Stability of a generalized Newtonian liquid falling film on an oscillating inclined planeстатья
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Аннотация:We consider the impact of periodical finite-amplitude perturbations induced byoscillations 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; fornon-Newtonian liquids, the mean parameters of the basic state depend on theplane’s oscillations. We solve the eigenvalue problem for linearized generalizedNavier-Stokes equations using long-waves expansion and Floquet theory. Weprovide results of calculations for shear-thinning and shear-thickening Carreauliquids. The plane oscillations stabilize or destabilize the flow depending ontheir frequency; the effect does not qualitatively depend on the amplitude. ForNewtonian liquid, diapasons of stabilizing and destabilizing frequency alternateup to infinity. For shear-thinning liquids, low-frequency oscillations destabilizethe flow, while high-frequency ones stabilize it increasing the critical Reynoldsnumber; shear-thickening liquids show the opposite behavior.