On lubrication models for vertical rivulet flows

Lopes, André von Borries; Borges, Robson; Matias, G. C.; Pimenta, Braulio G.; Siqueira, Ivan R.

doi:10.1007/s11012-022-01503-x

Meccanica

2022

DOI: 10.1007/s11012-022-01503-x

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On lubrication models for vertical rivulet flows

André von Borries Lopes

Robson Borges

G. C. Matias

et al.

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Cited by 2 publications

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“…Thin liquid films falling down walls have been investigated since many years ago under different boundary conditions. The stability of these flows is of interest because, when the film is not able to wet the wall, rivulets [4] may form and for some applications the film becomes useless. Usually it is difficult to control atmospheric temperature variations.…”

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Marangoni stability of a thin liquid film falling down above or below an inclined thick wall with slip

Dávalos-Orozco

2023

Meccanica

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The linear and nonlinear instability of a thin liquid film flowing down above or below (Rayleigh-Taylor instability) an inclined thick wall with finite thermal conductivity are investigated in the presence of slip at the wall-liquid interface. A nonlinear evolution equation for the free surface deformation is obtained under the lubrication approximation. The curves of linear growth rate, maximum growth rate and critical Marangoni number are calculated. When the film flows below the wall it will be subjected to destabilizing and stabilizing Marangoni numbers. It is found that from the point of view of the linear growth rate the flow destabilizes with slip in a wavenumber range. However slip stabilizes for larger wavenumbers up to the critical (cutoff) wavenumber. From the point of view of the maximum growth rate flow slip may stabilize or destabilize increasing the slip parameter depending on the magnitude of the Marangoni and Galilei numbers. Explicit formulas were derived for the intersections (the wavenumber for the growth rate and the Marangoni number for the maximum growth rate) where slip changes its stabilizing and destabilizing properties. From the numerical solution of the nonlinear evolution equation of the free surface profiles, it is found that slip may suppress or stimulate the appearance of subharmonics depending on the magnitudes of the selected parameters. In the same way, it is found that slip may increase or decrease the nonlinear amplitude of the free surface deformation. The effect of the thickness and finite thermal conductivity of the wall is also investigated.

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Marangoni stability of a thin liquid film falling down above or below an inclined thick wall with slip

Dávalos-Orozco

2023

Meccanica

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The effect of turbulence on the minimum thickness of a liquid film flowing down a vertical tube

Hughes

2024

Chemical Engineering Research and Design

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On lubrication models for vertical rivulet flows

Cited by 2 publications

References 36 publications

Marangoni stability of a thin liquid film falling down above or below an inclined thick wall with slip

Marangoni stability of a thin liquid film falling down above or below an inclined thick wall with slip

The effect of turbulence on the minimum thickness of a liquid film flowing down a vertical tube

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