Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-20T15:19:24.477Z Has data issue: false hasContentIssue false
  • English
  • Français

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

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 

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

Abkarian, M. & Viallat, A. 2008 Vesicles and red blood cells in shear flow. Soft Matt. 4, 653–657.Google Scholar
Abramowitz, M. & Stegun, I. A. 1972 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards.Google Scholar
Abreu, D. & Seifert, U. 2013 Noisy nonlinear dynamics of vesicles in flow. Phys. Rev. Lett. 110, 238103.Google Scholar
Alberts, B., Bray, D., Hopkin, K., Johnson, A., Lewis, J., Raff, M., Roberts, K. & Walters, P. 2004 Essential Cell Biology, 2nd edn. Garland Science.Google Scholar
Antonietti, M. & Forster, S. 2003 Vesicles and liposomes: a self-assembly principle beyond lipids. Adv. Mater. 15, 1323–1333.CrossRefGoogle Scholar
Batchelor, G. K. 1970 Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44, 419–440.Google Scholar
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
Blawzdziewicz, J., Cristini, V. & Loewenberg, M. 1999 Stokes flow in the presence of a planar interface covered with incompressible surfactant. Phys. Fluids 11, 251–258.Google Scholar
Boedec, G., Jaeger, M. & Leonetti, M. 2012 Settling of a vesicle in the limit of quasispherical shapes. J. Fluid Mech. 690, 227–261.Google Scholar
Boedec, G., Jaeger, M. & Leonetti, M. 2014 Pearling instability of a cylindrical vesicle. J. Fluid Mech. 743, 262–279.CrossRefGoogle Scholar
Boyd, S. P. & Vandenberghe, L. 2004 Convex Optimization. Cambridge University Press.Google Scholar
Callens, N., Minetti, C., Coupier, G., Mader, M., Dubois, F., Misbah, C. & Podgorski, P. 2008 Hydrodynmamic lift of vesicles under shear flow in microgravity. Europhys. Lett. 83, 24002.CrossRefGoogle Scholar
Dassios, G., Payatakes, A. C. & Vafeas, P. 2004 Interrelation between Papkovich–Neuber and Stokes general solutions of the stokes equations in spheroidal geometry. Q. J. Mech. Appl. Maths 57, 181–203.Google Scholar
de Gennes, P. G. 1974 Coil-stretch transition of dilute flexible polymers under ultrahigh velocity gradients. J. Chem. Phys. 60, 5030–5042.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
Gires, P. Y., Danker, G. & Misbah, C. 2012 Hydrodynamic interaction between two vesicles in a linear shear flow: asymptotic study. Phys. Rev. E 86, 011408.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
Helfrich, W. 1973 Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. C 28, 693–703.Google Scholar
Hobson, E. W. 1931 The Theory of Spherical and Ellipsoidal Harmonics. Cambridge University Press.Google Scholar
Hu, Y. T., Pine, D. J. & Leal, L. G. 2000 Drop deformation, breakup, and coalescence with compatibilizer. Phys. Fluids 12, 484–489.Google Scholar
Huang, H. L., Abkarian, M. & Viallat, A. 2011 Sedimentation of vesicles: from pear-like shapes to microtether extrusion. New J. Phys. 13, 035026.Google Scholar
Immordino, M. L., Dosio, F. & Cattel, L. 2006 Stealth liposomes: review of the basic science, rationale, and clinical applications, existing and potential. Intl J. Nanomed. 3, 297–315.Google Scholar
Janssen, J. J. M., Boon, A. & Agterof, M. W. G. 1997 Influence of dynamic interfacial properties on droplet breakup in plane hyperbolic flow. AIChE J. 43, 1436–1447.Google Scholar
Kantsler, V., Segre, E. & Steinberg, V. 2008a Critical dynamics of vesicle stretching transition in elongational flow. Phys. Rev. Lett. 101, 048101.Google Scholar
Kantsler, V., Segre, E. & Steinberg, V. 2008b Dynamics of interacting vesicles and rheology of vesicle suspension in shear flow. Europhys. Lett. 82, 58005.Google Scholar
Leal, L. G. 2007 Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes. Cambridge University Press.Google Scholar
Levant, M., Deschamps, J., Afik, E. & Steinberg, V. 2012 Characteristic spatial scale of vesicle pair interactions in a plane linear flow. Phys. Rev. E 85, 056306.Google Scholar
Levant, M. & Steinberg, V. 2012 Amplification of thermal noise by vesicle dynamics. Phys. Rev. Lett. 109, 268103.Google Scholar
Mader, M., Vitkova, V., Abkarian, M., Viallat, A. & Podgorski, T. 2006 Dynamics of viscous vesicles in shear flow. Eur. Phys. J. E 19, 389–397.Google Scholar
Medina, O. P., Zhu, Y. & Kairemo, K. 2004 Targeted liposomal drug delivery in cancer. Curr. Pharm. Des. 24, 2981–2989.CrossRefGoogle Scholar
Noireaux, V. & Libchaber, A. 2004 A vesicle bioreactor as a step toward an artificial cell assembly. Proc. Natl Acad. Sci. U.S.A. 101, 17669–17674.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Podgorski, T., Callens, N., Minetti, C., Coupier, G. & Misbah, C. 2011 Dynamics of vesicle suspensions in shear flow between walls. Microgravity Sci. Technol. 23, 263–270.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
Rallison, J. M. 1984 The deformation of small viscous drops and bubbles in shear flows. Annu. Rev. Fluid Mech. 16, 45–66.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
Seifert, U. 1997 Configurations of fluid membranes and vesicles. Adv. Phys. 46, 13–137.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
Sharma, A. & Sharma, U. S. 1997 Liposomes in drug delivery: progress and limitations. Intl J. Pharm. 154, 123–140.CrossRefGoogle Scholar
Spann, A. P.2013 Loop subdivision surface boundary integral simulations for vesicles in shear and extensional flows. PhD thesis, Stanford University.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.CrossRefGoogle Scholar
Spjut, J. E.2010 Trapping, deformation, and dynamics of phospholipid vesicles. MS thesis, University of California, Berkeley. Chap. 3.Google Scholar
Stone, H. A. 1994 Dynamics of drop deformation and breakup in viscous fluids. Annu. Rev. Fluid Mech. 26, 65–102.CrossRefGoogle Scholar
Stone, H. A., Bentley, B. J. & Leal, L. G. 1986 An experimental study of transient effects in the breakup of viscous drops. J. Fluid Mech. 173, 131–158.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.Google 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
Tran-Cong, T. & Blake, J. R. 1982 General solution of the Stokes’ flow equations. J. Math. Anal. Appl. 90, 72–84.Google Scholar
Veerapaneni, S. K., Gueyffier, D., Biros, G. & Zorin, D. 2009 A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows. J. Comput. Phys. 228, 7233–7249.Google Scholar
Vitkova, V., Mader, M., Polack, B., Misbah, C. & Podgorski, T. 2008 Micro-macro link in rheology of erythrocyte and vesicle suspensions. Biophys. J. 95, L33–L35.CrossRefGoogle ScholarPubMed
Vlahovska, P. M. & Gracia, R. S. 2007 Dynamics of a viscous vesicle in linear flows. Phys. Rev. E 75, 016313.Google Scholar
Vlahovska, P. M., Podgorski, T. & Misbah, C. 2009 Vesicles and red blood cells in flow: from individual dynamics to rheology. C. R. Phys. 10, 775–789.Google Scholar
Zabusky, N. J., Segre, E., Deschamps, J., Kantsler, V. & Steinberg, V. 2011 Dynamics of vesicles in shear and rotational flows: modal dynamics and phase diagram. Phys. Fluids 23, 041905.Google Scholar
Zhang, J., Zahn, J. D., Tan, W. & Lin, H. 2013 A transient solution for vesicle electrodeformation and relaxation. Phys. Fluids 25, 071903.Google Scholar
Zhao, H. & Shaqfeh, E. S. G. 2011 The dynamics of a vesicle in simple shear flow. J. Fluid Mech. 674, 578–604.Google Scholar
Zhao, H. & Shaqfeh, E. S. G. 2013a The dynamics of a non-dilute vesicle suspension in a simple shear flow. J. Fluid Mech. 725, 709–731.Google Scholar
Zhao, H. & Shaqfeh, E. S. G. 2013b The shape stability of a lipid vesicle in a uniaxial extensional flow. J. Fluid Mech. 719, 345–361.Google Scholar
Zhao, H., Spann, A. P. & Shaqfeh, E. S. G. 2011 The dynamics of a vesicle in a wall-bound shear flow. Phys. Fluids 23, 121901.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.CrossRefGoogle Scholar

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