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

  • Chi-Tuong Pham (a1), Stéphane Perrard (a2) and Gabriel Le Doudic (a3)

Abstract

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.

Copyright

Corresponding author

Email address for correspondence: pham@limsi.fr

References

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JFM classification

Type Description Title
UNKNOWN
Movies

Pham et al. supplementary movie 1
Below a critical volume (close to 15 mL), a 49 centimeter long drop, pinned at both ends, breaks up after a slow pinch-off dynamics. Pinch-off occurs about the center of the drop and both halves end up retracting, owing to surface tension (real time).

 Unknown (1.2 MB)
1.2 MB
UNKNOWN
Movies

Pham et al. supplementary movie 2
Close-up of the pinch-off region (real time) and remaining satellite drop after the break-up.

 Unknown (1.3 MB)
1.3 MB

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

  • Chi-Tuong Pham (a1), Stéphane Perrard (a2) and Gabriel Le Doudic (a3)

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