Dynamics of nearly spherical vesicles in an external flow

TL;DR

This paper analytically models the evolution of nearly spherical vesicles in external flow, revealing phase transitions between different dynamic states based on key dimensionless parameters.

Contribution

It introduces an analytical equation for vesicle dynamics near spherical shape and maps the phase diagram of vesicle behavior in flow.

Findings

Identifies transition curves for tank-treading to tumbling and trembling states.

Derives conditions for bifurcations in vesicle motion.

Provides a phase diagram on the S-Λ parameter plane.

Abstract

We analytically derive an equation describing vesicle evolution in a fluid where some stationary flow is excited regarding that the vesicle shape is close to a sphere. A character of the evolution is governed by two dimensionless parameters, $S$ and $\Lambda$, depending on the vesicle excess area, viscosity contrast, membrane viscosity, strength of the flow, bending module, and ratio of the elongation and rotation components of the flow. We establish the ``phase diagram'' of the system on the $S-\Lambda$ plane: we find curves corresponding to the tank-treading to tumbling transition (described by the saddle-node bifurcation) and to the tank-treading to trembling transition (described by the Hopf bifurcation).