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Related Experiment Video

Updated: Apr 23, 2026

Phase Behavior of Charged Vesicles Under Symmetric and Asymmetric Solution Conditions Monitored with Fluorescence Microscopy
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Diffuse interface models of locally inextensible vesicles in a viscous fluid.

Sebastian Aland1, Sabine Egerer1, John Lowengrub2

  • 1Institut für wissenschaftliches Rechnen, TU Dresden, 01062 Dresden, Germany.

Journal of Computational Physics
|September 24, 2014
PubMed
Summary

We developed a new diffuse interface model for inextensible vesicles, ensuring local inextensibility to accurately simulate fluid dynamics. This method prevents errors, improving predictions for vesicle behavior in flows.

Keywords:
Adaptive finite element methodHelfrich energyLocal relaxationMembraneNavier-Stokes flowPhase-field modelTank-treadingTumbling

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Area of Science:

  • Fluid Dynamics
  • Computational Mechanics
  • Biophysics

Background:

  • Simulating inextensible vesicles in viscous fluids is challenging due to maintaining interface integrity.
  • Existing diffuse interface models struggle with accurately enforcing local inextensibility, leading to errors in dynamics.

Purpose of the Study:

  • To introduce a novel diffuse interface model that accurately enforces local inextensibility for vesicle dynamics.
  • To develop and validate a robust numerical method for simulating these systems.

Main Methods:

  • Implementation of a local Lagrange multiplier to enforce local inextensibility.
  • Development of a local relaxation scheme to correct stretching/compression errors.
  • Adaptive finite element method with implicit coupling of Navier-Stokes and inextensibility equations.

Main Results:

  • The model converges to a relaxed sharp interface limit, verified by asymptotic analysis and numerical simulations.
  • Accurate local inextensibility enforcement prevents error accumulation, crucial for vesicle dynamics in tumbling and tank-treading regimes.
  • Simulations show local inextensibility inhibits fluid drainage between closely spaced vesicles.

Conclusions:

  • The new diffuse interface model effectively captures the dynamics of inextensible vesicles by accurately enforcing local inextensibility.
  • The local relaxation scheme is vital for preventing numerical artifacts and ensuring reliable simulations.
  • This model provides a more accurate framework for studying vesicle behavior in various flow conditions.