2007/05/24 by V. V. Lebedev, Lebedev, V. V., Konstantin Turitsyn +3 · 2 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Micro and Nano Robotics #Nonlinear Dynamics and Pattern Formation #Soft Condensed Matter (cond-mat.soft) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.0705.3543
openalex publication_date 2007/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.