Dynamics of a viscous vesicle in linear flows

Petia M. Vlahovska*, Ruben Serral Gracia

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

142 Scopus citations


An analytical theory is developed to describe the dynamics of a closed lipid bilayer membrane (vesicle) freely suspended in a general linear flow. Considering a nearly spherical shape, the solution to the creeping-flow equations is obtained as a regular perturbation expansion in the excess area. The analysis takes into account the membrane fluidity, incompressibility, and resistance to bending. The constraint for a fixed total area leads to a nonlinear shape evolution equation at leading order. As a result two regimes of vesicle behavior, tank treading and tumbling, are predicted depending on the viscosity contrast between interior and exterior fluid. Below a critical viscosity contrast, which depends on the excess area, the vesicle deforms into a tank-treading ellipsoid, whose orientation angle with respect to the flow direction is independent of the membrane bending rigidity. In the tumbling regime, the vesicle exhibits periodic shape deformations with a frequency that increases with the viscosity contrast. Non-Newtonian rheology such as normal stresses is predicted for a dilute suspension of vesicles. The theory is in good agreement with published experimental data for vesicle behavior in simple shear flow.

Original languageEnglish (US)
Article number016313
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number1
StatePublished - Jan 30 2007

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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