The role of tank-treading motions in the transverse migration of a spheroidal vesicle in a shear flow

The behaviour of a spheroidal vesicle, in a plane shear Bow bounded from one side by a wall, is analysed when the distance from the wall is much larger than the spheroid radius. It is found that tank-treading motions produce a transverse drift away from the wall, proportional to the spheroid eccentricity and the inverse square of the distance from the wall. This drift is independent of inertia, and is completely determined by the characteristics of the vesicle membrane. The relative strength of the contribution to drift from tank-treading motions and from the presence of inertial corrections, is discussed.