A film flow model for analysing gravity-driven, thin wavy fluid films

• The fluid film model is based on lubrication approximation but includes inertial terms.
• One grid cell over the film height combines accuracy with computational efficiency.
• Successful multivariate validation of the film flow model was performed.
• The film flow model is attractive for large-scale simulations of complex film runoff.
• Wave and contact line dynamics can be captured.

To analyse the physics underlying gravity-driven runoff of thin wavy films, a film flow model is developed, and is solved with computational fluid dynamics. This model is based on the lubrication theory, and takes into account the gravitational, wall shear and surface tension forces. A key characteristic of the model is that it assumes only one computational cell over the film height, which enables studying film flow on larger computational domains. A main aim of this study is to perform a detailed validation of the numerical model. The film flow model is validated against several experiments of gravity-driven, thin fluid films on smooth surfaces. The time-averaged film thickness and the fluid speed profiles predicted by the model show very good agreement with experimental results. Similarly, the film flow model is able to predict the wave speeds with sufficient accuracy. The energy spectra of the waves, where higher frequency waves are present in film flows at higher Reynolds numbers, show an exponentially decaying trend at these high frequencies. The model performs better than the Nusselt equation for film flows, which under-predicts the time-averaged film thickness and over-predicts the time-averaged fluid speeds, even for flows at low Reynolds numbers. The film flow model is compared qualitatively for fingering behaviour. This model also allows to investigate film flows on large surfaces, which can be rough, curved and of complex geometrical shape.