Nonlinear dynamics of a thin nonisothermal liquid film on an axially oscillating cylindrical surface

The nonlinear dynamics of a nonisothermal thin liquid film on a horizontal cylindrical surface subjected to axial harmonic vibration is investigated in this paper. It is found that the capillary instability of an axisymmetric film on a still cylinder can be saturated via the Marangoni effect by heating the film at the gas side, similar to the saturation of the Rayleigh-Taylor instability in the planar case. If the capillary instability is not saturated by the Marangoni effect, the combined capillary-Marangoni instability can be saturated by the harmonic axial forcing provided that the forcing amplitude exceeds a certain critical value depending on the rest of parameters. The critical amplitude is demonstrated to increase with the Marangoni number when other parameters are fixed. The critical forcing amplitude at a given forcing frequency is shown to be well approximated by a piecewise linear function of the Marangoni number.