Tank Treading and Unbinding of Deformable Vesicles in Shear Flow: Determination of the Lift Force

Deformation and tank-treading motion of flaccid vesicles in a linear shear flow close to a wall are quantitatively studied by light microscopy. Velocities of bounded vesicles obey Goldman’s law established for rigid spheres. A progressive tilt and a transition of unbinding of vesicles are evidenced upon increasing the shear rate, $\dot{\gamma }$. These observations disclose the existence of a viscous lift force, $F_l$, depending on the viscosity $\eta$ of the fluid, the radius R of the vesicle, its distance h from the substrate, and a monotonous decreasing function $f(1-v)$ of the reduced volume $v$, in the following manner: $F_l=\eta \dot{\gamma }(R^3/h)f(1-v)$. This relation is valid for vesicles both close to and farther from the substrate.