Skip to main content
×
Home
    • Aa
    • Aa

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)...
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.

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.

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

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.

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

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.

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

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.

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

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
Type Description Title
VIDEO
Movies

Alexander et al. supplementary movie
Movie 2. A numerical evolution of the Inviscid Langmuir Layer Stokesian Subfluid Model computed via a boundary integral method. The domain is originally a circle of radius 3. The domain is subject to a straining flow for 5 units of time and is allowed to relax for approximately 40 units of time. It gets stretched out to a length of 60. After the straining field is released, the domain assumes the classic bola shape, and eventually relaxes back to an ellipse approaching the energy-minimizing circular configuration. There are 32 frames per unit of time in the motion picture.

 Video (2.1 MB)
2.1 MB
VIDEO
Movies

Alexander et al. supplementary movie
Movie 1. Brewster Angle Microscopy images of a relaxing Langmuir layer. This movie shows a bola relaxing to a circular Langmuir domain. The brighter domains consist of about 5 layers of 8CB (Octylcyanobiphenyl), while the dark background consists of 3 layers of 8CB. First the fluid is sheared distorting the domain to a bola with a thin tether; this bola then slowly relaxes back to a circular shape. This is an 8 second movie of the relaxation of a bola. The image is approximately 4mm by 5mm. Note that the image is distorted as it is filmed at the Brewster Angle (approximately 53 degrees)

 Video (849 KB)
849 KB