James C.
Alexander Mathematics Case Western Reserve University |
Andrew J.
Bernoff Mathematics Harvey Mudd College |
Elizabeth K.
Mann Physics Kent State University |
Jacob Wintersmith in Elizabeth Mann's Lab in the Physics Department at Kent State. The Brewster Angle Microscope (BAM) used for our experiments is in the background. |

J. Adin
Mann, Jr Chemical Engineering Case Western Reserve University |
Jacob R. Wintersmith Physics '06 Harvey Mudd College |
Lu Zou Physics Kent State University |

We report on both experimental and
theoretical studies of molecularly-thin Langmuir films on the
surface of a quiescent subfluid. The film covers the entire fluid
surface, but several 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, primarily that of Stone &
McConnell (1995) and Lubensky & Goldstein (1996), identifying the
dominant effects via dimensional analysis, and reducing the system to a
more tractable form. The result is a free boundary problem where 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.

References:

References:

- D. K. Lubensky & R. E. Goldstein, "Hydrodynamics
of Monolayer Domains
at the Air-Water Interface"

Physics of Fluids**8**, 843 (1996). - H.A. Stone & H. M. McConnell, "Hydrodynamics of
Quantized Shape Transitions of Lipid Domains"

Proc. Roy. Soc. A 448 97 (1995).

Below we show a
series of Brewster Angle Microscopy photos (by Lu Zou) from Prof.
Elizabeth Mann's laboratory at Kent State University.

These
numerical simulations were developed by Jacob Wintersmith under the
supervision of Prof. Andrew Bernoff at Harvey Mudd College. They use a
boundary integral method for a hydrostatic Langmuir layer driven by a
line tension at the boundary and damped by a Stokesian subfluid.
Details can be found in the preprint above.

We
can determine the line tension from experimental observations by
digitizing the experimental images to determine the initial location of
the boundary, evolving the boundary forward with the boundary integral
code and then comparing the numerical results to the experiemntal
observations. The line tension determines how fast the Langmuir domain
relaxes; by minimizing the error between the experimental results
and the numerical evolution we can determine the line tension within a
few percent. The experiments were conducted by Lu Zou and the image processing and numerics were produced by Jacob Wintersmith

Below is a motion picture showing a comparison between the numerics and experiments.

These results have now appeared in an article:

- Jacob R. Wintersmith, Lu Zou, Andrew J. Bernoff, James C. Alexander, J. Adin Mann, Jr., Edgar E. Kooijman, and Elizabeth K. Mann

"Determination of interphase line tension in Langmuir films," Phys. Rev. E**75**, 061605 (2007). (Reprint)

Last Updated on 9-27-07