Nearly spherical vesicles in an external flow

TL;DR

This paper develops a dynamical model for nearly spherical vesicles in external flow, predicting different behavioral regimes and transition types based on flow and vesicle parameters.

Contribution

It introduces a new dynamical equation for nearly spherical vesicles, enabling phase diagram prediction of vesicle behaviors in flow conditions.

Findings

Identifies transition types: saddle-node and Hopf bifurcations.

Predicts phase diagram with regimes: tank-treading, tumbling, trembling.

Finds critical slowing near transition merging point.

Abstract

Tank-treading, tumbling and trembling are different types of the vesicle behavior in an external flow. We derive a dynamical equation for nearly spherical vesicles enabling to establish a phase diagram of the system predicting the regimes. The diagram is drawn in terms of two dimensionless parameters depending on the vesicle excess area, fluid viscosities, membrane viscosity and bending modulus, strength of the flow, and ratio of the elongational and rotational components of the flow. The tank-treading to tumbling transition occurs via a saddle-node bifurcation whereas the tank-treading to trembling transition occurs via a Hopf bifurcation. We establish a critical slowing near the merging point of the transition lines.