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
Effects of inertia and surface tension on a power-law fluid flowing down a wavy incline
Christian Heining,Nuri Aksel +1 more
TL;DR: In this paper, a thin film of a power-law liquid flowing down an inclined wall with sinusoidal topography is considered and an integral boundary-layer model for the film thickness and flow rate is derived.
54
Statistical analysis of pulsating non-Newtonian flow in a corrugated channel using Lattice-Boltzmann method
Hamid Hassanzadeh Afrouzi,Majid Ahmadian,Abouzar Moshfegh,Abouzar Moshfegh,Davood Toghraie,Ashkan Javadzadegan,Ashkan Javadzadegan +6 more
TL;DR: In this article, the Lattice Boltzmann Method (LBM) and Boundary Fitting Method (BFM) were used to study pulsating non-Newtonian flow in a corrugated channel.
53
Shear-imposed falling film
TL;DR: In this paper, the authors investigated the primary instability of a two-wave structure, which is normally a combination of kinematic and dynamic waves, and provided an analytical expression for the speed of a family of travelling waves as a function of the Froude number.
50
Interaction of three-dimensional hydrodynamic and thermocapillary instabilities in film flows
TL;DR: A model of three-dimensional wave patterns on the surface of a film flowing down a uniformly heated wall is shown to be robust and accurate in describing the competition between hydrodynamic waves and thermocapillary Marangoni effects for a wide range of parameters.
Wavy regimes of film flow down a fiber.
TL;DR: This work considers axisymmetric traveling waves propagating on the gravity-driven flow of a liquid down a vertical fiber using the two-equation model for the flow derived in the study by Ruyer-Quil et al.
49
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