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

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Abstract
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 (tR−t)2/5 and the film thickness decreases like (tR−t)1/5, where tR−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.