Late Stages of the “Pearling" Instability in Lipid Bilayers

Applying laser tweezers to cylindrical vesicles of lipid bilayers produces an instability which propagates down the vesicle leaving behind it a peristaltic state, which appears under the microscope as pearls on a string. We investigate the late stages of this “pearling” instability, where the pearls are observed to drift slowly towards the laser trap (the spot at which the tweezers are applied, into which the surfactant is drawn) where they jam up. We model the hydrodynamics of the drifting pearls as a combination of translation of the string of pearls, and “slipping” of the bilayer skin over the pearls, to relate the speed of the pearls to the underlying flux of surfactant into the trap. We find that the pearl drift is slower than the skin-slip speed by a factor of order a/R where a is the radius of the tethers connecting the pearls, and R is the pearl radius.