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Register a new userNonlinear periodic wavetrains in thin liquid films falling on a uniformly heated horizontal plate
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Added by
Alain Moise Dikande Pr.
Publication date
2018
fields
Physics
and research's language is
English
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A thin liquid film falling on a uniformly heated horizontal plate spreads into fingering ripples that can display a complex dynamics ranging from continuous waves, nonlinear spatially localized periodic wave patterns (i.e. rivulet structures) to modulated nonlinear wavetrain structures. Some of these structures have been observed experimentally, however conditions under which they form are still not well understood. In this work we examine profiles of nonlinear wave patterns formed by a thin liquid film falling on a uniformly heated horizonal plate. In this purpose, the Benney model is considered assuming a uniform temperature distribution along the film propagation on the horizontal surface. It is shown that for strong surface tension but relatively small Biot number, spatially localized periodic-wave structures can be analytically obtained by solving the governing equation under appropriate conditions. In the regime of weak nonlinearity, a multiple-scale expansion combined with the reductive perturbation method leads to a complex Ginzburg-Landau equation, the solutions of which are modulated periodic pulse trains which amplitude, width and period are expressed in terms of characteristic parameters of the model.
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Recent experiments of thin films flowing down a vertical fiber with varying nozzle diameters present a wealth of new dynamics that illustrate the need for more advanced theory. We present a detailed analysis using a full lubrication model that includes slip boundary conditions, nonlinear curvature terms, and a film stabilization term. This study brings to focus the presence of a stable liquid layer playing an important role in the full dynamics. We propose a combination of these physical effects to explain the observed velocity and stability of traveling droplets in the experiments and their transition to isolated droplets. This is also supported by stability analysis of the traveling wave solution of the model.
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We consider the deposition of a film of viscous liquid on a flat plate being withdrawn from a bath, experimentally and theoretically. For any plate speed $U$, there is a range of ``thick film solutions whose thickness scales like $U^{1/2}$ for small $U$. These solutions are realized for a partially wetting liquid, while for a perfectly wetting liquid the classical Landau-Levich-Derjaguin (LLD) film is observed, whose thickness scales like $U^{2/3}$. The thick film is distinguished from the LLD film by a dip in its spatial profile at the transition to the bath. We calculate the phase diagram for the existence of stationary film solutions as well as the film profiles, and find excellent agreement with experiment.
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