Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 16
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Kent-Dobias, Jaron and Bernoff, Andrew J. 2015. Energy-driven pattern formation in planar dipole-dipole systems in the presence of weak noise. Physical Review E, Vol. 91, Issue. 3,


    Bernardini, C. Stoyanov, S. D. Arnaudov, L. N. and Cohen Stuart, M. A. 2013. Colloids in Flatland: a perspective on 2D phase-separated systems, characterisation methods, and lineactant design. Chem. Soc. Rev., Vol. 42, Issue. 5, p. 2100.


    Gross, Markus and Varnik, Fathollah 2012. Critical dynamics of an isothermal compressible nonideal fluid. Physical Review E, Vol. 86, Issue. 6,


    Sriram, Indira and Schwartz, Daniel K. 2012. Line tension between coexisting phases in monolayers and bilayers of amphiphilic molecules. Surface Science Reports, Vol. 67, Issue. 6, p. 143.


    Volinsky, Roman Paananen, Riku and Kinnunen, Paavo K.J. 2012. Oxidized Phosphatidylcholines Promote Phase Separation of Cholesterol-Sphingomyelin Domains. Biophysical Journal, Vol. 103, Issue. 2, p. 247.


    Brown, Frank L. H. 2011. Continuum simulations of biomembrane dynamics and the importance of hydrodynamic effects. Quarterly Reviews of Biophysics, Vol. 44, Issue. 04, p. 391.


    Camley, Brian A. and Brown, Frank L. H. 2011. Beyond the creeping viscous flow limit for lipid bilayer membranes: Theory of single-particle microrheology, domain flicker spectroscopy, and long-time tails. Physical Review E, Vol. 84, Issue. 2,


    Camley, Brian A. Esposito, Cinzia Baumgart, Tobias and Brown, Frank L.H. 2010. Lipid Bilayer Domain Fluctuations as a Probe of Membrane Viscosity. Biophysical Journal, Vol. 99, Issue. 6, p. L44.


    Ramachandran, S. Komura, S. Imai, M. and Seki, K. 2010. Drag coefficient of a liquid domain in a two-dimensional membrane. The European Physical Journal E, Vol. 31, Issue. 3, p. 303.


    Tüzel, Erkan Pan, Guoai and Kroll, Daniel M. 2010. Dynamics of thermally driven capillary waves for two-dimensional droplets. The Journal of Chemical Physics, Vol. 132, Issue. 17, p. 174701.


    Iwamoto, Mitsumasa Yamamoto, Tetsuya Liu, Fei and Ou-Yang, Zhong-Can 2008. Shear-induced domain deformation in a tilted lipid monolayer: From circle to ellipse and kinked stripe. Physical Review E, Vol. 78, Issue. 5,


    Esposito, Cinzia Tian, Aiwei Melamed, Svetlana Johnson, Corinne Tee, Shang-You and Baumgart, Tobias 2007. Flicker Spectroscopy of Thermal Lipid Bilayer Domain Boundary Fluctuations. Biophysical Journal, Vol. 93, Issue. 9, p. 3169.


    Garza-Hume, C. E. and Padilla, P. 2007. Planar soap bubble clusters with a cavity. The European Physical Journal E, Vol. 23, Issue. 1, p. 7.


    Wintersmith, Jacob R. Zou, Lu Bernoff, Andrew J. Alexander, James C. Mann, J. Adin Kooijman, Edgar E. and Mann, Elizabeth K. 2007. Determination of interphase line tension in Langmuir films. Physical Review E, Vol. 75, Issue. 6,


    Zou, Lu Wang, Ji Basnet, Prem and Mann, Elizabeth K. 2007. Line tension and structure of smectic liquid-crystal multilayers at the air-water interface. Physical Review E, Vol. 76, Issue. 3,


    Schulz, S. G. Frieske, U. Kuhn, H. Schmid, G. Müller, F. Mund, C. and Venzmer, J. 2005. The Self-Assembly of an Amphiphilic Block Copolymer: A Dissipative Particle Dynamics Study. Tenside Surfactants Detergents, Vol. 42, Issue. 3, p. 180.


    ×
  • Journal of Fluid Mechanics, Volume 571
  • January 2007, pp. 191-219

Domain relaxation in Langmuir films

  • JAMES C. ALEXANDER (a1), ANDREW J. BERNOFF (a2), ELIZABETH K. MANN (a3), J. ADIN MANN (a4), JACOB R. WINTERSMITH (a5) and LU ZOU (a3)
  • DOI: http://dx.doi.org/10.1017/S0022112006003326
  • Published online: 25 January 2007
Abstract

We report on theoretical studies of molecularly thin Langmuir films on the surface of a quiescent subfluid and qualitatively compare the results to both new and previous experiments. The film covers the entire fluid surface, but domains of different phases are observed. In the absence of external forcing, the compact domains tend to relax to circles, driven by a line tension at the phase boundaries. When stretched (by a transient applied stagnation-point flow or by stirring), a compact domain elongates, creating a bola consisting of two roughly circular reservoirs connected by a thin tether. This shape will then relax slowly to the minimum-energy configuration of a circular domain. The tether is never observed to rupture, even when it is more than a hundred times as long as it is wide. We model these experiments by taking previous descriptions of the full hydrodynamics, identifying the dominant effects via dimensional analysis, and reducing the system to a more tractable form. The result is a free boundary problem for an inviscid Langmuir film whose motion is driven by the line tension of the domain and damped by the viscosity of the subfluid. Using this model we derive relaxation rates for perturbations of a uniform strip and a circular patch. We also derive a boundary integral formulation which allows an efficient numerical solution of the problem. Numerically this model replicates the formation of a bola and the subsequent relaxation observed in the experiments. Finally, we suggest physical properties of the system (such as line tension) that can be deduced by comparison of the theory and numerical simulations to the experiment. Two movies are available with the online version of the paper.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

R. Almgren 1996 Singularity formation in Hele-Shaw bubbles. Phys. Fluids 8, 344352.

R. Almgren , A. Bertozzi & M. P. Brenner 1996 Stable and unstable singularities in the unforced Hele-Shaw cell. Phys. Fluids 8, 13561370.

D. J. Benvegnu & H. M. McConnell 1992 Line tension between liquid domains in lipid monolayers. J. Phys. Chem. 96, 68206824.

P. Constantin , T. F. Dupont , R. E. Goldstein , L. P. Kadanoff , M. J. Shelley & S.-M. Zhou 1993 Droplet breakup in a model of the Hele-Shaw cell. Phys. Rev. E 47, 41694181.

R. DeKoker & H. M. McConnell 1993 Circle to dogbone—shapes and shape transitions of lipid monolayer domains. J. Phys. Chem. 97, 1341913424.

R. DeKoker & H. M. McConnell 1996 Stripe phase hydrodynamics in lipid monolayers. J. Phys. Chem. 100, 77227728.

P. G. Drazin & W. H. Reid 2004 Hydrodynamic Stability, 2nd Edn. Cambridge University Press.

T. F. Dupont , R. E. Goldstein , L. P. Kadanoff & S.-M. Zhou 1993 Finite-time singularity formation in Hele-Shaw systems. Phys. Rev. E 47, 41824196.

M. Edidin 2003 The state of lipid rafts: From model membranes to cells. Annu. Rev. Biophys. Biomol. Structure 32, 257283.

K. Glasner 2003 A diffuse interface approach to Hele-Shaw flow. Nonlinearity 16, 4966.

R. E. Goldstein , A. I. Pesci & M. J. Shelley 1993 Topology transitions and singularities in viscous flows. Phys. Rev. Lett. 70, 30433046.

F. C. Goodrich 1981 The theory of capillary excess viscosities. Proc. R. Soc. Lond. A 374, 341370.

D. Gottlieb & S. A. Orszag 1977 Numerical Analysis of Spectral Methods: Theory and Applications. Society for Industrial and Applied Mathematics.

P. Heinig , L. E. Helseth & T. M. Fischer 2004 Relaxation of patterns in 2D modulated phases. New J. Phys. 6, 189.

T. Hou , J. Lowengrub & M. Shelley 1994 Removing the stiffness from interfacial flow with surface tension. J. Comput. Phys. 114, 312338.

B. D. Hughes , B. A. Pailthorpe & L. R. White 1981 The translational and rotational drag on a cylinder moving in a membrane. J. Fluid Mech. 110, 349372.

J. Lauger , C. R. Robertson , C. W. Frank & G. G. Fuller 1996 Deformation and relaxation processes of mono- and bilayer domains of liquid crystalline langmuir films on water. Langmuir 12 (23), 56305635.

D. K. Lubensky & R. E. Goldstein 1996 Hydrodynamics of monolayer domains at the air-water interface. Phys. Fluids 8, 843854.

J. Lucassen , S. Akamatsu & F. Rondelez 1991 Formation, evolution, and rheology of 2-dimensional foams in spread monolayers at the air-water interface. J. Colloid Interface Sc. 144, 434448.

E. K. Mann , S. Hénon , D. Langevin , J. Meunier & L. Léger 1995 The hydrodynamics of domain relaxation in a polymer monolayer. Phys. Rev. E 51, 57085720.

E. K. Mann & S. Primak 1999 The stability of two-dimensional foams in Langmuir monolayers. Phys. Rev. Lett. 83, 53975400.

J. A. Mann Jr 1985 Dynamics, structure and function of interfacial regions. Langmuir 1, 1023.

J. A. Mann Jr, P. D. Crouser & W. V. Meyer 2001 Surface fluctuation spectroscopy by surface-light-scattering spectroscopy. Appl. Optics 40 (24), 40924112.

S. Mayor & M. Rao 2004 Rafts: Scale-dependent, active lipid organization at the cell surface. Traffic 5, 231240.

M. N. G. de Mul & J. A. Mann Jr 1998 Determination of the thickness and optical properties of a langmuir film from the domain morphology by Brewster angle microscopy. Langmuir 14, 24552466.

R. G. Parton & J. F. Hancock 2004 Lipid rafts and plasma membrane microorganization: Insights from Ras. Trends Cell Biol. 14 (3), 141147.

T. R. Powers , G. Huber & R. E. Goldstein 1990 Fluid-membrane tethers: Minimal surfaces and elastic boundary layers. Phys. Rev. E 65 (4), 041901.

C. Pozrikidis 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.

K. Simons & E. Ikonen 1997 Functional rafts in cell membranes. Nature 387, 569572.

P. Steffen , S. Wurlitzer & T. M. Fischer 2001 Hydrodynamics of shape relaxation in viscous langmuir monolayer domains. J. Phys. Chem. A 105 (36), 82818283.

H. A. Stone & H. M. McConnell 1995 Hydrodynamics of quantized shape transitions of lipid domains. Proc. R. Soc. Lond. A 448, 97111.

L. N. Trefethen 2000 Spectral Methods in MATLAB. Society for Industrial and Applied Mathematics (SIAM).

G. Tryggvason & H. Aref 1983 Numerical experiments on Hele–Shaw flow with a sharp interface. J. Fluid Mech. 136, 130.

S. Wurlitzer , P. Steffen & T. M. Fischer 2000a Line tension in langmuir monolayers probed by point forces. J. Chem. Phys. 112, 59155918.

S. Wurlitzer , P. Steffen , M. Wurlitzer , Z. Khattari & T. M. Fischer 2000b Line tension in langmuir monolayers probed by point forces. J. Chem. Phys. 113, 38223828.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax