Ph.D Student | Selin Duruk |
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Subject | Nonlinear Dynamics of Thin Liquid film on Vibrating Surfaces |

Department | Department of Mechanical Engineering |

Supervisor | Full Professor Oron Alexander |

Full Thesis text |

The goal of the present thesis is to analyze the nonlinear dynamics of thin liquid films on horizontally vibrating surfaces of several topological forms, in the high-frequency limit. The physical systems for the corresponding geometries are expressed with the help of Navier-Stokes equations and the appropriate boundary conditions to construct the mathematical model. This problem is treated in a way that enables reduction to a single partial differential equation, preserving the governing properties and nonlinear contributions. Each problem of the specific topology is first reduced to a dimensionless form to define the order of the parameters and choosing a small parameter from this set that would lead to possible reductions. Since our concern is focused on thin-film coatings, it is assumed that the film thickness is much smaller compared to the characteristic longitudinal wave length. The next step to reflect the effect of high-frequency oscillation is determined by two different time variables. To be able to investigate the changes of the dynamics of the system due to vibration, the relevant fields such as velocity, pressure and the film interface are decomposed into their averaged and pulsating components. The entire set of equations and the boundary conditions are split into two set of equations, in which the pulsating set represents a linear problem that can be solved explicitly and its nonlinear contributions emerge in the averaged set via the interaction of several pulsating components. Solution of these sets of problems results in a single nonlinear evolution equation describing the dynamics of the corresponding problem. This equation represents the focus of the research to understand the system dynamics resulting from the effect of the high-frequency tangential oscillations for the corresponding shape of the wall.

The spatiotemporal dynamics of the liquid film are examined based on the evolution equation. The cases, in which a base state can be derived, linear and weakly nonlinear analysis, are both carried out for flat and fiber coatings. The problems for corrugated walls, where exact base states are not available, the investigation of the stability of the steady states are examined after they are obtained numerically. For each specific case, the full set of data for each time step is obtained to visualize the evolution, the steady states, long-time behavior and rupture cases of the interface for both flat and corrugated surfaces. The stability properties of the thin films coating fibers are examined to show that it is possible to control the stabilization or destabilization in terms of the growth rates and the width of the instability range of unstable modes.

We conclude that the dynamics of these liquid films on flat, non-flat and cylindrical surfaces, subjected to high-frequency vibration can be manipulated in terms of their stability properties. This control mechanism related to vibration and the corresponding substrate enables to form humps (droplets) of a preferable size and shape, to saturate Rayleigh-Taylor instability, to coat a plate uniformly or to induce de-wetting of the substrate.