Vesicle behavior under unbounded axial Poiseuille flow is studied analytically. Our study reveals subtle features of the dynamics. It is established that there exists a stable off-centerline steady-state solution for low enough flow strength. This solution appears as a symmetry-breaking bifurcation upon lowering the flow strength and includes slipper shapes, which are characteristic of red blood cells in the microvasculature. A stable axisymmetric solution exists for any flow strength provided the excess area is small enough. It is shown that the mechanism of the symmetry breaking depends on the geometry of the flow: The bifurcation is subcritical in axial Poiseuille flow and supercritical in planar flow.
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