Three-dimensional vesicles under shear flow: numerical study of dynamics and phase diagram.

The study of vesicles under flow, a model system for red blood cells (RBCs), is an essential step in understanding various intricate dynamics exhibited by RBCs in vivo and in vitro. Quantitative three-dimensional analyses of vesicles under flow are presented. The regions of parameters to produce tumbling (TB), tank-treating, vacillating-breathing (VB), and even kayaking (or spinning) modes are determined. New qualitative features are found: (i) a significant widening of the VB mode region in parameter space upon increasing shear rate γ and (ii) a robustness of normalized period of TB and VB with γ. Analytical support is also provided. We make a comparison with existing experimental results. In particular, we find that the phase diagram of the various dynamics depends on three dimensionless control parameters, while a recent experimental work reported that only two are sufficient.

[1]  R. Skalak,et al.  Motion of a tank-treading ellipsoidal particle in a shear flow , 1982, Journal of Fluid Mechanics.

[2]  T. Biben,et al.  Tumbling of vesicles under shear flow within an advected-field approach. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  W. Helfrich.  Elastic Properties of Lipid Bilayers: Theory and Possible Experiments , 1973, Zeitschrift fur Naturforschung. Teil C: Biochemie, Biophysik, Biologie, Virologie.

[4]  M. Abkarian,et al.  Dynamics of viscous vesicles in shear flow , 2006, The European physical journal. E, Soft matter.

[5]  Hiroshi Noguchi,et al.  Dynamics of fluid vesicles in shear flow: effect of membrane viscosity and thermal fluctuations. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  George Em Karniadakis,et al.  A multiscale red blood cell model with accurate mechanics, rheology, and dynamics. , 2010, Biophysical journal.

[7]  Victor Steinberg,et al.  Orientation and dynamics of a vesicle in tank-treading motion in shear flow. , 2005, Physical review letters.

[8]  Chaouqi Misbah,et al.  Dynamics and Similarity Laws for Adhering Vesicles in Haptotaxis , 1999 .

[9]  Kyriacos A. Athanasiou,et al.  Principles of Cell Mechanics for Cartilage Tissue Engineering , 2004, Annals of Biomedical Engineering.

[10]  Udo Seifert,et al.  Configurations of fluid membranes and vesicles , 1997 .

[11]  Chaouqi Misbah,et al.  Vacillating breathing and tumbling of vesicles under shear flow. , 2006, Physical review letters.

[12]  Prosenjit Bagchi,et al.  Dynamics of nonspherical capsules in shear flow. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Alexander Farutin,et al.  Analytical progress in the theory of vesicles under linear flow. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Chaouqi Misbah,et al.  Rheology of a dilute suspension of vesicles. , 2007, Physical review letters.

[15]  Hiroshi Noguchi,et al.  Fluid vesicles with viscous membranes in shear flow. , 2004, Physical review letters.

[16]  G. B. Jeffery.  The motion of ellipsoidal particles immersed in a viscous fluid , 1922 .

[17]  Yaling Liu,et al.  Rheology of red blood cell aggregation by computer simulation , 2006, J. Comput. Phys..

[18]  Hiroshi Noguchi,et al.  Swinging and tumbling of fluid vesicles in shear flow. , 2007, Physical review letters.

[19]  P. Vlahovska,et al.  Dynamics of a viscous vesicle in linear flows. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  H Schmid-Schönbein,et al.  The red cell as a fluid droplet: tank tread-like motion of the human erythrocyte membrane in shear flow. , 1978, Science.

[21]  Michael H.G. Duits,et al.  Deformation of giant lipid bilayer vesicles in a shear flow , 1996 .

[22]  Udo Seifert.  Fluid membranes in hydrodynamic flow fields: Formalism and an application to fluctuating quasispherical vesicles in shear flow , 1999 .

[23]  Magalie Faivre,et al.  Swinging of red blood cells under shear flow. , 2007, Physical review letters.

[24]  M. Dupin,et al.  Modeling the flow of dense suspensions of deformable particles in three dimensions. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Victor Steinberg,et al.  Transition to tumbling and two regimes of tumbling motion of a vesicle in shear flow. , 2006, Physical review letters.

[26]  M. Bitbol.  Red blood cell orientation in orbit C = 0. , 1986, Biophysical journal.

[27]  V Steinberg,et al.  Dynamics of a vesicle in general flow , 2009, Proceedings of the National Academy of Sciences.

[28]  V V Lebedev,et al.  Dynamics of nearly spherical vesicles in an external flow. , 2007, Physical review letters.

[29]  Jingfang Huang,et al.  Krylov deferred correction accelerated method of lines transpose for parabolic problems , 2008, J. Comput. Phys..

[30]  Thomas Podgorski,et al.  Dynamics and rheology of a dilute suspension of vesicles: higher-order theory. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  F. C. Macintosh,et al.  Flow behaviour of erythrocytes - I. Rotation and deformation in dilute suspensions , 1972, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[32]  V. V. Lebedev,et al.  Nearly spherical vesicles in an external flow , 2007, 0705.3543.

[33]  Seifert,et al.  Fluid Vesicles in Shear Flow. , 1996, Physical review letters.

[34]  T W Secomb,et al.  Red blood cells and other nonspherical capsules in shear flow: oscillatory dynamics and the tank-treading-to-tumbling transition. , 2007, Physical review letters.

[35]  H. Ez‐zahraouy,et al.  On coupling between the orientation and the shape of a vesicle under a shear flow , 2007, The European physical journal. E, Soft matter.

[36]  V Steinberg,et al.  Phase diagram of single vesicle dynamical states in shear flow. , 2009, Physical review letters.

[37]  W. Helfrich,et al.  Bending energy of vesicle membranes: General expressions for the first, second, and third variation of the shape energy and applications to spheres and cylinders. , 1989, Physical review. A, General physics.