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Cooperation with: A. Münch (Humboldt-Universität zu Berlin, since Nov. 2003 also Heisenberg Fellow at the WIAS), C. Neto, K. Jacobs (Universität des Saarlandes, Saarbrücken), R. Seemann (Universität Ulm)
Description:
Dewetting of thin liquid films has attracted considerable attention due to its importance for technological applications and because it is a macroscopically observable process that is driven and influenced by the microscopic physics. Hereby, the focus has shifted from considering the stationary patterns that result from the dewetting to understanding the dynamical processes that lead to these states. This has introduced slippage as a relevant influence on the patterns that evolve ([3], [4], [5]); in particular, the appearance of finger instabilities at dewetting fronts has been associated with the possibility of even relatively short chain polymer films to slip on the substrate. Theoretical progress here depends strongly on the ability to develop, analyze, and solve lubrication-type models for the film dynamics, thereby addressing the presence of highly separated scales (in space as well as in time) and the fourth order of the involved partial differential equations. To this end, we have developed numerical methods that explore the special structure of the models to yield, in combination with spatial adaptivity and parallelization, efficient codes for the dewetting process, [1].
Using linear stability analysis, we showed that both under no-slip and full-slip boundary conditions, perturbations of the dewetting front are amplified, but the effect is greater by orders of magnitude in the full-slip case. Furthermore, the perturbations become much more asymmetrical under full-slip boundary conditions, while they develop symmetrical bulges under no-slip conditions, [2]. Additional computations that solve the lubrication model for the full three-dimensional flow confirm that these findings carry over into the nonlinear regime and are in good agreement with the experimental findings by C. Neto, K. Jacobs, and R. Seemann.
We are currently using multiple scale asymptotic techniques in order to formulate simpler problems that are able to resolve the small-scale structure in the vicinity of the apparent contact line and asymptotically match the inner solution to those solving the large-scale outer problem describing the shape and dynamics of the rim.
References:
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