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Absolute and convective instabilities in a liquid film over a substrate moving against gravity

par Pino, Fabio ;Mendez, M.A.;Scheid, Benoît
Référence Physical Review Fluids, 9, 10, 104002
Publication Publié, 2024-12-01

Article révisé par les pairs

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Résumé :

The drag-out problem for small Reynolds numbers (Re) admits the Landau-Levich-Derjaguin (LLD) solution for small capillary numbers (Ca), and Derjaguin's solution for large Ca. We investigate whether these solutions are absolutely or convectively unstable, solving the Orr-Sommerfeld eigenvalue problem. We show that the Derjaguin's solution is convectively unstable for Ka<17 and absolutely unstable for Ka≳0.15Re1.7 when Re>10. For water (Ka=3400), the LLD solution is always convectively unstable. The absolute instability is observed only when the dip-coated film is additionally fed from above.