We consider instability of a liquid film on a substrate structured by an array of gas-filled grooves. The instability is driven by disjoining pressure, while the effect of structuring on viscous flow in the film is modeled by a square-wave variation of the slip length along the substrate. Linear stability criteria are established analytically using Floquet theory and compared with the predictions of a straightforward numerical approach, all in the framework of a lubrication-type model. Then, stability is analyzed for a more general model based on Stokes flow approximation; validity of the lubrication-type approach is discussed. The structuring is found to enhance the instability for a wide range of conditions. Resonant interaction between the interfacial deformations and the substrate structuring pattern leads to discontinuities in the dispersion curves, a situation analogous to appearance of gaps in the energy spectra seen in the applications of Floquet theory in solid state physics.
ASJC Scopus subject areas
- Condensed Matter Physics