Skip to main content Accessibility help
×
Home
Hostname: page-component-568f69f84b-l2zqg Total loading time: 1.184 Render date: 2021-09-21T06:38:13.791Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

Water bells formed on the underside of a horizontal plate. Part 1. Experimental investigation

Published online by Cambridge University Press:  13 April 2010

GRAEME J. JAMESON*
Affiliation:
Centre for Multiphase Processes, University of Newcastle, Callaghan, New South Wales 2308, Australia
CLAIRE E. JENKINS
Affiliation:
Centre for Multiphase Processes, University of Newcastle, Callaghan, New South Wales 2308, Australia
ELEANOR C. BUTTON
Affiliation:
Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
JOHN E. SADER
Affiliation:
Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
*Corresponding
Email address for correspondence: graeme.jameson@newcastle.edu.au

Abstract

In this study we report discovery of a new type of water bell. This is formed by impinging a vertical liquid jet on to the underside of a large horizontal flat plate. After impact, the liquid spreads radially along the plate before falling at an abrupt unspecified radius. This falling liquid may then coalesce to form a curtain which encloses a volume of air. When the flow rate of the impinging jet is altered from the value at initial formation, a pronounced hysteretic effect in the water bell shape can be observed. We present detailed observations of these new phenomena, including the size and nature of the flow underneath the plate and the shape of the liquid curtain. These observations are interpreted theoretically in a companion paper (Part 2, Button et al. vol. 649, 2010, pp. 45–68).

Type
Papers
Copyright
Copyright © Cambridge University Press 2010

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

Aristoff, J. M., Leblanc, J. D., Hosoi, A. E. & Bush, J. W. M. 2004 Viscous hydraulic jumps. Phys. Fluids 16, S4.CrossRefGoogle Scholar
Aristoff, J. M., Lieberman, C., Chan, E. & Bush, J. W. M. 2006 Water bell and sheet instabilities. Phys. Fluids 18, S10.CrossRefGoogle Scholar
Baird, M. H. I. & Davidson, J. F. 1962 a Annular jets – I. Fluid dynamics. Chem. Engng Sci. 17, 467472.CrossRefGoogle Scholar
Baird, M. H. I. & Davidson, J. F. 1962 b Annular jets – II. Gas absorption. Chem. Eng. Sci. 17, 473480.CrossRefGoogle Scholar
Bark, F. H., Wallin, H.-P., Gällstedt, M. G. & Kristiansson, L. P. 1979 Swirling water bells. J. Fluid Mech. 90, 625639.CrossRefGoogle Scholar
Bond, W. N. 1935 The surface tension of a moving water sheet. Proc. Phys. Soc. B 47, 549558.CrossRefGoogle Scholar
Boussinesq, J. 1869 Théories des expériences de Savart, sur la forme que prend une veine liquide après s'être choquée contre un plan circulaire. C. R. Acad. Sci. Paris 69, 4548.Google Scholar
Bremond, N. & Villermaux, E. 2006 Atomization by jet impact. J. Fluid Mech. 549, 273306.CrossRefGoogle Scholar
Bridgman, P. W. 1931 Dimensional Analysis. Yale University Press.Google Scholar
Brunet, P., Clanet, C. & Limat, L. 2004 Transonic liquid bells. Phys. Fluids 16, 26682678.CrossRefGoogle Scholar
Brunet, P., Flesselles, J.-M. & Limat, L. 2001 Parity breaking in a one-dimensional pattern: a quantitative study with controlled wavelength. Europhys. Lett. 56, 221227.CrossRefGoogle Scholar
Brunet, P., Flesselles, J.-M. & Limat, L. 2007 Dynamics of a circular array of liquid columns. Eur. Phys. J. B 55, 297322.CrossRefGoogle Scholar
Buchwald, E. & König, H. 1936 Dynamic surface tension from liquid bells. Ann. Physik 26, 661U10.Google Scholar
Buckingham, R. & Bush, J. W. M. 2001 Fluid polygons. Phys. Fluids 13, S10.CrossRefGoogle Scholar
Bush, J. W. M., Aristoff, J. M. & Hosoi, A. E. 2006 An experimental investigation of the stability of the circular hydraulic jump. J. Fluid Mech. 558, 3352.CrossRefGoogle Scholar
Bush, J. W. M. & Hasha, A. E. 2002 On the collision of laminar jets: fluid chains and fishbones. J. Fluid Mech. 511, 285310.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
Clanet, C. 2000 Stability of water bells generated by jet impacts on a disk. Phys. Rev. Lett. 85, 51065109.CrossRefGoogle Scholar
Clanet, C. 2001 Dynamics and stability of water bells. J. Fluid Mech. 430, 111147.CrossRefGoogle Scholar
Clanet, C. 2007 Waterbells and liquid sheets. Annu. Rev. Fluid Mech. 39, 469496.CrossRefGoogle Scholar
Crapper, G. D., Dombrowski, N. & Pyott, G. A. D. 1975 Kelvin–Helmholtz wave growth on cylindrical sheets. J. Fluid Mech. 68, 497502.CrossRefGoogle Scholar
Dombrowski, N. & Fraser, R. P. 1954 A photographic investigation into the disintegration of liquid sheets. Phil. Trans. R. Soc. Lond. Ser. A 247, 101130.CrossRefGoogle Scholar
Dombrowski, N. & Hooper, P. C. 1964 Sprays formed by impinging jets in laminar and turbulent flow. J. Fluid Mech. 18, 392400.CrossRefGoogle Scholar
Ellegaard, C., Hansen, A. E., Haaning, A., Hansen, K., Marcussen, A., Bohr, T., Hansen, J. & Watanabe, S. 1998 Creating corners in kitchen sinks. Nature 392, 767768.CrossRefGoogle Scholar
Engel, O. G. 1966 Crater depth in fluid impacts. J. Appl. Phys. 37, 17981808.CrossRefGoogle Scholar
Finnicum, D. S., Weinstein, S. J. & Ruschak, K. J. 1993 The effect of applied pressure on the shape of a two-dimensional liquid curtain falling under the effect of gravity. J. Fluid Mech. 255, 647665.CrossRefGoogle Scholar
Gasser, J. C. & Marty, P. 1994 Liquid sheet modelling in an electromagnetic swirl atomiser. Eur. J. Mech. B/Fluids 13, 765784.Google Scholar
Giorgiutti, F. & Limat, L. 1997 Solitary dilation waves in a circular array of liquid columns. Physica D 103, 590604.CrossRefGoogle Scholar
Göring, W. 1959 Zur Abhängigkeit der Oberflächenspannung von der Bildungs – und Alterungsgeschwindigkeit der Oberfläsche. Z. Elektrochem., Ber. Bunsenges. physik. Chem. 63, 10691077.Google Scholar
Hopwood, F. L. 1952 Water bells. Proc. Phys. Soc. B 65, 25.CrossRefGoogle Scholar
Huang, J. C. P. 1970 The breakup of axisymmetric liquid sheets. J. Fluid Mech. 43, 305319.CrossRefGoogle Scholar
Jameson, G. J., Jenkins, C., Button, E. C. & Sader, J. E. 2008 Water bells created from below. Phys. Fluids 20, 091108.CrossRefGoogle Scholar
Jeandel, X. & Dumouchel, C. 1999 Influence of viscosity on the linear stability of an annular liquid sheet. Intl J. Heat Fluid Flow 20, 499506.CrossRefGoogle Scholar
Lance, G. N. & Perry, R. L. 1953 Water bells. Proc. Phys. Soc. B 66, 10671073.CrossRefGoogle Scholar
Lasheras, J. C. & Hopfinger, E. J. 2000 Liquid jet atomization in a coaxial gas stream. Annu. Rev. Fluid Mech. 32, 3352.CrossRefGoogle Scholar
Liu, H. 2000 Science and Engineering of Droplets: Fundamentals and Applications. William Andrew.Google Scholar
Liu, X. & Lienhard, J. 1993 The hydraulic jump in a circular jet impingement and in other thin liquid films. Exp. Fluids 15, 108116.CrossRefGoogle Scholar
Magnus, H. G. 1855 Hydraulische untersuchungen. Ann. Poggendorff 95, 159.Google Scholar
Mansour, A. & Chigier, N. 1990 Disintegration of liquid sheets. Phys. Fluids A 2, 706719.CrossRefGoogle Scholar
Olsson, R. G. & Turkdogan, E. T. 1966 Radial spread of a liquid stream on a horizontal plate. Nature 211, 813816.CrossRefGoogle Scholar
Parlange, J.-Y. 1967 A theory of water-bells. J. Fluid Mech. 29, 361372.CrossRefGoogle Scholar
Pirat, C., Mathis, C., Mishra, M. & Maïssa, P. 2006 Destabilization of a viscous film flowing down in the form of a vertical cylindrical curtain. Phys. Rev. Lett. 97, 184501.CrossRefGoogle ScholarPubMed
Rayleigh, Lord 1914 On the theory of long waves and bores. Proc. R. Soc. A 90, 324328.CrossRefGoogle Scholar
Savart, F. 1833 a Mémoire sur la constitution des veines liquides lancees par des orifices circulaires en mince paroi. Ann. de Chim. 53, 337386.Google Scholar
Savart, F. 1833 b Mémoire sur le choc de deux veines liquides animées de mouvements directement opposés. Ann. de Chim. 55, 257310.Google Scholar
Savart, F. 1833 c Mémoire sur le choc d'une veine liquide lancée contre un plan circulaire. Ann. de Chim. 54, 5687.Google Scholar
Savart, F. 1833 d Suite de Mémoire sur le choc d'une veine liquide lancée contre un plan circulaire. Ann. de Chim. 54, 113145.Google Scholar
Söderberg, L. D. & Alfredsson, P. H. 1998 Experimental and theoretical stability investigations of plane liquid jets. Eur. J. Mech. B/Fluids 17, 689737.CrossRefGoogle Scholar
Squire, H. B. 1953 Investigation of the instability of a moving liquid film. Br. J. App. Phys. 4, 167169.CrossRefGoogle Scholar
Taylor, G. I. 1959 a The dynamics of thin sheets of fluid. I. Water bells. Proc. R. Soc. A 253, 289295.CrossRefGoogle Scholar
Taylor, G. I. 1959 b The dynamics of thin sheets of fluid. II. Waves on fluid sheets. Proc. R. Soc. A 253, 296312.CrossRefGoogle Scholar
Thoroddsen, S. T. 2002 The ejecta sheet generated by the impact of a drop. J. Fluid Mech. 451, 373381.CrossRefGoogle Scholar
Watson, E. J. 1964 The radial spread of a liquid jet over a horizontal plane. J. Fluid Mech. 20, 481499.CrossRefGoogle Scholar
Wegener, P. P. & Parlange, J.-Y. 1964 Surface tension of liquids from water bell experiments. Zeit. Phys. Chem. 43, 245259.CrossRefGoogle Scholar
9
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.

Water bells formed on the underside of a horizontal plate. Part 1. Experimental investigation
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.

Water bells formed on the underside of a horizontal plate. Part 1. Experimental investigation
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.

Water bells formed on the underside of a horizontal plate. Part 1. Experimental investigation
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? *