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Pearling, wrinkling, and buckling of vesicles in elongational flows

Published online by Cambridge University Press:  15 July 2015

Vivek Narsimhan ,
Andrew P. Spann  and
Eric S. G. Shaqfeh
Vivek Narsimhan*
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Andrew P. Spann
Affiliation:
Department of Chemical Engineering, University of Texas at Austin, Austin, TX 78712, USA
Eric S. G. Shaqfeh
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA Institute of Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: vivekn12@mit.edu
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Abstract

Tubular vesicles in extensional flow can undergo ‘pearling’, i.e. the formation of beads in their central neck reminiscent of the Rayleigh–Plateau instability for droplets. In this paper, we perform boundary integral simulations to determine the conditions for the onset of this instability. Our simulations agree well with experiments, and we explore additional topics such as the role of the vesicle’s initial shape on the number of pearls formed. We also compare our simulations to simple physical models of pearling that have been presented in the literature, where the vesicle is approximated as an infinitely long cylinder with a constant surface tension and bending modulus. We present a complete linear stability analysis of this idealized problem, including the effects of non-axisymmetric deformations as well as surface viscosity. We demonstrate that, while such models capture the essential physics of pearling, they cannot capture the stability of these transitions accurately, since finite length effects and non-uniform surface tension effects are important. We close our paper with a brief discussion of vesicles in compressional flows. Unlike quasi-spherical vesicles, we find that tubular vesicles can transition to a wide variety of permanent, buckled states under compression. The idealized problem mentioned above gives the essential physics behind these instabilities, which to our knowledge has not been examined heretofore.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Instability: Instability Biological Fluid Dynamics: Membranes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 777 , 25 August 2015 , pp. 1 - 26
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Copyright
© 2015 Cambridge University Press 

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Footnotes

‡

V.N. and A.P.S. are joint first authors for this publication.

References

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, 294–320.CrossRefGoogle ScholarPubMed
Bentley, B. J. & Leal, L. G. 1986 An experimental investigation of drop deformation and breakup in steady two-dimensional linear flows. J. Fluid Mech. 167, 241–283.Google Scholar
Boedec, G., Jaeger, M. & Leonetti, M. 2014 Pearling instability of a cylindrical vesicle. J. Fluid Mech. 743, 262–279.Google Scholar
Chen, J. Z. Y. 2012 Pulling or compressing a vesicle by force: solution to the bending energy model. Phys. Rev. E 85, 061910.Google Scholar
Dechamps, J., Kantsler, V. & Steinberg, V. 2009 Phase diagram of single vesicle dynamical states in shear flow. Phys. Rev. Lett. 102, 118105.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, S1151–S1176.Google Scholar
Foltin, G. 1994 Dynamics of incompressible fluid membranes. Phys. Rev. E 49, 5243–5248.Google Scholar
Goldstein, R. E., Nelson, P., Powers, T. R. & Seifert, U. 1996 Front propagation in the pearling instability of tubular vesicles. J. Phys. II France 6, 767–796.Google Scholar
Gracia, R. S., Bezlyepkina, N., Knorr, R. L., Lipowsky, R. & Dimova, R. 2010 Effect of cholesterol on the rigidity of saturated and unsaturated membranes: fluctuation and electrodeformation analysis of giant vesicles. Soft Matt. 6, 1472–1482.Google Scholar
Gurin, K. L., Lebedev, V. V. & Muratov, A. R. 1996 Dynamic instability of a membrane tube. JETP 83, 321–326.Google Scholar
Happel, J. & Brenner, H. 1973 Low Reynolds Number Hydrodynamics. Noordhoff International Publishing.Google Scholar
Helfrich, W. 1973 Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. C 28, 693–703.Google ScholarPubMed
Kantsler, V.2007 Hydrodynamics of fluid vesicles. PhD thesis, Weizmann Institute of Science.Google Scholar
Kantsler, V., Segre, E. & Steinberg, V. 2007 Vesicle dynamics in time-dependent elongation flow: wrinkling instability. Phys. Rev. Lett. 99, 178102.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
Levant, M., Abreu, D., Seifert, U. & Steinberg, V. 2014 Wrinkling instability of vesicles in steady linear flow. Europhys. Lett. 107, 28001.Google Scholar
Lindberg, H. E. & Florence, A. L. 1987 Dynamic Pulse Buckling – Theory and Experiment. Springer Science and Business Media.Google Scholar
Lipowsky, R. & Dobereiner, H. G. 1998 Vesicles in contact with nanoparticles and colloids. Europhys. Lett. 43, 219–225.Google Scholar
Loewenberg, M. & Hinch, E. J. 1996 Numerical simulation of a concentrated emulsion in shear flow. J. Fluid Mech. 321, 395–419.Google Scholar
Menager, 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, 325–337.Google Scholar
Narsimhan, V.2014 Flow dynamics of fluid-filled particles with complex interfaces: a study of surfactant-contaminated droplets, red blood cells, and vesicles. PhD thesis, Stanford University.Google Scholar
Narsimhan, V., Spann, A. P. & Shaqfeh, E. S. G. 2014 The mechanism of shape instability for a vesicle in extensional flow. J. Fluid Mech. 750, 144–190.Google Scholar
Pan, J., Tristram-Nagle, S., Kucerka, N. & Nagle, J. F. 2008 Temperature dependence of structure, bending rigidity, and bilayer interactions of dioleoylphosphatidylcholine bilayers. Biophys. J. 94, 117–124.Google Scholar
Powers, T. R. 2010 Dynamics of filaments and membranes in a viscous fluid. Rev. Mod. Phys. 82, 1607–1631.Google Scholar
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.Google Scholar
Rawicz, W., Olbrich, K. C., McIntosh, T., Needham, D. & Evans, E. 2000 Effect of chain length and unsaturation on elasticity of lipid bilayers. Biophys. J. 79, 328–339.Google Scholar
Sanborn, J., Ogle, K., Krautb, R. S. & Parikh, A. N. 2013 Transient pearling and vesiculation of membrane tubes under osmotic gradients. Faraday Discuss. 161, 167–176.Google Scholar
Scriven, L. E. 1960 Dynamics of a fluid interface: equation of motion for newtonian surface fluids. Chem. Engng Sci. 12, 98–108.CrossRefGoogle Scholar
Seifert, U., Berndl, K. & Lipowsky, R. 1991 Shape transformations of vesicles: phase diagram for spontaneous curvature and bilayer-coupling models. Phys. Rev. A 44, 1182–1202.Google Scholar
Seifert, U. & Langer, S. A. 1993 Viscous modes of fluid bilayer membranes. Europhys. Lett. 23, 71–76.Google Scholar
Sinha, K. P., Gadkari, S. & Thaokar, R. M. 2013 Electric field induced pearling instability in cylindrical vesicles. Soft Matt. 9, 7274–7293.Google Scholar
Spann, A. P., Zhao, H. & Shaqfeh, E. S. G. 2014 Loop subdivision surface boundary integral method simulations of vesicles at low reduced volume ratio in shear and extensional flow. Phys. Fluids 26, 031902.Google Scholar
Stone, H. A. 1994 Dynamics of drop deformation and breakup in viscous fluids. Annu. Rev. Fluid Mech. 26, 65–102.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, 332–337.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
Turitsyn, K. S. & Vergeles, S. S. 2008 Wrinkling of vesicles during transient dynamics in elongational flow. Phys. Rev. Lett. 100, 028103.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 dynamics of a non-dilute vesicle suspension in a simple shear flow. J. Fluid Mech. 725, 709–731.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, 5280–5288.Google Scholar