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Settling of a vesicle in the limit of quasispherical shapes

Published online by Cambridge University Press:  20 December 2011

G. Boedec ,
M. Jaeger  and
M. Leonetti
G. Boedec
Affiliation:
M2P2, Aix-Marseille Univ., Technopole de Chateau-Gombert 13451 Marseille, France; M2P2, UMR CNRS 6181, 13451 Marseille, France; Centrale Marseille, 13451 Marseille, France
M. Jaeger
Affiliation:
M2P2, Aix-Marseille Univ., Technopole de Chateau-Gombert 13451 Marseille, France; M2P2, UMR CNRS 6181, 13451 Marseille, France; Centrale Marseille, 13451 Marseille, France
M. Leonetti*
Affiliation:
IRPHE, Aix-Marseille Univ., Technopole de Chateau-Gombert 13384 Marseille, France; IRPHE, UMR CNRS 6594, 13384 Marseille, France; Centrale Marseille, 13451 Marseille, France
*
†Email address for correspondence: leonetti@irphe.univ-mrs.fr
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Abstract

Vesicles are drops of radius of a few tens of micrometres bounded by an impermeable lipid membrane of approximately 4 nm thickness in a viscous fluid. The salient characteristics of such a deformable object are a membrane rigidity governed by flexion due to curvature energy and a two-dimensional membrane fluidity characterized by a local membrane incompressibility. This provides unique properties with strong constraints on the internal volume and membrane area. Yet, when subjected to external stresses, vesicles exhibit a large deformability. The deformation of a settling vesicle in an infinite flow is studied theoretically, assuming a quasispherical shape and expanding all variables of the problem onto spherical harmonics. The contribution of thermal fluctuations is neglected in this analysis. A system of equations describing the temporal evolution of the shape is derived with this formalism. The final shape and the settling velocity are then determined and depend on two dimensionless parameters: the Bond number and the excess area. This simultaneous study leads to three stationary shapes, an egg-like shape already observed in an analogous experimental configuration in the limit of weak flow magnitude (Chatkaew, Georgelin, Jaeger & Leonetti, Phys. Rev. Lett, 2009, vol. 103(24), 248103), a parachute-like shape and a non-trivial non-axisymmetrical shape. The final shape depends on the initial conditions: prolate or oblate vesicle and orientation compared with gravity. The analytical solution in the small deformation regime is compared with numerical results obtained with a three-dimensional code. A very good agreement between numerical and theoretical results is found.

JFM classification

Biological Fluid Dynamics: Capsule/cell dynamics Drops and Bubbles: Drops Low-Reynolds-number flows: Low-Reynolds-number flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 690 , 10 January 2012 , pp. 227 - 261
Copyright
Copyright © Cambridge University Press 2012

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