Impact of slippage on the morphology and stability of a dewetting rim
- Münch, Andreas
- Wagner, Barbara
2010 Mathematics Subject Classification
- 34E15 35B36 76D08
2008 Physics and Astronomy Classification Scheme
- 68.15.+e 47.54.+r 68.37.Ps
- asymptotic expansions, dewetting films, stability analysis
In this study lubrication theory is used to describe the stability and morphology of the rim that forms as a thin polymer film dewets from a hydrophobized silicon wafer. Thin film equations are derived from the governing hydrodynamic equations for the polymer to enable the systematic mathematical and numerical analysis of the properties of the solutions for different regimes of slippage and for a range of time scales. Dewetting rates and the cross sectional profiles of the evolving rims are derived for these models and compared to experimental results. Experiments also show that the rim is typically unstable in the spanwise direction and develops thicker and thinner parts that may grow into ``fingers''. Linear stability analysis as well as nonlinear numerical solutions are presented to investigate shape and growth rate of the rim instability. It is demonstrated that the difference in morphology and the rate at which the instability develops can be directly attributed to the magnitude of slippage. Finally, a derivation is given for the dominant wavelength of the bulges along the unstable rim.
- J. Phys.: Condens. Matter, 23 (2011) pp. 184101/1--184101/12.