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Intermediate-asymptotic structure of a dewetting rim with strong slip
Institute of Mathematics, Humboldt University of Berlin Unter den Linden 6, 10099 Berlin, Germany E-mail address: pevans{at}mathematik.hu-berlin.de
School of Mathematical Sciences, University of Nottingham Nottingham NG7 2RD, UK E-mail address: john.king{at}nottingham.ac.uk
Institute of Mathematics, Humboldt University of Berlin Unter den Linden 6, 10099 Berlin, Germany E-mail address: muench{at}mathematik.hu-berlin.de
When a thin viscous liquid film dewets, it typically forms a rim which spreads outwards, leaving behind a growing dry region. We consider the dewetting behavior of a film, when there is strong slip at a liquid-substrate interface. The film can be modeled by two coupled partial differential equations (PDEs) describing the film thickness and velocity. Using asymptotic methods, we describe the structure of the rim as it evolves in time and the rate of dewetting, in the limit of large slip lengths. An inner region emerges, closest to the dewetted region, where surface tension is important; in an outer region, three subregions develop. This asymptotic description is compared with numerical solutions of the full system of PDEs.