Stability of a generalized Newtonian liquid falling film on an oscillating inclined plane

•Oscillations of the supporting plane strongly affect the stability of a falling film.•Complex liquid rheology enhances the effect of the oscillations.•Depending on frequency, the oscillations stabilize or destabilize the flow.•Inertia plays a major role for the oscillations effect on the film stability. We consider the impact of periodical finite-amplitude perturbations induced by oscillations of the supporting plane on the natural instability of a falling film. The oscillations change the basic state of the flow from steady to periodical; for non-Newtonian liquids, the mean parameters of the basic state depend on the plane’s oscillations. We solve the eigenvalue problem for linearized generalized Navier-Stokes equations using long-waves expansion and Floquet theory. We provide results of calculations for shear-thinning and shear-thickening Carreau liquids. The plane oscillations stabilize or destabilize the flow depending on their frequency; the effect does not qualitatively depend on the amplitude. For Newtonian liquid, diapasons of stabilizing and destabilizing frequency alternate up to infinity. For shear-thinning liquids, low-frequency oscillations destabilize the flow, while high-frequency ones stabilize it increasing the critical Reynolds number; shear-thickening liquids show the opposite behavior.