Browsing by Author "King, John R."
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- ItemIntermediate-asymptotic structure of a dewetting rim with strong slip(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Evans, Peter L.; King, John R.; Münch, AndreasWhen a thin viscous liquid film dewets, it typically forms a rim which spreads outwards, leaving behind a growing dry region. We consider the dewetting behaviour of a film, when there is strong slip at a liquid-substrate interface. The film can be modelled 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.
- ItemLinear stability analysis of ta sharp-interface model for dewetting thin films(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) King, John R.; Münch, Andreas; Wagner, BarbaraThe topic of this study concerns the stability of the three-phase contact-line of a dewetting thin liquid film on a hydrophobised substrate driven by van der Waals forces. The role of slippage in the emerging instability at the three-phase contact-line is studied by deriving a sharp-interface model for the dewetting thin film via matched asymptotic expansions. This allows for a derivation of travelling waves and their linear stability via eigenmode analysis. In contrast to the dispersion relations typically encountered for the finger-instabilty, where the dependence of the growth rate on the wave number is quadratic, here it is linear. Using the separation of time scales of the slowly growing rim of the dewetting film and time scale on which the contact line destabilises, the sharp-interface results are compared to earlier results for the full lubrication model and good agreement for the most unstable modes is obtained.