Abstract
We study the shape of vesicles being dragged through their viscous environment by a homogeneous force, using a numerical method to treat Stokes hydrodynamics around the vesicle. Due to the mobile boundaries, the uniqueness theorem does not apply here, and we have obtained a catalog of the various stationary solutions. Vesicles can be bean-like and pear-like, the latter being unstable with respect to perturbations breaking their axisymmetry. Oblate ellipsoids are stabilised by a sufficiently strong drag. A 2d flow of lipids in the membrane is induced for non-axisymmetric shapes. As the drag force becomes too strong, no more stationary solutions exist. For very deflated vesicles, an "S"-shaped solution appears, coupling rotational and translational motion.