Stokes theory of thin-film rupture

The structure of the ow induced by the van der Waals destabilization of a non-wetting liquid film placed on a solid substrate is studied by means of theory and numerical simulations of the Stokes equations. Our analysis reveals that lubrication theory, which yields hmin / 1=5 where hmin is the minimum film thickness and is the time until breakup, cannot be used to describe the local flow close to rupture. Instead, the slender lubrication solution is shown to experience a crossover to a universal self-similar solution of the Stokes equations that yields hmin / 1=3, with an opening angle of 37º off the solid.The authors thank J. Rivero-Rodríguez and B. Scheid for key numerical advice, A.L. Sánchez, C. Martínez-Bazán and J.M. Gordillo for their enduring teaching and encouragement, W. Coenen for carefully reading the manuscript, and H.A. Stone for sharing his insights, and for his kind hospitality at the Complex Fluids Group, Princeton. This research was funded by the Spanish MINECO, Subdirección General de Gestión de Ayudas a la Investigación, through project DPI2015-71901-REDT, and by the Spanish MCIU-Agencia Estatal de Investigación through project DPI2017- 88201-C3-3-R, partly nanced through FEDER European funds. A.M.-C. also acknowledges support from the Spanish MECD through the grant FPU16/02562 and to its associated program Ayudas a la Movilidad 2018 during his stay at Princeton University