Instability of multi-layered liquid films

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Abstract
The stability of an n‐layered liquid film flowing steadily down an inclined plane is investigated using linear theory. Neutral curves of all competing modes of instability have been obtained for various ratios of viscosity, density, and thickness. The interfacial mode instability due to the local downward step increase in density is found to occur only when such a density increase is large enough to provide sufficient gravitational potential. A local downward decrease in density seems to always be unstable. The interfacial mode instability associated with the local downward increase in viscosity is found to occur only if the Reynolds number is sufficiently small. The interfacial mode instability associated with the local downward step decrease in viscosity is found to be absent if the wavenumbers of the disturbances are smaller than a cutoff wavenumber.