Understanding why red blood cells (RBCs) move with an asymmetric shape (slipperlike shape) in small blood vessels is a long-standing puzzle in blood circulatory research. By considering a vesicle (a model system for RBCs), we discovered that the slipper shape results from a loss in stability of the symmetric shape. It is shown that the adoption of a slipper shape causes a significant decrease in the velocity difference between the cell and the imposed flow, thus providing higher flow efficiency for RBCs. Higher membrane rigidity leads to a dramatic change in the slipper morphology, thus offering a potential diagnostic tool for cell pathologies.

The migration of a suspended vesicle in an unbounded Poiseuille flow is investigated numerically in the low Reynolds number limit. We consider the situation without viscosity contrast between the interior of the vesicle and the exterior. Using the boundary integral method we solve the corresponding hydrodynamic flow equations and track explicitly the vesicle dynamics in two dimensions. We find that the interplay between the nonlinear character of the Poiseuille flow and the vesicle deformation causes a cross-streamline migration of vesicles towards the center of the Poiseuille flow. This is in a marked contrast with a result [L.G. Leal, Ann. Rev. Fluid Mech. 12, 435 (1980)] according to which the droplet moves away from the center (provided there is no viscosity contrast between the internal and the external fluids). The migration velocity is found to increase with the local capillary number (defined by the time scale of the vesicle relaxation towards its equilibrium shape times the local shear rate), but reaches a plateau above a certain value of the capillary number. This plateau value increases with the curvature of the parabolic flow profile. We present scaling laws for the migration velocity.