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The mechanism of shape instability for a vesicle in extensional flow

Published online by Cambridge University Press:  02 June 2014

Vivek Narsimhan ,
Andrew P. Spann  and
Eric S. G. Shaqfeh
Vivek Narsimhan
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA
Andrew P. Spann
Affiliation:
Institute of Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA
Eric S. G. Shaqfeh*
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA Institute of Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: [email protected]
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Abstract

When a flexible vesicle is placed in an extensional flow (planar or uniaxial), it undergoes two unique sets of shape transitions that to the best of the authors’ knowledge have not been observed for droplets. At intermediate reduced volumes (i.e. intermediate particle aspect ratio) and high extension rates, the vesicle stretches into an asymmetric dumbbell separated by a long, cylindrical thread. At low reduced volumes (i.e. high particle aspect ratio), the vesicle extends symmetrically without bound, in a manner similar to the breakup of liquid droplets. During this ‘burst’ phase, ‘pearling’ occasionally occurs, where the vesicle develops a series of periodic beads in its central neck. In this paper, we describe the physical mechanisms behind these seemingly unrelated instabilities by solving the Stokes flow equations around a single, fluid-filled particle whose interfacial dynamics is governed by a Helfrich energy (i.e. the membranes are inextensible with bending resistance). By examining the linear stability of the steady-state shapes, we determine that vesicles are destabilized by curvature changes on its interface, similar to the Rayleigh–Plateau phenomenon. This result suggests that the vesicle’s initial geometry plays a large role in its shape transitions under tension. The stability criteria calculated by our simulations and scaling analyses agree well with available experiments. We hope that this work will lend insight into the stretching dynamics of other types of biological particles with nearly incompressible membranes, such as cells.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Instability: Instability Low-Reynolds-number flows: Low-Reynolds-number flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 750 , 10 July 2014 , pp. 144 - 190
Copyright
© 2014 Cambridge University Press 

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Narsimhan et al. supplementary movie

This movie illustrates the asymmetric dumb-bell instability for a reduced volume ν = 0:65 vesicle at Capillary number 4 and matched viscosity ratio (i.e., λ = 1). This instability corresponds to the shape transitions observed by Spjut and Muller (2008).

Download Narsimhan et al. supplementary movie(Video)
Video 9.5 MB

Narsimhan et al. supplementary movie

This movie shows the evolution of a vesicle when the extension rate is above the critical Capillary number Cacrit where a steady-state shape no longer exists. The reduced volume is ν = 0:57, viscosity ratio is λ = 1, and the Capillary number is Ca = 2.

Download Narsimhan et al. supplementary movie(Video)
Video 5.6 MB

Narsimhan et al. supplementary movie

This movie illustrates pearling, which is when the central neck of the vesicle forms beads with a characteristic size of the neck's radius. The reduced volume is ν = 0:49, the viscosity ratio is λ = 1, and the Capillary number is Ca = 4.

Download Narsimhan et al. supplementary movie(Video)
Video 15.3 MB