Influence of shear flow on vesicles near a wall: A numerical study

We describe the dynamics of three-dimensional fluid vesicles in steady shear flow in the vicinity of a wall. This is analyzed numerically at low Reynolds numbers using a boundary element method. The area-incompressible vesicle exhibits bending elasticity. Forces due to adhesion or gravity oppose the hydrodynamic lift force driving the vesicle away from a wall. We investigate three cases. First, a neutrally buoyant vesicle is placed in the vicinity of a wall that acts only as a geometrical constraint. We find that the lift velocity is linearly proportional to shear rate and decreases with increasing distance between the vesicle and the wall. Second, with a vesicle filled with a denser fluid, we find a stationary hovering state. We present an estimate of the viscous lift force that seems to agree with recent experiments of Lorz et al. [Europhys. Lett. 51, 468 (2000)]. Third, if the wall exerts an additional adhesive force, we investigate the dynamical unbinding transition that occurs at an adhesion strength linearly proportional to the shear rate.