| Περίληψη: | The gravity-driven film flow over a flat inclined surface is a fundamental problem in fluid mechanics. This flow appears in many significant industrial, environmental and biomedical processes. Although this flow is a classic problem in fluid mechanics, nevertheless, in the real world, the substrates on which the films move exhibit some kind of roughness, either accidentally or intentionally. The interaction between the underlying topography and the fluid layer triggers a complicated dynamical behavior that favors the formation of eddies inside the bottom undulations and resonant standing waves at the free surface of the flow. Even the small fluctuations of the substrate can significantly affect the shape of the free surface. Besides the topological variations, the rheology of the material can affect the fluid flow since the liquids involved are often polymer solutions which generally exhibit non-Newtonian properties. Moreover, a fully wetting state cannot always be achieved. Recent studies indicate that the wetting state of the substrate depends both on its geometrical and liquid properties, while air inclusions can be formed during the coating process of these surfaces resulting in products of inferior quality. Regarding the calculation of the critical parameters for the onset of interfacial instabilities, the existing literature is mainly limited to the Newtonian case. However, the polymeric properties may affect the stability of the flow significantly. Due to the widespread usage of polymer solutions in industrial applications, the understanding of the mechanisms leading to the stabilization/destabilization of the flow is of the utmost importance, while the latter gives the potential for instability control through the development of appropriately tailored substrates.
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