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Applied Mathematics Colloquium
Friday, September 26, 11:30 am
Cullimore Lecture Hall II
New
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Domain Evolution and Relaxation in Langmuir Films
Andrew Bernoff
Department of Mathematics
Claremont, CA
Abstract
We report on an experimental and theoretical study of Langmuir layers, defined
as a molecularly thin polymer layer on the surface of a
subfluid. Langmuir layers can have multiple phases (e.g. fluid, gas, liquid crystal, isotropic or anisotropic solid); at phase
boundaries a line tension force is observed. We first consider two co-existing fluid phases; specifically a localized phase embedded
in an infinite secondary phase. When the localized phase is stretched (by a transient stagnation flow), it takes the form of a bola
consisting of two roughly circular reservoirs connected by a thin tether. This shape then relaxes 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 thin. We
model these experiments by taking previous descriptions of the full hydrodynamics (primarily those of Stone & McConnell and Lubensky &
Goldstein), 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. The
problem has a boundary integral formulation which allows us to numerically simulate the tether relaxation; comparison with the
experiments allows us to estimate the line tension in the system, often to within 1%. As time allows we will also report on some other
phenomena observed in Langmuir systems, including collapse of gas phase bubbles, creation of foams, co-existence of three or more fluid
phases, elastic buckling of surface layers, and formation of dogbone and labyrinth patterns due to dipolar repulsion in the layer.