The Lift on a Tank-Treading Ellipsoidal Cell in a Shear Flow

The lift on a strongly non-spherical vesicle in a bounded shear flow, is studied in the case the membrane moves with a velocity, which is a linear function of the coordinates. The magnitude of the induced drift is calculated as a function of the axes lengths, of the distance from the wall, and of the ratio of the cell to the solvent viscosity. It appears that the main mechanism for lift, in the presence of tank-treading motions, is the fixed orientation of the vesicle with respect to the flow. Tank-treading vesicles in suspensions, flowing through narrow gaps under small Reynolds number conditions: $Re=Lv/\nu < 1$ (with $L$ the gap width, v the flow velocity and $\nu$ the viscosity) migrate away from the walls, with a velocity that is $\O(Re^{-1})$ larger than predicted by inertia.