-----------------------------------------------------------
Applied Mathematics Colloquium
Friday, May 1, 11:30 am
Cullimore Lecture Hall II
-----------------------------------------------------------
Beyond Wrinkles: Stress
and Fold Localization in Thin Elastic Membranes
Ka Yee Lee
Department of Chemistry, James Franck Institute, Materials
Research Science and
Chicago, IL
Abstract
Thin elastic membranes supported on fluid or elastic foundations deviate from
their flat geometries upon compression. We demonstrate that the periodic and
much studied wrinkled state is but one possible solution for such strained
membranes. Folds, sharply localized solutions, appear whenever the membrane is
compressed beyond a third of its initial wrinkle wavelength. Eventually the
surface transforms into a symmetry broken state with flat regions of membrane
coexisting with locally folded points, reminiscent of a crumpled unsupported
membrane. We study this transition in many systems including lipid monolayers on liquid subphases of
differing viscosity and use neutron and x-ray reflectivity to elucidate the
role of the subphase in setting the wrinkle and fold
size. The folding transition is particularly important for lung surfactant monolayers, allowing for the creation of a 3D reservoir
that is associated with a 2D film so that the collapsed materials at the end of
exhalation can be easily reincorporated into the film for the next breathing
cycle.