Similarity solutions for van der Waals rupture of a thin film on a solid substrate

Rupture of a thin viscous film on a solid substrate under a balance of destabilizing van der Waals pressure and stabilizing capillary pressure is shown to possess a countably infinite number of similarity solutions in each of which the horizontal lengthscale decreases like (t(R)-t)(2/5) and the film thickness decreases like (t(R)-t)(1/5), where t(R)-t is the time remaining before rupture. Only the self-similar solution corresponding to the least oscillatory curvature profile is observed in time-dependent numerical simulations of the governing partial differential equation. The numerical strategy employed to obtain the self-similar solutions is developed from far-field asymptotic analysis of the similarity equations. (C) 1999 American Institute of Physics. [S1070-6631(99)03509-6].