Sedimentation of vesicles: from pear-like shapes to microtether extrusion

We study the sedimentation of buoyant giant lipid vesicles in a quiescent fluid at velocities ranging from 5 to 20 μm s-1. Floppy vesicles are deformed by the flow. Their bottom (upstream) part remains spherical, while their top (downstream) part narrows down and elongates along the direction of motion, resulting in pear-like shapes or in the reversible formation of a micron-size tube at the vesicle top. The sedimentation velocity of a vesicle is very similar to that of a rigid sphere. Using a thermodynamic approach, we show that the hydrodynamic force acting at the top of a floppy vesicle can exceed the critical force needed to draw a membrane tube. We predict that the tube radius scales as the power 1/3 of the ratio of the bending energy to the typical hydrodynamic stress, ηU/R, where η is the fluid viscosity, U the sedimentation velocity and R the vesicle radius. This result is consistent with the previously reported experimental data. The tensions of vesicles exhibiting a tube and of pear-like shape are deduced from the thermodynamic approach.