Free Surface Model Derived From the Analytical Solution of Stokes Flow in a Wedge

The formation of a thin liquid film onto a moving substrate is a commonly encountered industrial process, and one that is encountered in lubrication, oil extraction processes, and coating flows. The formation of such a film is analyzed via the analytical Stokes flow solution for the flow in a wedge bounded on one side by a free surface and on the other by a moving surface. The full solution is obtained by numerically integrating a set of ordinary differential equations from far downstream, in the region of the final film thickness. The results show excellent agreement with the results obtained by the Bretherton equation, the Ruschak equation, the Coyne and Elrod model, and a two-dimensional free surface finite element simulation of the problem.