Skip to main content Accessibility help
×
Home
Hostname: page-component-99c86f546-vl2kb Total loading time: 0.38 Render date: 2021-12-01T10:43:25.977Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

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*
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: rkb29@cam.ac.uk

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.

Type
JFM Rapids
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Avedisian, C. T. & Zhao, Z. 2000 The circular hydraulic jump in low gravity. Proc. R. Soc. Lond. A 456, 21272151.CrossRefGoogle Scholar
Bhagat, R. K. & Wilson, D. I. 2016 Flow in the thin film created by a coherent turbulent water jet impinging on a vertical wall. Chem. Engng Sci. 152, 606623.CrossRefGoogle Scholar
Bidone, G. 1819 Le remou et sur la propagation des ondes. Rep. R. Sci. Acad. Turin 12, 21112.Google Scholar
Bohr, T., Dimon, P. & Putkaradze, V. 1993 Shallow-water approach to the circular hydraulic jump. J. Fluid Mech. 254, 635648.CrossRefGoogle Scholar
Bush, J. W. M. & Aristoff, J. M. 2003 The influence of surface tension on the circular hydraulic jump. J. Fluid Mech. 489, 229238.CrossRefGoogle Scholar
Button, E. C., Davidson, J. F., Jameson, G. J. & Sader, J. E. 2010 Water bells formed on the underside of a horizontal plate. Part 2. Theory. J. Fluid Mech. 649, 4568.CrossRefGoogle Scholar
Godwin, R. P. 1993 The hydraulic jump (shocks and viscous flow in the kitchen sink). Am. J. Phys. 61 (9), 829832.CrossRefGoogle Scholar
Hager, W. H. 2013 Energy Dissipators and Hydraulic Jump, vol. 8. Springer.Google Scholar
Hansen, S. H., Hørlück, S., Zauner, D., Dimon, P., Ellegaard, C. & Creagh, S. C. 1997 Geometric orbits of surface waves from a circular hydraulic jump. Phys. Rev. E 55 (6), 70487061.Google Scholar
Jameson, G. J., Jenkins, C. E., Button, E. C. & Sader, J. E. 2010 Water bells formed on the underside of a horizontal plate. Part 1. Experimental investigation. J. Fluid Mech. 649, 1943.CrossRefGoogle Scholar
Kasimov, A. R. 2008 A stationary circular hydraulic jump, the limits of its existence and its gasdynamic analogue. J. Fluid Mech. 601, 189198.CrossRefGoogle Scholar
Kurihara, M. 1946 On hydraulic jumps. In Proceedings of the Report of the Research Institute for Fluid Engineering, Kyusyu Imperial University, vol. 3 (2), pp. 1133.Google Scholar
Mathur, M., DasGupta, R., Selvi, N. R., John, N. S., Kulkarni, G. U. & Govindarajan, R. 2007 Gravity-free hydraulic jumps and metal femtoliter cups. Phys. Rev. Lett. 98 (16), 164502.CrossRefGoogle ScholarPubMed
Lord Rayleigh 1914 On the theory of long waves and bores. Proc. R. Soc. Lond. A 90 (619), 324328.CrossRefGoogle Scholar
Rojas, N., Argentina, M. & Tirapegui, E. 2013 A progressive correction to the circular hydraulic jump scaling. Phys. Fluids 25 (4), 042105.CrossRefGoogle Scholar
Sun, N., Shi, L., Lu, F., Xie, S. & Zheng, L. 2014 Spontaneous vesicle phase formation by pseudogemini surfactants in aqueous solutions. Soft Matt. 10 (30), 54635471.CrossRefGoogle ScholarPubMed
Tani, I. 1949 Water jump in the boundary layer. J. Phys. Soc. Japan 4 (4–6), 212215.CrossRefGoogle Scholar
Vazquez, G., Alvarez, E. & Navaza, J. M. 1995 Surface tension of alcohol water + water from 20 to 50 °C. J. Chem. Engng Data 40 (3), 611614.CrossRefGoogle Scholar
Wang, T., Davidson, J. F. & Wilson, D. I. 2015 Flow patterns and cleaning behaviour of horizontal liquid jets impinging on angled walls. Food Bioprod. Process. 93, 333342.CrossRefGoogle Scholar
Watson, E. J. 1964 The radial spread of a liquid jet over a horizontal plane. J. Fluid Mech. 20 (3), 481499.CrossRefGoogle Scholar
Wilson, D. I., Le, B. L., Dao, H. D. A., Lai, K. Y., Morison, K. R. & Davidson, J. F. 2012 Surface flow and drainage films created by horizontal impinging liquid jets. Chem. Engng Sci. 68 (1), 449460.CrossRefGoogle Scholar

Bhagat et al. supplementary movie 1

Hydraulic jump in water propanol solution

Download Bhagat et al. supplementary movie 1(Video)
Video 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 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 MB
30
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

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

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

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

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

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

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *