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One-dimensional capillary jumps

Published online by Cambridge University Press:  15 January 2015

M. Argentina ,
A. Cohen ,
Y. Bouret ,
N. Fraysse  and
C. Raufaste
M. Argentina*
Affiliation:
Université Nice Sophia Antipolis, CNRS, INLN, UMR 7335, 06560 Valbonne, France Institut Universitaire de France, 75005 Paris, France
A. Cohen
Affiliation:
Université Nice Sophia Antipolis, CNRS, LPMC, UMR 7336, 06100 Nice, France
Y. Bouret
Affiliation:
Université Nice Sophia Antipolis, CNRS, LPMC, UMR 7336, 06100 Nice, France
N. Fraysse
Affiliation:
Université Nice Sophia Antipolis, CNRS, LPMC, UMR 7336, 06100 Nice, France
C. Raufaste
Affiliation:
Université Nice Sophia Antipolis, CNRS, LPMC, UMR 7336, 06100 Nice, France
*
†Email address for correspondence: [email protected]
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Abstract

In flows where the ratio of inertia to gravity varies strongly, large variations in the fluid thickness appear and hydraulic jumps arise, as depicted by Rayleigh. We report a new family of hydraulic jumps, where the capillary effects dominate the gravitational acceleration. The Bond number – which measures the importance of gravitational body forces compared to surface tension – must be small in order to observe such objects using capillarity as a driving force. For water, the typical length should be smaller than 3 mm. Nevertheless, for such small scales, solid boundaries induce viscous stresses, which dominate inertia, and capillary jumps should not be described by the inertial shock wave theory that one would deduce from Bélanger or Rayleigh for hydraulic jumps. In order to get rid of viscous shears, we consider Plateau borders, which are the microchannels defined by the merging of three films inside liquid foams, and we show that capillary jumps propagate along these deformable conduits. We derive a simple model that predicts the velocity, geometry and shape of such fronts. A strong analogy with Rayleigh’s description is pointed out. In addition, we carried out experiments on a single Plateau border generated with soap films to observe and characterize these capillary jumps. Our theoretical predictions agree remarkably well with the experimental measurements.

JFM classification

Interfacial Flows (free surface): Capillary flows Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 765 , 25 February 2015 , pp. 1 - 16
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Copyright
© 2015 Cambridge University Press 

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Argentina et al. supplementary movie

Capillary hydraulic jump formation following the drop coalescence. The permanent regime is established on a distance comparable to the drop radius. The image real width is 8.2 mm. The movie is slowed down 100 times.

Download Argentina et al. supplementary movie(Video)
Video 193 KB

Argentina et al. supplementary movie

Capillary hydraulic jump formation following the drop coalescence. The permanent regime is established on a distance comparable to the drop radius. The image real width is 8.2 mm. The movie is slowed down 100 times.

Download Argentina et al. supplementary movie(Video)
Video 38.2 KB

Argentina et al. supplementary movie

Close-up focused on the capillary hydraulic jump in the permanent regime. The shape is stationary and the traveling velocity is constant. The image real width is 6.7 mm. The movie is slowed down 500 times.

Download Argentina et al. supplementary movie(Video)
Video 1.1 MB

Argentina et al. supplementary movie

Close-up focused on the capillary hydraulic jump in the permanent regime. The shape is stationary and the traveling velocity is constant. The image real width is 6.7 mm. The movie is slowed down 500 times.

Download Argentina et al. supplementary movie(Video)
Video 233.5 KB