Film rupture in the diffuse interface model coupled to hydrodynamics

The process of dewetting of a thin liquid film is usually described using a long-wave approximation yielding a single evolution equation for the film thickness. This equation incorporates an additional pressure term—the disjoining pressure—accounting for the molecular forces. Recently a disjoining pressure was derived coupling hydrodynamics to the diffuse interface model [L. M. Pismen and Y. Pomeau, Phys. Rev. E $62,$ 2480 (2000)]. Using the resulting evolution equation as a generic example for the evolution of unstable thin films, we examine the thickness ranges for linear instability and metastability for flat films, the families of stationary periodic and localized solutions, and their linear stability. The results are compared to simulations of the nonlinear time evolution. From this we conclude that, within the linearly unstable thickness range, there exists a well defined subrange where finite perturbations are crucial for the time evolution and the resulting structures. In the remainder of the linearly unstable thickness range the resulting structures are controlled by the fastest flat film mode assumed up to now for the entire linearly unstable thickness range. Finally, the implications for other forms of disjoining pressure in dewetting and for spinodal decomposition are discussed.