The role of external influences in the formation of waves on the surface of a flowing-down film of a viscious fluid

The example of two non-stationary forces is used to study the impact of external influences leading to the occurrence of additional ponderomotive forces on the wave modes of the film freely flowing down a vertical surface. In the first case, the ferromagnetic fluid film is affected by the electric field. For the given forces, in the case of small flow rates, the problem is reduced to the solution of a model equation for the perturbation of the film thickness. The numerical solutions of the problem are obtained, and several characteristic scenarios of evolution of periodical perturbations are considered. It is shown that changes in the boundaries of the region of linear stability of the unperturbed flow with a flat free surface under the influence of ponderomotive forces has a great impact on the flow.