Transient and self-similar dynamics in thin film coarsening

We study coarsening in a simplified model of one-dimensional thin films of viscous fluids 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)N(t)=O(t−2/5) long-time statistical 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 versus heterogeneous dewetting and use these as initial conditions for the CDS simulations that yield characteristic “staircasing” transients. Transients 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.