The behavior of closed inextensible membranes in linear and quadratic shear flows

The dynamics of a spheroidal vesicle, bounded by an inextensible membrane, is analyzed as a function of the enclosed fluid viscosity, and of the membrane mechanical properties. The two situations in which a bending rigidity and a shear elasticity are the potential energy source in the membrane have been compared, and the stability properties of quasi-spherical vesicle shapes discussed. The transition from tank-treading to flipping motion in an external shear flow, has been studied as a function of the vesicle internal viscosity and of the strength of the shear quadratic component. The transverse lift strength has been calculated in both cases of a tank-treading and of a flipping motion regime.