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

Published online by Cambridge University Press:  19 February 2013

Hong Zhao  and
Eric S. G. Shaqfeh
Hong Zhao*
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
Eric S. G. Shaqfeh
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Biological Fluid Dynamics: Capsule/cell dynamics Instability: Instability Low-Reynolds-number flows: Low-Reynolds-number flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 719 , 25 March 2013 , pp. 345 - 361
Copyright
©2013 Cambridge University Press

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References

Alpert, B. K. 1999 Hybrid Gauss–trapezoidal quadrature rules. SIAM J. Sci. Comput. 20 (5), 1551–1584.CrossRefGoogle Scholar
Biben, T., Farutin, A. & Misbah, C. 2011 Three-dimensional vesicles under shear flow: numerical study of dynamics and phase diagram. Phys. Rev. E 83, 031921.Google Scholar
Deschamps, J., Kantsler, V. & Steinberg, V. 2009 Phase diagram of single vesicle dynamical states in shear flow. Phys. Rev. Lett. 102, 118105.Google Scholar
Farutin, A., Biben, T. & Misbah, C. 2010 Analytical progress in the theory of vesicles under linear flow. Phys. Rev. E 81, 061904.Google Scholar
Frigo, M. & Johnson, S. G. 2005 The design and implementation of FFTW3. Proc. IEEE 93 (2), 216–231.CrossRefGoogle Scholar
Helfrich, W. 1973 Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. C 28 (11), 693–703.Google Scholar
Kantsler, V., Segre, E. & Steinberg, V. 2008 Critical dynamics of vesicle stretching transition in elongational flow. Phys. Rev. Lett. 101, 048101.Google Scholar
Mader, M., Vitkova, V., Abkarian, M., Viallat, A. & Podgorski, T. 2006 Dynamics of viscous vesicles in shear flow. Eur. Phys. J. E 19, 398–397.Google Scholar
Misbah, C. 2006 Vacillating breathing and tumbling of vesicles under shear flow. Phys. Rev. Lett. 96, 028104.Google Scholar
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.Google Scholar
Rallison, J. M. & Acrivos, A. 1978 A numerical study of the deformation and burst of a viscous drop in an extensional flow. J. Fluid Mech. 89, 191–200.Google Scholar
Veerapaneni, S. K., Gueyffier, D., Biros, G. & Zorin, D. 2009 A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows. J. Comput. Phys. 228, 7233–7249.Google Scholar
Zhao, H., Isfahani, A. H. G., Olson, L. & Freund, J. B. 2010 A spectral boundary integral method for micro-circulatory cellular flows. J. Comput. Phys. 229 (10), 3726–3744.Google Scholar
Zhao, H. & Shaqfeh, E. S. G. 2011 The dynamics of a vesicle in simple shear flow. J. Fluid Mech. 674, 578–604.Google Scholar
Zhong-can, O. Y. & Helfrich, W. 1989 Bending energy of vesicle membranes: general expressions for the first, second, and third variation of the shape energy and applications to spheres and cylinders. Phys. Rev. A 39 (10), 5280–5288.Google Scholar