  The levelling of a thin liquid film has been analysed experimentally,
theoretically, and numerically. The purpose of this contribution is to compare
solutions from two different finite element models: one based on the 2D
Navier-Stokes equations, and the other based on a simplification thereof, known
as the lubrication approximation. The latter is significantly less
computationally expensive, hence it is desirable to know in which parameter
range this approximation is valid. As a benchmark problem, we consider the
classical dam-break problem. This paper establishes the validity window of the
lubrication approximation in terms of the Reynolds number, Froude number, and
film aspect ratio. To validate the solutions produced by the solver,
experimental data has been obtained for the levelling of silicone oil. The free
surface velocity measured experimentally is compared to that produced by the
two numerical models and found to have relatively good agreement. The
lubrication approximation is then compared with the Navier-Stokes model for a
range of Reynolds and Froude numbers, and for a range of film aspect ratios.
The results show that the lubrication approximation is remarkably robust and
particularly accurate for low Reynolds and Froude numbers, for which inertial
effects are negligible. Using fixed Reynolds and Froude numbers of 100 and 0.01
respectively, the lubrication approximation is accurate for aspect ratios up to
1%.

Fluid Dynamics