Vesicle tumbling inhibited by inertia

Vesicles under flow constitute a model system for the study of red blood cells (RBCs) dynamics and blood rheology. In the blood circulatory system the Reynolds number (at the scale of the RBC) is not always small enough for the Stokes limit to be valid. We develop a numerical method in two dimensions based on the level set approach and solve the fluid/membrane coupling by using an adaptive finite element technique. We find that a Reynolds number of order one can destroy completely the vesicle tumbling motion obtained in the Stokes regime. We analyze in details this phenomenon and discuss some of the far reaching consequences. We suggest experimental tests on vesicles.

[1]  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.

[2]  Dominique Barthès-Biesel,et al.  Capsule motion in flow: Deformation and membrane buckling , 2009 .

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

[4]  T Biben,et al.  Analytical analysis of a vesicle tumbling under a shear flow. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Isabelle Cantat,et al.  Lift Force and Dynamical Unbinding of Adhering Vesicles under Shear Flow , 1999 .

[6]  Aymen Laadhari,et al.  Modélisation numérique de la dynamique des globules rouges par la méthode des fonctions de niveau , 2011 .

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

[8]  Petia M. Vlahovska,et al.  Vesicles in Poiseuille flow. , 2008, Physical review letters.

[9]  Hiroshi Noguchi,et al.  Dynamical regimes and hydrodynamic lift of viscous vesicles under shear. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  G. Biros,et al.  Analytical and numerical solutions for shapes of quiescent two-dimensional vesicles , 2009 .

[11]  Udo Seifert.  Hydrodynamic lift on bound vesicles , 1999 .

[12]  T. Biben,et al.  Steady to unsteady dynamics of a vesicle in a flow. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[15]  Petia M. Vlahovska,et al.  Vesicles and red blood cells in flow: From individual dynamics to rheology , 2009 .

[16]  David Salac,et al.  A level set projection model of lipid vesicles in general flows , 2011, J. Comput. Phys..