Journal Article10.1007/S100510051137
Improved modeling of flows down inclined planes
412
TL;DR: In this article, a second-order 2D model of film flows down inclined planes was derived by combining a gradient expansion at first or second order to weighted residual techniques with polynomials as test functions.
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Abstract: New models of film flows down inclined planes have been derived by combining a gradient expansion at first or second order to weighted residual techniques with polynomials as test functions. The two-dimensional formulation has been extended to account for three-dimensional flows as well. The full second-order two-dimensional model can be expressed as a set of four coupled evolution equations for four slowly varying fields, the thickness h, the flow rate q and two other quantities measuring the departure from the flat-film semi-parabolic velocity profile. A simplified model has been obtained in terms of h and q only. Including viscous dispersion effects properly, it closely sticks to the asymptotic expansion in the appropriate limit. Our new models improve over previous ones in that they remain valid deep into the strongly nonlinear regime, as shown by the comparison of our results relative to travelling-wave and solitary-wave solutions with those of both direct numerical simulations and experiments.
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Citations
Influences of a uniform electric field on the stability of film flows along an inclined wavy wall
HU Guo-hui
Abstract: The stability of two-dimensional film flow along an inclined wavy wall in the presence of a normal electric field was investigated theoretically,as well as the characteristics of steady flow.To analyze the influences of the electric field and the wavy structures,a set of evolution equations describing the effect of electrical field on the liquid film was derived based on the WRIBL approach.In the case of small amplitude of wall,the capillary is helpful for stabilizing the film flows,whereas the electric field promotes the development of the linear perturbations.An equilibrium condition for the two competing effects was proposed,and results indicate that the wall structure will enhance these effects.The investigations on the steady flows show the dependence of the relative amplitude and the phase difference on the physical parameters,and indicate that the electric field is benefit for suppressing the resonant phenomenon in film down a structured wall.
The effect of wall slip on the dewetting of ultrathin films on solid substrates: Linear instability and second-order lubrication theory
TL;DR: In this article, the influence of wall slip on the instability of a nonwetting liquid film placed on a solid substrate is analyzed in the limit of negligible inertia, and a parabolic model is developed to accurately predict the linear dynamics of the film for arbitrary slip lengths.
Shear imposed falling film with odd viscosity effects
TL;DR: In this paper , the authors examined the behavior of a thin liquid film flowing on an inclined plane subject to imposed shear stress and determined the model's critical Reynolds number through linear stability analysis.
Rheology of thin films from flow observations
Bruno Figliuzzi,Dominique Jeulin,Anaël Lemaître,Gabriel Fricout,Jean-Jacques Piezanowski,Paul Manneville +5 more
TL;DR: In this paper, the authors present a method for characterizing the film rheology based on measurements at regular time intervals of the film surface topography, which allows them to validate a model of Rheology for the thin fluid film and to determine the physical parameters specific to this model.
Film flow over heated wavy inclined surfaces
TL;DR: In this paper, the gravity-driven laminar flow of a thin layer of fluid down a heated wavy inclined surface is discussed, and the coupled effect of bottom topography, variable surface tension and heating has been investigated both analytically and numerically.
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