The metastability of lipid vesicle shapes in uniaxial extensional flow

TL;DR

This study analyzes the shape stability of deflated lipid vesicles under uniaxial extensional flow, revealing metastability, bifurcation points, and conditions for unbounded elongation through analytical and numerical methods.

Contribution

It provides a detailed analysis of vesicle shape metastability and bifurcation behavior in flow, combining analytical derivations with numerical simulations.

Findings

All stationary vesicle configurations are metastable.

Bifurcation leads to unbounded elongation at critical extension rates.

Stationary vesicle length remains finite at bifurcation point.

Abstract

In this work, we investigate the elastic properties of deflated vesicles and their shape dynamics in uniaxial extensional flow. By analysing the Helfrich bending energy and viscous flow stresses in the limit of highly elongated shapes, we demonstrate that all stationary vesicle configurations are metastable. For vesicles with small reduced volume, we identify the type of bifurcation at which the stationary state is lost, leading to unbounded vesicle elongation in time. We show that the stationary vesicle length remains finite at the critical extension rate. The critical behaviour of the stationary vesicle length and of the growth rates of small perturbations is obtained analytically and confirmed by direct numerical computations. The beginning stage of the unbounded elongation dynamics is simulated numerically, in agreement with the analytical predictions.