On the breakup of fluid films of finite and infinite extent

We study the dewetting process of thin fluid films that partially wet a solid surface. Using a long-wave (lubrication) approximation, we formulate a nonlinear partial differential equation governing the evolution of the film thickness, h. This equation includes the effects of capillarity, gravity, and an additional conjoining/disjoining pressure term to account for intermolecular forces. We perform standard linear stability analysis of an infinite flat film, and identify the corresponding stable, unstable, and metastable regions. Within this framework, we analyze the evolution of a semi-infinite film of length L in one direction. The numerical simulations show that for long and thin films, the dewetting fronts of the film generate a pearling process involving successive formation of ridges at the film ends and consecutive pinch-off behind these ridges. On the other hand, for shorter and thicker films, the evolution ends up by forming a single drop. The time evolution as well as the final drops pattern show a competition between the dewetting mechanisms caused by nucleation and by free surface instability. We find that precise computations, requiring quadrupole precision of computer arithmetic, are often needed to avoid spurious results.