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Gravity-Driven Film Flow: Design of Bottom Topography

C. Heining[1] and N. Aksel[1]

[1]Applied Mechanics and Fluid Dynamics, University of Bayreuth, Bayreuth, Germany

We study the gravity-driven film flow of a Newtonian liquid down an inclined plane. Many applications such as heat- and mass exchangers and evaporators or film coaters require undulated or rippled bottom topographies. In these cases, the interplay of gravity, surface tension and inertia leads to a response of the interface which furthermore strongly depends on the shape of the bottom topography. Instead of determining the free surface position as in the case of the direct problem, we prescribe a free surface shape and seek the corresponding bottom topography. Furthermore, we consider the stability of the system and derive conditions for the onset of instabilities at the free surface in form of surface waves.