Pattern formation in unstable thin liquid films under the influence of antagonistic short-and long-range forces

Abstract

Various stages of evolution of the surface instability and pattern formation are investigated for unstable thin (<100 nm) fluid films subjected to the long-range van der Waals repulsion and a shorter range attraction. The complete three-dimensional morphology is resolved based on numerical solutions of the nonlinear 2D thin film equation. In the first phase of evolution, initial random nonhomogeneities are quickly reorganized into a small amplitude undulating structure consisting of long "hills" and "valleys." Different types of patterns are formed thereafter, depending on the initial mean thickness vis-à-vis location of the minimum in the intermolecular force curve. Dewetting of relatively thick films occurs by circular isolated holes which grow and coalesce to form a large-scale structure with intervening pools and ridges of the liquid, which eventually decay into increasingly circular droplets. In thinner films, the shallow depressions merge and the long ridges of the bicontinuous structure mature, fragment, and directly transform into increasingly circular droplets, which continue to grow by ripening and merger. The characteristics of a pattern, its pathway of evolution, and the morphology at the onset of dewetting thus depend crucially on the form of the intermolecular potential in an extended neighborhood of the initial thickness. The linear and 1D nonlinear analyses used hitherto fail completely in prediction of morphological patterns, but can predict their length scales rather well.