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The levelling of a thin liquid film has been analysed experimentally,theoretically, and numerically. The purpose of this contribution is to comparesolutions from two different finite element models: one based on the 2DNavier-Stokes equations, and the other based on a simplification thereof, knownas the lubrication approximation. The latter is significantly lesscomputationally expensive, hence it is desirable to know in which parameterrange this approximation is valid. As a benchmark problem, we consider theclassical dam-break problem. This paper establishes the validity window of thelubrication approximation in terms of the Reynolds number, Froude number, andfilm aspect ratio. To validate the solutions produced by the solver,experimental data has been obtained for the levelling of silicone oil. The freesurface velocity measured experimentally is compared to that produced by thetwo numerical models and found to have relatively good agreement. Thelubrication approximation is then compared with the Navier-Stokes model for arange of Reynolds and Froude numbers, and for a range of film aspect ratios.The results show that the lubrication approximation is remarkably robust andparticularly accurate for low Reynolds and Froude numbers, for which inertialeffects are negligible. Using fixed Reynolds and Froude numbers of 100 and 0.01respectively, the lubrication approximation is accurate for aspect ratios up to1%.

Comparison of Lubrication Approximation and Navier-Stokes Solutions for Dam-Break Flows in Thin Films