Thin-film free boundary problems for partial wetting
We present a novel framework to solve thin-film equations with an explicit non-zero contact angle, where the support of the solution is treated as an unknown. The algorithm uses a finite element method based on a gradient formulation of the thin-film equations coupled to an arbitrary LagrangianEulerian method for the motion of the support. Features of this algorithm are its simplicity and robustness. We apply this algorithm in 1D and 2D to problems with surface tension, contact angles, and gravity.
free boundary problem thin films numerical methods