Surface waves along liquid cylinders. Part 1. Stabilising effect of gravity on the Plateau-Rayleigh instability - Laboratoire Interdisciplinaire des Sciences du Numérique Accéder directement au contenu
Article Dans Une Revue Journal of Fluid Mechanics Année : 2020

Surface waves along liquid cylinders. Part 1. Stabilising effect of gravity on the Plateau-Rayleigh instability

Résumé

We study the shape and the geometrical properties of sessile drops with translational invariance (namely 'liquid cylinders') deposited upon a flat superhydrophobic substrate. We account for the flattening effects of gravity on the shape of the drop using a pendulum rotation motion analogy. In the framework of the inviscid Saint-Venant equations, we show that liquid cylinders are always unstable because of the Plateau-Rayleigh instability. However, a cylindrical drop deposited upon a superhydrophobic non-flat channel (here, wedge-shaped channels) is stabilised beyond a critical cross-sectional area. The critical threshold of the Plateau-Rayleigh instability is analytically computed for various profiles of the channel. The stability analysis is performed in terms of an effective propagation speed of varicose waves. Experiments are performed in order to test these analytical results. We measure the critical drop size at which breakup occurs, together with the decreasing effective propagation speed of varicose waves as the threshold is approached. Our theoretical predictions are in excellent agreement with the experimental measurements.
Fichier principal
Vignette du fichier
reshaped_JFM1_preprint.pdf (2.02 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03863941 , version 1 (29-11-2022)

Identifiants

Citer

Chi Tuong Pham, Stéphane Perrard, Gabriel Le Doudic. Surface waves along liquid cylinders. Part 1. Stabilising effect of gravity on the Plateau-Rayleigh instability. Journal of Fluid Mechanics, 2020, ⟨10.1017/jfm.2020.114⟩. ⟨hal-03863941⟩
23 Consultations
126 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More