Journal of Fluid Mechanics

Papers

The shape stability of a lipid vesicle in a uniaxial extensional flow

Hong Zhaoa1 c1 and Eric S. G. Shaqfeha1a2

a1 Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA

a2 Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA

Abstract

The dynamics of a lipid vesicle in a uniaxial extensional flow are investigated by using a spectral boundary integral equation method. The vesicle at its stationary state assumes an axisymmetric shape of mirror symmetry, with its surface velocity vanishing everywhere. When the reduced volume of the vesicle is less than 0.75, there exists a critical capillary number, beyond which the stationary shape is unstable. The most unstable mode breaks the mirror symmetry of the shape so that the vesicle deforms into a dumbbell shape with two unequally sized ends. This is followed by the formation of a thin tube bridging the two dumbbell ends, whose length increases with time. The numerical results are in qualitative agreement with experimental observations.

(Received June 24 2012)

(Revised October 27 2012)

(Accepted December 31 2012)

(Online publication February 19 2013)

Key words

  • capsule/cell dynamics;
  • instability;
  • low-Reynolds-number flows

Correspondence

c1 Email address for correspondence: hongzhao@stanford.edu

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