Coarsening: transient and self-similar dynamics in 1-D

Monday, March 23, 2009 - 12:15pm - 1:00pm
EE/CS 3-180
Thomas Witelski (Duke University)
Motivated by the dewetting of viscous thin films on hydrophobic
substrates, we study models for the coarsening dynamics of interacting
localized structures in one dimension.
For the thin films problem, lubrication theory
yields a Cahn-Hilliard-type governing PDE which describes spinodal dewetting
and the subsequent formation of arrays of metastable fluid droplets.
The evolution for the masses and positions of the droplets can be reduced
to a coarsening dynamical system (CDS) consisting of a set of coupled
ODEs and deletion rules. Previous studies have established that the number
of drops will follow a statistical scaling law, N(t)=O(t-2/5). We derive
a Lifshitz-Slyozov-Wagner-type (LSW) continuous model for the drop size distribution and compare it with discrete models derived from the CDS.
Large deviations from self-similar LSW dynamics are examined on short- to
moderate-times and are shown to conform to bounds given by Kohn and Otto.
Insight can be applied to similar models in image processing and other
problems in materials science. Joint work with M.B. Gratton (Northwestern
Applied Math).
MSC Code: