Coarsening dynamics of dewetting films

Abstract

Lubrication theory for unstable thin liquid films on solid substrates is used to model the coarsening dynamics in the long-time behavior of dewetting films. The dominant physical effects that drive the fluid dynamics in dewetting films are surface tension and intermolecular interactions with the solid substrate. Instabilities in these films lead to rupture and other morphological changes that promote nonuniformity in the films. Following the initial instabilities, the films break up into near-equilibrium droplets connected by an ultrathin film. For longer times, the fluid will undergo a coarsening process in which droplets both move and exchange mass on slow time scales. The dynamics of this coarsening process will be obtained through the asymptotic reduction of the long-wave PDE governing the thin film to a set of ODEs for the evolution of the droplets. From this, a scaling law that governs the coarsening rate is derived.

A Nonlocal Continuum Model for Biological Aggregation

“…This is the hallmark of many pattern-forming systems in nature. Non-biological examples include the Cahn-Hilliard equation, which models the spinodal decomposition of binary alloys (Cahn, 1968;Eilbeck et al, 1989;Bates and Fife, 1990), droplet formation in dewetting fluid films (Bertozzi et al, 2001;Oron and Bankoff, 2001;Glasner and Witelski, 2003), and self-aggregation of finite-sized particles (Holm and Putkaradze, 2005). These models are well-known to exhibit coarsening dynamics, in which small localized clumps form and merge into larger clumps over time.…”

Thin film dynamics: theory and applications

“…As suggested by Figure 12, this time scale increases, T C → ∞, as ǫ → 0, a dramatically different dependence on ǫ than the droplet formation time-scale, T D → 0. A model for the coarsening dynamics, in terms of droplet motion and mass transfer, is developed in [49].…”

Blowup and dissipation in a critical-case unstable thin film equation

“…In these cases, stable configurations of n steady-state dropletsH 0 (x) exist. Numerical simulations of these problems remains an open question since the solutions are extremely sensitive to the mass, any perturbation of the mass will lead to blow-up as the end-product of a merging (coarsening [14,35]) instability, see § 6.4. Issues related to the numerical solution of the PDE with compact initial data and the interaction of droplet solutions are discussed further below.…”