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Pearling instability of a cylindrical vesicle

Published online by Cambridge University Press:  04 March 2014

G. Boedec ,
M. Jaeger  and
M. Leonetti
G. Boedec*
Affiliation:
Aix-Marseille Université, CNRS, IRPHE UMR 7342, Centrale Marseille, Technopôle de Château-Gombert, 49, Rue Frédéric Joliot-Curie, 13384 Marseille, France
M. Jaeger
Affiliation:
Aix-Marseille Université, CNRS, M2P2 UMR 7340, Centrale Marseille, Technopôle de Château-Gombert, 38, Rue Frédéric Joliot-Curie, 13451 Marseille, France
M. Leonetti
Affiliation:
Aix-Marseille Université, CNRS, IRPHE UMR 7342, Centrale Marseille, Technopôle de Château-Gombert, 49, Rue Frédéric Joliot-Curie, 13384 Marseille, France
*
†Email address for correspondence: boedec@irphe.univ-mrs.fr
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Abstract

A cylindrical vesicle under tension can undergo a pearling instability, characterized by the growth of a sinusoidal perturbation which evolves towards a collection of quasi-spherical bulbs connected by thin tethers, like pearls on a necklace. This is reminiscent of the well-known Rayleigh–Plateau instability, where surface tension drives the amplification of sinusoidal perturbations of a cylinder of fluid. We calculate the growth rate of perturbations for a cylindrical vesicle under tension, considering the effect of both inner and outer fluids, with different viscosities. We show that this situation differs strongly from the classical Rayleigh–Plateau case in the sense that, first, the tension must be above a critical value for the instability to develop and, second, even in the strong tension limit, the surface preservation constraint imposed by the presence of the membrane leads to a different asymptotic behaviour. The results differ from previous studies on pearling due to the consideration of variations of tension, which are shown to enhance the pearling instability growth rate, and lower the wavenumber of the fastest growing mode.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Low-Reynolds-number flows: Low-Reynolds-number flows Biological Fluid Dynamics: Membranes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 743 , 25 March 2014 , pp. 262 - 279
Copyright
© 2014 Cambridge University Press 

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