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 in 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 in 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.