@misc{StermanCohenBestehornOron, author = {Sterman-Cohen, Elad and Bestehorn, Michael and Oron, Alexander}, title = {Rayleigh-Taylor instability in thin liquid films subjected to harmonic vibration}, series = {Physics of Fluids}, volume = {29}, journal = {Physics of Fluids}, number = {5}, issn = {1089-7666}, doi = {10.1063/1.4984082}, pages = {052105-1 -- 052105-17}, abstract = {The dynamics of the Rayleigh-Taylor instability of a two-dimensional thin liquid film placed on the underside of a planar substrate subjected to either normal or tangential harmonic forcing is investigated here in the framework of a set of long-wave evolution equations accounting for inertial effects derived earlier by Bestehorn, Han, and Oron ["Nonlinear pattern formation in thin liquid films under external vibrations," Phys. Rev. E 88, 023025 (2013)]. In the case of tangential vibration, the linear stability analysis of the time-periodic base state with a flat interface shows the existence of the domain of wavenumbers where the film is unstable. In the case of normal vibration, the linear stability analysis of the quiescent base state reveals that the instability threshold of the system is depicted by a combination of distinct thresholds separate for the Rayleigh-Taylor and Faraday instabilities. The nonlinear dynamics of the film interface in the case of the static substrate results in film rupture. However, in the presence of the substrate vibration in the lateral direction, the film interface saturates in certain domains in the parameter space via the mechanism of advection induced by forcing, so that the continuity of the film interface is preserved even in the domains of linear instability while undergoing the time-periodic harmonic evolution. On the other hand, sufficiently strong forcing introduces a new inertial mode of rupture. In the case of the normal vibration, the film evolution may exhibit time-periodic, harmonic or subharmonic saturated waves apart of rupture. The enhancement of the frequency or amplitude of the substrate forcing promotes the destabilization of the system and a tendency to film rupture at the nonlinear stage of its evolution. A possibility of saturation of the Rayleigh-Taylor instability by either normal or unidirectional tangential forcing in three dimensions is also demonstrated.}, language = {en} } @misc{StermanCohenBestehornOron, author = {Sterman-Cohen, Elad and Bestehorn, Michael and Oron, Alexander}, title = {Ratchet flow of thin liquid films induced by a two-frequency tangential forcing}, series = {Physics of Fluids}, volume = {30}, journal = {Physics of Fluids}, number = {2}, issn = {1089-7666}, doi = {10.1063/1.5010262}, pages = {022101-1 -- 022101-13}, abstract = {A possibility of saturating Rayleigh-Taylor instability in a thin liquid film on the underside of a substrate in the gravity field by harmonic vibration of the substrate was recently investigated [E. Sterman-Cohen, M. Bestehorn, and A. Oron, Phys. Fluids 29, 052105 (2017); Erratum, Phys. Fluids 29, 109901 (2017)]. In the present work, we investigate the feasibility of creating a directional flow of the fluid in a film in the Rayleigh-Taylor configuration and controlling its flow rate by applying a two-frequency tangential forcing to the substrate. It is shown that in this situation, a ratchet flow develops, and the dependence of its flow rate on the vibration frequency, amplitude, its periodicity, and asymmetry level is investigated for water and silicone-oil films. A cause for the emergence of symmetry-breaking and an ensuing flow in a preferred direction is discussed. Some aspects of a ratchet flow in a liquid film placed on top of the substrate are discussed as well. A comparison with the case of a neglected fluid inertia is made, and the differences are explained.}, language = {en} }