Application of Floquet theory to the stability of liquid films on structured surfaces

Vladimir Sergeevich Ajaev, Elizaveta Ya Gatapova, Oleg A. Kabov

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12 Citations (Scopus)


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.

Original languageEnglish
Article number122102
JournalPhysics of Fluids
Issue number12
Publication statusPublished - 2 Dec 2013

ASJC Scopus subject areas

  • Condensed Matter Physics

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