Relaxation dynamics of a compressible bilayer vesicle containing highly viscous fluid

TL;DR

This study investigates the relaxation dynamics of a compressible bilayer vesicle with asymmetric internal and external viscosities, revealing how viscosity influences stability, mode coupling, and relaxation times.

Contribution

The paper introduces a comprehensive model for vesicle relaxation considering viscosity asymmetry and membrane coupling, extending previous theories with new insights into instability and mode behavior.

Findings

Higher internal viscosity shifts the cross-over mode to larger values.

Approaching instability slows down relaxation dynamics significantly.

Model reduces to known results in limiting cases.

Abstract

We study the relaxation dynamics of a compressible bilayer vesicle with an asymmetry in the viscosity of the inner and outer fluid medium. First we explore the stability of the vesicle free energy which includes a coupling between the membrane curvature and the local density difference between the two monolayers. Two types of instabilities are identified: a small wavelength instability and a larger wavelength instability. Considering the bulk fluid viscosity and the inter-monolayer friction as the dissipation sources, we next employ Onsager's variational principle to derive the coupled equations both for the membrane and the bulk fluid. The three relaxation modes are coupled to each other due to the bilayer and the spherical structure of the vesicle. Most importantly, a higher fluid viscosity inside the vesicle shifts the cross-over mode between the bending and the slipping to a larger value. As the vesicle parameters approach toward the unstable regions, the relaxation dynamics is dramatically slowed down, and the corresponding mode structure changes significantly. In some limiting cases, our general result reduces to the previously obtained relaxation rates.