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, ̇ \.γ. These observations disclose the existence of a viscous lift force, Fₗ, depending on the viscosity η 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: Fₗ0ex0ex=0ex0exη ̇ \.γ(R³/h)f(1-v). This relation is valid for vesicles both close to and farther from the substrate.