Dynamics of wrinkles on a vesicle in external flow

TL;DR

This paper develops a theoretical model describing how wrinkles form and evolve on vesicle membranes in external flow, linking negative surface tension to instability and validating scaling laws through analysis and simulations.

Contribution

It introduces a new theory connecting membrane instability to wrinkle formation, providing analytical expressions and numerical confirmation for the dynamics of wrinkled vesicles.

Findings

Identified the instability threshold for wrinkle formation.

Derived scaling laws for wrinkle wavelength evolution.

Confirmed scaling laws through numerical simulations.

Abstract

Recent experiments by Kantsler et. al. (2007) have shown that the relaxational dynamics of a vesicle in external elongation flow is accompanied by the formation of wrinkles on a membrane. Motivated by these experiments we present a theory describing the dynamics of a wrinkled membrane. Formation of wrinkles is related to the dynamical instability induced by negative surface tension of the membrane. For quasi-spherical vesicles we perform analytical study of the wrinkle structure dynamics. We derive the expression for the instability threshold and identify three stages of the dynamics. The scaling laws for the temporal evolution of wrinkling wavelength and surface tension are established and confirmed numerically.