Linear stability analysis of a sharp-interface model for dewetting thin films
- King, John R.
- Münch, Andreas
- Wagner, Barbara
2010 Mathematics Subject Classification
- 76M45 34B15 65M06
2008 Physics and Astronomy Classification Scheme
- sharp-interface model, slippage, stability, dewetting, fingering, Lubrication models, rim
The 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.
- J. Engrg. Math., 63 (2009) pp. 177--195.