Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-28T21:09:56.941Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. & Stegun, I. A.(ed.) 1972 In Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables Dover Publications.Google Scholar
Amarouchene, Y., Bonn, D., Meunier, J. & Kellay, H. 2001 Inhibition of the finite-time singularity during droplet fission of a polymeric fluid. Phys. Rev. Lett. 86, 3558–3561.Google Scholar
Ardekani, A. M., Sharma, V. & McKinley, G. H. 2010 Dynamics of bead formation, filament thinning and breakup in weakly viscoelastic jets. J. Fluid Mech. 665, 46–56.Google Scholar
Bar-Ziv, R. & Moses, E. 1994 Instability and ‘pearling’ states produced in tubular membranes by competition of curvature and tension. Phys. Rev. Lett. 73, 1392–1395.Google Scholar
Bar-Ziv, R., Moses, E. & Nelson, P. 1998 Dynamic excitations in membranes induced by optical tweezers. Biophys. J. 75 (1), 294–320.CrossRefGoogle ScholarPubMed
Bar-Ziv, R., Tlusty, T. & Moses, E. 1997 Critical dynamics in the pearling instability of membranes. Phys. Rev. Lett. 79, 1158–1161.Google Scholar
Bar-Ziv, R., Tlusty, T., Moses, E., Safran, S. A. & Bershadsky, A. 1999 Pearling in cells: a clue to understanding cell shape. Proc. Natl Acad. Sci. 96 (18), 10140–10145.Google Scholar
Bhat, P. P., Appathurai, S., Harris, M. T., Pasquali, M., McKinley, G. H. & Basaran, O. A. 2010 Formation of beads-on-a-string structures during break-up of viscoelastic filaments. Nat. Phys. 6, 625–631.Google Scholar
Boedec, G., Jaeger, M. & Leonetti, M. 2013 Sedimentation-induced tether on a settling vesicle. Phys. Rev. E 88, 010702.Google Scholar
Campelo, F. & Hernández-Machado, A. 2007 Model for curvature-driven pearling instability in membranes. Phys. Rev. Lett. 99, 088101.Google Scholar
Chaïeb, S. & Rica, S. 1998 Spontaneous curvature-induced pearling instability. Phys. Rev. E 58, 7733–7737.Google Scholar
Clasen, C., Eggers, J., Fontelos, M. A., Li, J. & McKinley, G. H. 2006 The beads-on-string structure of viscoelastic threads. J. Fluid Mech. 556, 283–308.Google Scholar
Dimova, R., Aranda, S., Bezlyepkina, N., Nikolov, V., Riske, K. A. & Lipowsky, R. 2006 A practical guide to giant vesicles. probing the membrane nanoregime via optical microscopy. J. Phys.: Condens. Matter 18 (28), S1151.Google ScholarPubMed
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71 (3), 036601.Google Scholar
Evans, E., Bowman, H., Leung, A., Needham, D. & Tirrell, D. 1996 Biomembrane templates for nanoscale conduits and networks. Science 273 (5277), 933–935.Google Scholar
Fygenson, D. K., Marko, J. F. & Libchaber, A. 1997 Mechanics of microtubule-based membrane extension. Phys. Rev. Lett. 79, 4497–4500.Google Scholar
Goldstein, R. E., Nelson, P., Powers, T. & Seifert, U. 1996 Front propagation in the pearling instability of tubular vesicles. J. Phys. II France 6, 767–796.Google Scholar
Goveas, J. L., Milner, S. T. & Russel, W. B. 1997 Late stages of the ‘pearling’ instability in lipid bilayers. J. Phys. II France 7 (9), 1185–1204.Google Scholar
Granek, R. & Olami, Z. 1995 Dynamics of Rayleigh-like instability induced by laser tweezers in tubular vesicles of self-assembled membranes. J. Phys. II France 5 (9), 1349–1370.Google Scholar
Gurin, K. L., Lebedev, V. V. & Muratov, A. A. 1996 Dynamic instability of a membrane tube. J. Expl Theor. Phys. 83 (2), 321–326.Google Scholar
Hansen, S., Peters, G. W. M. & Meijer, H. E. H. 1999 The effect of surfactant on the stability of a fluid filament embedded in a viscous fluid. J. Fluid Mech. 382, 331–349.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
Ménager, C., Meyer, M., Cabuil, V., Cebers, A., Bacri, J. -C. & Perzynski, R. 2002 Magnetic phospholipid tubes connected to magnetoliposomes: pearling instability induced by a magnetic field. Eur. Phys. J. E 7 (4), 325–337.Google Scholar
Nelson, P., Powers, T. & Seifert, U. 1995 Dynamical theory of the pearling instability in cylindrical vesicles. Phys. Rev. Lett. 74, 3384–3387.Google Scholar
Oliveira, M. S. N. & McKinley, G. H. 2005 Iterated stretching and multiple beads-on-a-string phenomena in dilute solutions of highly extensible flexible polymers. Phys. Fluids 17 (7), 071704.Google Scholar
Olmsted, P. D. & MacIntosh, F. C. 1997 Instability and front propagation in laser-tweezed lipid bilayer tubules. J. Phys. II France 7 (1), 139–156.Google Scholar
Palierne, J. F & Lequeux, F. 1991 Sausage instability of a thread in a matrix; linear theory for viscoelastic fluids and interface. J. Non-Newtonian Fluid Mech. 40 (3), 289–306.Google Scholar
Plateau, J. 1873 Statique Expérimentale et Théorique des Liquides Soumis aux Seules Forces Moléculaires. Gauthier-Villars.Google Scholar
Powers, T. R. 2010 Dynamics of filaments and membranes in a viscous fluid. Rev. Mod. Phys. 82, 1607–1631.Google Scholar
Powers, T. R. & Goldstein, R. E. 1997 Pearling and pinching: propagation of Rayleigh instabilities. Phys. Rev. Lett. 78, 2555–2558.Google Scholar
Rayleigh, L. 1878 On the instability of jets. Proc. Lond. Math. Soc. s1–10 (1), 4–13.CrossRefGoogle Scholar
Rayleigh, L. 1892a XIX. On the instability of cylindrical fluid surfaces. Phil. Mag. Ser. 5 34 (207), 177–180.Google Scholar
Rayleigh, L. 1892b XVI. On the instability of a cylinder of viscous liquid under capillary force. Phil. Mag. Ser. 5 34 (207), 145–154.Google Scholar
Sanborn, J., Oglecka, K., Kraut, R. S. & Parikh, A. N. 2013 Transient pearling and vesiculation of membrane tubes under osmotic gradients. Faraday Discuss. 161, 167–176.Google Scholar
Timmermans, M.-L. E. & Lister, J. R. 2002 The effect of surfactant on the stability of a liquid thread. J. Fluid Mech. 459, 289–306.CrossRefGoogle Scholar
Tomotika, S. 1935 On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid. Proc. R. Soc. Lond. A 150 (870), 322–337.Google Scholar
Tsafrir, I., Sagi, D., Arzi, T., Guedeau-Boudeville, M.-A., Frette, V., Kandel, D. & Stavans, J. 2001 Pearling instabilities of membrane tubes with anchored polymers. Phys. Rev. Lett. 86, 1138–1141.Google Scholar
Vlahovska, P., Podgorski, T. & Misbah, C. 2009 Vesicles and red blood cells in flow: from individual dynamics to rheology. C. R. Phys. 10 (8), 775–789.Google Scholar
Whitaker, S. 1976 Studies of the drop-weight method for surfactant solutions: III. Drop stability, the effect of surfactants on the stability of a column of liquid. J. Colloid Interface Sci. 54 (2), 231–248.Google Scholar
Yanagisawa, M., Imai, M. & Taniguchi, T. 2008 Shape deformation of ternary vesicles coupled with phase separation. Phys. Rev. Lett. 100, 148102.Google Scholar
Zhao, H. & Shaqfeh, E. S. G. 2013 The shape stability of a lipid vesicle in a uniaxial extensional flow. J. Fluid Mechan. 719, 345–361.Google Scholar