Waves on down-flowing fluid films: Calculation of resistance to arbitrary two-dimensional perturbations and optimal downflow conditions

Wavy downflow of viscous fluid films is studied. The full Navier–Stokes equations are used to calculate the hydrodynamic characteristics of the flow. The stability of calculated nonlinear waves to arbitrary two-dimensional perturbations is considered within the framework of the Floquet theory. It is shown that, for small values of the Kapitza number, the waves are stable over a wide range of wavelengths and values of the Reynolds number. It is found that, as the Kapitza number increases, the parameter range where nonlinear waves are calculated is divided into a series of alternating zones of stable and unstable solutions. A large number of narrow zones where the solutions are stable are revealed on the wavelength-Reynolds number parameter plane for large values of the Kapitza number. Optimal regimes of film downflow that correspond to the minimum value of average film thickness for nonlinear waves with different wavelengths are determined. The basic characteristics of these waves are calculated in a wide range of Reynolds and Kapitza numbers.