Pearling, wrinkling, and buckling of vesicles in elongational flows

Tubular vesicles in extensional flow can undergo ‘pearling’, i.e. the formation of beads in their central neck reminiscent of the Rayleigh–Plateau instability for droplets. In this paper, we perform boundary integral simulations to determine the conditions for the onset of this instability. Our simulations agree well with experiments, and we explore additional topics such as the role of the vesicle’s initial shape on the number of pearls formed. We also compare our simulations to simple physical models of pearling that have been presented in the literature, where the vesicle is approximated as an infinitely long cylinder with a constant surface tension and bending modulus. We present a complete linear stability analysis of this idealized problem, including the effects of non-axisymmetric deformations as well as surface viscosity. We demonstrate that, while such models capture the essential physics of pearling, they cannot capture the stability of these transitions accurately, since finite length effects and non-uniform surface tension effects are important. We close our paper with a brief discussion of vesicles in compressional flows. Unlike quasi-spherical vesicles, we find that tubular vesicles can transition to a wide variety of permanent, buckled states under compression. The idealized problem mentioned above gives the essential physics behind these instabilities, which to our knowledge has not been examined heretofore.