When   Monday, May 18, 2009   Time   4:00 PM - 5:00 PM  
Where   Technological Instit M 416 2145 Sheridan Rd.   map it
Audience   - Faculty/Staff - Student - Public
Contact   Molly E Scanlon   +1 847 491 5586  
Group   McCormick-Colloquia Engineering Sciences and Applied Mathematics

Applied Math Colloquium

Title: Transient and self-similar dynamics in thin film coarsening

Speaker: Dr. Michael Gratton, Northwestern University

Abstract:

We study coarsening in a simplified model of one-dimensional thin viscous films on hydrophobic substrates. Lubrication theory shows that such films are unstable and dewet to form droplets that then aggregate over long timescales. The masses and positions of the droplets can be described by a coarsening dynamical system (CDS) consisting of ODEs and deletion rules. We develop discrete and continuous mean-field models that reproduce the well-known N(t)=O(t^{-2/5}) long-time power law for the number of drops. A Lifshitz-Slyozov-Wagner-type (LSW) continuous model predicts the self-similar distribution of drop masses matching with histograms produced by CDS simulations and the discrete mean field model. We also describe the distribution of drops following homogeneous vs. heterogeneous dewetting and use these as initial conditions for the CDS simulations that yield characteristic ``staircasing'' transients. These can also include recurring spike formation behavior in the mass distribution. For idealized initial conditions, we show that the transient dynamics can span the full coarsening process, bypassing the power law regime entirely.