Prof. Alex Oron, Department of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, IL

Mo., 5.11.2012, 15:30 Uhr
Stability analysis of a thin liquid film on a axially oscillating cylindrical surface

Several intriguing experimental results related to the behavior of liquid films and drops on forced solid substrates have been recently reported in literature. They sparked various activities on the modeling front.
Stability of an axisymmetric liquid film on a horizontal cylindrical surface subjected to axial harmonic forcing is investigated in both high- and low-frequency limits. Using long-wave asymptotic expansions we derive and analyze the nonlinear evolution equations describing the nonlinear dynamics of this physical system in terms of the time-averaged film thickness in the case of a high-frequency limit and the film thickness in the case of a low-frequency limit.
In the high-frequency limit, we carry out the linear stability analysis for a film of a constant thickness which shows that axial forcing of the cylinder may result in either stabilization or destabilization of the system with respect to the unforced one, depending on the choice of the parameter set. The analysis is extended to the weakly nonlinear stage and reveals that the system may bifurcate from the equilibrium either subcritically or supercritically depending on the parameters of the problem, but independently on the forcing amplitude. The weakly nonlinear analysis suggests that in the supercritical regime, the amplitude of a steady state decreases with an increase in the forcing frequency.
In the low-frequency limit, we find that the capillary long-time film rupture typical for the case of a film on a static cylinder can be arrested in the nonlinear stage if the substrate is forced with a sufficiently high amplitude and/or frequency. The threshold for the rupture prevention is determined by the product of the dimensionless amplitude and frequency of forcing, whereas the critical value of this product is independent of forcing parameters. This threshold delineates the borderline between the ruptured and nonruptured subdomains.