nd edn. Ishiyaku (in Japanese).
Tsubota, K., Wada, S. & Liu, H. 2014 Elastic behavior of a red blood cell with the membrane’s nonuniform natural state: equilibrium shape, motion transition under shear flow, and elongation during tank-treading motion. Biomech. Model. Mechan. 13 (4), 735746.
Turlier, H., Fedosov, D. A., Audoly, B., Auth, T., Gov, N. S., Sykes, C., Joanny, J. F., Gompper, G. & Betz, T. 2016 Equilibrium physics breakdown reveals the active nature of red blood cell flickering. Nat. Phys. 12 (5), 513519.
Veerapaneni, S. K., Gueyffier, D., Zorin, D. & Biros, G. 2009 A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D. J. Comput. Phys. 228 (7), 23342353.
Walter, J., Salsac, A.-V., Barthès-Biesel, D. & Le Tallec, P. 2010 Coupling of finite element and boundary integral methods for a capsule in a Stokes flow. Int. J. Numer. Meth. Eng. 83 (7), 829850.
Westergren, A. 1921 Studies of the suspension stability of the blood in pulmonary tuberculosis. Acta Med. Scand. 54 (1), 247282.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Type Description Title

Matsunaga et al. supplementary movie
Sedimentation of a single red blood cell under Bond number Bo=2.5×101 and viscosity ratio (a) λ=1.0 and (b) λ=5.0. The initial orientation angle is Θ0=π/4, and the animation shows up to non-dimensional time (aΔρg)t/μ =300. Note that camera is also settling with the cell.

 Video (234 KB)
234 KB

Reorientation of a single red blood cell during sedimentation

  • D. Matsunaga (a1), Y. Imai (a2), C. Wagner (a3) and T. Ishikawa (a1) (a4)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed