Hostname: page-component-7c8c6479df-ph5wq Total loading time: 0 Render date: 2024-03-29T12:21:59.475Z Has data issue: false hasContentIssue false

On the cusps bordering liquid sheets

Published online by Cambridge University Press:  30 July 2014

J. M. Gordillo
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingenería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, Avenida de los Descubrimientos s/n 41092, Sevilla, Spain
H. Lhuissier
Affiliation:
Université Paris Diderot, CNRS, Matière et Systèmes Complexes UMR 7057, 75205 Paris, France
E. Villermaux*
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384 Marseille, France
*
Institut Universitaire de France, Paris, France. Email address for correspondence: villermaux@irphe.univ-mrs.fr

Abstract

The edge of a stationary radially expanding liquid sheet and the receding rim bordering a plane sheet are naturally indented. It presents a collection of cusps at the extremity of which the liquid concentrates and is expelled. An experimental description of these cusps for a stationary flat inviscid Savart sheet is given. We identify the stable node–jet structure responsible for the deflection of the incoming flow at the rim and demonstrate how these cusps are the structures that accommodate for both mass and momentum conservation at the sheet edge. Their shape, their number around the sheet, and the residual momentum carried by the ejected liquid are computed.

Type
Rapids
Copyright
© 2014 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

Aldbrege, R. C. & Killingsworth, N. J. 2004 Experimental evaluation of Markstein-number influence on thermoacoustic instability. Combust. Flame 137, 178197.Google Scholar
Bremond, N. & Villermaux, E. 2006 Atomization by jet impact. J. Fluid Mech. 549, 273306.CrossRefGoogle Scholar
Clanet, C. & Villermaux, E. 2002 Life of a smooth liquid sheet. J. Fluid Mech. 462, 307340.CrossRefGoogle Scholar
Culick, F. E. C. 1960 Comments on a ruptured soap film. J. Appl. Phys. 31, 11281129.CrossRefGoogle Scholar
D’Angelo, Y., Joulin, G. & Boury, G. 2000 On model evolution equations for the whole surface of three-dimensional expanding wrinkled premixed flames. Combust. Theor. Model. 4, 317338.CrossRefGoogle Scholar
Dressaire, E., Courbin, L., Delancy, A., Roper, M. & Stone, H. A. 2013 Study of polygonal water bells: inertia-dominated thin-film flows over microtextured surfaces. J. Fluid Mech. 721, 4657.CrossRefGoogle Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.CrossRefGoogle Scholar
Huang, J. C. P. 1970 The break-up of axisymmetric liquid sheets. J. Fluid Mech. 43, 305319.CrossRefGoogle Scholar
Lhuissier, H. & Villermaux, E. 2009 Soap films burst like flapping flags. Phys. Rev. Lett. 103, 054501–(4).CrossRefGoogle ScholarPubMed
Lhuissier, H. & Villermaux, E. 2011 The destabilization of an initially thick liquid sheet edge. Phys. Fluids 23 (9), 091705; 091704.CrossRefGoogle Scholar
Lhuissier, H. & Villermaux, E. 2013 ‘Effervescent’ atomization in two dimensions. J. Fluid Mech. 714, 361392.CrossRefGoogle Scholar
Michelson, D. M. & Sivashinsky, G. I. 1982 Thermal-expansion induced cellular flames. Combust. Flame 48, 211217.CrossRefGoogle Scholar
Plateau, J. 1873 Statique Expérimentale et Théorique des Liquides Soumis aux Seules Forces Moléculaires. Gauthiers Villars.Google Scholar
Savart, F. 1833 Mémoire sur la constitution des Veines liquides lancées par des orifices circulaires en mince paroi. Ann. Chim. France 53, 337386.Google Scholar
Taylor, G. I. 1959 The dynamics of thin sheets of fluid. II. Waves on fluid sheets. Proc. R. Soc. A 253 (1274), 296312.Google Scholar
Villermaux, E. & Clanet, C. 2002 Life of a flapping liquid sheet. J. Fluid Mech. 462, 342363.CrossRefGoogle Scholar
Villermaux, E., Pistre, V. & Lhuissier, H. 2013 The viscous Savart sheet. J. Fluid Mech. 730, 607625.CrossRefGoogle Scholar