WAVES ON A LIQUID FILM FLOWING DOWN THE LOWER SURFACE OF AN INCLINED PLANE
Yu.Ya. Trifonov
Kutateladze Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences (IT SB RAS), Novosibirsk, Russia
Keywords: viscous film flow, stability, nonlinear wave, interface
Abstract
The wave flow of a viscous liquid film along the lower surface of an inclined plane is investigated. Flow regimes with steadily traveling waves are identified, and their stability with respect to periodic linear perturbations with the same wavelength as in the nonlinear solution is examined. Calculations are performed using the full Navier-Stokes equations. Bifurcation lines are calculated for various inclination angles and Kapitsa numbers. Their structure is found to depend strongly on the Kapitsa number and only weakly on the inclination angle. At large inclination angles, a change in the bifurcation type from the wave-free solution occurs, and the film thickness vanishes at a certain distance from the bifurcation point. The critical angle at which film detachment occurs is determined as a function of the Kapitsa and Reynolds numbers.
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