Steady‐state traveling waves on the surface of a viscous liquid film falling down on vertical wires and tubes

Abstract

Abstract Various nonlinear wavy regimes of a viscous liquid film flowing down vertical wires and tubes were calculated using the integral method. The linear stability analysis of the trivial smooth solution was compared with the results published previously. In the region of linear instability, the competition among the gravity, viscous and capillary forces formed the steady‐state traveling solutions of finite amplitudes. At least two families of waves were shown to be parameterized by the wave number for given values of external parameters (Reynolds number, cylinder radius and physical characteristics of liquid). The basic waves characteristics depended on external parameters and on wave number. The intensity of wavy processes increased with decreasing cylinder radius. The calculations show the catastrophic growth of wave amplitude, when the system flows down a vertical tube of sufficiently small radius and moves into the linear, unstable region.