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
Spatio-temporal evolution of evaporating liquid films sheared by a gas
Omair A. A. Mohamed
- 04 Nov 2021
TL;DR: In this paper, a Benney-like equation was derived for the long-wave limit of an evaporating liquid film and a shearing gas, and the temporal and spatiotemporal characteristics of the flow were investigated both in the linear regime using the analytically derived dispersion relationship, and in the nonlinear regime by solving the governing equation numerically.
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Dynamics of co-current gas-liquid film flow through a slippery channel
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Bifurcations of a weighted-residual integral boundary-layer model for nonlinear dynamics of falling liquid films
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- 01 Apr 2007
TL;DR: In this paper, the nonlinear dynamics of thin liquid films falling on a vertical plane is investigated numerically using the first-order time-dependent weighted-residual integral boundary layer (WRIBL) equations derived by Ruyer-Quil and Manneville (2000).
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On wave families in a two-layer falling film
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TL;DR: In this paper, the authors used an approximate method to find families of non-linear steady-traveling periodic waves in a two-layer falling film and found that these waves have qualitatively similar behavior as that of those found in homogeneous films but the quantitative characteristics of the waves strongly depend on additional similarity parameters in the two layer films.
Mathematical modelling of wavy surface of Liquid film falling down a vertical plane At moderate Reynolds'' numbers
TL;DR: Prokudina-la et al. as mentioned in this paper, L.A. Salamatov, Yevgeny.salamatov et al., YEVgeny, Y.salamaatov.
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