Fluid Vesicles and Red Blood Cells in Capillary Flow

5 Fluid Vesicles and Red Blood Cells in Capillary Flow 

The deformation of single RBCs and single fluid vesicles in capillary flows were studied theoretically by lubrication theories [214-216] and boundary-integral methods [217-219]. In most of these studies, axisymmetric shapes which are coaxial with the center of the capillary were assumed and cylindrical coordinates were employed. In order to investigate non-axisynunetric shapes as well as flow-induced shape transformations, a fully three-dimensional simulation approach is required. 

We focus here on the behavior of single red blood cells in cscpASaxy flow [187], as described by a triangulated surface model for the membrane (compare Sect. 11.2.4) immersed in a MFC solvent (see Sect. 11.3). The radius of the capillary. Reap, is taken to be slightly larger than the mean vesicle or RBC radius, Rq = where 

S is the membrane area. Snapshots of vesicle and RBC shapes in flow are shown in Fig. 32 for a reduced volume of V = 0.59, where the vesicle shape at rest is a discocyte. For sufficiently small flow velocities, the discocyte shape is retained. However, the discocyte is found not in a coaxial orientation instead the shortest eigenvalue of the gyration tensor is oriented perpendicular to the cybnder axis [187]. Since two opposite sides of the rim of the discocyte are closer to the wall where the flow velocity is small, the rotational symmetry is slightly disturbed and the top view looks somewhat triangular, see Fig. 32a. With increasing flow velocity, a shape transition to an axisymmetric shape occurs. In the case of fluid vesicles this is a 

The fundamental difference between the flow behaviors of fluid vesicles and red blood cells at high flow velocities is due to the shear elasticity of the spectrin network. Its main effect for jiRq/ k 1 is to suppress the discocyte-to-prolate transition, because the prolate shape would acquire an elastic energy of order fiR. In comparison, the shear stress in the parachute shape is much smaller. 

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H. Noguchi and G. Gompper, Shape transitions of fluid vesicles and red blood cells in capillary flows, Proc. Natl. Acad. Sci. USA 102, 14159 (2005). 

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