Comparison of models for wave regimes of liquid film downflow in the linear approximation

A number of the most well-known models of the wave flow of thin liquid films down a vertical plane are considered. For each model, a linear stability analysis of plane-parallel motion is carried out. Neutral stability curves, dispersion relations, and disturbed flow patterns for various values of problem parameters are constructed. It is found that, among all the models of the first order of accuracy in terms of a small parameter, i.e., the ratio of the film thickness to the length of characteristic disturbances, the proposed divergent system of equations provides the most adequate description of the flows of interest.