DYNAMICS AND RHEOLOGY OF HIGHLY DEFLATED VESICLES

We study the dynamics and rheology of a single two-dimensional vesicle embedded in a linear shear flow by means of numerical simulations based on the boundary integral method. The viscosities inside and outside the vesicle are supposed to be identical. We explore the rheology by varying the reduced area, i.e. we consider more and more deflated vesicles. Effective viscosity and normal stress differences are computed and discussed in detail, together with the inclination angle and the lateral membrane velocity (tank-treading velocity). The angle is found, surprisingly, to reach a zero value (flow alignment) at a critical reduced area even in the absence of viscosity contrast. A Fast Multipole Method is presented that enables to run efficiently simulations with a large number of vesicles. This method prevails over the direct summation for a number of mesh points beyond a value of about 10 3 . This offers an interesting perspective for simulation of semi-dilute and concentrated suspensions.

[1]  C. Pozrikidis.  Boundary Integral and Singularity Methods for Linearized Viscous Flow: Index , 1992 .

[2]  L Greengard,et al.  On the Efficient Implementation of the Fast Multipole Algorithm. , 1988 .

[3]  Leslie Greengard,et al.  A fast algorithm for particle simulations , 1987 .

[4]  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.

[5]  C. Pozrikidis,et al.  Interfacial dynamics for Stokes flow , 2001 .

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

[7]  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.

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

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

[10]  Thierry Biben,et al.  An advected-field method for deformable entities under flow , 2002 .

[11]  Ramani Duraiswami,et al.  Fast multipole method for the biharmonic equation in three dimensions , 2006, J. Comput. Phys..

[12]  S. Chien.  Red cell deformability and its relevance to blood flow. , 1987, Annual review of physiology.

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

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

[15]  Emmanuel Maitre,et al.  Applications of level set methods in computational biophysics , 2009, Math. Comput. Model..

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

[17]  A. Einstein.  Eine neue Bestimmung der Moleküldimensionen , 1905 .

[18]  P. S. Ramalho.  Microcirculation and hemorheology. , 1983, Acta medica portuguesa.

[19]  George Biros,et al.  A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D , 2009, J. Comput. Phys..

[20]  W. Zimmermann,et al.  Lateral migration of a two-dimensional vesicle in unbounded Poiseuille flow. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  R. G. Cox,et al.  Particle motions in sheared suspensions XXV. Streamlines around cylinders and spheres , 1968 .

[22]  Albert Einstein,et al.  Berichtigung zu meiner Arbeit: „Eine neue Bestimmung der Moleküldimensionen”︁ [AdP 34, 591 (1911)] , 2005, Annalen der Physik.

[23]  T. Biben,et al.  Optimal lift force on vesicles near a compressible substrate , 2004 .

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

[25]  C. Misbah,et al.  Vesicles in haptotaxis with hydrodynamical dissipation , 2003, The European physical journal. E, Soft matter.

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

[27]  John F. Brady,et al.  The Einstein viscosity correction in n dimensions , 1983 .