Journal Article10.1007/S100510051137
Improved modeling of flows down inclined planes
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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
•Dissertation
Computational study of liquid film flows along flat and undulated substrates
Phuc-Khanh Nguyen
- 01 Jan 2012
TL;DR: Nguyen and Bontozoglou as mentioned in this paper presented a computational study of the gravity-driven liquid film flowing along either a flat wall, or a wall with periodic corrugations, and showed that at short intrinsic separations, a continuous oscillation around the mean separation takes place.
2
Experimental Validation of Falling Liquid Film Models: Velocity Assumption and Velocity Field Comparison
TL;DR: In this paper, the experimental validation of film models by comparing constructed and experimental velocity fields based on model and elementary experimental data is presented, where the velocity fields are reconstructed based on different film flow model velocity profile assumptions such as experimental film thickness, flow rates, and their derivatives.
2
•Dissertation
Flow Down a Wavy Inclined Plane
Kelly A. Ogden
- 29 Mar 2011
TL;DR: In this article, the authors compared three models for flow down a wavy, inclined plane with the goal of determining which best predicts features of the flow, and found that the weighted residual model (WRM) most accurately models the flow.
2
Electrostatic control of the Navier-Stokes equations for thin films
TL;DR: In this article , a robust control scheme for the Navier-Stokes equations for two-dimensional multiphase flow of a thin film underneath an inclined solid surface is derived.
2
Hopf instability of a Rayleigh–Taylor unstable thin film heated from the gas side
Michael Bestehorn,Alexander Oron +1 more
TL;DR: In this paper , the authors derived a dimension-reduced set of three coupled evolution equations where nonlinearities of both the Navier-Stokes and the heat equation are included, and found that the first bifurcation from the motionless state is oscillatory which sets in with a finite but small wave number.
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