Stability of Falling Film Flow
project by Dipl.-Math. Christoph Albert
A falling film is a thin layer of water or any other liquid which, driven by gravity, is running down a vertical plane. They are employed in a large variety of different applications, e.g. in the food industry, in the pharmaceutical industry or in nuclear reactors. The small thickness of the film facilitates the heat transfer between the wall and the liquid, whereas mass transport between the liquid and the surrounding gas is enhanced by the large area of the free surface. The critical Reynolds number of the fundamental, steady velocity profile depends, among other things, on the angle of inclination of the plane. A film on a vertical plane is even unstable at every positive Reynolds number, and will therefore, under perfectly ordinary conditions, exhibit waves that evolve into a rich variety of patterns. The pioneering experiments in  were actually conducted with tap water in the kitchen of the house in which Pyotr Kapitza and his son were held under arrest. The appearance of waves on the surface of a film is known to have a huge impact on the rates at which transport processes to and from the film take place. The goal of this project is to increase the understanding of transport processes in wavy falling films, and to gain insight on the influence additional physics, like Marangoni effects and non-Newtonian rheological behaviour, have on the critical Reynolds numbers.
In order to perform highly resolved Direct Numerical Simulations of falling films, we employ the Finite Volume Code Free Surface 3D (FS3D) . An immediate goal is the extension of this solver to incorporate the additional physical effects.
It was found that high interfacial curvatures in the capillary wave region of the film pose a serious challenge for the treatment of surface tension. Since the interface is especially thin in this area, spurious oscillations, so called parasitic currents, can easily dominate the whole flow there. In simulations performed with traditional approaches for surface tension, like the Continuum Surface Stress (CSS) model, we noticed unphysical vortex structures in the film. Reliable results, which do not behave unphysical after grid refinement, could only be achieved by utilizing a balanced Continuum Surface Force (CSF) algorithm, together with second order accurate curvature calculations via height functions.The results of these simulations were validated by comparison to the experimental data in  and .
-  Kapitza, P.L., Kapitza, S.P. (1949). Wave flow of thin liquid layers. Zh.Eksp.Teor. Fiz., 19, 105-120
-  Rieber, M., PhD-Thesis, ITRL-Stuttgart, 2004
-  Nosoko, T., Yoshimura, P. N., Nagata, T., Oyakawa, K. (1996). Characteristics of two-dimensional waves on a falling liquid film. Chem. Eng. Sci., 51, 725 – 732
-  Dietze, G., Flow separation in falling liquid films, Sierke Verlag, 2010.