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On the origin of the circular hydraulic jump in a thin liquid film

Published online by Cambridge University Press:  31 July 2018

Rajesh K. Bhagat Open the ORCID record for Rajesh K. Bhagat [Opens in a new window] ,
N. K. Jha ,
P. F. Linden  and
D. Ian Wilson
Rajesh K. Bhagat*
Affiliation:
Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, Cambridge CB3 0AS, UK
N. K. Jha
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Wilberforce Road, Cambridge CB3 0WA, UK
P. F. Linden
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Wilberforce Road, Cambridge CB3 0WA, UK
D. Ian Wilson
Affiliation:
Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, Cambridge CB3 0AS, UK
*
†Email address for correspondence: [email protected]
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Abstract

This study explores the formation of circular thin-film hydraulic jumps caused by the normal impact of a jet on an infinite planar surface. For more than a century, it has been believed that all hydraulic jumps are created due to gravity. However, we show that these thin-film hydraulic jumps result from energy loss due to surface tension and viscous forces alone. We show that, at the jump, surface tension and viscous forces balance the momentum in the liquid film and gravity plays no significant role. Experiments show no dependence on the orientation of the surface and a scaling relation balancing viscous forces and surface tension collapses the experimental data. A theoretical analysis shows that the downstream transport of surface energy is the previously neglected critical ingredient in these flows, and that capillary waves play the role of gravity waves in a traditional jump in demarcating the transition from the supercritical to subcritical flow associated with these jumps.

JFM classification

Waves/Free-surface Flows: Capillary waves Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 851 , 25 September 2018 , R5
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Copyright
© 2018 Cambridge University Press 

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Bhagat et al. supplementary movie 1

Hydraulic jump in water propanol solution

Download Bhagat et al. supplementary movie 1(Video)
Video 8.9 MB

Bhagat et al. supplementary movie 2

) Formation of a hydraulic jump due to vertical impingement of a liquid jet on a horizontal surface

Download Bhagat et al. supplementary movie 2(Video)
Video 6.1 MB

Bhagat et al. supplementary movie 3

Change in jump radius by changing the surface tension

Download Bhagat et al. supplementary movie 3(Video)
Video 4.3 MB