The dynamics of a vesicle in a wall-bound shear flow

Abstract

The three-dimensional dynamics of a lipid vesicle in a wall-bound shear flow is simulated by a Stokes-flow boundary integral equation method. When the vesicle is far away from the wall, the wall induces a lift velocity that is proportional to the wall normal component of the particle stresslet and is inversely proportional to the square of its centroid height. When the vesicle is in close contact with the wall under the action of gravity, its bottom surface height scales linearly with the shear rate, with a scaling constant that depends strongly on its nonsphericity. The numerical results are in quantitative agreement with the experimental measurements. The wall boundary causes the particle shear stress and normal stress differences to increase, but the effect diminishes when the centroid height is more than twice the vesicle radius. The simulation shows that the presence of the wall delays the transition (i.e., creates higher critical viscosity ratios) from the tank-treading motion to trembling and tumbling.