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

Abstract

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, $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}$. These observations disclose the existence of a viscous lift force, ${F}_{l}$, depending on the viscosity $\ensuremath{\eta}$ of the fluid, the radius R of the vesicle, its distance h from the substrate, and a monotonous decreasing function $f(1\ensuremath{-}v)$ of the reduced volume $v$, in the following manner: ${F}_{l}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\eta}\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}({R}^{3}/h)f(1\ensuremath{-}v)$. This relation is valid for vesicles both close to and farther from the substrate.