The mechanism of shape instability for a vesicle in extensional flow

When a flexible vesicle is placed in an extensional flow (planar or uniaxial), it undergoes two unique sets of shape transitions that to the best of the authors’ knowledge have not been observed for droplets. At intermediate reduced volumes (i.e. intermediate particle aspect ratio) and high extension rates, the vesicle stretches into an asymmetric dumbbell separated by a long, cylindrical thread. At low reduced volumes (i.e. high particle aspect ratio), the vesicle extends symmetrically without bound, in a manner similar to the breakup of liquid droplets. During this ‘burst’ phase, ‘pearling’ occasionally occurs, where the vesicle develops a series of periodic beads in its central neck. In this paper, we describe the physical mechanisms behind these seemingly unrelated instabilities by solving the Stokes flow equations around a single, fluid-filled particle whose interfacial dynamics is governed by a Helfrich energy (i.e. the membranes are inextensible with bending resistance). By examining the linear stability of the steady-state shapes, we determine that vesicles are destabilized by curvature changes on its interface, similar to the Rayleigh–Plateau phenomenon. This result suggests that the vesicle’s initial geometry plays a large role in its shape transitions under tension. The stability criteria calculated by our simulations and scaling analyses agree well with available experiments. We hope that this work will lend insight into the stretching dynamics of other types of biological particles with nearly incompressible membranes, such as cells.