טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentNovbari Elena
SubjectNonlinear Dynamics of Thin Liquid Films on an Inclined
Oscillating Plate
DepartmentDepartment of Mechanical Engineering
Supervisors Professor Oded Gottlieb
Professor Alexander Oron


Abstract

Two-dimensional spatiotemporal nonlinear dynamics of thin liquid films falling on a periodically oscillating solid vertical plane is studied within the framework of longwave integral boundary layer theory. A set of two pertinent nonlinear evolution equations (WRIBL) that were recently derived for the non-modulated case, is extended to incorporate harmonic boundary excitation. These equations, referred to as the temporally modulated weighted-residual integral boundary layer equations (TMWRIBL), are investigated numerically.

The solutions obtained for film dynamics via both forced and unforced time-dependent models are validated by comparison to those documented for direct numerical simulations of the Navier-Stokes equations, to the Benney (BE) and temporally modulated Benney (TMBE) equations and to experimental results.

Similar to the BE (TMBE), the bifurcation structure of the WRIBL (TMWRIBL) equations is found to include three distinct regions: linearly stable, bounded wave flows and spurious solutions. Spurious solutions of WRIBL (TMWRIBL) exhibit a negative flow rate which represents locally reverse flow against gravity. The threshold for emergence of these reverse-flow solutions is a zero local flow rate.

However, the WRIBL (TMWRIBL) equations display bounded solutions for larger values of Reynolds number than the BE (TMBE). Analysis of the WRIBL equations reveals the existence of both periodic traveling wave (TW) and aperiodic non-stationary wave (NSW) flows, whereas film evolution, as described by the modulated TMWRIBL equations, yields quasiperiodic tori and several types of chaotic strange attractors. It is shown that periodic in-plane boundary excitation does not alter the spatial topological structure of the interfacial waves and the fundamental unforced bifurcation structure.